The Nature of Water 

'As from the said pool of blood proceed the veins which spread their branches through the human body, in just the same manner the ocean fills the body of the earth with an infinite number of veins of water! 

If a drop of water falls into the sea when this is calm, it must of necessity be that the whole surface of the sea is raised imperceptibly, seeing that water cannot be compressed within itself like air. c.a. 20 r. a 

Whether the surface of the air is bounded by the fire, as is the water by the air and the earth by the water, and whether the surface of the air takes waves and eddies as does the surface of the water, and whether in proportion as the body of the air is thinner than that of the water the revolutions of its eddies are greater in number: of the eddies of the water some have their centres filled with air, others with water. I do not know whether it is the same with the eddies of the surface of the fire. Of the eddies of the water all those which begin at the surface are filled with air, and those that have their origin within the water are filled with water; and these are more lasting because water within water has no weight as water has when it is above the air; therefore the eddies of the water round the air have weight and speedily perish. c.a. 42 r. a 


The deluges of rivers are created when the mouths of the valleys 
cannot afford egress to the waters that they receive from these valleys 
as rapidly as the valleys receive them. 

The progress of the water is swifter when it falls at a greatei angle. 





The wave is the recoil of the stroke, and it will be greater or less in 
proportion as the stroke itself is greater or less. A wave is never found 
alone, but is mingled with as many other waves as there are uneven 
places in the object where the said wave is produced. At one and the 
same time there will be moving over the greatest wave of a sea innum- 
erable other waves proceeding in different directions. If you throw a 
stone into a sea with various shores, all the waves which strike against 
these shores are thrown back toward where the stone has struck, and 
on meeting others advancing they never interrupt each other's course. 
Waves of equal volume, velocity and power, when they encounter each 
other in opposing motion, recoil at right angles, the one from the stroke 
of the other. That wave will be of greater elevation which is created by 
the greater stroke, and the same is true of the converse. The wave pro- 
duced in small tracts of water will go and return many times from the 
spot which has been struck. The wave goes and returns so many more 
times in proportion as the sea which produces it contains a less quantity 
of water, and so conversely. Only in the high seas do the waves advance 
without ever turning in recoil. In lesser tracts of water the same stroke 
gives birth to many motions of advance and recoil. The greatest wave 
is covered with innumerable other waves moving in different direc- 
tions; and these have a greater or less depth as they are occasioned by a 
greater or less power. The greatest wave is covered with various waves, 
which move in as many different directions as there were different 
places from which they separated themselves. The same wave produced 
within a small tract of water has a greater number of other waves pro- 
ceeding over itself, in proportion to the greater strength of its stroke 
and recoil from the opposite shores. Greater is the motion of the wave 
than that of the water of which it is composed. Many waves turned in 
different directions can be created between the surface and the bottom 
of the same body of water at the same time. The eddying movements 
can accompany the direct movements of each wave. All the impressions 
caused by things striking upon the water can penetrate one another 
without being destroyed. One wave never penetrates another; but they 
only recoil from the spot where they strike. c.a. 84 v. a 



The movement of water within water proceeds like that of air 
within air. c.a. 108 v. a 

Among irremediable and destructive terrors the inundations caused 
by rivers in flood should certainly be set before every other dreadful 
and terrifying movement, nor is it, as some have thought, surpassed by 
destruction by fire. I find it to be the contrary, for fire consumes that 
which feeds it and is itself consumed with its food. The movement of 
water which is created by the slopes of the valleys does not end and die 
until it has reached the lowest level of the valley; but fire is caused by 
what feeds it, and the movement of water by its wish to descend. The 
food of the fire is disunited, and the mischief caused by it is disunited 
and separated, and the fire dies when it lacks food. The slope of the 
valley is continuous and the mischief done by the destructive course 
of the river will be continuous until, attended by its valleys, it ends 
in the sea, the universal base and only resting place of the wandering 
waters of the rivers. 

But in what terms am I to describe the abominable and awful evils 
against which no human resource avails? Which lay waste the high 
mountains with their swelling and exulting waves, cast down the 
strongest banks, tear up the deep-rooted trees, and with ravening waves 
laden with mud from crossing the ploughed fields carry with them the 
unendurable labours of the wretched weary tillers of the soil, leaving 
the valleys bare and mean by reason of the poverty which is left there. 

Among irremediable and destructive terrors the inundations caused 
by impetuous rivers ought to be set before every other awful and terrify- 
ing source of injury. But in what tongue or with what words am I to 
express or describe the awful ruin, the inconceivable and pitiless havoc, 
wrought by the deluges of ravening rivers, against which no human 
resource can avail? c.a. 108 v. b 

Prove and draw up the rule for the difference that there is between 
a blow given by water upon water, and by water falling upon some- 
thing hard; and consider well also that as water falls upon other water, 
and it yields space to the blow, the percussion making the water open 
as it receives the blow, so the same result will occur in a vase when the 
water which is contained within it has been struck, for it will be the 



same as when falling water has struck against a hard substance which 
resists the blow. c.a. 153 v. d 


Among straight rivers which occur in land of the same character, 
with the same abundance of water and with equal breadth, length, 
depth, and declivity of course, that will be the slower which is the more 

This may be proved with straight rivers. That will be most winding 
which is the oldest, and that which winds will become slower as it 
acquires greater length. 

Of waters which descend from equal altitudes to equal depths that 
will be the slower which moves by the longer way. 

Of rivers which are at their commencement that will be the slower 
which is the more ancient, and this arises from the fact that the course 
is continually acquiring length by reason of the additional meander- 
ings of the river; and the reason of this is explained in the twelfth 
section. c.a. 156 r. a 

The cause which moves the humours in all kinds of living bodies 
contrary to the natural law of their gravity, is really that which moves 
the water pent up within them through the veins of the earth and dis- 
tributes it through narrow passages; and as the blood that is low rises 
up high and streams through the severed veins of the forehead, or as 
from the lower part of the vine the water rises up to where its branch 
has been lopped, so out of the lowest depths of the sea the water rises 
to the summits of the mountains, and finding there the veins burst 
open it falls through them and returns to the sea below. Thus within 
and without it goes, ever changing, now rising with fortuitous move- 
ment and now descending in natural liberty. 

So united together it goes ranging about in continual revolution. 

Rushing now here now there, up and down, never resting at all in 
quiet either in its course or in its own nature, it has nothing of its own 
but seizes hold on everything, assuming as many different natures as 
the places are different through which it passes, acting just as the 
mirror does when it assumes within itself as many images as are the 
objects which pass before it. So it is in a state of continual change, 



sometimes of position and sometimes of colour, now enclosing in itself 
new scents and savours, now keeping new essences or qualities, show- 
ing itself now deadly now lifegiving, at one time dispersing itself 
through the air, at another suffering itself to be sucked up by the heat, 
and now arriving at the region of cold where the heat that was its guide 
is restricted by it. 

And as when the hand under water squeezes a sponge so that the 
water that escapes from it creates a wave that passes through the other 
water, even so does the air that was mingled with the water when the 
cold * is squeezed out, flee away in fury and drive out the other air; 
this then is the course of the wind. 

And as the hand which squeezes the sponge under water when it is 
well soaked, so that the water pent up within it is compelled to flee 
away and therefore is driven by force through the other water and 
penetrates it, and this second mass perceiving itself to be struck de- 
parts in a wave from its position, even so the new . . . makes . . . 

c.a. 171 r. a 

The sharp bends made in the embankments of rivers are destroyed 
in the great floods of the rivers because the maximum current drives 
the water in a straight course. But as this diminishes it resumes its 
winding course, during which it is being continually diverted from 
one bank to another, and as it thus grows less the embankment of the 
river becomes hollowed out. 

But in this lesser depth the water does not move with uniform 
course, because the greater current leaps from one hollow to another 
of the opposite banks, and the sides of the water which border upon 
the embankment have the shortest course. 

The rotundities in the islands of shingle formed by the angles of the 
embankment trace their origin to the chief eddies of the rivers, which 
extend with their revolutions among the concavities and convexities 
which are found alternately in the embankments of the rivers; and 
from these spring the tiny brooks, interposed between the sandbanks 
of the rivers and their embankments, and placed opposite to the hol- 
lows of the embankments of these rivers. 

1 MS., quella del jreddo. 



The entry of river into river produces the first meanderings of the 

The meanderings of rivers in plains are occasioned by the rivers 
emptying themselves there. 

If the winding river be altogether removed from its ancient bed and 
set in a straight channel, it is necessary that the rivers which pour 
themselves into it from two sides increase in length on the one side 
as much as they lose it on the other, the one that acquires length losing 
in swiftness, this swiftness being transferred to the one that grows 

Cause the lesser rivers to enter into the greater rivers at acute angles; 
the advantage of this will be that the current of the greater river di- 
verts the line of entry of the lesser river and does not suffer it to strike 
against the opposite bank. 

Should however the lesser river be in flood at the time when the 
waters of the greater river are low the percussion of the lesser river 
will break the opposite bank of this greater river. 

The largest of the curves of a river in a valley will always have its 
convex side facing the lower part of the breadth of the valley. 

The meanderings of rivers are always greater in proportion as they 
are nearer to the spot where the lesser river enters the greater. 

The waves of earth formed by the embankment of the rivers are 
continually changing their positions, the former being created anew 
where the latter have been washed away. c.a. 185 r. b 

Prove whether a triangle thrown into still water makes its wave of 
perfect roundness in the end. c.a. 199 v. b 

[Sketch — figure of bubble resting on water] 

Why the bubbles which the water makes are half-spheres and those 
of the air are perfect spheres. Why the sides of the base of the half- 
sphere are spherical rectangles, and the contact which each has with 
the water does not cause it to form a projection above it but on account 
of its weight it has to bend and curve. c.a. 209 r. a 

[With drawing] 

The water that falls down from a height, will create a deep pool, 
which will continually increase, and its banks will often fall in. And 



the reason of this is that the water, which falls upon the other water, 
by the swiftness of its blow and by its weight causes it to give place, 
and passes down to its depths where it forms a hollow space, and 
through the stroke and the air, which as it falls is buried with it, it 
comes to rise up again and raise itself to a height by various channels, 
which expand like an opening bud, and the stroke of the water upon 
the bank proceeds in a circle and thus continuing it will gnaw and 
consume the surrounding shores. c.a. 215 v. d 

The air by its nature does not flee away beneath the water; but the 
water which is supported round about it presses it out of itself and 
drives it forth. 

Therefore one element does not flee away of itself out of the other 
element, but is driven out by it. c.a. 244 v. a 


The flow and ebb of the sea are due to the course of the rivers, which 
give the water back again to the sea with slower movement than the 
movement of their own current; and on this account necessity causes 
the water to rise to a height. And this river covers up its current again 
with the swift wave which in its recoil goes to meet the descending 
current of the river. 

The wave of the river flows back against its current when the sea 
is at its ebb. After the return of the wave to the shore it there acquires 
new power from the approach of the river. 

The flow and ebb of the sea are not caused by the moon or the sun, 
but by the greatest wave as it advances and falls back. But since the 
recoil is weaker than the advancing movement, as it is deprived of 
support, this hesitating movement would consume itself if it were not 
renewed by the help of the rivers; for these being immediately swollen 
by the approaching wave of the aforesaid tide, the wave produced by 
this swollen river becomes added to this ebb, and it strikes the opposite 
shores of the islands set over against it, and then leaps back, and so 
returns in its former course, and so continues, as has been said above. 

This experience has taught us, for it is seen continually in every 
river, and especially as it strikes against the sides of its bays. 

c.a. 281 r. a 



The spiral or rotary movement of every liquid is so much the swifter 
in proportion as it is nearer to the centre of its revolution. 

This that we set forth is a circumstance worthy of note; since move- 
ment in the circular wheel is so much slower as it is nearer to the centre 
of the revolving object. But this same circumstance is shown in the 
similarity of movement both as to speed and length in each complete 
revolution of the water, both in the circumference of its greater and of 
its lesser circle; but the curve of the lesser circle is as much less than 
that of the greater as the greater circle is more curved than the lesser. 
And so this water is of uniform movement in all the processes of its 
revolution, and if it were not so the concavity would instantly be filled 
up again. But because the lateral weight of this eddying mass 1 is two- 
fold, such concavity has no permanent movement, and of such dupli- 
cation of weight the first comes into being in the revolving movement 
of the water, the second is created in the sides of this concavity, and it 
supports itself there and finally falls headlong down upon the air which 
has filled up the aforesaid cavity with itself. 

The movements of the air through the air are two, that is straight in 
the form of a column upwards, and with revolving movement. 

But water makes this movement downwards, and makes it in the 
form of a pyramid, and makes it so much the more swiftly as the 
pyramid is more pointed. c.a. 296 v. b 


There were many of the chief towns of the districts which, through 
being placed upon their chief rivers, have been consumed and de- 
stroyed by these rivers, as was Babylon by the Tigris, by means of 
Cyrus . . . and so with an infinite number of regions; and the science 
of water gives exact information as to their defences. c.a. 305 r. a 

Water falling perpendicularly into running water makes a curve as 
it enters and a curve as it rises. The summit of the part that rises in the 
air will not be in the centre of the base of this cavity, and this base will 
be oval. c.a. 343 v. a 

1 MS. circiilazion revertiginosa. 




The water falls in whatever is the line of the summit of its wave, 
and it moves more swiftly where this fall has less slant, and breaks 
more into foam where it meets with more resistance. 

There, according to what has been stated, the waves break against 
the course of the river and never in the direction of its course, because 
water falling upon flowing water can never create a rebound upon 
something that flies away and does not await the stroke; but in the 
case of the opposite descent towards the course of the water, the water 
in the wave as it falls against the course of the river does not come 
upon water which flies away from its stroke, but upon water which is 
proceeding in the opposite direction to this fall; and consequently as 
the wave in its fall has four degrees of velocity and the water that 
comes to meet it is also of four degrees of velocity, the impetus of the 
wave acquires eight degrees of velocity, and therefore waves of rivers 
break against their current, and that of the sea breaks against the water 
that flies back from the shore against which it has struck, and not 
against the wind that drives it. c.a. 354 r. b 


Every movement of water creates flow and ebb in every part of the 
river where the swiftness of its course checks it. 

This is proved by the fact that where the course of the river is steeper 
it is swifter; and where it is more level it is slower. Therefore the level 
sea receives more water than it discharges; for which reason it is nec- 
essary for the water of the sea to rise to such a height that its weight 
overcomes the water that drives it; and then this water which has been 
driven descends from its height round about the base of the aforesaid 
hill, and that part which descends against the current mentioned before 
swells this current up in such a way that the upper part of its water is 
retarded, until the water that follows becoming more abundant subdues 
the ebb and creates a new flow. c.a. 354 r. e 

The impetus made in the great current of the water preserves its line 
among the motionless waves as the solar ray may do in the course of 
the winds. 



At one time the wave of the impetus is motionless amid the great 
current of the water, at another it is extremely swift in the motionless 
water, that is on the surface of the swamps. 

Why does a blow upon the water create many waves? c.a. 354 v. a 

The river which has always depth at the centre of its course will keep 
within its banks. 

Where the channel is more confined, there the water runs more 
strongly than elsewhere, and as it issues from the straight it spreads 
itself furiously, and strikes and wears away the near banks which lie 
across its course, and often changes its course from one place to another. 

c.a. 361 r. b 

The movement of the wind resembles that of the water. 

What is the difference between water which is drawn and water 
which is driven? 

Water which is drawn is when the Ocean as it falls draws after it the 
water of the Mediterranean Sea. 

Water driven is that caused by the rivers which, as they come into the 
sea, drive its water. 

Amid all the causes of the destruction of human property, it seems 
to me that rivers on account of their excessive and violent inundations 
hold the foremost place. And if as against the fury of impetuous rivers 
any one should wish to uphold fire, such a one would seem to me to be 
lacking in judgment, for fire remains spent and dead when fuel fails it, 
but against the irreparable inundation caused by swollen and proud 
rivers no resource of human foresight can avail; for in a succession of 
raging and seething [waves], gnawing and tearing away the high 
banks, growing turbid with the earth from the ploughed fields, destroy- 
ing the houses therein and uprooting the tall trees, it carries these as its 
prey down to the sea which is its lair, bearing along with it men, trees, 
animals, houses and lands, sweeping away every dike and every kind of 
barrier, bearing with it the light things, and devastating and destroying 
those of weight, creating big landslips out of small fissures, filling up 
with its floods the low valleys, and rushing headlong with insistent and 
inexorable mass of waters. 

What a need there is of flight for whoso is near! O how many cities, 
how many lands, castles, villas and houses has it consumed! 



How many of the labours of wretched husbandmen have been ren- 
dered idle and profitless! How many families has it brought to naught, 
and overwhelmed! What shall I say of the herds of cattle which have 
been drowned and lost! 

And often issuing forth from its ancient rocky beds it washes over 
the tilled [lands] . . . c.a. 361 v. a 

Where the channel of the river is more sloping the water has a 
swifter current; and where the water is swifter it wears the bed of its 
river more away and deepens it more and causes the same quantity of 
water to occupy less space. 

The shorter the course of the rivers the greater will be their speed. 
And so also conversely it will be slower in proportion as their course has 
greater length. 

Where the superabundance of the water is not received within the 
depth of its channel, necessity causes it to fall precipitately outside its 

No part of an element possesses weight within its element unless it is 
either moved within it with impetus, or falls down within it, being 
drawn by it from within another element. c.a. 365 r. a 

The course of a smaller flood of water conforms to that of the larger 
of the great floods, and changes course and keeps company with it and 
ceases to delve under the banks. 

The proof of this is seen in the Po. For when it is low its water runs 
many times in cross-currents, and called by the low places and directing 
its way towards these it takes its course and strikes the bank in its 
foundations, and hollows these out causing wide destruction. But when 
it flows in full stream the lesser quantity which formerly with its cross- 
current had beaten upon the banks and hollowed them, abandons its 
course, being dragged in company with the greater volume of water 
and advancing along the line of its base it forbears to damage its banks. 

a 23 v. 

The water which falls by the line nearest to the vertical is that which 
descends most rapidly and gives itself with greatest blow and greatest 
weight to the spot on which it strikes. 



Every stream of water when near to its fall will have the curve of the 
descent commencing on the surface before it commences in the depth. 

a 24 r. 

Water is by its weight the second element that encompasses the earth, 
and that part of it which is outside its sphere will seek with rapidity to 
return there. And the farther it is raised above the position of its ele- 
ment the greater the speed with which it will descend to it. Its qualities 
are dampness and cold. It is its nature to search always for the low- 
lying places when without restraint. Readily it rises up in steam and 
mist, and changed into cloud falls back again in rain as the minute 
parts of the cloud attach themselves together and form drops. And at 
different altitudes it assumes different forms, namely water or snow 01 
hail. Constantly it is buffeted by the movement of the air, and it 
attaches itself to that body on which the cold has most effect, and it 
takes with ease odours and flavours. a 26 r. 

It is not possible that dead water should be the cause of movement 
either of itself or of anything else. a 43 r. 


Man has been called by the ancients a lesser world, and indeed the 
term is rightly applied, seeing that if man is compounded of earth, 
water, air and fire, this body of the earth is the same; and as man has 
within himself bones as a stay and framework for the flesh, so the world 
has the rocks which are the supports of the earth; as man has within 
him a pool of blood wherein the lungs as he breathes expand and con- 
tract, so the body of the earth has its ocean, which also rises and falls 
every six hours with the breathing of the world; as from the said pool 
of blood proceed the veins which spread their branches through the 
human body, in just the same manner the ocean fills the body of the 
earth with an infinite number of veins of water. In this body of the 
earth there is lacking, however, the sinews, and these are absent because 
sinews are created for the purpose of movement, and as the world is 
perpetually stable within itself no movement ever takes place there, and 
in the absence of any movement the sinews are not necessary; but in 
all other things man and the world show a great resemblance. 




Clearly it would seem that the whole surface of the ocean when not 
fleeted by tempest is equally distant from the centre of the earth, and 
that the tops of the mountains are as much farther removed from this 
centre as they rise above the surface of the sea. Unless therefore the 
body of the earth resembled that of man it would not be possible that 
the water of the sea being so much lower than the mountains should 
have power in its nature to rise to the summit of the mountains. We 
must needs therefore believe that the same cause that keeps the blood at 
the top of a man's head keeps water at the summit of mountains. 



Where there is life there is heat, and where there is vital heat there is 
movement of vapour. This is proved because one sees that the heat of 
the element of fire always draws to itself the damp vapours, the thick 
mists and dense clouds, which are given off by the seas and other lakes 
and rivers and marshy valleys. And drawing these little by little up to 
the cold region, there the first part halts, because the warm and moist 
cannot exist with cold and dryness; and this first part having halted 
receives the other parts, and so all the parts joining together one to 
another form thick and dark clouds. 

And these are often swept away and carried by the winds from one 
region to another, until at last their density gives them such weight 
that they fall in thick rain; but, if the heat of the sun is added to the 
power of the element of fire, the clouds are drawn up higher and come 
to more intense cold, and there become frozen and so produce hail- 

So the same heat which holds up so great a weight of water as is seen 
to fall in rain from the clouds sucks it up from below from the roots of 
the mountains and draws it up and confines it among the mountain 
summits, and there the water finds crevices, and so continuing it issues 
forth and creates rivers. a 54 v. 

If heat is the cause of the movement of moisture cold stops it. This 
has been already shown by the example of the cold region which stops 



the clouds drawn by the hot element. As for the proof that the heat 
draws the moisture it is shown as follows: — heat a jug and set it in a 
vase with the mouth downwards, and place there some charcoal which 
has been lighted. You will see that the moisture as it retires before the 
heat will rise and fill the jug with water, and the air which was 
enclosed in this jug will escape through its opening. 

Also if you take a wet cloth and hold it to the fire you will see the 
damp of the cloth leave its place, and that part of the moisture which 
has least substance will rise up, drawn by the proximity of the fire 
which from its nature rises towards the region of its element. In this 
way the sun draws up the moisture. 



I say that it is just like the blood which the natural heat keeps in the 
veins at the top of the man, and when the man has died this blood 
becomes cold and is brought back into the low parts, and as the sun 
warms the man's head the amount of blood there increases, and it 
grows to such an excess there with the humours as to overload the veins 
and frequently to cause pains in the head. It is the same with the 
springs which ramify through the body of the earth and, by the natural 
heat which is spread through all the body that contains them, the 
water stays in the springs and is raised to the high summits of the 
mountains. And the water that passes through a pent-up channel within 
the body of the mountain like a dead thing will not emerge from its 
first low state, because it is not warmed by the vital heat of the first 
spring. Moreover the warmth of the element of fire, and by day the 
heat of the sun, have power to stir up the dampness of the low places 
and draw this to a height in the same way as it draws the clouds and 
calls up their moisture from the expanses of the sea. a 56 r. 

Of the opinion held by some that the water of some seas is higher 
than the highest summits of the mountains and that the water was 
driven up to these summits: 

Water will not move from one spot to another unless to seek a lower 
level, and in the natural course of its current it will never be able to 



return to an elevation equal to that of the spot whence it first issued 
forth from the mountains and came into the light. That part of the sea 
which by an error of imagination you state to have been so high as to 
have flowed over the summits of the high mountains for so many 
centuries, would be consumed and poured out in the water that has 
issued from these same mountains. You can well imagine that during 
all the time that the Tigris and the Euphrates have flowed from the 
summits of the Armenian mountains, 1 one may suppose the whole of 
the water of the ocean to have passed a great many times through their 

Or do you not believe that the Nile has discharged more water into 
the sea than is at present contained in all the watery element? Surely 
this is the case. If then this water had fallen away from the body of the 
earth, the whole mechanism would long since have been without water. 
So therefore, one may conclude that the water passes from the rivers to 
the sea, and from the sea to the rivers, ever making the self-same round, 
and that all the sea and the rivers have passed through the mouth of the 
Nile an infinite number of times. a 56 r and v. 



Water which falls from a height into other water imprisons within 
itself a certain quantity of air, and this through the force of the blow 
becomes submerged with it. Then with swift movement it rises up 
again and arrives at the surface which it has quitted, clothed with a fine 
veil of moisture spherical in form, and proceeds by circles away from 
the spot where it first struck. Or the water which falls down upon other 
water runs away from the spot where it strikes, in various different 
branches, bifurcating and mingling and interlacing one with another; 
and some, being hollow, are dashed back upon the surface of the water; 
and so great is the force of the weight, and of the shock caused by this 
water, that through its extreme swiftness the air is unable to escape into 
its own element, but on the contrary is submerged in the manner that 
I have stated above. 

1 Text is not de monti eruini, as given in M. Ravaisson-Mollien's transcript, but de 
moti ermjnj {de monti ertnini), as given by Dr. Richter. 




The movement of water tends always to wear away its support; and 
the part which is the softest offers the least resistance, and as it vacate: 
its place it leaves various hollows in which the water, whirling round 
in divers eddies, wears away and hollows out and increases these 
chasms, and striking against the newly-bared dikes leaps back and 
strikes upon the banks, consuming and eating away and destroying 
whatever stands in its path, changing its course in the midst of the 
havoc it has made, dragging with it in its course the lightest of the soil 
and then depositing it in the parts that are more tranquil. As it raises 
its bed the quantity and force of the water is lessened and its fury is 
transferred to the opposite side, and when it reaches the bank it eats it 
away and lays its foundations bare until with great destruction it has 
uncovered new ground. If it should find a plain it covers it, and carry- 
ing away and hollowing out it forms a new bed, and if it should come 
upon buried stones it uncovers them and lays them bare. But it often 
happens that these, because of their size, make resistance to the 
impetuous flood, and so after being driven against the rocks that are 
in the middle of its course it leaps back towards the opposite side, break- 
ing and destroying the opposite bank. a 59 r. 


Water which falls in the manner stated does not enlarge its pit, foi 
as the fact of it falling perpendicularly shows, there is but little force in 
the water that drives it from behind, and this is why it falls all broken 
and in fine spray almost in a perpendicular line. And the air which is 
amidst this broken water having an almost equal weight above it cannot 
escape so quickly as not to be submerged by the weight together with 
the blow. But, since air cannot be disunited from its element without 
violence, after yielding to the fury of the blow and the weight, it rises 
again quickly and returns to the surface in round bubbles near to the 
spot that was struck, and so as it does not move any distance from this 
spot it does not cause any damage to the banks of the pit. But when the 



rushing river, swollen by recent rains, scours its banks, it falls in tiny 
into the lower waters, and no longer as formerly descending peacefully 
ill a shower mingled with air upon the other water but united and 
strong, strikes and tears open the smitten depths right down to their 
rocky bed, uncovering and carrying away the buried stones, setting up 
for itself a new barrier in the shingle carried from the pit which it has 
made it throws itself upon it and falls back beaten, and divides at the 
blow into two different streams which separate and form half-circles, 
devouring and consuming every obstacle and enlarging their bed in the 
form of a circle. 

To put it more exactly — when the rivers are in flood, the falls of the 
water are less abrupt, and therefore, as the mass of water strikes the 
lower levels, the water which follows the blow does not hasten with 
the violence of that which falls, and this being the case it offers resist- 
ance and thus offering resistance the water rises and the fall becomes 
shorter. In consequence it does not imprison so much air, because the 
lower parts of the water are hardly separated from the rest in its fall 
and, owing to this, very little air can enter, and therefore the blow and 
weight of the water meet with no resistance, and the blow proceeds 
without diminishment right down to the bottom, displacing the gravel 
that is there and surrounding and clothing the stones with itself and 
increasing the depth of the pools. a 59 r. and v. 


The reason is that in the beds of rivers there are always found stones 
of different sizes, and as the water, coming to the largest, sinks down 
behind them and smites the spot on which it falls, the blow dislodges 
the lesser stones from the spot on which it strikes, and the bed is made 
larger. As the fall increases it becomes more powerful and hollows out 
even more the pit which has been begun; and this occurs because the 
rivers constantly gnaw the mud of their bed and constantly uncover 
and lay bare rocks of different forms and sizes. 




The reason of this is that just as a pair of stockings which cover the 
legs reveal what is hidden beneath them, so the part of the water which 
lies on the surface reveals the nature of its base, inasmuch as that part 
of the water which bathes its base, finding there certain protrusions 
caused by the stones, strikes upon them and leaps up raising with it all 
the other water which flows above it. a 59 v. 




The reason of this is that the water which strikes this rock afterwards 
descends and makes a kind of pit, in which in its course it searches for 
the hollow and then leaps back to a height and again falls down to the 
bottom and does the same, so continuing many times, like a ball that is 
thrown on the ground which before it finishes its course makes many 
bounds each smaller than the one before it. 



All the movements of the wind resemble those of the water. 

Universally all things desire to maintain themselves in their natural 
state. So moving water strives to maintain the course pursuant to the 
power which occasions it, and if it finds an obstacle in its path it com- 
pletes the span of the course it has commenced, by a circular and revolv- 
ing movement. 

So when water pours out of a narrow channel and descends with fury 
into the slow-moving currents of mighty seas — since in the greater bulk 
there is greater power, and greater power offers resistance to the lesser — 
in this case, the water descending upon the sea beats down upon its 
slow-moving mass, and this cannot make a place for it with sufficient 
speed because it is held up by the rest of the water; and so the water 
that descends, not being willing to slacken its course, turns round after 
it has struck, and continues its first movement in circling eddies, and so 



fulfils its desire down in the depth; for in these same eddies it finds 
nothing more than its own movement, which is attended by a suc- 
cession of circles one within the other; and by thus revolving in circles 
its course becomes longer and more continuous, because it meets with 
no obstacle except itself; and this motion eats away and consumes the 
banks, and they fall headlong in ruin. ... a 60 r. 


The reason of this is that, if the circles which above are large become 
reduced to a point as they are submerged, and then continue their 
movement in the direction in which it began, the water will at the 
bottom make a movement contrary to that above when it separates 
itself from its centre. 

Although the sounds which traverse the air proceed from their 
sources by circular movements, nevertheless the circles which are pro- 
pelled by their different motive powers meet together without any 
hindrance and penetrate and pass across one another, keeping always 
their causes as their centres. 

Since, in all cases of movement, water has great conformity with air, 
I will offer it as an example of the above-mentioned proposition. I say 
that, if at the same time you throw two small stones into a large lake of 
still water at a certain distance one from another, you will observe two 
distinct sets of circles form round the two points where they have 
struck; and as these sets of circles grow larger they come to meet 
together and the circles intersect one with another, always keeping as 
their centres the spots which were struck by the stones. The reason of 
this is that although some show of movement may be visible there, the 
water does not depart from its place because the openings made there 
by the stones are instantly closed; and the movement occasioned by the 
sudden opening and closing of the water makes a certain shaking 
which one would define as a quivering rather than a movement. That 
what I say may be more evident to you, just consider those pieces of 
straw which on account of their lightness float on the surface of the 
water and are not moved from their position by the wave that rolls 
beneath them as the circles widen. This disturbance of the water, there- 



fore, being a quivering rather than a movement, the circles cannot 
break one another as they meet, for, as all the parts of water are of a 
like substance, it follows that these parts transmit the quivering from 
one to another without changing their place, for, as the water remains 
in its position, it can easily take this quivering from the parts near to it 
and pass it on to other parts near to it, its force meanwhile steadily 
decreasing until the end. a 6i r. 

The winding courses of the water caused by the rebounds of the 
percussions which they make against the banks will cause the bed of the 
river below them to be more hollowed out than any other part; and in 
their percussions they will become of great depth; and the water that is 
whirled round near to these deep places will serve to undermine and 
destroy the banks against which it strikes. 

One both clearly sees and recognises that the waters which strike the 
banks of the rivers act in the same way as balls which, when they are 
struck against walls, rebound from these at angles similar to those at 
which they strike, and proceed to strike against the opposite sides of the 
walls. So these waters after having first struck against the one bank, 
leap back towards the opposite one and strike upon it and hollow it out 
with vigour, because there is a greater confluence of water in this spot. 
The reason of this is that the water which leaps back from one bank to 
another hollows out that part of the bed of the river which finds itself 
beneath it; and the other water of the river which cannot be received in 
this low part remains repulsed and thrown back somewhat by the direct 
course of the river. And having no way of escape, it returns to its 
natural course, that is, that, as the bed of the river finds itself lower 
under the winding ways made by the above-mentioned percussions of 
the waters, this second water, which has lost its adventitious means of 
escape, resumes its natural course, falls into the lower parts of the river 
and strikes the banks at the same spot as that which witnessed the per- 
cussion of the aforesaid rebounds. As this bank is thus assailed by two 
entirely different sets of percussions a larger hollow is caused in it, for, 
while the first strike the bank above, the others descending more 
steeply devour and lay it bare at its base, and this is the cause of the 
aforesaid destruction and subsidence of the banks. a 6$ v. 




No part of the watery element will raise itself or make itself more 
distant from the common centre except by violence. No violence is last- 
ing, c 15 r. 


This is because [confined] water when struck by a blow cannot make 
its impetus pass from circle to circle as it would in a great lake; and 
since the water when struck finds near to itself the edges of the bucket, 
which are harder and more resisting than the other water, it cannot 
expand itself, and consequently it comes about that the whole of its 
impetus is turned upwards; and therefore water struck by a stone 
throws its drops up higher when its waves are confined than when they 
have a wide space. c 22 r. 

[Of the motion of water] 

Water or anything falling upon water causes the water that receives 
the blow to spread itself out beneath the blow and to surround it, and 
having passed over the cause of this blow it continues above it in pyra- 
midal shape and then falls back to the common level. 

The reason of this is that when a drop of water falls from a roof 
upon other water, the part that receives the blow cannot find room or 
escape within the rest of the water with the speed with which it has 
been attacked, because it would be necessary for it to support too much 
weight in order to enter under so great a quantity of water. Having 
therefore to obey its own course as well as the action of that which 
drives it from its place, and finding that as the adjacent water does not 
receive the blow and is not ready for a similar flight it cannot penetrate 
it, it seeks instead the shortest way and flows through the substance 
that offers it less resistance, namely the air. 

And as this first circle that surrounds the place which has been struck 
closes up with fury, because it was raised above the common surface of 
the water, it reduces the water that escapes upwards to the form of a 



And if you think that the water which falls was the same as that 
which leaps up, make a small stone drop into the water and you will 
see the water leap up in the same way and not the stone. c 22 v. 

Every part of water within other water that is without movement 
lies equally at rest with that situated at the same level. 

Here experience shows that if there were a lake of very great size 
which lay without movement of wind either entering or departing, and 
if you were to remove a very small part of the height of the bank which 
is below the surface of the water, all the water that is above the top of 
the bank that was cut away will pass through this cutting, but will not 
set in movement or draw with it out of the lake any part of the water 
that lay there before this water moved and went away. 

In this instance nature is constrained by the workings of its law 
which lives infused within it, namely, that all the parts of that surface 
of the waters which are supported by the banks without any opening or 
exit are situated at an equal distance from the centre of the earth. 

c 23 v. 



Know that stones are rolled over by water because this water either 
surrounds or flows over them. If it surrounds them it meets again 
beyond them and intersects, hollowing out the soil or sand beyond the 
stone, and this after being thus laid bare begins to roll of itself. And if 
the water flows over the stone, then after it has done so it falls in the 
same line, and by the force of its impetus penetrates from the surface to 
the base of the other water, and gnaws and tugs and drags away the 
stone from the opposing obstacles with the result that this also begins 
to roll, and so continues from place to place until it traverses the whole 
river. And if a lesser stone should stand in its path the water uncovers 
it by the same process and does the same, and in this way stones are 
rolled over in the beds of flowing rivers. c 24 v. 

A horse or man or any other creature that makes its way through 
stagnant water of medium depth will cause this water to rise and cover 



a quantity of the shore towards which this creature is directing its 

This may be clearly demonstrated; for if you take a step in this water 
you will find that it makes a wave which directs its course and moves 
in the same direction as that in which the creature is travelling; nor 
does it pause until it has achieved its desire and covered a small part of 
the shore. 

A second step creates another wave which has a similar result, and 
the same with the third and all the steps; each of itself creating a wave 
that travels as far as the shore, in such a way that this shore which 
formerly was uncovered finds itself covered by water over a great dis- 
tance — then when you have emerged from this water you will see it 
returning to its former position in swift course. c 25 r. 

Waves of rivers that flow against the courses of the winds will be of 
greater height than others. 

The rivers that move against the courses of the winds will have a 
greater current below than above, as their surface on being driven by 
the winds becomes slower than it was at first. 

The reason of this is that if the rivers, being of equal depth and 
breadth, are of uniform current at the bottom and on the surface, the 
resistance made by the wind to the current on the surface must neces- 
sarily cause it to turn back, and as it does not suffice these waves to 
raise themselves a little, falling at last they enter underneath the others 
and proceed to the bottom. Finding there the other current of the bot- 
tom it accompanies it, and as the bank is not capable of containing this 
increase it is necessary that at the bottom the current doubles itself; if 
it were not so one would see the water rising far above the banks of the 
rivers. c 25 v. 

The stone placed in the level and smooth beds of flowing rivers 
becomes the cause of their inequality and deterioration. 

When an object which is dropping down strikes upon another object 
harder than itself it suddenly makes a rebound which is so much 
greater as it has had a greater fall. When therefore a stone is situated 
beneath the surface of running rivers, the greater its size the greater is 
the percussion that takes place when water falls from its summit upon 



the beds of the rivers, and on account of this it comes to produce a 
deeper hollow in the place struck by this water. 

After this first percussion many rebounds will follow, and these will 
become larger in size and less powerful as they are farther removed 
from the first. 

The embankment which sends forth the trunk of the tree that it has 
nourished, to project into the waves of the rapid rivers, will become the 
cause of the destruction of the opposite bank. 

The cause of this effect is that the water that flows in the rivers 
always goes leaping from bank to bank. If nothing projects in this bank 
many lines of water gather there and unite together and leap in a mass 
on the opposite bank, and twist themselves in with the other lines 
which they meet with on their way; and having reached the embank- 
ment they gnaw and destroy it. And there are yet new lines produced 
there which leap back and damage the other bank; and so from place 
to place they begin to form eddies of varying depths, and hence it 
comes about that straight rivers become winding and crooked. 

c 26 r. 


Of the four elements water is the second least heavy and the second 
in respect of mobility. It is never at rest until it unites with its maritime 
element, where, when not disturbed by the winds, it establishes itself 
and remains with its surface equidistant from the centre of the world. 
It is the increase and humour of all vital bodies. Without it nothing 
retains its first form. It unites and augments bodies by its increase. 

Nothing lighter than itself can penetrate it without violence. 

It readily raises itself by heat in thin vapour through the air. Cold 
causes it to freeze. Stagnation make it foul. That is, heat sets it in move- 
ment, cold causes it to freeze, immobility corrupts it. 

It assumes every odour, colour and flavour, and of itself it has noth- 
ing. It percolates through all porous bodies. Against its fury no 
human defence avails, or if it should avail it is not for long. In its rapid 
course it often serves as a support to things heavier than itself. It can lift 
itself up by movement or bound as far as it sinks down. It submerges 
with itself in headlong course things lighter than itself. The mastery 



of its course is sometimes on the surface, sometimes in the centre, 
sometimes at the bottom. One portion rises over the transverse course 
of another, and but for this the surfaces of the running waters would 
be without undulations. Every small obstacle whether on its bank or in 
its bed will be the cause of the falling away of the bank or bed opposite 
to it. When the water is low it does more damage to the bank in its 
course than it does when it flows in full stream. Its parts do not weigh 
upon the parts placed beneath them. No river will ever keep its course 
in the same direction between its banks. Its upper parts do not impart 
weight to the lower. 

[An experiment] 


I wish to show you in what manner water can be supported by air 
while being divided and separated from it. Certainly if you have reason 
in you, I believe that you will not deny that if there be a leather bag 
placed at the bottom of the water in a well, so as to touch all its sides, 
in such a way that the water cannot pass beneath, if this leather bag be 
filled with air it will not exert less force in rising to the surface of the 
water to find the other air than the water makes in its desire to touch 
the bottom of the well. And if this leather bag desires to rise up it will 
push up the water that is placed above it, and by raising this water it 
will take its weight from ofT the bottom of the well. For this reason 
therefore it is almost as though the well were bottomless. 

Where and why the movement of the water ought to hollow out the 
sand of the surface of the beds of flowing rivers — but to speak first of 
the percussion on the surface: 

The more rapid the current of the water along the slope of a smooth 
canal the more powerful will be its percussion against whatever opposes 

For all the elements when removed from their natural position desire 
to return to it, especially fire, water and earth; and the shorter the line 
along which this return is made, the straighter its course, and the 
straighter its course the greater the percussion upon whatever opposes 



The same effect is produced by the wind blowing through streets 
of uniform width. c 26 v. 



Define first of all what is height and depth, also how the elements are 
situated one within the other. Then what is solid weight and liquid 
weight; but first of all what weight and lightness consist of in them- 
selves. Then describe why water moves, and why its motion ceases; 
then why it becomes slower or more rapid, and in addition to this how 
it continually descends when in contact with air that is lower than 
itself; and how the water rises in the air through the heat of the sun 
and then falls back in rain. Further, why the water springs from the 
summits of the mountains, and whether any spring of water higher 
than the ocean can pour forth water higher than the surface of this 
ocean; and how all the water that returns to the ocean is higher than 
the sphere of the water: and how the water of the equinoctial seas is 
higher than the northern waters, and is higher beneath the body of the 
sun than in any other part of the circle of the equator; for when the 
experiment is made under the heat of a burning brand, the water boils 
as the effect of the brand, and the water around the centre of where 
it boils descends in a circular wave. And how the waters of the north 
are lower than the other seas, and more so as they become colder, until 
they are changed into ice. e 12 r. 


That river which stretches itself out most by long tortuous windings 
is the one which becomes filled up most rapidly with matter. This is 
proved by the twelfth, which says: — the water that loiters most dis- 
charges most rapidly the matter that it carries. Therefore the river 
which by meandering more makes itself longer by means of its twists 
and turns makes itself so much slower in proportion as it makes itself 
longer. e 66 v. 

Of the difference that exists between the accidents of water and 
the accidents of air and fire: 

Water is not capable in itself of being either condensed or rarefied, 
but it exists in as great quantity in front of the fish that penetrates it as 




behind it, and it opens itself up as much in front of that which pene- 
trates it as it closes up behind this penetrating thing. And the impetus 
of the fish is of briefer duration than that of the bird in the air, 
although the muscles of the bird are very powerful in relation to their 
quantity; because the fish is all muscle and this is very necessary 
because it is in a heavier substance than the air. But although the water 
is not itself capable of being condensed it is of a nature to acquire 
gravity and levity. It acquires gravity at the destruction of the impetus 
which raises it in the air at the creation of the wave, and levity by the 
creation of the impetus that lightens the water and causes it to move 
contrary to the natural course of heavy things. 



The valley interposed between the waves is lower than the general 
surface of the water, as one sees when the water turns back in order to 
fill up the places that have been struck by the water-spouts. 

e 71 v. 


Of those that take up the whole of this height and of the moving and 
the fixed. Of the long and the round. Of those that change their move- 
ment and those that divide, and those that become merged in those 
[eddies] to which they unite themselves, and those that are mingled 
with the falling and reflex water and make it spin around. 

Which are the eddies that cause light things to whirl round on the 
surface and do not submerge them? Which are those that submerge 
them and cause them to spin round upon the bottom and then deposit 
them upon this bottom ? Which are those that separate the things from 
the bottom and throw them back to the surface of the water? Which 
are the slanting eddies, which are the straight, which are the shallow? 

f 2 r. 




When you put together the science of the movements of water 
remember to put beneath each proposition its applications, so that such 
science may not be without its uses. 

Of the usefulness of the courses that the swimmer ought to follow 
with regard to the surface revolutions of the waters and as to their 
eddies which submerge these swimmers. Then how he ought to direct 
himself when submerged in order to save himself, and so forth. 

And at the end of each book notice the things that are most remark- 
able, as how to break through the thickness of the eddies in any direc- 
tion. Of what measures one ought to take when swimming in a 
rough sea, and how to avoid being dashed against the rocks and on the 
rudders of ships. f 2 v. 

Of the things carried by the water, that will make the greatest 
revolution which is of least size : 

This happens because the great revolutions of eddies are infrequent 
in the currents of rivers and the small eddies are almost numberless, 
and large objects are only turned round by large eddies and not by 
small ones, whereas small objects revolve both in small eddies and 

Of objects equal in length and breadth carried by the current of the 
waters, those will make fewest revolutions which are deepest. 

This happens because these revolutions vary greatly from the surface 
to the bottom of the water, in which as many revolutions are produced 
as there is depth to cause them. Wherefore of necessity an object borne 
by the water when it buries itself deeply is buffeted by many revolu- 
tions at different degrees of altitude; and for this reason it remains in 
a state of hesitance and many times obeys none or if it obeys then it 
obeys the most powerful. 

Of objects equal in shape and size, that which is buried deepest will 
obey least the revolutions of the water. f 3 r. 

Book ten. Of the different recesses and roundnesses that exist in 
reservoirs, before the exits of the water from these reservoirs, with the 



varying rates of speed, sizes, depths and breadths; and the shapes of the 
holes, high or low, wide or narrow; and the walls thick or thin. 

f 4 v. 

Book nine. Of the water that passes through a reservoir, of which 
the walls are full of holes of various sizes, shapes and positions, at dif- 
ferent heights, varying from the entrance to the exit and conversely; 
and so also the reservoir of different shapes, depths, lengths, and 
breadths; and the water more or less powerful and swift, great and 
small. f 5 r. 

The flow and ebb is double in the same sheet of water, because it 
will be many times at the mouth of this sheet of water before there is 
a decrease in the great sheet of water; this occurs because the wave of 
the first flow runs strongly in the sheet of water, and during the time 
when this wave follows its impetus that at the mouth makes its ebb. 
Before the wave, penetrating into the neck, feels the ebb at this mouth 
of the sheet of water g a, the flow starts again at this mouth, and in this 
time the wave, which has penetrated into the neck, pauses, slackening 
its impetus in proportion as the second penetration by the second wave 
begins afresh. Thus so many of these waves enter the neck that the 
sheet of water is raised and its waters come back with impetus behind 
the ebb that recedes from this mouth, and [this ebb] does not pene- 
trate farther in the third or fourth wave, so that the first water is not 
thrust out of the entrance. f 6 v. 

In the big wide eddies, the water raises and uncovers the soil heaped 
up in its centre. 

In the small eddies of water, the water bores down and makes a 
hollow in the centre of the eddy. 

Of objects borne by the water upon its bed, the lighter makes a 
longer path in the same time. 

A river does not remain uniform, for after the current it unloads 
shingle, and after this it produces another current, of which the move- 
ment is directed either to the bank or the centre or to as many different 
spots as there are different slopes of the mounds of shingle left at the 
bottom by the aforesaid currents. f 7 r. 

The depth of the sheet of water which receives the fall of the water 



will always have the shape of a quarter of a hollow sphere, if the soil be 
of uniform resistance. 

And this arises out of what has gone before, where it is stated that the 
straight course of the water is higher and swifter in the middle than on 
the sides; and the greater speed sends its fall more forward than does 
the slower speed. ... f 7 v. 

Given the depth of the fall of the water and its slant, with the power 
of the wheel that is its object, one seeks the height of the fall of this 
water in order to make itself equal to the power of the wheel. 

The water that strikes upon the objects sometimes leaps up con- 
siderably, sometimes only a little, and sometimes it descends, and this 
arises from the objects being small or large, or the descent in front of 
these objects being greater or less, or from the current that strikes these 
objects being more or less powerful. f 8 v. 



Why the eddies of the water are hollowed in the centre by their 

Why the impressions produced on the surface of the water will main- 
tain themselves for some time, on being carried by the course of the 

Why the movements of the impressions of the waters penetrate each 
other without change of their first shape. 

Rule as to the measurements of water and what breadth, depth, and 
rapidity of movement a given space of current ought to have in a given 

Given the resistance of a wheel and given the slant and descent in 
the fall of the water, one asks how great must its volume be to be 
equal to the said resistance. 

Given the volume of the fall of the water and its length and slant, 
one asks whether the power of the wheel is equal to this power of the 

Given the resistance of the wheel and the slant of the water and its 
volume, one asks the length of the fall. f 9 r. 












Water that pours out through the same-sized mouth may vary in 
extent in a greater or less degree in [various] ways, of which the first is 
that the surface of the water may be either a greater or less distance 
above the mouth through which it pours, the second that the water 
passes with greater or less speed beyond the bank where this mouth is 
made, the third that the side below the thickness of the mouth where 
the water passes may be either more or less slanting, the fourth in the 
variety of slant of the sides of this mouth, fifth in the thickness of the 
lip of this mouth, sixth as to the shape of the mouth, that is whether it 
be round or square, or rectangular or elongated, seventh according as 
this mouth is placed at a greater or less slant of bank in its length, 
eighth as this mouth is placed in a greater or less slant of bank in its 
height, ninth according as it is situated in the concave or convex parts 
of the bank, tenth as it may be placed towards the greater or less width 
of the canal, eleventh if the top of the canal has more speed at the top 
of the mouth or more slowness than elsewhere, twelfth if the bed have 
round bosses and hollows opposite to this mouth or higher or lower, 
thirteenth according to whether the water that passes through this 
mouth takes the wind or not, fourteenth if the water that falls out of 
this mouth falls through the air shut in on one side or on all except the 
front, fifteenth as the water that falls thus enclosed is deep within its 
vessel or shallow, sixteenth whether the enclosed water which falls 
makes a long fall or a short one; seventeenth whether the sides of the 
canal where this water descends are hollow or protuberant or straight 
or curving. f 9 v. 

Of the eddies of water which frequently turn their revolving move- 
ment backwards : 

Of the falling and the reflex eddies. The eddy sometimes grows in 
power and diminishes in diameter, and sometimes diminishes in 
strength and increases in diameter. 

The first movement is when the water flows away by its base, as the 
water that forms the eddy becomes swifter when it is lower, because 
it has a greater weight of water above it and therefore becomes swifter; 



and because the water pushes downwards more than upwards it 
restricts this void in the eddy more and more; and it bends because it 
directs itself to whether the sheet of water has its outlet. f 12 r. 

Water with an uneven bed makes contrary movements from the sur- 
face to the bed. The unevenness in the beds of rivers springs from the 
bends in the banks or from substances that have fallen from these banks 
to their feet. f 12 v. 


When the hand is turned in circular movement in a vase half-filled 
with water it causes an accidental eddy which will expose the bottom of 
this vase to the air, and when its motive power is at rest this eddy will 
follow the same movement but it will diminish continually until the- 
end of the impetus imparted to it by its motive power. f 13 r. 


The eddy with the deeper hollow will be that produced in water of 
swifter movement. 

And that eddy will have a smaller hollow if it is produced in deeper 
water which has not the same movement but is slower. 

And with water of equal speed that will keep a larger hollow where 
a greater depth of water turns with its movement. 

This is said because many times the eddies are produced in a straight 
current in a great expanse of slowly moving water; and as this water is 
partly supported by the eddy which revolves in a thin coil between it 
and the air of the hollow, this lateral water being of great weight 
pushes upon the sides of the eddy where it is leaning and finding them 
weak compresses them. f 13 v. 

[Of eddies] 

If water higher than air acquires weight, as is shown in the seventh 
of the ninth, why is it that the water of the sides of the eddies is higher 
than the bottom of the eddy which up to this point is full of air. 

You have the fourth of the seventh which proves that every heavy 
substance is only of weight along the line of its movement and in no 
other direction; and here you see very deep eddies after the manner of 



great pits in rivers, the sides of which are of water, which is every- 
where higher than the air of this eddy; and these banks of water are 
without weight except by this line of their movement, during the time 
in which they possess the strength given them by their motive power. 

What produces eddies and why some are hollow at the centre and 
others are not. 

Whether water poured into the hollow of eddies would fill them 
or no, or would escape by the bottom and enter into the current at the 

Which natural eddies are of considerable depth and which of slight 
depth; which change their position and which do not move; which 
while moving turn in an opposite direction and which keep their move- 
ment in one direction; which become duplicated and which do not; 
which unite in contrary movements. f 14 v. 


Write first of the simple hollows made by the simple falls of water 
upon a bed of a uniform substance, and then upon a bed of various 
substances. Then with obstacles placed in the course that the water takes 
in its descent, then with obstacles in the place where it has struck, that 
is, upon its bed; then in its reflex movement, and first at the beginning 
of its fall. Then describe in what part of the edge of the sheet of water 
this water will take its course; and what substances will be carried away 
or deposited in different parts of the bed of this sheet of water; and 
what will be the speed or slowness of movement of the water in various 
parts of the surface, and so also from the surface to the bottom at 
various depths and breadths; and thus you will do as far as the bottom. 

f 15 v. 
[Movements of water] 

Of the parts of the same water that rises through the air at different 
angles, that which has least slant falls back nearer to where it started. 

The rising motions of the water which it makes from the bottom to 
the surface of the sheet of water will never fall back towards the bot- 
tom, because not entering into the air and not acquiring weight they 
cannot penetrate to the bottom, by the seventh of the ninth. 

The water alwavs rises and descends with a disconnected movement 



of speed, and this is caused by the air that it penetrates and the air that 
is mingled with it. f 16 v. 


It is possible for there to be less depth underneath the current than 
before it or on the sides. 

Let o c n be the current and a an eddy of double strength according 
to the ninth concerning eddies. Since in addition to its revolution it 
strikes against the bank and leaps up into the air, and falling back upon 
the rest of the water penetrates it and strikes and hollows out the bed in 
sudden chasm, for, in addition to the force of the blow, there is joined 
the spiral drilling made by the aforesaid revolution, by means of which 
what has been shaken by the blow is stirred up and carried away; and 
it becomes more powerful as it is more turbid. 

And this is the most powerful method that can be made use of in 
order to dislodge and carry away the soil and so create a great chasm. 

Beneath the current the bed will become raised when the course of 
this current dies in stagnant water. 

By the sixth of the ninth — where the course of the water fails, there 
remains that which the water has brought. f 17 v. 

Of a volume of water that has struck upon an object, the lower part 
is the first to strike the bottom and it is instantly reflected to the 
surface. That which is in the middle does not descend to the bottom, 
but encountering the first part reflected it strikes upon it, and is 
knocked and so it also is bent back in the same lines and revolutions. 

And the two bodies of water when the lower encounters the higher 
unite and revolve together at their contact. 

Of the water that falls into other water that which is nearest the 
centre of the fall slants most and that nearest the extremities is the 
straightest. f 18 v. 


When water strikes other water at a considerable angle the part 
which strikes first is immediately bent back and delays, and that which 
succeeds to it veils it with a thin covering and runs swiftly upon that 
which first slackens and so it is then bent and slackens at the same 



bpot as the foregoing. And the water that follows does the same upon 
it, and so in succession each new wave follows its course. 

The turbid running water, if it is high at its start and at its entry 
into the sheet of water, flows for a considerable distance at the height 
of its first impetus before it buries itself or becomes mingled with the 
other water. f 19 v. 

Definition of the half-cylindrical wave and what part of its volume 
has a greater or less slant, and how it commences and ends, and where 
it is more or less wide or more or less high or I would say deep; and the 
differences that there are in it when it is large or small or swift or slow. 

The waters flow one above another without mingling for a long 
space, when their entrance in the sheet of water is higher and swifter 
in the one case than in the other. f 20 r. 

Where the water has only slight movement the half-cylindrical waves 
will keep their direction when they intersect. 

Where it is swifter they will curve. 

And where the rates of speed are unequal their curves will vary 
towards the end. f 20 v. 

Of the eddies one is slower at the centre than on the sides, another 
is swifter at the centre than on the sides; others there are which turn 
back in the opposite direction to their first movement. 

That eddy is slower at the centre than on the sides which makes a 
great revolution, and this deposits a considerable quantity of matter in 
the centre of its circle and leaves it in the form of a mound. 

The eddy which is swift at the centre of its revolution carries air and 
water in its base, which it hollows out and bores down after the fash- 
ion of a well. f 21 r. 

Every impression of the water is maintained over a long space and 
this is so much the longer as it is swifter. 

Write of the things worthy of remark that are found in water; and 
what revolutions they make when they are of different shapes and the 
water makes different revolutions. f 21 v. 

Of the different rates of speed of currents from the surface of water 
to the bottom. 



Of the different cross slants between the surface and the bottom. 

Of the different currents on the surface of the waters. 

Of the different currents on the bed of the rivers. 

Of the different depths of the rivers. 

Of the different shapes of the hills covered by the waters. 

Of the different shapes of the hills uncovered by the waters. 

Where the water is swift at the bottom and not above. Where the 
water is slow at the bottom and swift above. 

Where it is slow below and above and swift in the middle. Where it 
is slow in the middle and swift below and above. 

Where the water in the rivers stretches itself out and where it con- 
tracts. Where it bends and where it straightens itself. 

Where it penetrates evenly in the expanses of rivers and where 
unevenly. Where it is low in the middle and high at the sides. 

Where it is high in the middle and low at the sides. 

Where the current goes straight in the middle of the stream. Where 
the current winds, throwing itself on to different sides. 

Of the different slants in the descents of the water. f 23 v. 


Of the waters that cross at different angles in their reflex move- 
ments, and of those that cross on the summits of the waves; those that 
cross the descending wave and those that cross in the trough of the 

Some cross at different angles, great reflex movement with small 
reflex movement, and similarly a great wave with a small one, or fall- 
ing movement with that in the valley or with reflex movement, small 
with large. 

Sometimes there is reflex with falling movement, sometimes valley 
with wave, sometimes falling movement with reflex, small and large, 
and at different angles. 

Sometimes rapid waters with slow, sometimes eddies with waves or 
valleys or reflexes, or the falling movements of water flowing along 
different lines crossing one another. 

Courses by different lines one above the other. 



Eddies with different movements which have to meet and enter into 
one another. 

Lengths of different curves of eddies from the surface of the water 
to its bed as they intersect one another. 

Intersection of falling and reflex eddies. 

Of the waters that are interposed in any direction between the said 
accidents of the waters. f 24 r. 

[Boo\s of the Treatise on Water] 

Book nine of the shapes of the eddies. 

Book ten of the action of the eddies. 

Book eleven of things that aid the eddies. 

Book twelve of things that injure the eddies. 

Book thirteen of the percussions of the waters one with another as 
they leap up within the air at different rates of speed. 

Book of the waters that spring up within the air at different angles 
and with the same speed. 

Book of the waters that spring up within the air and the different 

Water more slanting, striking that less slanting and more powerful 
and less deep. 

Water less deep and more slanting and more powerful than the 
deeper and less slanting. 

Shallow water driven through the air by greater power than the 
deeper water. f 24 v. 

Of the waters falling through the air which intersect with various 
depths and lengths of movement and power. 

The reflex movement will never be of the height of the beginning 
of the falling movement unless it strikes as does the wave on the rock 
of the sea. f 25 r. 

[Of the waves] 

In proportion as the waves of the sea are higher than the ordinary 
height of the surface of its water, so the bottoms of the valleys that lie 
between the waves are lower; and this is due to the fact that the great 
fall of the great waves creates the great hollows of the valleys. 

f 25 v. 




Here follows the proof of what is said on the opposite page: 

I say that no part of the surface of water moves of itself unless it 
descends, therefore as the sphere of water has not the power to descend 
in any part of its surface, it follows from the first conception that it 
does not move of itself. And if you carefully consider each minute 
particle of this surface you will find it surrounded by other similar 
particles which are at an equal distance between them from the centre 
of the earth, and at the same distance from this centre is that particle 
which is surrounded by them; therefore, by the third conception, that 
particle of the water will not move of itself because it is surrounded by 
edges of equal height. And thus every circle formed of such particles 
makes itself a vessel for the particles enclosed within this circle, which 
vessel has the circle formed by its edges of equal height; and in this 
respect this particle resembles all the other similar ones of which the 
surface of the sphere of the water is composed. Of necessity it will be 
without movement of itself, and in consequence each being at equal 
height from the centre of the world, necessity makes their surface 
spherical, but it is not necessary that they should be spherical below, as 
reason and experience show. 

That which is said of the surface of the water that borders on the air 
is understood to be said of the surface of the air that borders on the 
fire, which would be such as often to evaporate after the manner of 
clouds drawn by the heat of the sun, as does the water drawn through 
the air by the same heat in the form of clouds; and in the same way 
the fire drawn by a greater heat than its own, that is to say by the sun, 
it being proved in the sixth that it is warm by essence and not by 
virtue, as many would have it. 

So having proved by the testimony of these spheres that the flexible 
elements are spherical, it is my purpose to investigate nature both in its 
universal aspect and in the particulars of each of its elements, and first 
of fire, then of air, and then of water. f 26 v. 

Book thirty-two. Of the movement that fire makes when it pene- 
trates the water at the bottom of the boiler: 

It runs bubbling to the surface of this water by different ways and 



according to the movements that the water makes when struck by the 
penetration of the fire. By means of this experiment you can investigate 
the hot vapours which are exhaled from the earth and pass through the 
water, twisting themselves about because the water checks their move- 
ment, vapours which afterwards penetrate through the air in straighter 

And this experiment you will make with a square glass vessel, keep- 
ing your eye at about the centre of one of these walls; and in the 
boiling water with slow movement you may drop a few grains of 
panic-grass because by means of the movement of these grains you can 
quickly know the movement of the water that carries them with it. 
And from this experiment you will be able to proceed to investigate 
many beautiful movements which result from one element penetrating 
into another. f 34 v. 


The water that falls from the cloud is sometimes dissolved into such 
minute particles that by reason of the friction that it has with the air it 
cannot divide the air but seems to change itself into air. Sometimes in 
descending it multiplies, because it finds the minutest particles of water 
which by reason of their lightness were of slow descent, and becomes 
incorporated with them, and at every stage of its descent acquires a new 
quantity of water. Sometimes the winds bend the rain and so cause its 
descent to be slanting, and for this reason the descent becomes slow and 
protracted, and it frequently happens that it is converted into such fine 
particles that it can no longer descend and so remains in the air. 

[Treatise on water] 

Write how the clouds are formed and how they dissolve, and what 
it is that causes vapour to rise from the water of the earth into the air, 
and the cause of mists and of the air becoming thickened, and why it 
appears more blue or less blue at one time than at another. Write in 
the same way of the regions of the air and the cause of snow and hail, 
and how water contracts and becomes hard in the form of ice, and of 
the new shapes that the snow forms in the air, and of the trees in cold 
countries with the new shapes of the leaves, and of the pinnacles of ice 
and hoar-frost that form new shapes of plants with strange leaves, the 



hoar-frost serving almost as the dew ready to nourish and sustain the 
said leaves. f 35 r. 

No surface of water that borders upon the air will ever be lower than 
that of the sea. 

The wave that the motive power makes before it in the air or be- 
tween the surface and the bed of the water is in the shape of a half 

The wave made by the motive power on the surface of the water is 
in the shape of a half-circle, and towards the bottom it has the shape 
of a quarter-circle. 

Why the movement made by the motive power on the surface of the 
water makes a wave before it, and does not do so when it moves be- 
tween the surface of the water and its bed. What one asks occurs 
because the water of the surface borders on the air, whereas the water 
that is between the surface of the water and its bed borders on the 
water that is above and the water that is below. f 41 r. 

Of the water that falls from the weirs of rivers, that part will have 
its straight course shut in which has the most powerful fall: 

This comes about because water with a powerful fall hollows out the 
soil of the spot on which it strikes and deposits it where its course is 
more feeble than beneath the reflex movement of the water; this as it 
moves towards the sky becomes more feeble with each degree of its 
movement until at last it loses all its power. 

And as in this reflex action its power ebbs it lets fall below it all the 
things of weight taken from the spot where it has struck, and after this 
inundation the water becomes lowered and finds itself shut in between 
the matter which it formerly carried and the bank from which it has 

Of the waters that descend in torrents from the weirs of rivers only 
that will preserve its straight course beyond this torrent of which the 
fall was feeblest and slowest. 

This happens because that which moves slowly strikes feebly, and 
therefore it follows that it only raises itself a little from the bed on 
which it strikes, and in consequence deposits but little in the reflex 
movement of the water. And this is why after this deluge the bank here 



remains low, and all the water that falls follows its course where the 
bank is lower, and consequently the straight course of all the water of 
the river will remain with the water that has a feeble fall. f 42 v. 

Of the things borne by the water which have part of themselves in 
the air and part in the water: 

If a thing is borne by the water being half in the water and half in 
the air, and the air moves with a speed equal to the speed of the water, 
then this movable thing will be in the first stage of swiftness of move- 

If the air is slower than the movement of the water which moves in 
the same direction as the air, the movement of the movable thing will 
be slower than if these movements of air and water were equal, and it 
will be so much slower in proportion as these movements of air and 
water are more different. 

If the movement of the air is swifter than that of the water 1 which 
moves in the same direction, then this movement of the object will be- 
come more rapid, and the more so as this air is swifter than the water. 1 

If the movement of the air against the course of the water is of equal 
speed to that of this water against the air, the movable thing will follow 
the course of the water if it has more contact with the water than with 
the air: it will do the contrary if it has more contact with the air than 
with the water. f 43 v. 

How a leaf is whirled about along different lines in the depth of the 
water : 

This movable thing revolves along different lines, high and low, 
turning itself over or not turning over, and doing the same in the 
width of the water which moves it. And this springs from the different 
movements of the water with its different slanting and eddying courses. 
Here one may place objects of different shapes, and one will have made 
a good experiment in 2 . . . by the leaves of the trees which are borne 
in considerable quantities from the surface to the depth of the flowing 
and transparent waters. f 44 r. 

1 MS. aria. 

2 Words erased in MS. 




To set forth the conditions of the waters that spring forth within the 
air, and their percussions made with different degrees of power, quan- 
tity, length of movements and variety of slant, I will institute a com- 
parison between the four principal winds, namely: north, south, east 
and west; and with these conditions I shall equip myself to give 
information as to the aforesaid movements of the water within the air; 
as a result this description will be briefer and more expeditious. 

f 45 r. 

These are the four ways in which the waters moving in the same 
manner penetrate one another with lines that slant towards the centre 
of the earth. 

These four demonstrations are sufficient to prove the four principal 
effects that the waters produce as they strike one another within the 
air. Of which the first is that in which the more slanting penetrates the 
less slanting, and penetrates it in part and carries with it the part that 
has been struck. 

In the second demonstration the less slanting penetrates the more 
slanting in part and carries with it the part that has been struck. In 
the third demonstration the more slanting water carries away with it 
entirely the less slanting water. The fourth does the opposite, in that 
the less slanting water carries away with it entirely the more slanting. 

f 45 v. 

If the earth were [not] spherical no part of it would be uncovered 
by the sphere of the water. 

You will never find a flat piece of the earth without the water upon 
it being of convex shape standing in the middle of this level surface. 
And this water will never move towards the extremities of this plain. 
Therefore upon a surface that is absolutely flat there may be water of 
varying degrees of depth. 

It is impossible to find any flat part in the surface of any very great 
expanse of water. 

The deep recesses in the ocean bed are everlasting, the summits of 
the mountains are the contrary: it follows that the earth is spherical 
and all covered with water and that it will be inhabitable. 



An object which is carried by the course of the water ... in the 
course of less power: if it is slanting below it will move towards the 
bottom, and so it will move according to the direction of its slant. 

Of the objects carried between two currents of water only that one 
will proceed without being turned upside down which is in the middle 
of two currents of equal movement. 

But that will be in continual revolution over and over which is in 
the middle of two unequal currents. 

An object will not make any lateral revolution when it moves be- 
tween currents equal in movement; and so conversely. f 52 v. 

Of the movement of a thing that slants irregularly in water which 
has a regular current: it will proceed to turn continually when below 
the surface of the water, and that in which the slant is regular will not 
make any turn. 

When the upper part of the straight side of the object and the lower 
part are struck by an equal current this object will make a lateral 
revolution. f 53 v. 

[The percussion of water] 

All water after it has struck against an object is divided into four 
different and principal movements, namely right and left, high and 
low; and the low movement causes injury to its bed. 

Of the four principal movements which water makes as it divides 
in its reflex action, that will be more rapid which is reflected at a more 
acute angle. f 54 r. 


Of the things carried by the course of the waters that which has a 
larger part of itself in the air responds to the movement of the air 
more than to that of the water; and so conversely that which has a 
larger part of itself in the water will follow the course of this water 
more than that of the air. 

See in the windings of the canals where the water is swifter below, 
in the middle, and above, and of this make a book. 

The pipe by which water is drawn to a height receives less damage 
than that pipe along which water is driven; and this is due to the fact 



that in the first case the motive power is above and in the second it is 

Where the water is most rapid, it wears away most the bed on which 
it rubs. 

Where the water is most shut in, it becomes most rapid and in its 
passage wears away its bed most. f 65 r. 

The object always changes the order of the nature of the waves thai 
have been commenced. 

The current a b has one order and the object which receives its per- 
cussion throws it over completely and changes it to another figure. 

If you wish to form a correct impression of all the shapes of the 
waves and the courses of the waters, observe the clear water where it 
is shallow beneath the rays of the sun, and you will see, by means of 
this sun, all the shadows and lights of the said waves and of the things 
carried by the water. 

The sphere of the water increases and decreases sensibly or insensi- 
bly, according to the greater or less, more universal or less universal 
deluges of the waters given back to this sphere of the water. 

f 65 v. 


Eddies are always the intermingling of two streams of water, that 
is, the falling and the reflex. 

All the water which in the currents of the rivers tarries behind the 
objects in these currents has no other exit than by contact with the 
aforesaid currents. 

The eddies which turn back are always those of the swiftest water, 

And the eddies that are turned in the direction that the stream is 
flowing are those of the water which tarries in the stream's course. 

Here the law of the waters in their eddies does not fail, because the 
water that becomes slow, turns back, and makes the eddies in the op- 
posite direction to its movement, as do the eddies of the swiftest water. 
And for this reason these eddies, whether of the slow or of the rapid 
water, mingle together and redouble their power; but not entirely 
because the slow eddy in mingling with the swift becomes swifter than 



at first, and the swift eddy as it embraces and unites with that which 
is slower acquires slowness. 

The hollow in the swift waters caused by the submersion of the 
eddies will point towards the approach of the waters, and in the slow 
waters it will point in the direction in which they are flowing. 

f 66 r. 


A drop is that which does not detach itself from the rest of the water 
unless the power of its weight is more than its adhesion to the water 
with which it is joined. 

That drop is formed more slowly which has a slower movement of 
water at its creation. 

All the movements made on the surface of water are also made at 
each successive stage of its depth, and likewise in each part of its 
length; and this is learnt from the grasses that grow on the beds of 
the streams. f 66 v. 

Water that falls in the air separates itself with difficulty from its 
bulk, and the sign of this is found in the curve that it produces and 
the winding of one of its parts round the other, between which the 
film of water is interposed. f 67 r. 

If the earth covered by the sphere of the water is more or less heavy 
than if it were not so covered: 

I reply that the heavy substance weighs more which is in the middle 
of the lighter. 

Therefore the earth which is covered by air is heavier than that 
which is covered by water. 

I say: — the centre of gravity of the pyramid being placed at the 
centre of the earth, it will change its centre of gravity if it is sub- 
sequently covered in part by the sphere of the water, and I give an 
example with two cylindrical weights that are equal and similar, of 
which one is half in the water and the other entirely in the water: I 
say that that which is half out of the water is the heavier, as has been 

Suppose there to be a straight line equal to the diameter of the. 



sphere of the water, which touches the surface of the sphere of water 
in the centre of its length. One asks what is the difference between 
each of the miles of the descent which the surface of this sphere makes 
below the said line. f 69 r. 

f Centre of the earth and watery sphere} 

Because the centre of the natural gravity of the earth ought to be in 
the centre of the world the earth is always growing lighter in some 
part, and the part that becomes lighter pushes upwards, and submerges 
as much of the opposite part as is necessary for it to join the centre of 
its aforesaid gravity to the centre of the world; and the sphere of the 
water keeps its surface steadily equidistant from the centre of the 

Where the sun is straight above, the earth grows light; covered by 
the air, the waters and the snows have been lacking to it, and on the 
opposite side the rains and the snows have made the earth heavy 
again and drive it towards the centre of the world, and thrust the parts 
that have become lightened to a greater distance from this centre; so 
therefore the sphere of this water preserves an equality of distance 
from the centre of its sphere but not of gravity. 

Water poured in the air at a concave angle becomes spread out in a 
sheet, and it remains spread out in a sheet more on the side of the 
angle where this water makes more contact; and on the opposite side 
the sheet of water will leap up and make its union at first in the form 
of an open sheath. f 70 r. 

[Water of the sea and of rivers~\ 

The sea beneath the equinox is raised by the heat of the sun, and 
acquires movement over every part of the hill or portion of the water 
that rises in order to give equality and restore perfection to its sphere. 

If an outlet of water with sixteen ounces descent in each mile yields 
me sixteen measures of water, how much will the same outlet afford 
with eight ounces descent per mile? 

The revolutions of the cross-eddies acquire size and slowness at each 
stage of their length. 

The convulsions of the reflex movements of the water at the bottom 
of rivers destroy the circling movements of the longitudinal eddies. 

The water of the sea and of the turbid rivers is heavier than the 




other waters, and as a consequence offers more resistance to the 
weights it carries. 

The water of the sea offers more resistance because the weight of the 
salt that is mixed with it is liquefied, and it is inseparable from it with- 
out the heat that dries up the water; but the turbid part of the water 
is separated from it by heat and when the water is at rest. f 70 v. 

\Movement of water in the air and in the water] 

The movement that water makes in the air follows for some distance 
the line of the sides of the small holes through which it descends. It is 
not thus with the discontinuous quantity that the stone shows itself to 
be when thrown by the circular movement of the man's arm; this fol- 
lows the straight movement; which the water does not do on account 
of it being spread out in a sheet, for this in a long space of movement 
collects all the parts of the water together. 

The impressions of the movements made by the water within the 
water are more permanent than the impressions that the water makes 
within the air; and this takes place because water within water is de- 
void of weight, as is proved in the fifth, but only the impetus weighs 
and this moves this water that has no weight until it is itself con- 

The impressions of the movements of water are more permanent 
when the water carried by the impetus enters into a sheet of water 
(pelago) with slower movement, and conversely. 

The impressions made by the water within the air are destroyed in 
the first movement that they make towards the earth, because the im- 
petus is consumed in the natural movement that is produced in the 
water. f 71 r. 


The falls of water that intersect in the air become filled with air in 
their reflex movement. 

Of the falls of water which strike each other within the air being of 
equal thickness, that which descends from a higher part of its reservoir 
will join itself to the course of that which is lower and will complete 
its course with it. 

Falling water which then runs over terraces breaks its bed very 
much at the end of these terraces. 



This proceeds from the fact that when the current of the water 
reaches the last stage of these terraces it falls and raises itself from the 
bottom, burying itself so much the more as its fall is deeper, because 
the fall is more powerful in great descents than in lesser ones. 

All water, when it strikes the bottom or upon another object, divides 
and runs in different directions. 

All water, when it surges up, divides at the surface and runs in dif- 
ferent directions, and so much the more as the sheet of water is more 
tranquil. f 71 v. 

The simple movements of the waters are those which act simply with 
their simple movement of whatever kind it may be. 

Composite movements are created by different movements and 
these are very powerful in different functions. 

The wave is slower at the summit than upon its sides. 

The falling movement is more rapid than the reflex. 

Joined together, the greatest and the least slowness of the waves, that 
is of the wave in itself with its sides and summits, become equal to 
the common course of their stream, and this is to be adduced in the 
conclusions, that is to say to prove them. f 72 r. 

[Of the raising of water in nature and by artifice] 

If the water which gushes forth from the high summits of the 
mountains comes from the sea, the weight of which drives it up there 
so that it is higher than these mountains, why has this portion of water 
the capacity of raising itself to so great a height, and of penetrating 
the earth with such difficulty and length of time, while it has not been 
granted to the rest of the element of water to do the same, although 
this borders on the air which would not be able to resist it and so 
prevent the whole from rising to the same height as the aforesaid part? 

You who have found such an invention must needs return to the 
study of natural things, for you will be found lacking in cognate 
knowledge, and of this you have made great provision by means of the 
property of the friar of which you have come into possession [P]. 1 

1 Ravaisson-Mollien says: 'Cette phrase signifie peut-etre: Si tu as trouve a inventer 
une imitation de l'elevation de l'eau dans la Nature, aux cimes des monts, en ayant cm 
beaucoup t'instruire a cet egard avec le fonds de livres, dessins, etc., du frere [moine] 
un tel, que tu possedes, cette instruction-la te trouvera bientot en defaut. et il te faudra 
de nouveau etudier les choses de la Nature.' 



Water falling into a channel of width equal to the width of the 
water that falls will make a deep hollow within the surface of the 

Water falling into [a channel] where the width is greater than the 
said fall will not make a very great hollow in the surface of the 
water, on account of the eddies, which cause the water to bend in the 
hollow caused by this fall. 

Water which clears away the bottom on which it hurls itself rap- 
idly or slowly in all its width, depth or narrowness, its seething mass 
being tossed back by the bed of the watery expanse, is in part caught 
up again to the surface of the water, there to make its various falling 
and reflex movements, in part returns to where was its first fall, bury- 
ing itself there with it and then returning up in lateral eddies, and in 
part falling back in the middle of the seething mass and spreading 
itself out with slow movement round the centre of its fall. 

f 72 v. and r. 
[Movements of water] 

Between the current and the eddy is the sand. 

Between the sand and the eddy is a smooth valley where the eddy 

In the eddy are pieces of timber and other light things. 

If the air is motionless an object borne on the surface of the water 
will be slower than one that is below its surface. 

Where the water issues forth by a level bed beneath the sluices it 
hollows out the bed before and behind these sluices. f 77 r. 


A wide object borne by the current of the river between the surface 
and the bed of the river, if it should meet with water that is slower 
than that which bears it and should find itself at that time slanting 
in the direction of the approaching river, will immediately leap from 
the bed to the surface of the water; and if this slant is pointing in the 
opposite direction to the course of the water then in encountering 
the slow current it will suddenly precipitate itself towards the bottom; 
and if this slant looks to the right or left of the breadth of the stream 



it will throw itself to this right or left side of the stream and so will 
continue in any direction. 1 7S r. 



If the mountains had not remained in great part uncovered by the 
waters, the courses of the rivers would not have been able to carry so 
much mud into the sea as exists at a great elevation, mingled with the 
animals which have been enclosed by it. 

The revolutions of the reflex water in returning to the current of its 
river penetrate it more in its lower parts than on its surface; and this 
proceeds from the fact that the current, by the seventh, is swifter above 
than below, and is in consequence more powerful above, and therefore 
less penetrated by the percussion of this reflex water above than below. 

The eddies formed by the percussion of the reflex water in the course 
of the falling water are of two kinds, of which one is produced towards 
the bottom and revolves vertically through the length of the stream, 
the other is upon the surface and revolves right and left through the 
breadth of the stream. The lower is produced by the falling down 
again of the seething mass towards the bottom, and that on the surface 
by the revolving movement striking into the surface current, f 78 v. 

Water turns before falling water like the wheel of a mill, f 81 r. 

Of the surfaces surrounding the water that is poured through the 
air from an expanse of water, and also what the water does in these 

Of the movements of the things that have fallen with the water which 
moves in the air, and also what they do in this expanse of water. 

Of the things that float upon the middle water, and how they 
become submerged when they find themselves between the centre of 
the middle water and the fall, and they become submerged together 
with this fall which takes place in the expanse of water, and strike 
against the bottom and break in pieces. 

Write therefore all the effects of the things that become submerged 
in any extremity of this middle water, which always submerges its 
extremities because it is in the centre of all the reflex movements 
towards the bottom of its expanse of water. f 81 v. 



Of the earth. Every heavy substance tends to descend, and the lofty 
things will not retain their height but with time they will all descend, 
and thus in time the earth will become a sphere, and as a consequence 
will be completely covered with water, and the underground channels 
will remain without movement. 

Of the convex wave. If the wave created by the fall of the water 
of a canal of uniform breadth and depth will be of long movement 
or no. 

Of the concave wave. If the concave wave created by the water that 
falls abruptly from the open canal under a sluice will be of long 
movement in a canal of uniform breadth and depth. f 84 r. 

Water which runs through a canal of uniform emptiness and fills 
all its first smooth part, will fill all the other straight and slanting 
parts and will move with equal swiftness. 

The movements of the heavy elements are not to the centre in order 
to go to this centre, but because the medium in which they are cannot 
resist them, and when they find resistance in their element this body 
no longer has weight and does not seek to penetrate to the centre. 

Water in air weighs and descends by the shortest path. It divides 
and opens the air which is below its centre of gravity with all its parts 
equally, and it does not divide the air that is upon its sides because it 
is not situated above it. And because of this it makes a hollow in the 
air of very short length until it reaches that which resists it; and as 
this resistance is that of water the water that falls through the air no 
longer seeks to go the centre, because it no longer divides the water 
as it did with the air; therefore the heavy substance moves downwards 
where it meets with no resistance, and not in order to go to the centre. 

f 86 v. 

Write first of all water in each of its movements, then describe all 
its beds and the substances in them, adducing always the propositions 
as to the aforesaid waters, and let the order be good as otherwise the 
work will be in confusion. 

Describe all the shapes that water assumes, from its largest to its 
smallest wave, and their causes. f 87 v. 




If with a sluice the larger body of water is divided by the narrower 
and the movement of the water is from the narrower to the larger, 
the water which rises under the sluice will leap on to the larger water, 
and by its falling back it will hollow the bed of the canal in several 
places with different leaps. p 88 r. 

[Treatise on water] 

Describe what water does in each defined instance between its sur- 
face and the bottom. And what part of the water is slower or more 

Of the lateral objects placed upon the banks of winding rivers. 

Of the intersections that the waves make one with another on being 
bent back by the opposite banks of the rivers. 

Of the elevation of the waves formed by the intersection of other 
cylindrical waves. f 89 r. 

Of the various breadths of the transversal interpositions set in the 
middle of the breadths of rivers. 

Of the various projections of the lateral objects set upon the banks 
of rivers. 

Of the different slants placed in the middle of the widths of rivers. 

Of the different juxtapositions of the fronts of the lateral objects 
placed upon the banks of rivers. f 89 v. 

[Boo\ of the treatise on water] 

If the cylindrical wave shall strike the eddies produced about one 
of the extended banks, these pent-up eddies will be contracted and 
acquire great power to excavate beneath the bank and cause it to fall 

Order of the book. 

Put at the beginning what a river can do of equal depth and slant 
of bed on its bank, where lie objects of various kinds. Then place these 
objects two by two. Then place them to face the opposite bank, in the 
same variety, and describe what the waters do when they intersect one 
another in the centre of the stream, and the obstacle they afford to the 
water reflected by the opposite bank. And then describe what each does 
in its bed, that is how it rises and settles itself. 



The side of the wave when it makes its rapid tailing movement is 
the end of the slow reflex movement. It follows that the movement of 
the valley of the wave is swift and the crest of the wave is slow. 

f 90 v. 


If the course of the river is contracted on one of its sides it produces 
a half-cylindrical wave which is swift; and the eddies which are pro- 
duced between the contracted bank and the cylindrical wave occasion 
the laying bare and crumbling away of this contracted bank. 

If the banks should contract equally on each side of the current and 
opposite, then the cylindrical waves will intersect, and after this inter- 
section they will descend and strike upon the bank and cause it to fall 

But if the contraction of one bank should be lower than that of the 
other, then the upper cylindrical wave can enter under the lower. 

Here it is necessary, in the commentary, to define the distances of 
the contractions of the banks and their breadths. f 91 r. 

[Of canals, rivers and eddies] 

The bank which is made to curve inwards in order to give greater 
breadth to the canal is the cause of the sudden forming of an eddy, 
and this bores down and makes a deep hole at the base of the bank 
and so becomes the cause of its fall. 

This is proved by the first of the third, which shows that the river 
in acquiring sudden breadth of space acquires also sudden breadth of 
water, and the water thus widened comes also to lower itself in depth; 
and so it suddenly creates a current which hurls itself upon the bank 
where it has been widened, and striking it divides itself into two 
eddies, one of which (the more powerful, as c b a) in order to be 
enclosed throws itself vigorously straight towards the bottom; and by 
the ninth which says that as the eddy will be most easily penetrated 
which has the lips of its mouth least slanting, it will have them quite 

Water brings about the fall of that bank of which the canal acquires 
a sudden breadth. 

If the canal gains on each side sudden breadth it produces eddies on 



each side; if these are united at the centre of the breadth of this canal 
it will make of itself a sudden and great depth. 
All these figures have to result from experience. f 91 v. 

[Cylindrical waves] 

The more the half-cylindrical wave moves the more it descends, and 
the more it spreads itself out the swifter it becomes. 

When there are two unequal cylindrical waves of which the larger 
comes into existence before the smaller, this smaller wave intersects 
the larger and passes above it. And this happens because the larger 
which is created first, when it is opposite to the smaller, is spread out 
and lowered, and the lesser which strikes it, being high, strikes the 
lowness of the greater one, and not finding any obstacle as high as 
itself runs over it and falls headlong on the opposite side and follows 
its initial impetus. 

But if the lesser of the unequal cylindrical waves starts higher in the 
river than the greater, then this greater follows its natural course, and 
the lesser follows the course of the greater. f 92 r. 

If the cylindrical waves clash and do not intersect as far as the cen- 
tre, the middle part which clashes leaps back and passes above the 
part that does not clash. 

When two cylindrical waves of equal size and power clash abso- 
lutely they each turn back Completely without any penetration one of 
the other. 

But if the cylindrical waves are unequal in size, neither the larger 
nor the smaller will observe their law, because the larger does not 
bend and the lesser unites with the larger. 

But if when the waves are equal the rise of the one is before that 
of the other, their blows will not be delivered with equal power; 
consequently the course of the second will bend before that of the 
first. f 92 v. 

Water that moves between a bank and a straight smooth bed will 
not make a wave of any kind. 

What is thus stated takes place because a wave is only created by a 
reflex movement, and the reflex movement arises from the percussion 
of the falling movement which is made upon the particular object at 



the bottom or the sides of the canal; and if in these places there are no 
particular objects then by what has been said it will not create any 
wave, this water being made by minute upward movements which 
only raise themselves a little from the bottom, so that they do not 
make waves by coming to the surface. 

The simple half-cylindrical wave is formed upon some small object 
that is joined to the bank; the water that strikes it there makes a long 
wave in the shape of a half-column which takes its course slantwise 
towards the opposite bank, and dies there and is reborn. 

Let a be the object, placed upon the bank a o of the canal n o m p. 

I say that the water which strikes upon this object will make a wave 
which by its being continually reformed will also make itself continu- 
ous; and it would be always so if it were not interrupted by the com- 
mon course of the water of the canal, which all strikes on this wave 
and drives it unceasingly in every stage of its length, so that at the 
end it directs it according to its ordinary course. f 93 v. 

\ Currents and falls of water] 

In water of ordinary speed the middle water will have tiny ripples. 

The water that is interposed between the mean of the surface and its 
bed is not of the nature of the mean; whereas this mean of the surface 
receives the percussion of the falling and the reflex; for the one and 
the other to be within the boundary falls upon the other water, making 
percussion of the air as of a heavy thing, and as a heavy thing it pene- 
trates within the other water struck by it. 

The water falls at first, rises up again, and raises itself with its semi- 
cylindrical wave above the semi-cylindrical wave opposite which made 
its fall more slanting. f 94 r. 

[The current of rivers] 

Water that descends in a straight river moves always by a slanting 
course, from the centre to the opposite banks and from these opposite 
banks to the centre of the river. This is proved by the ninth of this 
where it is stated: — The course of straight rivers is always higher in 
the centre of their width and upon the sides than it is between the 
centre of their width and these sides. And this was proved by the sev- 
enth in which it was stated: — The water of straight rivers never flows 
in a straight line because it is so much swifter as its obstruction is 



farther removed from the banks. And this was confirmed where I 
said : — Where the falling movement is impeded there the reflex move- 
ment is created; and by the tenth of this: Always between the falling 
and the reflex movement is the maximum depression in the expanse of 
the rivers; and by the eleventh :— After the last height of the reflex 
water there is produced the beginning of the falling movement; and 
by the twelfth: — The falling movement of the waters does not change 
into the reflex movement without percussion against the bed or the 
bank of the river. Where the water strikes the bed or the bank of 
the river there the soil of the bed or the bank of the river becomes 

Always under the falling movement the bed of the river becomes 
raised and its height is restored under the reflex movement. 

The lateral slants of the waters which move continually in straight 
rivers are of a greater or less degree [of slant] according as these wa- 
ters have a more or less rapid current. g 14 v. 

[Density of water — fresh and salt] 


The Ocean does not penetrate within the earth, and this we learn 
from the many and varied springs of fresh water which in various 
places of this Ocean penetrate from the bottom to its surface. The same 
thing also is shown us by the wells, made at a distance of more than a 
mile from the said Ocean, which are filled with fresh water; and this 
takes place because the fresh water is lighter than the salt water and as 
a consequence more penetrating. 

Which weighs more, water that is frozen or water that is not frozen ? 

Fresh water penetrates more into salt water than salt water does into 
fresh water. 

That fresh water penetrates farther into salt water than salt water 
does into fresh is shown us by a thin cloth, dry and old, that hangs 
with its opposite ends at an equal depth in two different bodies of 
water, of which the surfaces are equally low; you will then see how 
the fresh water will raise itself so much higher up on this piece of 
cloth than the salt water, as it is lighter than it. g 38 r. 




The course that the water takes when issuing from a lake into a dry 
river-bed is so much slower or swifter as the river is wider or more 
confined or in a more level position in one place than in another. 

By what is set forth the flow and ebb of the sea which enters from 
the Ocean into the Mediterranean, and of the rivers that contend with 
it, raises their waters so much the more or less as the sea is more or less 
confined. g 48 r. 


Pliny says in his second book, in the hundred and third chapter, 
that the water of the sea is salt because the heat of the sun scorches 
and dries up the moisture and sucks it up, and thereby greatly increases 
the salt savour of the sea. 

But this cannot be admitted, because if the saltness of the sea were 
caused by the heat of the sun there is no doubt that the lakes and pools 
and marshes would be more salt in proportion as their waters have less 
movement and depth, but, on the contrary, experience shows us that 
the waters of these marshes are entirely free from saltness. It is also 
stated by Pliny in the same chapter that this saltness might arise be- 
cause, after the subtraction of every sweet and tenuous portion such as 
the heat readily draws to itself, the more bitter and coarser portion 
will be left behind, and in consequence the water on the surface is 
sweeter than that at the bottom. But this is contradicted by the reasons 
given above, whence it follows that the same thing would happen with 
marshes and other tracts of water which become dried up by the heat. 
It has also been said that the saltness of the sea is the sweat of the 
earth, but to this we may reply that then all the springs of water which 
penetrate through the earth would be salt. 

The conclusion therefore is that the saltness of the sea is due to the 
numerous springs of water, which in penetrating the earth find the 
salt mines, and dissolving parts of these carry them away with them 
to the Ocean, and to the other seas from whence they are never lifted 
by the clouds which produce the rivers. So the sea would be more salt 
in our times than it has ever been at any time previously; and if it 



were argued by the adversary that in an infinite course of time the 
sea would either become dried up or congealed into salt, to this I reply 
that the salt is restored to the earth by the setting free of the earth 
which is raised up together with the salt it has acquired, and the 
rivers restore it to the earth over which they flow. 

But — to express this better — if it be granted that the world is ever- 
lasting it must needs be that its population also will be everlasting; 
and that therefore the human race has perpetually been and will be 
consumers of salt; and if the whole mass of the earth were composed 
of salt it would not suffice for human food. And for this reason we 
are forced to conclude either that the substance of the salt is everlast- 
ing as is the world, or that it dies and is renewed together with the 
men who consume it. But since experience teaches us that it does not 
die, as is shown from the fact of fire not consuming it, and from 
water becoming more salt in proportion as it is dissolved in it, and 
from the fact that when water evaporates the original quantity of salt 
remains, there must needs pass through human bodies as urine or 
perspiration or the other excretions that are found there as much salt 
as is brought every year into the cities. And therefore we may say 
that the rains which penetrate through the earth are what carry back 
underneath the foundations of cities and their peoples through the 
passages of the earth the saltness taken from the sea; and that the 
change in the position of the sea which was over all the mountains has 
left the salt in the mines that are to be found in these mountains. 

As a third and last reason we may say that salt is in all created 
things; and we may learn this from passing water through ashes and 
the refuse of things which have been burnt, and from the urine of 
animals and the excretions which proceed from their bodies, and the 
earth into which by corruption all things are changed. 

g 48 v. and 49 r. 


The subterranean courses of the waters like those which are made 
between the air and the earth are those which unceasingly wear away 
and deepen the beds of their courses. 

1 MS. della vibratio dell a terra. 



The soil carried away by the rivers is deposited in the ultimate parts 
of their courses; or rather the soil carried away by the high courses of 
the rivers is deposited in the ultimate descents of their movements. 

Where fresh water is rising to the surface of the sea it is a manifest 
portent of the creation of an island which will be uncovered more 
slowly or more rapidly as the quantity of the water that rises is less or 
greater in amount. And this island is produced by the quantity of 
earth or deposit of stones made by the subterranean course of the 
water in the places through which it flows. c 49 v. 


The falls that the waters make at their banks always wear away the 
bases of these banks and cause them to fall headlong on their founda- 
tions. This is proved: — if the height of the bank a c from which falls 
the water a n, striking and consuming the place struck m n c, be the 
centre of the percussion upon which are divided the reflex movements 
n m o and neb, which in each direction consume the bank that is 
chafed by their revolving movements, then as the banks find them- 
selves thus consumed their supports collapse on the side on which their 
prop fails. 

The water which falls from a h to n m will proceed to deepen all 
the bed from where it falls as far as the lowest level of the place where 
it falls, from a b to c d. g 50 v. 


The water of the sea cannot penetrate from the roots to the summits 
of the mountains which border upon it but only raises itself as far as 
the aridity of the mountain 1 draws it. And if on the contrary the rain 
which penetrates from the summit of the mountain to its roots which 
border on the sea, descends and softens the opposite slope of the same 
mountain, and draws the water continually as does the syphon which 
pours through its longest side, it must be this which draws up to a 
height the water of the sea; thus if s n were the surface of the sea and 

1 MS. monte. So Richter. Ravaisson-Mollien reads mondo. 



the rain descends from the summit of the mountain a to n on one side 
of it and descends on the other side from a to ra, this without doubt 
would be the method of distillation of a filter or as happens through 
the tube called a syphon; and the water which has softened the moun- 
tain by the great rain which descends from the two opposite sides 
would constantly attract the rain a n on its longest side together with 
the water of the sea, if the side of the mountain a m were longer than 
the side a n; but this cannot be because no part of the earth that is not 
submerged by the ocean can be lower than this ocean. c 70 r. 

[With drawings] 

These convolutions must be made with coloured water falling 
blindly into clear water. g 90 v. 

Running water has within itself an infinite number of movements 
which are greater or less than its principal course. 

This is proved by the things supported within two streams of water 
which are equal to the water in weight. If the waters are clear they 
show well the true movement of the waters that conducts them, be- 
cause sometimes the fall of the wave towards the bottom bears them 
with it so that they strike upon this bottom; and they would be re- 
flected back with it to the surface of the water if the floating body 
were spherical; but it frequently happens that the wave does not bear 
them back, because they are wider or narrower in one direction than 
in the other, and being thus irregular in shape they are struck upon 
the side that is largest by another reflex wave which proceeds to roll 
over and over this movable thing which moves wherever it is carried, 
its movement being sometimes swift and sometimes slow, and turning 
sometimes to right and sometimes to left, at one instant upwards at 
another downwards, turning over and turning back upon itself, now 
in one direction and now in another, obeying all the forces that have 
power to move it, and in the struggles carried on by these moving 
forces going always as the booty of the victor. g 93 r. 

There can be no flow and ebb unless several rivers discharge them- 
selves in the same expanse of water. g 95 r. 

In the course of the year the amount of the water that rises will be 
as great as of that which descends in the rivers and the air. h 29 v. 



\ Course of rivers] 

Ail the things which are lighter than sand will be left in the lower 
part of the river underneath the beginning of the fall of the wave. 

Where the water has least movement the surface of the bottom will 
be of the finest mud or sand. 

Where the course of turbid water meanders among the gnarled 
roots of thickets it will deposit much sand or mud through the many 
twists of its eddies. h 30 r. 



The water which gives less weight to its course is swifter. 

The water which is swifter drives its wheel faster. 

That gives less weight to its course which is straighter. 

The water of the mills ought to strike the blades of the wheels at 
right angles. 

That water which flows with less slant will strike the wheel farther 
from the perpendicular of its fall. 

That water which strikes farther from the perpendicular of its fall 
gives a less blow. h 30 v. 

The wave created by the percussion of water upon the bed of a river 
will make a movement from below contrary to that from above. 

The wave is slower at the end of its elevation than at any other part. 

The parts of the wave which move most swiftly will be near the end 
of its fall. 

The sand remains higher underneath the highest part of the wave 
than under its lower part. h 31 r. 

When a stone is thrown into still water it will create ripples that 
expand equally if the water is of uniform depth. 

If two stones are thrown one near to the other within the space of a 
braccio, the circles of the water will increase equally one within the 
other without the one destroying the other. 

But if the bottom is not level the circles will not expand in uniform 
movement except on the surface. 

When an object of long shape is thrown into water it will create an 
oval undulation. 



A round object thrown into running water will create an oval undu- 
lation in two movements. h 31 v. 

Where the water is higher it has more weight upon its bed and its 
course is more undulating. 

That part of the bed or of the bank which projects with the sharpest 
angles into the straight course of the waters suffers most damage in the 
flow of the water. h 35 v. 

Water which strikes on an angle deepens the former sides, h 36 r. 

Every part of the surface of the water desires to be situated at an 
equal distance from the centre of the elements, and if one part of the 
surface be raised above another this so happens because of the contrary 
movements which are taking place between it and the bottom. 

H 37 r. 

Where the current is in the centre of the full stream the ridge will 
not be between the point of union of the eddies and of where the water 
rebounds; it is all deep. 

The large pebbles remain in the deepest part of the current. 

H 37 v. 

Where the channel of the water grows narrower it digs its bed 
deeper and flows more swiftly. h 38 r. 

Iron which receives continually the impact of flowing water never 
rusts but is consumed by being burnished. h 39 r. 

In proportion as the object dividing the water is more distant from 
the surface it leaves less sand behind it. h 39 v. 

Where one body of water joins another at a sharp angle it will make 
a great depth. h 40 v. 

[Of things carried by the water] 

Where the water makes less movement there when laden it deposits 
its weight. h 46 v. 

If a long object uniform in weight and thickness finds itself in the 
middle of an even descent, its length will move according to the length 
of the course of the water. 


Royal Library, Windsor 



When a long object moves in a channel midway between the middle 
and the contact of the bank it will move slantwise. 

The long object which is nearer to the side than to the centre will 
proceed to revolve upon the water. h 47 r. 

Where water has less movement there it deposits its weight more 

The eddies of water after it has struck the ground at an angle turn 
in contrary movement. h 47 v. 

Water will be in perpetual movement if its surface is not equidistant 
from the centre of the earth. 

Sand and other light objects follow and obey the twists and turns of 
the eddies of the water while the large stones move in a straight line. 

h 50 [2] r. 

Water which falls into smooth water causes it to become slanting, 
consequently its descent becomes swifter. h 50 [2] v. 

Measure the height of the falling water and multiply it by the height 
to which you wish to raise it, and as many times as the extent of the 
fall of the water enters into the height to which it has been raised, so 
many times is it thinner than that which rises; and this is the last and 
greatest amount that can be raised. h 51 [3] v. 

Water which rises continually because of the movement of other 
water will be so much the thinner as that which moves it is of greater 
length. h 52 [4] r. 

Turbid water does more harm to the banks than clear water, and 
more at the base than at the top, because it is heavier and thicker. 

h 52 [4] v. 

The line of the water which has the greater movement breaks that 
of the lesser movement and buries itself beneath it. 

That part of the sand which is nearest to the impact of the falling 
water will be finer than the rest. 

The large shingle will be farthest away from the blow, h 53 [5] r. 

I ask whether the water which emerges underneath comes from the 
surface or no. 



The first depth will be where the sum of the blow of the second 
water makes its way into the course of the eddies; the lesser where the 
second base is, is where the revolving water encounters it in its course. 

h 53 [5] v. 

After the descent of water that which was above remains below; the 
lower part becomes changed into the upper part. 

After the most rapid descent of the water the lower part remains of 
more rapid movement than the upper part. h 54 [6] r. 

Of waters that flow upon beds of equal slant that will have the less 
depth which has the greater breadth. 

Of waters that flow between banks of equal breadth that will have 
less depth which possesses the more rapid course. h 54 [6] v. 

Water in its movement drags with it the air which borders on it. 

And the bed offers more resistance : this is why it moves more on the 
surface than at the bottom. 

All the upper part of the water which finds itself at the beginning 
of its fall will be lower than the other after this fall. h 55 [7] r. 

Water which flows in falls of equal slant will move more strongly at 
the bottom of the canal than at its surface. h 56 [8] v. 

Waters which fall from the same level with an equal slant in an 
equal length of movement will be of equal swiftness, h 58 [10] v. 

Of waters which fall from the same level by channels of equal slant, 
that will have the swifter course which has the greater length. 

Of waters which fall the same distance from the same level, that 
will be slower which is longer. h 59 [n] r. 

The percussion of the water upon the wheel will be at the highest 
degree of its power when it strikes within equal angles. 

The percussion made between equal angles will be of the greatest 
power when the current of the water and the movement of the wheel 
are in the same direction. h 63 [15] r. 

The sand moved by two light currents of water settles itself upon 
the steep bank in a square ridge. h 63 [15] v. 



Water which has struck against a round body will create equal 
hollows beyond the sides of this body. 

Gravel dug up by the blows of the water will settle where the move- 
ments made by the blows meet. 

That face of the triangle which is interposed between more nearly 
equal angles in the course of the water will be the cause of a great 
hollow in the water that strikes there. h 64 [16] r. 

Water which moves by a uniform slant will be swifter at the surface 
than at the bottom. 

The wave that is caused by a blow will be higher at the beginning 
than in the middle. 

Waves that are caused by the wind will be higher in the middle 
than at the beginning; that is the fourth [will be higher] than the 
third. h 67 [19] v. 

These back-currents eat away the banks of the canals; you will 
therefore make screens of wood to extend for the whole of their im- 
pact, h 68 [20] r. 

[Movement of water] 

Water which exceeds the general depth and breadth of rivers moves 
in contrary movement. 

The wave of the water will swell between the cause of the move- 
ment and its end. 

Water which moves by reason of the undulation of the wind will 
make a contrary movement at the bottom to that at the surface. 

Water does not weigh less crosswise than in the line of its per- 

Every movement of liquid weighs more in the direction in which 
through a hole of equal size its vase empties itself more rapidly; the 
centre of the bottom of the vase receives a greater weight of water 
than any other place. h 68 [20] v. 

The free movement made by the upper part of water will not make 
angles of any kind except in the percussion. 
All the upper lines made by the movement of water are curved. 
The wave follows the movement of the air which touches it. 



The object enclosed between the air and the wave does not follow 
the movement of the one or the other. 

The water that is expelled from the spot which the vessel occupies 
weighs as much as all the remainder of the ship which displaces it. 

h 69 [21] r. 

Streams of water equal in current and angle of descent which move 
one against the other, penetrate and pass through each other without 
turning aside from their natural course. h 69 [21] v. 

Water which moves against motionless water attacks and destroys its 

The water with the greater movement penetrates and traverses the 
lesser movement of other water, like air. h 70 [22] r. 

The line made by the course of water after its percussion leaps back 
at equal angles. h 71 [23] r. 

The farther water is away from its bed the freer will it be in it? 
natural movement. h 72 [24] r. 

Where the water has a stronger current the shingle is larger. All 
the detached shingle will turn its largest side slantwise against the 
course of the water. h 74 [26] v. 

All light things gather together in the centre of the eddies that is at 
the bottom. h 75 [27] r. 

Every portion of water desires its parts to be as the whole element, 
equally distant from its centre. h 76 [28] r. 

The water which flows near the bed of the stream between the banks 
will be slower than the rest because of the percussions made by the 
eddies. h 77 [29] v. 

[Error as to buying water] 

You who buy water by the ounce know that you may greatly deceive 
yourselves. In fact if you take an ounce in stagnant water and an 
ounce in flowing water, against the hole of your ounce, an ounce near 
the surface, one near the bottom, one across the current . . . 



In proportion as the natural movement separates itself from its cause 
so it becomes more rapid. h 78 [30] r. 

That wheel of the water will be better turned when the water that 
turns it does not leap back after its percussion. 

The blow will be of the greatest force when the movement which 
causes it is straighter and longer. h 79 [31] v. 

[Sand and water] 

All the hollows of the furrows visible in the sand will be between 
equal angles, according to the movement of the water, h 80 [32] r. 


The wave is less sloping and of slower movement in its rise than in 
its descent. h 81 [33] r. 

The surface of the water of rivers desires to be equidistant from the 
centre; as it leaps it weighs down and consumes the bed because it 
grows thicker in the course of its intersections and increases in weight 
as it enters the air, and in consequence falls and bursts through the 
bed. h 81 [33] v. and 82 [34] r. 

In water that has no movement the leaves that ranged through every 
part of the water rest upon its bed. h 82 [34] r. 

The back-currents which are formed in the midst of the expanse 
of the falling water are situated between the leap of the water and 
its banks. h 82 [34] r. 

The back-currents made by the water after the expense of its fall will 
be between the surface and the bottom, between the upper and the 
lower part. h 83 [35] r. 

If the beds of two canals are of equal slant and breadth, and contain 
an equal volume of water, and one is restricted to two thirds of its 
breadth in the middle of its course and the other is uniform in breadth, 
I ask which will discharge more water. 

Water that falls into other water strikes against its bed and raises 
itself farther in the air than does the general surface, and then falls 
back and lessens its bounds. h 83 [35] v. 



The lines of the water as it leaps after its percussion will not be in a 
straight course but will bend in a curve. h 84 [36] r. 

A straight canal of uniform depth and slant will make within a 
short time a deeper hollow in its centre than near the bank. 

The water in the middle of straight canals flows more rapidly than 
it does at the sides. 

Where the water has more movement it is lighter if it is of the same 

Water which has been pent up will burst the bank and the bottom 
after its fall. h 84 [36] v. 

Every canal of water of uniform declivity, depth and breadth, which 
is pent up for a certain space, will burst its bed and its bank after the 
passage of this restricted area. 

This is due to the fact that where water is pent up it rises behind this 
barrier and after passing through this narrow place it presses on furi- 
ously; as it descends it comes upon the water below which does not 
flow and so it receives a check. After this it follows the line of its 
descent and goes to the bottom and burrows there and turns with a 
circular movement towards the banks, and hollowing these out from 
below it makes them fall in ruin, as is shown in the drawing above. 

h 85 [37] r. 
[With drawing] 

Water below obeys its natural course less than that above. 

This comes about because the water that borders on the air is not 
made heavy by any weight, so that simply and without any restraint it 
obeys its natural course c d. 

That below is weighted and pressed and acts as is shown at a b. See 
that as it forms an angle at a and above at c it cannot form anything 
but a curved line. 

All the waters some distance below the surface intersect after their 
percussion. h 85 [37] v. 

That water will turn in contrary course which exceeds the general 
breadth and depth of the rivers. 

Waters of equal breadth and unequal depth will be of equal move- 
ment on the surface. 



Among the currents of water of equal slant that which is the 
straightest will be the swiftest. h 87 [39 J r. 

Water which exceeds in depth or breadth the general breadth and 
depth of the river will turn against its first course. h 87 [39J v. 


Remember when discoursing about water to adduce first experience 
and then reason. h 90 [42] r. 

Of streams of water equal in length, breadth and declivity, the 
swiftest will be the one of greatest depth. h 92 [44] v. 

All the movements of streams of water which are equal in depth 
and declivity will be more swift at the surface than at the bottom, and 
more at the centre than at the sides. h 93 [45] r. 

Water, which is the vital humour of the terrestrial machine, moves 
by its own natural heat. h 95 [47 v.] r. 

[The circulation of water] 

The water which from the lowest depths of the sea entering by the 
force of its mover is driven to the high summits of the mountains, there 
finding the severed veins, hurls itself headlong and returns by the 
shortest way to the depths of the sea; and again it raises itself through 
the ramification o£ its veins and again falls back, and thus, coming and 
going, sometimes high and sometimes low, inwards and outwards, it 
revolves with natural or accidental movement after the manner of a 
screw, while the water that is poured away through its severed branches 
and falls back upon itself rises again through its courses and returns to 
the same points of descent. h ioi [42 r.] v. 

Where three currents of water meet together there will be created a 
sudden depth, for they rise and acquire weight and then movement 
with force, and this breaks in the percussion that it makes upon the 
bottom. 1 61 [13] v. 

[Of the fall of a river] 

If the bottom of the bed of the river from which the water hurls 
itself is hollow in the centre, the water which moves from the sides and 
directs itself towards this centre will raise itself before falling. 



If the river as it flows strikes against some rock, it will leap up, and 
the place that it strikes in its fall will be of the nature of a well. 

i 62 [14] r. 

If the rock in a river projects above and divides the course of the 
water which rejoins after this rock, the interval that is found to exist 
between the rock and the reunion of the water will be the place where 
the sand becomes deposited. 

But if the rock that divides the course of the waters is covered by the 
flowing waters only in its lower parts, the water that passes above will 
fall behind it and form a hollow at its feet and cause it to turn; and the 
water that falls headlong into this chasm turns in vortex upwards and 
downwards, for the uniting of the two streams of water which had 
been divided by the rock does not suffer the water immediately to 
pursue its journey. 1 67 [19] v. 

Every natural and continuous movement desires to preserve its 
course on the line of its inception, that is however its locality varies it 
proceeds according to its beginning. 

This movement aforesaid occurs in the course of rivers, which always 
attack and destroy whatever opposes the direct line of their course. 

But if these rivers were straight, with equal breadth, depth and slant, 
you would find that with each degree of movement they would acquire 
degrees of speed. 

Consequently if there is a change or difference in their slant there 
is a difference in their course; and where there is less inequality in 
breadth they become deeper; and given an equal slant, where they are 
wider they become slower. Therefore the waters which desire a straight 
course, and to make themselves swifter at each stage of their move- 
ment, finding the places through which they pass wider and deeper 
become slower and break the bed or the bank. 1 68 [20] r. 



The movement of the rebound of water is swifter than that of the 
percussion when the water that strikes is much mingled with the air. 

1 68 [20] v. 



For the air is capable of being compressed, and the more it is com- 
pressed the more it has weight within the other air; and the greater its 
weight the greater its percussion against its object, as is seen with the 
winds which are constrained from great breadth to pass through a nar- 
row defile of the mountains : if there were no opening above them they 
would not fill up the spaces of the things in front of them, but they are 
able to expand above with great facility because there are great spaces 
between the hills . . . and below readily, and the wind flies easily 
towards the height. Remember how Augustus made a vow in Gaul to 
the wind Cirrius because for just such an impetus he had to lose his 
army, and there he made a temple. 1 68 [20] v., 69 [21] r. and v. 

Water will leap up far higher than it has fallen, through the violent 
movement caused by the air which finds itself shut in within the 
bubbles of the water, and which afterwards rises and floats like bells 
upon the surface of the water. Returning to the place where it strikes, 
the water is again submerged by the blow, so that the air finds itself 
hemmed in between the water which drives it down and that which 
encounters it, and being pressed upon with such fury and violence 
suddenly bursts through the water which serves it as a covering, and 
like a thunderbolt emerging from the clouds so this air emerges from 
the water carrying with it a part of the water 1 which previously formed 
its covering. 1 69 [21] v. 

[Water in canals] 

When water in some part of its passage through a narrow canal 
becomes wider it immediately becomes shallow and swifter because it 
finds a slope where it moves vigorously. And along the course it has 
commenced it directs itself to the foot of its dike and strikes it. 

After which percussion it turns upwards and proceeds with a whirl- 
ing movement hollowing out the foundation of the bank until it 
returns upwards. And this process of hollowing it out gives it the shape 
of the hull of a ship, narrow at the commencement and the end and in 
the centre deep and wide. 1 70 [22] r. 

Here arise the bubblings or wellings up of water in the middle of 

1 MS. has aria, air. 



the higher eddies. And it may be asked whether the movement of the 
eddies starts because it runs towards the percussion of the water, which 
is lower than in any other adjacent part; or because the thrust of the 
water that flows in the centre of the breadth of the surface is that which 
as it strikes the other waters raises them and makes a hill with the 
other water, and then returns towards its entry in the expanse of water; 
or if the water struck by the other waters in its stream and pressed by 
it gushes up and leaps back to the place from which the current comes. 

i 71 [23] r. 


The name pelago (sea, large lake) is applied to an area large and 
deep in form in which the waters lie with little movement. Gorgo 
(whirlpool) is of the same nature as the pelago except for a certain 
difference, and this is that the waters that enter into the pelago do so 
without percussions while those of the gorgo are made up of great 
falls and bubblings up and surgings occasioned by the continuous 
revolutions of the waters. Fiume (river) is that which occupies the 
site of the lowest part of the valleys and which flows continuously. A 
torrent is that which flows only with rains : it also makes its way in the 
low parts of the valleys and joins itself to the rivers. 

Canal is the term applied to waters regulated within their banks by 
human aid. Fonti (sources) is the name given to the birthplaces of 
rivers. Argine (bank) is that which with its abrupt height withstands 
the widening of rivers canals and torrents. The ripa (bank) is higher 
than the argine. The riva (shore) is lower than the argine. The 
spiaggia (beach) is among the lowest of the parts which form bounda- 
ries with the waters. Lago (lake) is that in which the waters of the 
rivers assume great width. Paludi (marshes) are stagnant waters. 
Grotte (caves) are hollows formed in the banks of rivers by the course 
of the river; their length follows the line of the course of the water; 
they have some depth and also find their way under the foundations of 
the bank, losing their shape as they near the end of their course. 
Caverns are of the shape of ovens which enter far beneath the bank, 
and the waters in them are in a state of wild turmoil and are constantly 

Pozzi (wells) are the sudden depths of rivers. Stagni (pools) are the 



places of refuge for the waters of floods or storms, their beds being firm 
and duck SO that the soil can neither drink in nor dry up these waters. 
Baratri (chasms) are also places where the water suddenly becomes 
deep. Procelle (storms) are tempests of water. Polulamenti e surgimenti 
(bubblings and wellings up) are the beginnings of the waters; but the 
former come from below upwards and the latter merely in transverse 
movement which falls from some grotto. Sommergere (submersion) is 
understood to refer to things which enter under the water; inter segati- 
one d acqiie (intersection of waters) takes place when one river cuts 
the other. 1 1 7 2 [ 2 4l r - and v - 

When the general courses of the rivers are contracted, as they issue 
from the valleys and enter amid the defiles of the mountains, the water 
will heap itself up in its wide part; and it will make great descent and 
movement through the said contracting of the mountains, and after 
passing the middle of this contracted part it will make a great hollow, 
and then having entered again in the broad part it will lack depth, in 
just such proportion as the wide part increases in such a way that the 
waters become of equal course. 

And the said depth will be lacking after the leap of the waters, be- 
cause it will become filled up with shingle beneath the greater altitude 
of the leap of the said waters. 

If the fall is of the same width as the river, the water that strikes the 
bottom will leap up and then fall back again by each line that departs 
from the centre of the surging mass, and the farther they descend from 
this surging mass the more they spread out. And part is moved by the 
course of the stream, and as a consequence it is necessary for it to make 
three movements, each of which consumes a considerable portion of the 
foot of the bank. 

For that which descends from the summit of the surging mass 
throws itself towards the bottom, and since such descent is slanting it 
acquires a movement towards the bottom of the bank; and as this 
descent follows in part the general movement of the river, this surging 
mass falls with a threefold descending movement, one proceeding 
downwards, another towards the bank, another towards the course of 
the river. And all three consume the base of the bank, by reason of the 

*A list of words is added, descriptive of movement of water. 



great displacement occasioned by so much impetus; for if the river 
were to flow for a long way hugging the bank it would be able to find 
some stone which at some spot would protect a piece of this bank near 
to it; but this movement proceeds downward towards the bottom, for- 
ward towards the bank, downward towards the course of the stream, in 
such a way that each stone is struck by three different movements and 
on three different sides. 

From which it follows that if the soil is friable it crumbles away 
in a short time. I 74 O 6 ] v -> 75 [ 2 7] r - 

[Of the movement of water — bubbles} 

When one sees mountains rising in the running waters, rising in the 
form of bubbles, it serves as a sign of the great depth from which these 
bubbles spring after the percussion made by the water upon the bot- 
tom; and by the speed of its rebound it bores through and penetrates 
the other water and then turns towards the surface of the running 
water and passes through it, rising up in this way; thereafter acquiring 
weight it loses its first impetus and falls down again by each line round 
its centre, and returns again towards its bed. i 76 [28] v. 


Of the difference water makes in its course if its sides strike on a 
strand, a bank, or other water, that is in passing by a piece of stagnant 
water or running water crosswise. 

One should also observe what differences there are in rivers if they 
fall upon beds of different natures, namely upon stone or earth, or tufa 
or clay, sand or mud, or stagnant or running water, and this crosswise 
or slanting or opposite, or by the same line as the water itself, that is by 
the line of the same current but slower or swifter than that which it 
strikes, or more level or more slanting. 


One asks why the percussion of water within water makes lines of 
circular movements and eddies, and its leap is not straight as is that 
other which beats upon its shores and banks. 

Why bubbles are not continuous when the falls of the water are: 



The reason is that the water which flows above alter falling is swifter 

than that which flows below; and when that below precipitates itselt 
in some chasm it raises itself towards the surface with almost the same 
impetus, and sometimes subdues and overcomes the water that flows 
above and sometimes is subdued by it. 

Being thus in a state of equilibrium as to its power of movement 
sometimes one conquers and sometimes the other. 

1 77 [29] r. and v. 

Things lighter than water do not follow the course of the rebound 
and intersection of the water, but pass along the centre of its current or 
near the parts as they are found at the entrance of the currents, and are 
not impeded unless by equal pressure, because if the right wave of the 
rebound meets with the left, it is necessary, if they are of equal power, 
that the place of their percussion be thrown back equally. 

Consequently things in this place which move upon the water, not 
being driven more by one percussion than by the other remain in the 
same line of current. But if one of the forces of the wave be greater 
than the other, that is by the swiftness of its current, I do not mean 
force arising from a greater quantity of water, for if the one water was 
much less thick than the other this would not matter: for let us sup- 
pose one body of water to be less than double the other in volume and 
to acquire double its speed; now since these bodies of water clashing 
together are of equal size in their contact, as I have proved in the third 
of the fifth, the larger being a square braccio and the lesser of a half 
braccio, the lesser does not strike the greater unless it is in its half, and 
in the same way the greater strikes the lesser with its half, so that the 
contacts made by the percussions are equal in quantity and unequal in 
that the power is double, the speed of the one being double that of the 


Sometimes there are many eddies which have a great current of 
water in the middle of them, and the more they approach the end of 
the current the greater they are. These are created on the surface by the 
waters that turn back after the percussion that they make in the most 
rapid current, for the front portions of these waters, being themselves 



slow, on being struck by the swift movement, are suddenly transformed 
into the said speed. Consequently the water which touches them behind 
is attached and drawn by force, and torn away from the other, so that it 
turns all in succession, one (wave) following the other with a like 
swiftness of movement, if it were not that such current at first cannot 
receive it so that at any rate it does not rise above it, and as this cannot 
be it is necessary for it to turn back and consume in itself these swift 
movements. From that time the said eddies with various revolving 
movements proceed to consume the impetus that has been begun. And 
they do not remain in the same positions, but after they have been 
formed thus, turning, they are borne by the impetus of the water in 
the same shape, in which they come to make two movements; the one 
is made in itself by its own revolution, the other as it follows the course 
of the water which is carrying it along all the time that it is destroy- 
ing it. i 78 [30] r. and v., 79 [31] r. 

[Air and water] 

The water which by a slight movement encloses, a little way below 
its surface, the air which is submerged with it, turns with a slight 
impetus out of the surface, carrying with it such covering of water that 
being of equal weight with this air it stands above it in the form of a 
half-spherical figure. 

But if this air is submerged with impetus it comes back out of the 
water with fury for the length of the movement made beneath the 
water; and pressed by its weight it leaps out of the water, breaks its 
surface with its impetus and flows on with straight course after the 
manner of wind emerging from bellows which discharges itself in a 
stream through the air; and therefore it does not, as does the former as 
it floats upon the water, remain enveloped in its surface. 

1 80 [32] v. 

How all the air which leaps back with the water does not remain on 
the surface but by its impetus submerges itself anew amid the revolu- 
tions of the waters: 

How the movements of the waters among the other waters are not 
obliged to move more by a straight line than a curved one, and how 
after leaping back as they wished these waters are not obliged to be at 
rest, but in order to return to a low place and with a revolving move- 



mcnt thcv go attending the course of the river until they have dis- 
charged the air that is enclosed within them on the surlace ol the 
sheet of water. I 81 [33 1 r. 


\Of water flowing into water] 


If the entry of the water into the sheet of water (pelago) is of circular 
shape the concavity of its base will be of the form of a crescent, receiv- 
ing the shingle within its circumference or within the two horns of this 

I ask whether if the current should make some bend it will become 
hollow at the bottom or in the middle or above, and the same thing as 
regards the leaps which follow afterwards against the bank of the rivers, 
the bed being of uniform substance, and also as to the bank where it is 
raised, where it leans and the methods of effecting its repair. 

1 81 [33] v. 
[ Of falling water] 

I ask as to the shape that water assumes in the different slants of its 
descent in each of its falls, and what shape the concavity will have when 
the water strikes upon a bed of uniform substance; and I ask as to the 
shape the shingle will take which is left after the percussion of each of 
these, and the remedies when they are injured. 1 82 [34] r. 


Because the straighter the river the swifter will its course be, and the 
more vigorously will it gnaw and consume the bank and its bed, it is 
therefore necessary either to enlarge these rivers considerably or to send 
them through many twistings and turnings or to divide them into a 
number of branches. 

And if the river through many twistings and turnings becomes slow 
and marshy through its many detours you ought then to straighten it, 
in such a way that the waters acquire sufficient movement and do not 
cause destruction to the banks or dikes; and if there should be depth 
near to some dike you ought to fill up the spot with gabions together 



with fascines and shingle, so that it may not become hollowed out by 
movement under the dike, and so by causing it to crumble the river 
may afterwards proceed to make a bend in your land or villa and there 
straighten its course. i 82 [34] v. 

f Of the earth carried by water] 

When the water in the floods commences to find a place where it 
can flow, it begins with its feeble inundation to strip and carry away 
the lightest things, and deposits them where its course becomes feeble, 
then as it grows it carries away the heavier things such as sand, and 
carries them over the former things and there leaves them, and even 
though the water should not increase, by the mere fact of its continu- 
ance it proceeds by degrees to carry away the things from the place 
where it flows; but by reason of their weight it cannot carry them so 
far forward as the first lighter things, and if it then carries away the 
heavier things it deposits them proportionately near to the spot from 
whence it took them. 

How to restore the soil to the places that have been uncovered and 
stripped bare by the courses of the waters on a hill or mountain or in 
sandy places. 

For the rains, or to provide an outlet for other waters, one ought to 
construct canals or mouths of rivers, for the places where they pass in 
so great current that they tend to become turbid by reason of the earth 
they carry with them and to be changed; then when they are at the 
place where you wish that they rid themselves of the soil, these canals 
of water are divided into many small channels of water, after the man- 
ner of furrows, and their violence is lessened and they grow clear again. 

1 83 [35] r. 
[Of flowing water] 

Where the river is constricted, it will have its bed stripped bare of 
earth, and the stones or tufa will remain uncovered by the soil. 

Where the river widens, the small stones and the sand will be 

Where the river widens considerably, there will be discharged the 
mud or the ooze and bits of timber and other light things. 

Where several currents of water run together, there will instantly be 
formed a hollow that will be navigable. 



Where the waters separate, the sand and ooze will be deposited and 

the bed will be raised in the shape of the halt oi a ship inverted. 

Beneath the rebounds of the water, there will be formed hills of sand 
or stones. 

Beneath the repercussions, that which rests under the rebound will 
become raised. 

Where the water finds the place higher, which forms an obstacle 
beneath it, it makes a greater and higher wave and then forms a deeper 
hollow. 1 83 [35] v. 

Where you find much sand you will find at the end of it in front or 
behind shingle or bare tufa. 

Sand is discharged when waters meet in their course, for in such a 
spot nothing can remain that offers resistance to a current so reinforced; 
light waves drop their sand at the sides of the said current, and the 
sand as the current becomes less swift forms a cover to the shingle. 

Sometimes the lesser floods carry branches covered with leaves from 
the plains and deposit them in their small movements, and then, 
becoming stronger, heap sand upon the edges of these branches and still 
increasing carry there shingle and tall large stones. 1 84 [36] r. 

[The rebounds of water] 

The rebounds that water makes which rise through the percussion 
of water which has fallen upon other water, are not carried between the 
equal angles of its percussion, but will leap to the surface by the shortest 
way, through the air that was submerged together with the water. 

1 84 [36] v. 

If a stone is thrown into still water it will form circles equidistant 
from their centre; but if into a moving river the circles formed will 
lengthen out and be almost oval in shape, and will travel on together 
with their centre away from the spot where it was first made, following 
the course of the [stream] ... 1 87 [39] r. 


The waves are of [twelve] kinds, of which the first is made in the 
upper parts of the waters; the second is made above and below by the 
same path; the third is made above and below by contrary paths, and is 



not in the centre; the fourth is made so that from its centre upwards it 
runs in one direction and from this centre downwards it makes the 
opposite movement; the fifth flows downwards and not upwards; the 
sixth flows downwards and above has a contrary movement; the 
seventh is that of the submersions of waters by means of a spring that 
enters into the earth; the eighth is that of the submersions by means of 
eddies which are narrow above and wide below; the ninth is that of the 
eddies wide at the surface and narrow at the base; the tenth is of cylin- 
drical eddies; the eleventh of eddies that bend in regular curves 1 ; the 
twelfth is of the slanting eddies. Make here all the waves together, and 
all the movements by themselves, and all the eddies by themselves. 
Arrange thus the series in order separated one from the other. And so 
also the rebounds of how many kinds they are in themselves and also 
the falls. And set down the differences that there are in turbid waters, 
in their movements and percussions, and those that are clear; and 
similarly in waters that are violent and those that are sluggish; in those 
that are swollen and those that are shallow; and between the fury of 
pent-up rivers and those with a wide course; and of those that run over 
great stones or small ones or sand or tufa; and of those that fall from a 
height striking upon different stones with various leaps and bounds, 
and of those that fall by a straight path touching and resting upon a 
level bed; and of those that fall from a great height alone through the 
air; and of those that fall through the air in shapes that are round or 
thin or wide or separated or united. And then write down the natures 
of all the percussions : on the surface, in the centre, and at the bottom, 
and of their different slants, and the different natures of the objects and 
different shapes of the objects. 

And if you give movement to a sheet of water, whether by opening 
its sluices above, or in the middle, or below, show the differences that 
are caused by it falling or moving on the surface, and what effect it 
makes in entering with such fall upon the ground or in stagnant water, 
and how that by which it is moved at first maintains itself in a channel 
level or uneven, and how it produces all at once eddies and their re- 
cesses, as one sees in the basins of Milan, and the nature of the sudden 
rush of the rivers, and so also with those that grow little by little; of 
die waters also that cannot in the great floods pass through the arches 

1 MS. d equal nacuita. 



of the bridges which surmount them, and how the water that passes 
through these arches increases the impetus through having a great 
weight above. 87 [39] v -> 88 I-H r - and v - 

[The water of mills] 

I ask whether if the impetus of the waters that turn the mills creates 
a protuberance either across above or below near the place of percus- 
sion, this percussion will have the same force as if this water ran in a 
straight line. 1 89 [41] r. 


Rivers when straight flow with a much greater impetus in the centre 
of their breadth than they do at their sides. 

When the water has struck on the sides of rivers with equal percus- 
sion, if it find a part of the river narrower it will leap towards the 
middle of the river and these waves will make a new percussion be- 
tween themselves; as a consequence they will return again towards the 
banks, equally, and that water of conical shape, which is enclosed 
between the first percussion made upon the bank and the second made 
in the centre of the stream, will slacken at its base and be swift near to 
its crest. Striking the bottom they will afterwards rise equally to the 
height of the intersection; but always that of the centre will be swifter 
than that which leaps back. 

Water which moves along an equal breadth of river and on an equal 
bed will have as many different thicknesses as there are different slants 
in the bed where it runs; and by as much as it is swifter in one place 
than another so proportionately it will be more shallow. 

1 105 [57] v., 106 [58] r. 


Water which falls from the height of a fathom will never return to 
the same height except in small drops, which will leap much higher 
because the motion of leaping back will be much more rapid than that 
of the descents. In fact when the water falls it buries with it a great 
quantity of air, and after the (other) water has been struck it leaps 
back towards its surface with a force which creates a movement almost 
as rapid as was that of the descent; but not actually so for the reason 



given in the second of the seventh, where it is stated that the movement 
of the rebound will never be so swift as was the descent of the substance 
which rebounds; or thus: — a succeeding rebound will never be equal to 
that which precedes it. So that in consequence the rebound which the 
water makes proceeds from the base where it has been created, almost 
with the speed of the descent that has given it birth; and in addition to 
this there is added to it a second momentum which augments this 
motion, namely that of the air that is submerged by the fall of the 
water. This air clothed around with water bounds up with fury and 
leaps into its element like wind driven by the bellows; it carries with it 
the last of the water which is close to the surface, and by such an in- 
crease causes it to leap up much farther than its nature demanded. 

i 108 [60] v., 109 [61] r. 

The farther the circular wave is removed from its cause the slower 
will it become. 1 114 [66] r. 

[The meeting of water-courses] 

If the courses of two lines of water which cross each other in the 
middle or in a part of their river-beds pass either the one into the other 
or the one over the other, do they then each leap back after the per- 
cussion ? Certainly they leap, because it is impossible for the two bodies 
to pass one through the other. 

But after the two bodies have clashed together they will widen 
themselves at their point of contact, and after having struck they will 
recoil to an equal distance from the centre of the percussion. And that 
body which goes upwards follows its nature, and the other body below 
the centre of the impact which would wish to go downwards and 
cannot, increases that above. 1 114 [66] v. 


Make one side of the channel of glass and the remainder of wood; 
and let the water that strikes there have millet or fragments of papyrus 
mixed in it, so that one can see the course of the water better from their 
movements. And when you have made the experiment of these re- 
bounds fill the bed with sand mixed with small shingle; then smooth 



this bed and make the water rebound upon it; and watch where it rises 
ami where it settles down. 

Then make the bank on the wooden side of mud, and watch its 
effects through the glass, and make it again in flowing water. 

1 115 [67] r. 
[Movements of water] 

If the water was a quantity endowed with sense * as it is a continuous 
one, the movement that it makes between the extreme elevations and 
depressions of its waves would be unequal. 

In effect the part that rises acquires degrees of slowness in each 
degree of movement, in such a way that at its greatest elevation it is 


in the extreme stage of slowness. 


And afterwards in descending it acquires degrees of speed in every 
degree of movement, so that at its lowest depth it acquires greater 
movement; therefore the resistance that ends its descent is that which 
receives the hurt, and that which ends the height of its elevation has no 

But if the quantity is continuous : the continuous quantity has equal 
movements when its river is of equal size and depth, because being all 
united together it is necessary that in all the parts of its movement each 
part draws and is drawn, pushes and is pushed, or drives and is driven. 
And it is necessary that this be with equal movement and power; and 
if it were not so the water would multiply more where it was slowest 
and would fail where it had most movement. 

1 115 [6y] v., 116 [68] r. 

Where the water divides it rises; and afterwards as it falls down 
again it strengthens its course by the increased descent that follows. 

Where the waters join they rise; and then the near movement that 
follows becomes slow. 1 116 [68] 

When in the courses of rivers there are two currents of water, com- 
mencing the one far from the other, which meet in a place where they 
clash together, they will rise up after this percussion, and their bed will 
be but little consumed because they depart from it; and afterwards they 
will fall back again as they separate, and fall asunder, and falling back 

1 MS. disscreta. 



again they will strike and scrape upon their bed. By reason then of this 
percussion, which beats and scrapes the bed with its movement, a depth 
will be produced there; and this happens in the great currents of rivers. 

i 117 [69] r. 

[The height and depth of the waves] 


The greatest elevation of the waves will not wear away its bed be- 
neath itself; in effect it touches it but little, by the fifth of the sixth 
which says that everything weighs by the line of its movement; from 
which we may say that this wave moves towards the air that flies from 
its percussion and weighs towards the air. If however the amount of 
friction is slight, it will have but little force and will consume the bed 
but little. 



Whatever obstacle forms the chief cause in breaking the straight 
course of the water will be most consumed and displaced by it. 

Therefore we may say that if the air were the cause why the straight- 
ness of the elevation of the wave is broken it would be consumed by 
this percussion of water. But this air is not the cause of the breaking of 
such a course; the only cause of it is the force which the water acquires 
as it emerges from its element. And it would relax its pace in such a 
position if it were a sensitive quantity, but being as it is a continuous 
quantity it is necessary that one body of water pushes and the other 
draws, because they are united. 1 117 [69] v. 

If the water moves more swiftly in the falling of the wave than in its 
rising, and at what point this water delays most. 

The water that moves in the formation of the waves will find itself 
of as great speed during its ascent as that of its descent, and it will have 
as much in the middle of its lowest depth as that of its greatest height. 
And if it was not of equal movement it would not be of equal depth or 
breadth; and if however it was of equal length and depth but not of 
equal movement it would form a great height in the place where it 
slackened most. 1 118 [70I r. 



The water {lows more strongly at the sides of a covered rock than 
above it and after it has passed it, and for this reason it twists the 
waves made hv its rebounds, producing on its surface crescent-shaped 
figures, 1 I2 3 [75] r - 

[The different sorts of rebounds of water] 

The rebounds of the waters are of two kinds, that is they are formed 
from two causes; one is that of the lumps of the bed on which the water 
passes, the other is when the parts of the water that strike against the 
lumpy parts of the bank leap back to the opposite bank. These masses 
of water on striking leap back to the opposite bank and press and drive 
themselves upon the first wave that they meet, and swelling leap 
towards the sky; and each flies equally from the place where it has 
struck, until another wave drives it back and afterwards another drives 
it forward. 

So in succession they fill the surface of the rivers with a trellis pat- 
tern, always raising themselves to the positions of the above-mentioned 
percussions. 1 127 [79] v. 

[Ride as to rebounds: experiment] 

I ask concerning the rebound: if the first rebound is ten braccia tell 
me how far will the second be. Dye the ball so that it marks the spot 
where it strikes upon the marble or other hard substance, study the 
position of each of the rebounds in succession, and so deduce the rule. 

1 128 [80] r. 

If you throw sawdust down into a running stream, you will be able 
to observe where the water turned upside down after striking against 
the banks throws this sawdust back towards the centre of the stream, 
and also the revolutions of the water and where other water either joins 
it or separates from it; and many other things. Kir. 



Water is nature's carter, it transforms the soil and carries to ... a 
great part . . . double. k 2 r. 




Simple movement: Many rivers there are that increase their waters 
at every state of movement without loss. 

Simple movement: Many there are that lose without ever acquiring. 

Composite movement: And there are a considerable number which 
acquire more than they lose. 

Composite movement: And a considerable number lose more than 
they acquire. k 60 [n] v. 

I have written in how many ways water hollows out the bottom, and 
in how many ways it deposits earth upon the bottom. And the same of 
the banks: where it raises them and where it forms them, and in how 
many ways it hollows out the soil of the banks, and the estates where 
during its floods it goes spreading itself beyond its banks. 

k 65 [18] r. 

The eddies of water are always produced in the middle water. 

The middle water is that above the mouth of the water which is bent 
across near to where it runs into the canal. 

The middle water is that between the water that is falling and that 
which is thrown back. k 93 [13] v. 

Should two streams of water encounter each other and then bend 
together in the same flight, the middle water will be found bevond this 
flight upon the current that has less power. 

The surface of the water which bends in leaving the straight line of 
its course for the lateral outlet will be always higher in the centre than 
at the sides. k 94 [14] r. 

Of the water that is poured through a hole of uniform size situated 
at the bottom of its reservoir, the part that is nearest to the wall of this 
hole will have greater height and greater movement than the lateral 
part. k 94 [14] v. 

When water is poured in different streams from one reservoir into 
another that will be higher above its hole which is poured through a 
hole of less width, and the proportion of the height will be the same 
as that of the width of the holes. k 94 [15] r. 



When two streams of water encounter each other and then pour 
through the same channel to the bed of a river, eddies are created there 
on the right hand and on the left, and sometimes these eddies of the 
right and left become reunited. k. 9 6 l l6 J r - 

The water which moves in a river is either summoned or driven or 
moves of itself. If it is summoned or as one may say requisitioned 
what is it that requisitions it? If it is driven what is it that drives it? If 
it moves of itself this shows it to have a reasoning power; but in bodies 
which undergo continual change of shape it is impossible that there 
should be reasoning power, for in these bodies there is no judgment. 

k 101 [21] v. 


All the embankments of rivers against which the waters strike ought 
to be so much the more slanting as the percussion of the water is of 
greater power. 

Water rises higher upon the bank against which it strikes when it 
finds this bank more slanting; and consequently descends with greater 
impetus to strike against the opposite bank. k 102 [22] v. 

What difference there is between the percussion of the same quantity 
of water when it falls through the air or falls shut up in a conduit : 

The water which falls in a perpendicular line becomes shrill at 
some stage of its descent. When it falls through a conduit this is left 
empty, and here the air fights with the water as will be said in its 
place. You should not forget however to say that this descent of the 
water is checked by the condensation of the air in the conduit where 
the water is. k 103 [23] v. 

If the waters that enter into a reservoir or issue forth from it have 
the holes of exit equal to the holes of entry, and the fall of the entry is 
longer than that of the exit, the entry will then be greater than the 
exit until the water of the basin rises, and then they will become equal. 

k 104 [24] r. 

And if the fall of the entry is more beneath the surface than the 
fall of the exit, although they are of the same size, the entry will be 
greater than the exit until their powers equalise themselves. 



But if in this case the exit covers a longer space of the surface than 
the entry does then the exit will be greater than the entry. 

K I0 4 [24] V. 

What shape will the same quantity of water moving along the same 
slant have in order that it may be as swift as possible? 

Let it have that which will make least contact with the bottom, that 
is a half-circle. 

That water will be swifter when the part that makes eddies through 
striking upon the bottom and the sides is less in bulk than the rest; 
and this is the greatest river. k 105 [25] r. 

[Relation of wave and wind] [Diagram] 

The wave increases because the wind increases. 

D b e f the wind, strikes e f the water, and causes it to overflow; d a 
e c the second part of the same wind finds c e prepared to overflow, 
having come from e /, and comes behind it with its power; and dou- 
bles the power t v e f and so makes the wave double, k 106 [26] v. 

Whether the percussion made by the water upon its object, is equal 
in power to the whole mass of the water that strikes when it finds itself 
in the air, or no. 

Which is the easier, to raise the sluice of the mill with the water 
flowing, up or down or across, or when the water is still. 

k 117 [37] r. 

Vessels of equal capacity and full of water in double proportion and 
which empty themselves by holes made in their lowest depth, in each 
degree of time will change the degrees of proportions in the copious- 
ness of their discharges. 

I maintain that if at the commencement of the discharge the water 
is of double quantity, the amount of the discharge is immediately 
double in the one case what it is in the other, varying immediately; in 
such a way that if the descents are divided in six stages in the lesser 
vessel and twelve in the larger one, when the lesser vessel has had a 
drop of five stages and the greater five also, this lesser vessel is left 
with one stage of height of water and the larger with seven, which is 
in proportion seven times as great. k 128 [48] r. 



\ Fill I of water] 

Water which falls in the form of a pyramid by a perpendicular line 
upon a level surface will leap up again to a height and will end its 
point towards the base of this pyramid, and will then intersect and 
pass beyond it and fall down. l i r. 

[ Air replacing water] 

Why the air which fills up the void in a globe from whence the 
water emerges, enters with the same impetus as that of the water which 
is poured out. Whatever is resting upon this water turns in contrary 
movement to that of the water. l 17 v. 

[ Rivers] 

The long thing of uniform thickness swells as much in its two 
opposite sides as it is lowered in its two other opposite sides. 

Here the water which is confined in the parallel river increases as 
much in height as it is lacking in breadth; consequently as it falls it 
hollows out the place where it has struck. 

The parallel rivers may at some part of their length be confined in 
two ways, namely between their surface and their bed or upon their 
opposite sides. l 30 r. 

[Falls of water] 

When two streams of water meet at an extremely sharp angle the 
more powerful hollows out its side of the base most, and makes a sud- 
den depth. 

This is the true way of giving the fall while conserving the bank to 
the water which descends from the said bank. l 31 v. 

[The course of rivers] 

The beds of the rivers uncovered naturally, do not give true indica- 
tions of the nature and quantity of the objects carried by the waters, 
because in the deep waters many places are filled with sand, and after- 
wards in the particular lateral courses of the rivers these deposits of 
sand are borne above the shingle on which they rested or laid bare 
beneath, so causing the continual subsidence of the raised bank of this 
sand which by reason of its lightness accompanies it in its course and 
is then deposited where the current of the water becomes more 




The twistings of rivers in flood are such as to burst every dike and 
all the order that the river keeps when low. l 32 r. 

[Falls and courses of water] 

Water that has fallen with great impetus from its dam reproduces 
die twistings of the rivers according to the line of its fall, but when the 
waters subside, although the line a b keeps its place even if this river 
should swell again, the canal a b will become filled with sand, and the 
volume of the water will follow its natural course. l 32 v. 

[Water in percussion] 

When water strikes it rises, and it acquires weight in proportion as 
it leaps out of its common surface; this fallen back upon, the other 
water strikes it and penetrates as far as its bed, which it consumes 
perpetually; and such a hollow is formed in the length of the sides of 
the object struck. 

To guard against this a flat surface may be formed round any 
column which has a firm base and is of such breadth that the water 
that falls back is compelled to find it. l 33 r. 

The less curved the bank where the leap of the river strikes it the 
farther removed will the second leap be from the spot from which the 
first departed. l 36 v. 

The eddies of rivers are of several kinds; of these some are hollow 
in the centre after the manner of a concave pyramid; others full in the 
centre like a raised cone; some throw things up from the bottom, 
others submerge things borne on the surface of the water; and the one 
creates a hollow underneath the bank which forms its side, the other 
fills it up. 

These eddies serve the purpose by their revolutions and delays of 
equalising the excessive speed of the rivers; and as therefore the eddies 
at the side are not sufficient, by reason of the narrowness of the rivers, 
it becomes necessary that new kinds of eddies should be created which 
shall turn the water over from the surface to the bottom and at various 
different angles; of these some meet at the bottom and churn up all 
the soil which the eddy of the surface has in course of time deposited. 
And the other eddies do the same against the banks of the rivers. 

b.m. 30 v. 



A book of how to drive back armies by the fury of floods caused by 
the letting loose of waters. 

A book of how to inundate armies by closing the outlets of the 

A book to show how the waters bring down in safety logs hewn in 
the mountains. 

A book of how boats are forced against the rush of the rivers. 

A book of how to raise great weights by the simple increase of the 

A book of how to guard against the rush of rivers so that cities may 
not be struck by them. b.m. 35 r. 

Of the inequality in the hollow of a ship. 

Book of the inequality of the curve of the sides of ships. 

Book of the inequality in the position of the helm. 

Book of the inequality in the keel of ships. 

Book of the difference in the holes through which water is poured 

Book of the water contained in vessels with air and of its move- 

Book of the motion of water through a syphon. 

Book of the clashing together and concourse of water proceeding 
from different directions. 

Book of the varying shapes of the banks along which the rivers pass. 

Book of the various shoals formed below the locks of the rivers. 

Book of the twistings and bendings of the currents of the rivers. 

Book of the different places whence the waters of the rivers are 

Book of the shapes of the banks of the rivers and their permanence. 

Book of the perpendicular fall of water upon various objects. 

Book of the course of water when impeded in various positions. 

Book of the various shapes of the obstacles which impede the course 
of the waters. 

Book of the hollow or rotundity formed at the bottom round the 
various obstacles. 

Book of how to conduct navigable canals over or beneath the rivers 
which intersect them. 



Book of the soils which drink up the waters of the canals and of the 
means of protection. 

Book of the creation of channels for rivers which quit their bed 
when it is filled up with soil. b.m. 45 r. 

[Of water] 

This wears away the lofty summits of the mountains. It lays bare 
and carries away the great rocks. It drives away the sea from its ancient 
shores for it raises its base with the soil that it carries there. It shatters 
and devastates the high banks; nor can any stability ever be discerned 
in these which its nature does not suddenly bring to naught. It seeks 
out with its rivers every sloping valley where it may carry off or de- 
posit fresh soil. Wherefore many rivers may be said to be those through 
which all the element has passed, and the sea has gone back many 
times to the sea, and no part of the earth is so high but that the sea 
has been at its foundations, and no depth of the ocean is so low but 
that the loftiest mountains have their bases there. And so it is some- 
times sharp and sometimes strong, sometimes acid and sometimes bit- 
ter, sometimes sweet and sometimes thick or thin, sometimes it is seen 
bringing hurt or pestilence, sometimes health-giving, sometimes poi- 
sonous. So one would say that it suffers change into as many natures 
as are the different places through which it passes. And as the mirror 
changes with the colour of its object so it changes with the nature of 
the place through which it passes: — health-giving, noisome, laxative, 
astringent, sulphurous, salt, incarnadined, mournful, raging, angry, 
red, yellow, green, black, blue, greasy, fat, thin. Sometimes it starts a 
conflagration, sometimes it extinguishes one; is warm and is cold; 
carries away or sets down, hollows out or raises up, tears down or es- 
tablishes, fills up or empties, raises itself up or burrows down, speeds 
or is still, is the cause at times of life or death, of increase or privation, 
nourishes at times and at times does the contrary, at times has a tang 
of salt, at times is without savour, at times submerges the wide valleys 
with great floods. With time everything changes. b.m. 57 r. 

At times it goes twisting to the northern parts, eating away the base 
of its bank; at times it overthrows the bank opposite on the south; at 
times it turns towards the centre of the earth consuming the base 
which supports it; at times leaps up seething and boiling towards the 



sky; at times revolving in a circle it confounds its course; at times it 
extends on the western side robbing the husbandmen of their tilth; at 
times it deposits the soil it has carried away in the eastern parts. And 
thus at times it digs out, and at times fills in where it has taken away 
and where it has made a deposit. Thus without any rest it is ever re- 
moving and consuming whatever borders upon it. So at times it is 
turbulent and goes ravening in fury, at times clear and tranquil it 
meanders playfully with gentle course among the fresh verdure. At 
times falls from the sky in rain or snow or hail; at times forms great 
clouds out of fine mist. At times moved of itself, at times by the force 
of others; at times gives increase to things that are born by its life- 
giving moisture, at times shows itself either fetid or full of pleasant 
odours. Without it nothing can exist among us. At times it is bathed 
in the hot element and dissolving into vapour becomes mingled with 
the atmosphere, and drawn upwards by the heat it rises until having 
found the cold region it is pressed closer together by its contrary na- 
ture, and the minute particles become attached together. And as when 
the hand under water squeezes a sponge which is well saturated so 
that the water shut up in it as it escapes through the crevices is driven 
into the rest and drives this from its position by its wave, so it is with 
the cold which the warm moisture compresses, for when it has reduced 
it to a more solid form the air that is pent up within it breaks by 
force the weakest part, and hisses just as though it was coming out of 
bellows when they are pressed down by an insupportable weight. And 
thus in various positions it drives away the lighter clouds which form 
obstacles in its course. b.m. 57 v. 

. . . stage of declivity. Water initiates its own movement. 

Book of the various ways of levelling waters. 

Book of how to divert rivers from places where they do damage. 

Book of how to straighten the course of rivers which cover too much 

Book of how to divide rivers into many branches and make them 

Book of how waters pass through seas with different movements. 

Book of how to deepen the beds of rivers by different currents of 



Book of how to control rivers so that the small beginnings of the 
damage they cause may not increase. 

Book of the different movements of waters which pass through 
channels of different forms. 

Book of how to prevent the small rivers diverting a larger one as 
their waters strike it. 

Book of how to ascertain the lowest level in the current of the sur- 
face of rivers. 

Book of the origin of rivers which flow from the lofty summits of 
the mountains. 

Book of the variety of the movements of waters in their rivers. 

b.m. 122 r. 

[Why the beds of straight rivers are deeper in the centre than at the 

The current of a straight river is higher in the centre than at the 
sides, and rises towards the sky with greater waves and turns in greater 
depth towards the centre of the earth. 

And this occurs because the current is the clashing together or inter- 
section of the reflex movement of the waves, which leap back after 
striking against the bank and running back to the opposite bank 
clash with the contrary movements, and these resisting each other and 
neither being able to penetrate into the other leap back high out of 
the water, and then falling back — having acquired weight while in the 
air — plunge beneath the water there where they strike it. 

b.m. 135 v. 

How rivers widen their valleys and wear away the roots of the 
mountains at their sides: 

The bases of the hills as their valleys grow deeper are bent back 
towards the course of the river, as though they should wish to de- 
mand back from the speeding river the soil of which it has despoiled 

This proceeds from the nineteenth of this treatise which says: the 
current of the river eats away the base of the mountain on one side 
where it strikes and gives it back to the opposite side to which it is 

In great valleys the river changes its bed. 



The rivers in great valleys make greater changes in their heds in 
proportion as they are farther away from the roots of the mountains. 
This is proved by the ninth of this which says: the largest rivers flow 
through the largest valleys which have been made by them, and by 
reason of their size they are continually consuming the waves that flow 
from their banks, carrying them always back to the current of the 


The mouths of rivers are continually bending and descending behind 
the course of their principal stream, and this proceeds from the former 
[rule] which says: water takes away with its wave from the bank 
where it strikes and gives back to the opposite bank where it is 

Valleys are continually growing deeper. 

Valleys continually grow wider and deeper and rivers continually 
change their position. b.m. 161 r. 



The water which falls in a perpendicular line through a round pipe 
upon a level place will make a circumambient wave round the site of 
its percussion, within the circumference of which the water will move 
very rapidly and be spread very thinly round about this place which 
has been struck, and at the end it will strike into the wave produced 
by it which seeks to return to the place of the percussion. 

b.m. 167 v. 

Water is that which serves the vital humour of this arid earth. 

It is the cause which moves it through its veins contrary to the 
natural course (desire) of weighty things; it is like that which moves 
the humours in all kinds of living bodies, and . . . 

And as the water is driven up from the lower part of the vine 
towards its severed stems and afterwards falls back to its roots, pene- 
trates these and rises again anew, so from the lowest depth of the sea 
the water rises to the tops of the mountains, and falls down through 
their burst veins and returns to the sea and rises again anew. Thus up 



and down, in and out, unresting, now with fortuitous, and now with 
natural motion, now in its liberty and now constrained by its mover, it 
goes revolving and, after returning in force to its mover, rises again 
anew and then falls anew; so as one part rises the other descends. 

Thus from the lowest depths of the sea the water rises up to the 
summits of the mountains and falls down low through the burst veins, 
and at the same time other water is rising: so the whole element 
ranges about and makes its passage many times through the rivers 
that fall into the sea. 

At one time it becomes changed to the loftiest clouds, and afterwards 
it is pent up within the deep caverns of the earth. 

It has nothing of itself, but moves and takes everything, as is clearly 
shown when it is distilled. 

Thus hither and thither, up and down, it ranges, never resting at all 
in quietude, always flowing to help wherever the vital humour fails. 

Now taking away the soil, now adding to it, here depositing logs 
there stones here bearing sand there mud, with nothing stable in bed 
or bank: 

Now rushing on with headlong course, now descending in tran- 
quillity, now showing itself with fierce aspect, now appearing bright 
and calm, now mingling with the air in fine spray, now falling down 
in tempestuous rain; now changed to snow or storms of hail, now 
bathing the air with fine rain; so also now turning to ice and now hot; 
never keeping any stability; now rising aloft in thin cloud, compressing 
the air where it shuts it in, so that it moves through the other air after 
the fashion of a sponge squeezed beneath the water, when what is 
enclosed within it is driven out through the rest of the water. 

b.m. 210 r. 

The heat that is poured into animated bodies moves the humours 
which nourish them. 

The movement made by this humour is the conservation of itself 
and the vivification of the body which contains it. 

Water is that which serves the vital humour of the arid earth; it is 
poured within it, and flowing with unceasing vigour through the 
spreading veins it replenishes all the parts that depend of necessity on 
this humour. 



And it flows from the vast depths of the mighty ocean in the deep 
wide caverns that lie hid within the bowels of the earth, whence 
through the spreading veins upwards against its natural course in con- 
tinual ascent to the high summits of the mountains it returns through 
the burst veins to the deep. 

Water is that which serves the vital humour of the arid earth; and 
the cause which moves it through the veins is just that which moves 
the humours in all the different species of animated bodies. 

b.m. 234 r. 

Water which serves as the vital humour of the arid earth and for 
this same cause moves through the spreading veins, is poured into it 
and works within it as does the blood in human bodies. 

The same cause moves the water through its spreading veins as that 
which moves the blood in the human species, and as through the burst 
veins in the top of a man the blood from below issues forth, so through 
the burst veins in the summits of the mountains the waters from below 
are poured out. 

Water after having issued forth from the veins of the earth is aban- 
doned by the moving cause which led it there. 

Water in falling from the high summits observes in its movement 
the desire of all the other heavy things. b.m. 234 v. 

And that which with the utmost admiration of those who contem- 
plate it raises itself from the lowest depth of the sea to the highest 
summits of the mountains, and pouring through the broken veins re- 
turns to the shallow parts of the sea, and again rises with swiftness 
and returns in like descent, and thus in course of time its whole ele- 
ment circulates. 

So from high to low, so passing in and out, now with natural and 
now with fortuitous movement it proceeds, together and united. So 
with continual revolution it goes ranging round, after the manner of 
the water of the vine, which as it pours through its severed branches 
and falls back upon its roots rises again through the passages, and 
falling back returns in a similar revolution. 

The water which sees the air through the broken veins of the high 
summits of the mountains, is suddenly abandoned by the power which 



led it there; and when the water escapes from the forces which raise it 
to a height it resumes in liberty its natural course. 

In the same way, so does the water that rises from the low roots of 
the vine to its lofty summit, and falling through the severed branches 
upon the primal roots mounts anew to the place whence it fell. 

b.m. 235 r. 

Water is just that which is appointed to serve as the vital humour of 
this arid earth, and the cause which moves it through its spreading 
veins, contrary to the natural course of heavy things, is just what 
moves the humours in all the species of animated bodies. 

This it is which to the complete stupefaction of the beholders rises 
from the lowest depths of the sea to the highest summits of the moun- 
tains, and pouring out through the burst veins returns to the depths of 
the sea and rises again swiftly and again descends as aforesaid. So 
from the outer parts, to the inner, so turning from the lower to the 
higher, at times it rises in fortuitous movement, at times rushes down 
in natural course. So combining these two movements in perpetual 
revolution it goes ranging through the channels of the earth. 

b.m. 236 v. 


Either the water has weight or it has not weight. And if it has 
weight, why does not it bend the leaves borne on the bed where it 
rests? And if it does not bend them, it does not give its gravity to the 
bottom of the water. And if it does not give its gravity, what supports 
it? Its bed supports it, but it does not receive weight, because it is 
proved that water has no weight except above an element lighter than 
itself such as air and fire, and other liquids such as oil and the like. 
And if this is the case, why does a vase in the air weigh more when 
full of water than when full of air? The water does not weigh on 
their sides, but the vase when filled has weight in the air, which it 
would not have under water except to the extent of the weight of the 
material of which the vase is made. And the sea does the same upon 
its vase the earth, and the shores uncovered to the air are the lips of 
the vase that receives it. Which vase, being conjoined to the rest of 
the earth, throws its weight upon the air of its antipodes in the increase 



of the- sea, because such antipodean seas balance each other in their 
weights through being opposite; and the inequality produced their 
weights, and from this caused the sea to be changing its position con- 
tinually, the centre of gravity of the earth together with the water 
also changing its position. b.m. 266 v. 


Because n c is of a width similar to a 0, and in like manner because 
m i is slightly less, these waters will be almost all at one level. 

Forster in 32 v. 

The water a b will be very considerably higher than the water d e. 

The water r m will be almost equal, and the part o of the back-cur- 
rent will be extremely shallow and will hollow out the bed; p will be 
higher by reason of the percussion, x lower at the mill . . . 

Forster in 33 r. 


When within the smooth water you see a spreading eddy there is a 
fall and rebound of water. Forster m 40 r. 


Why do the lines of the water pouring into a hole not direct them- 
selves to its centre? Forster in 75 v. 

Why do the circles of the water not break when they intersect? 

Forster in 76 r. 

Why the water is higher in one part of the sea or river than in an- 
other, and why in many rapidly moving eddies the water is lower in 
the centre of the eddies than at the sides. 

On the Movements of Liquids by Galen. Quaderni 11 16 r. 

Water cannot move of itself unless it descends, and if it moves with- 
out descending it is moved by something else, and if it moves without 
being moved by anything else it is a reflex movement and of short life. 

Quaderni 11 16 v. 



On how to bend the course of a river through its valley. 

And you who desire to control the course of the river and to be 
obeyed by it, you only need to cause its current to bend, for where 
this bends it wears away the bottom and draws after it all the rest of 
the water of its river. Quaderni iv 2 r. 



The current of water is the concourse of the reflections which re- 
bound from the bank of the river towards its centre, in which con- 
course the two streams of water thrown back from the opposite banks 
of the river encounter each other; and these waters as they encounter 
each other produce the biggest waves of the river, and as these fall 
back into the water they penetrate it and strike against the bottom as 
though they were a substance heavier than the rest of the water, and 
rub against the bottom, ploughing it up and consuming it, and carry- 
ing ofiE and transporting with them the material they have dislodged. 
And therefore the greatest depth of the water of a river is always be- 
low the greatest current. 

It is possible for water in a brief time to perforate and make a passage 
through stone. Quaderni iv 2 r. 

Watch the movement of the surface of water, how like it is to that 
of hair, which has two movements, one following the undulation of 
the surface, the other the lines of the curves: thus water forms whirl- 
ing eddies, part following the impetus of the chief current, part the 
rising and falling movement. Windsor: Drawings 12579 r. 

The movement of the wave is swifter than the movement of the 
water that produces it. This is seen by throwing a stone into still water, 
for it creates around the spot where it strikes a circular movement 
which is swift, and the water which creates this circular swelling does 
not move from its position nor do the objects which float on the sur- 
face of the water. Leic. 14 v. 

[With drawing of section of river in which are the words 'Arno\ 
l Rifredi\ i Mugnone > ] 

When a lesser river pours its waters into a greater and this greater 



flows from the opposite bank, the course of the lesser river will be bent 
by the onset of the greater. And this occurs because when this greater 
river fills up the whole of its bed with water it comes to form an eddy 
under the mouth of this river, and thus drives with it the water that 
has been poured out by the lesser river. When the lesser river pours 
its waters into the greater river which has its current crossing the 
mouth of the lesser river, its waters will bend in the direction of the 
current of the greater river. Leic. 15 r. 


Book 1 of water in itself 

Book 2 of the sea 

Book 3 of the springs 

Book 4 of rivers 

Book 5 of the nature of the depths 

Book 6 of the objects 

Book 7 of different kinds of gravel 

Book 8 of the surface of water 

Book 9 of the things that move in it 

Book 10 of the means of repairing [the banks of] rivers 

Book 11 of conduits 

Book 12 of canals 

Book 13 of machines turned by water 

Book 14 of how to make water ascend 

Book 15 of the things which are consumed by water. Leic. 15 v. 


Whether the flow and ebb are caused by the moon or sun, or are the 
breathing of this machine of the earth. How the flow and ebb differ in 
different countries and seas. 

How in the end the mountains will be levelled by the waters, seeing 
that they wash away the earth which covers them and uncover their 
rocks, which begin to crumble and are being continually changed into 
soil subdued alike by heat and frost. The waters wear away their bases 



and the mountains bit by bit fall in ruin into the rivers which have 
worn away their bases, and by reason of this ruin the waters rise in a 
swirling flood and form great seas. 

How in violent tempests the waves throw down every light thing 
and suck much earth into the sea, which causes the water of the sea 
to be turbid over a wide space. 

How loose stones at the base of wide steep-sided valleys when they 
have been struck by the waves become rounded bodies, and many 
things do the same when pushed or sucked into the sea by these 

How the waves quiet down and make long stretches of calm water 
within the sea without any movement when two opposite winds meec 
together at this spot; thus at these meeting places various shapes made 
up of calm sea are visible surrounded by the tiny waves of a moderate 
sea. Leic. 17 v. 


Water of itself does not move unless it descends. 

That water will be highest which is farthest removed from the centre 
of its sphere. And that surface of water is said to be lowest which is 
nearest to the centre of its sphere. 

No surface of water which is contiguous to the air is lower than the 
surface of its sphere. The waters of the salt seas are fresh at their maxi- 
mum depth. The waters range with perpetual movement from the 
lowest depths of the seas to the topmost summits of the mountains, 
not following the law of heavy things; and in this instance its action 
resembles that of the blood of animals which is always moving from 
the sea of the heart and flowing towards the summit of their head; 
and so when a vein there has burst open, as one sees if a vein bursts in 
the nose, the whole of the blood from below rises up to the height 
where the vein has burst. 

When the water gushes forth from the burst vein in the earth it 
follows the law of other things which are heavier than the air and so 
always seeks the low places. 

That water will be swifter which descends by the less slanting line. 
And that water will be slower which moves along a more slanting line. 



The Nile and the other rivers of great size have very many times 
poured out the whole of the element of water and restored it to the 
sea. The veins flow with infinite ramifications through the body of the 
earth. The waters assume as many different natures as the places are 
different through which they pass. If it were possible to make a well 
which should pass through the earth on the opposite side and for a 
river to descend through this well, the head of the river which entered 
there first would descend through this well and pass the centre of the 
elements without making any reflex movement, and it would pour as 
much water on the far side of this centre as it had from the opposite 

And if, because of some deep valley, the line on the opposite side of 
the well were shorter than on this side, this water would fill up the 
valley, however large it was, until it equalled the weight of the water 
in the well, although in some part the centre (of gravity) of the water 
and of the earth united together would move somewhat from its fipt 
position through the weight of the water, which would be increased 
on the opposite side of the earth where it was not at first. The centre 
(of gravity) of the water and earth joined together is moved when 
the weight of the sea moves because it is carried by the winds. 

Leic. 21 v. 


How the bottoms of rivers and ditches become trampled by big 
animals and this causes the muddy waters to escape and they thus 
leave in their course the soil in which they were loitering. How in the 
manner described above canals may be constructed through level lands. 
How to convey away the soil from canals which have become choked 
up with mud by the opening of certain sluices which are moved up- 
wards by the canal. 

How one ought to straighten rivers. How one ought so to provide 
that rivers do not sweep away other men's possessions. How one ought 
to maintain the beds of rivers. How one ought to maintain the banks. 
How the banks when broken should be repaired. How one ought to 
regulate the impetus of rivers in order to strike terror into the enemy 
so that he may not enter the valleys of this river to damage them. 

How the river in order to be crossed by your army ought to be con- 



verted into many small branches. How one ought to ford rivers below 
the rows of horses so that they may protect the infantry from the rush 
of the water. 

How by the use of wine-skins an army is able to cross a river by 
swimming. How the shores of all the seas that touch one another are 
of equal height, and are the lowest part of the land which meets the 
air. Of the manner of swimming of fishes; of the way in which they 
leap out of the water as may be seen with dolphins, for it seems a 
marvellous thing to make a leap upon something which does not stand 
firm but slips away. 

Of the manner of swimming of animals of long shape such as eels 
and the like. Of the way of swimming against the currents and great 
falls of rivers. Of the way in which fishes swim when they are round 
in shape. How animals which do not have the hoof cleft asunder are 
not able to swim. How all the other animals which have feet with toes 
ar^by nature able to swim, except man. In what way a man ought to 
learn to swim. Of the way in which a man should rest upon the water. 
How a man ought to defend himself against the whirlpools or eddies 
of the waters which suck him down to the bottom. How a man when 
sucked down to the bottom has to seek the reflex current which will 
cast him out of the depths. How he ought to propel himself with his 
arms. How he ought to swim on his back. 

How he can only remain under water for such time as he can hold 
his breath. 

How by an appliance many are able to remain for some time under 
water. How and why I do not describe my method of remaining under 
water for as long a time as I can remain without food; and this I do 
not publish or divulge on account of the evil nature of men who 
would practice assassinations at the bottom of the seas by breaking the 
ships in their lowest parts and sinking them together with the crews 
who are in them; and although I will furnish particulars of others they 
are such as are not dangerous, for above the surface of the water 
emerges the mouth of the tube by which they draw in breath, sup- 
ported upon wine-skins or pieces of cork. 

How the waves of the seas continually consume their promontories 
and rocks. How the shores of the seas grow continually towards the 



centre of the sea. The reason why the gulfs of the seas are created. The 
cause why the gulfs become tilled up with earth or seaweed. 

The cause why round about the shores of the seas there is found a 
large high bank called the mound of the sea. 

Why the waves are higher when they touch the bottom nearer to the 
shore than they are on the high sea. 

How at the mouths of certain valleys the gusts of wind strike down 
upon the waters and scoop them out in a great hollow, and carry the 
water up into the air in the shape of a column and of the colour of 

And this same thing I once saw taking place on a sand-bank in the 
Arno, where the sand was hollowed out to a depth of more than a 
man's stature, and the gravel of it was removed and whirled a great 
distance apart, and assumed in the air the form of a mighty campanile; 
and the summit of it grew like the branches of a great pine, and then 
it bent on meeting the swift wind which passed over the mountains. 

How the wave is least towards the approaching wind because the 
bank serves it as a shield. 

How the water that finds itself between the percussions of the waves 
of the sea becomes changed into mist. 

Of eddies wide at the mouth and narrow at the base. 

Of eddies very wide at the base and narrow above. 

Of eddies of the shape of a column. 

Of eddies formed between two masses of water that rub together. 

Leic. 22 v. 

How waves do not penetrate one another but leap back from the 
place where they have struck; and every reflex movement flies away 
at equal angles from the striking place. 

The reflex movement of water within water will always be of the 
same shape as its falling movement. By this reflex movement I do not 
mean that which springs back within the air but that which follows 
along its surface. 

As the wave of the sand moves considerably more slowly than the 
wave of the water that produces it, so the wave of the water created by 
the wind is much slower than the wave of the wind that produces it, 
that is the wave of the air. The wave of the air performs the same 



function within the element of fire as does the wave of the water 
within the air, or the wave of the sand, that is earth, within the water; 
and their movements are in the same proportion one to another as is 
that of the motive powers within them. 

The more powerful current will cleave asunder the less powerful 
and pass through the middle of it. Currents of equal power which 
clash together leap back from the site of their percussion. A whole 
mass of water in its breadth, depth and height is full of innumerable 
varieties of movements, as is shown on the surface of water of a mod- 
erate degree of turbulence, in which one sees continually gurglings 
and vortices, with various eddies formed of the more turbid water 
from the bottom that rises to the surface. How every seven years the 
waters of the Adige rise and then fall, and it makes a famine as it 
rises. Leic. 23 r. 

How water has tenacity in itself and cohesion between its particles. 
This is seen from the fact that a drop before separating itself from the 
remainder stretches itself out as far as it can, and offers resistance in 
its union until it is conquered by the excessive weight of the water 
which is continually increasing upon it. How water serves as a magnet 
for other water. This is seen in the process of a drop becoming de- 
tached from the remainder, this remainder being stretched out as far as 
it can through the weight of the drop which is extending it; and after 
the drop has been severed from this mass the mass returns upwards with 
a movement contrary to the nature of heavy things. It may be seen 
how the larger drop of water instandy takes up into itself the smaller 
drops which come into contact with it; and the minute particles of 
moisture diffused through the air act in the same way, for they be- 
come compressed, making themselves a magnet one for another until 
at last their weight so increases as to conquer the resistance of the air 
that first sustained them, and so they descend in the form of rain. 

It may be shown with a bubble of water how this water is of such 
uniform fineness that it clothes an almost spherical body formed out 
of air somewhat thicker than the other; and reason shows us this 
because as it breaks it makes a certain amount of noise. Leic. 23 v. 



It is possible to devise obstructions which will preserve the embank- 
ment against the friction of the current. 

You should therefore cause blocks of coarse shingles to be con- 
structed ten braccia apart; and let them be ten braccia wide with 
height varying according to the height of the embankment and of a 
thickness of three braccia. And they should be set to slant in the direc- 
tion from which the water comes; and each of itself will serve as a 
shield to the water and throw it back towards the centre of the stream. 

When the obstruction covered by the water slants very considerably 
in the direction from which the water comes, the stroke of the water 
will only cause a small hollow in front of this obstruction and it will 
deposit a considerable quantity of soil behind it. 

If the obstruction is entirely upright and the water flows over it it 
will form a deep hollow in front of it and will only deposit a small 
amount of soil behind it. And if the obstruction has a lesser obstruc- 
tion in front of it which leans against it there will be no hollow in 
front of this lesser obstruction for so far as its bulk extends. If the 
obstruction have another near behind it the hill of sand will be sud- 
denly cut and dug out in a new hollow. 

How the rivers, in their great floods, fill up all their greatest depths 
with sand or stones, except the places where the river is confined, as 
when it passes through the arches of bridges or other constricted 
places; and it does this because behind these arches it strikes against 
the front of their columns, and rises in a swirling flood, and raises it- 
self, and so with fury makes up for the delay that has taken place 
before the said bridge or other object. Leic. 24 r. 

If the obstructions of the waters are permanent the deep places of 
the rivers caused by them will also be permanent. And if the obstruc- 
tion of these waters is movable the deep places caused by it will also 
be movable. And if the movable obstruction is near the bank of the 
river it immediately will become the cause of bending the whole 
river; and this is due to the fact that the water which passes between 
the obstruction and the bank hollows out this bank. And even though 
the obstruction proceed upon the bed of the river behind the current 
of the waters, it does not follow that the concavity already made in 
the bank will not proceed continually to grow and increase because 



of the water that ranges within it, as is shown by the fourth of the 
third; and that the water which leaps back from it to the opposite 
bank will not create another similar concavity in this bank; and this 
will then proceed continuously to increase, and then it returns leaping 
back beneath the first concavity; and so it proceeds time after time 
until this impetus is consumed amid the universal current of the river. 

Leic. 24 v. 


These are the cases that have to stand in the beginning: 
The air which is submerged together with the water which has 
struck upon the other water returns to the air, penetrating the water 
in sinuous movement, changing its substance into a great number of 
forms. And this occurs because the light thing cannot remain under 
the heavy, rather is it continually pressed by the part of the liquid 
which rests upon it; and because the water that stands there perpen- 
dicular is more powerful than the other in its descent, this water is 
always driven away by the part of the water that forms its coverings, 
and so moves continually sideways where it is less heavy and in conse- 
quence offers less resistance, according to the fifth of the second. And 
because this has to make its movement by the shortest way it never 
spreads itself out from its path except to the extent to which it avoids 
that water which covers it above. 

When the air enclosed within the water has arrived at its surface it 
immediately forms the figure of a half-sphere, and this is clothed with 
an extremely thin film of water. This occurs of necessity because water 
has always cohesion in itself, and this is the more potent as the water 
is more sticky; and this air having reached the opening of the surface 
of the water and not finding there any further weight to press upon 
it, raises its head through the surface of the water with as great a 
weight of water joined to it as the aforesaid tenacity can have; and 
it stops there in a perfect circle as the base of a half sphere, which 
has the aforesaid perfection because its surface has been uniformly 
expanded by the uniform power of the air. And it cannot be more 
than a half-sphere because spherical bodies attain their greatest width 
at their diameter; and if this air that is enclosed were more than a 
half-sphere the base would be less than where the diametral line is, 



and consequently the arc of this half-sphere would not have shoulders 
or real resistance in its weakest, that is its widest part, and therefore 
it would come about that it would break in this spot of its greatest 
width, because the weakest part of any arc is always the end of its 
greatest width. 

The air emerges with impetus in spherical form clothed with an 
extremely thin film of water, away from the body of the water; and 
this air by reason of the weight that it has acquired cannot pour itself 
into the other air, but held back by the adhesiveness of the water with 
which this film was formed falls down again by its excess of weight, 
continually growing in circumference, because the amount of the air 
which at first was in the whole of the aforesaid spherical body is after- 
wards reduced by half, and this is of itself capable of containing all 
this air, so that this spherical body goes on descending so far towards 
the surface of the water that it unites with it, finding there as I have 
said before greater width than in its own diametral line. 

Nor has the air clothed with a thin film of water perfect sphericity 
in the aforesaid instance, because the part of the water with which 
this air is clothed, is heavier where it is more perpendicular to the 
centre of the circle, which makes itself the base of this half-sphere, 
and therefore in this position it lowers itself more; because that part of 
a thing supported in its extremities is so much weaker as it is more 
distant from its foundation, and that thing descends more rapidly 
which has the weaker support. That part of the air clothed by a film 
of water will be of most perfect sphericity which is least in size; this 
is proved by the reason stated above, because these bodies are clothed 
with films of equal thickness: for if the air that escaped from the sur- 
face of the water was small in amount it raised up a small quantity of 
this film, and clothed itself in it; and since its lesser 1 altitude is nearer 
its foundation than was that of a greater, it maintains itself more than 
this greater. The air which is subdued by the weight of the film of 
water which clothes it penetrates in minute particles through this film, 
and these, for the reason stated, cannot be separated from their state 
of connection or adhesion to it, and therefore through the weight it 
has thus acquired it descends from the sides of this body, and remains 

1 MS. has tnaggiore. 



joined to the base of the middle sphere of air from whence it 

It breaks the middle sphere of the air clothed by the water in the 
third part of its curve; this is proved with the arches of walls, and 
therefore I will not treat of it in these notes, but I will place it in the 
book where it is necessary. 

That part of the water is higher which is more remote from the 
centre of the sphere of fire and of the air and of the water, but not of 
the earth, because this has not a mathematical spherical shape; and 
for this reason the centre of its gravity is not concentric with the centre 
of the spheres of the other three elements. 

The water of itself does not move unless it descends : therefore, when 
it is in its sphere it does not have one part of itself lower than an- 
other, and therefore of itself it will not move unless it is moved by 
others: and the two aforesaid proofs are sufficient to prove that water 
is spherical and of itself without movement; and as a consequence all 
the waters that move of themselves are lower at one extremity than at 
the other, that is in their surface; so finding the descent it runs there 
because there is no support for it there. 

How the air can never of itself remain beneath the water but always 
wishes to be above in its contact: in proof of this let it be supposed that 
there are three elements and that the earth is nothing and that one 
allows a quantity of water to fall through the air; this cannot stay 
above the air, because the weaker liquid body cannot support the 
heavier, and consequendy the air since it is a body thinner than the 
water and therefore is not able to support it will give it place; and this 
it will continue to do until the water has reached its lowest depth, that 
is assuming that it has not become evaporated or changed into air 
through its long friction with the air; but let us suppose that so much 
turns that a part arrives there: I say that after consuming its impetus 
between the reflex and falling movements which it would make 
around its centre it would come to a stop at this centre under all the 
sphere of air equally, because the centre of the elements is the lowest 
part that can be found in them, since the lowest is that part which is 
farthest removed from the greatest height of its whole. This is the 

Water attracts other water to itself when it touches it : this is proved 



from the bubble formed by a reed with water and soap, because the 
hole, through which the air enters there into the body and enlarges it, 
immediately closes when the bubble is separated from the reed, run- 
ning one of the sides of its lip against its opposite side, and joins itself 
with it and makes it firm. 

Also a small drop enters into the body of the other water. If you 
should grant me by the proof of these bubbles of water that water has 
tenacity though it be small and thin, you grant me that that which 
makes the part will make its whole. 

The bubble formed within the air by a reed, through which it is 
blown, does not fall in spherical shape, when it becomes detached be- 
cause its excess of water runs below and makes it heavier there than 
elsewhere, and consequently the movement there is hurried, and 
breaks it above at a third. Leic. 25 r. 

Every current has three central lines, which are situated in the 
middle of its greatest power : of these one is at the contact made by the 
water with the bed that receives it; the second is at the middle of its 
depth and width; the third is formed on the surface; but that of the 
middle is the principal one for it guides the whole course and divides 
all the reflex movements and turns them to their appointed directions. 
The higher central line of the current of the water is the upper line of 
the falling movement, and the lower of the reflex whirling movement, 
that is that which turns itself over and falls down upon the falling 
movement upon which it takes its leap; but let us leave the revolutions 
of the waters and their changes from below upwards as far as con- 
cerns these definitions, and speak only of the water remaining on the 
surface, that is as far as concerns its central lines. The central line of 
the surface of the current is always in the most prominent part of the 
water which surrounds the object struck by it; and the central line is 
only that which after striking upon a smooth-faced object falls back 
upon itself. The central line of the bottom of the current after striking 
upon the smooth object, is turned over towards the centre of the earth, 
and rambles about so much in scraping the bed that it makes a hollow 
large enough to contain its revolutions; and all the other lateral lines 
slope to the bed and hollow it. [To consider] whether the wave of 
the water causes the formation of the wave of sand above its bed or 



whether the wave of the bed is the cause of the wave on the surface of 
the water. [To consider the] difference between the waves, from 
knowing their depth: which may always be discovered between the 
falling and the reflex movement of the waters. [To consider] how 
the least depth within the banks of any expanse of water will be 
found at the end of its reflex movement. How also the least depths of 
rivers will be found at the sides of the currents where they unite with 
other currents. [To consider] how in between two currents there are 
always shallows. The highest part of the surface of the water that 
strikes the object will strike it in its centre if it be of smooth front 
or pointed with sides of equal slant and length. But unless the angle is 
in the middle of the front of the object the highest elevation of the 
wave that strikes it will no longer be in the centre of this front but 
opposite to the aforesaid angle. The water of the surface that is moved 
in tiny ripples by the wind, always moves so much more swiftly than 
the wave of the water, in proportion as the wave is swifter than the 
natural movement of the water, and as the natural movement of the 
water is swifter than the wave of the sand, and as the wave of the 
sand is swifter than the wave of the earth that forms the river bank. 
But I ought first to say that the movement of the free air is so much 
swifter than the movement of the air that strikes the water, because 
that part of the wind that strikes the water is checked by the resistance 
of the surface of the water. All the waves of the sand which travel 
with the water are as much slower than the waves of the sand that 
travel with the wind as the movement of the water is slower than the 
movement of the wind. Leic. 25 v. 

In these eight sheets there are seven hundred and thirty conclusions 
as to water. 

When the wave has been driven on to the shore by the force of the 
wind it forms a mound by putting its upper part at the bottom, and 
turns back on this until it reaches the spot where it is beaten back anew 
by the succeeding wave which comes below it and turns it over on its 
back, and so overthrows the mound and beats it back again on the 
shore mentioned before; and so continues time after time; turning 
now to the shore with its upper movement and now with its lower 
fleeing away from it. 



How it is Dot possible to describe the process of the movement of 
water unless one first defines what gravity is and how it is created or 

As the wave after striking on the sea shore turns back along the 
bed of the sea behind its mound, it encounters the following wave 
which comes from the high sea, and breaks itself upon it and divides 
itself; part leaping towards the sky and then falling down and turn- 
ing back, part towards the bed of the sea; and this continues towards 
the sea, carrying with it the lower part of the water that struck upon 
it. Were it not for it doing thus the seaweed and the wrack of the 
tempests would not be able to be carried from one shore and deposited 
upon another. If the water of the sea turns towards the sea above its 
bed after the percussion made upon its shore, how can it carry with 
it the shells, molluscs, 'buovoli', snails and other similar things pro- 
duced in the bed of the sea, and throw them upon this shore? This 
movement of the aforesaid things towards the shore commences when 
the percussion of the falling wave divides the reflex wave into the 
aforesaid two parts, for the things raised from the bottom often leap 
up in the wave that returns to the shore, and being solid bodies are 
driven towards the mound, which then draws them back with it 
towards the sea; and so continues in succession until the storm begins 
to abate, and stage by stage it leaves them where the greater wave 
reaches, that is that as the succeeding wave does not return to the 
same mark where it had deposited the booty that it carried, this booty 
remains where it has been left by the wave; and this process continues 
as the waves grow less. There remain the things cast up by the sea 
within the space that lies between the first mound of the wave upon 
the shore and the mound made by the wave that comes from the deep 
sea. If the whole sea rests and supports itself upon its bed the part of 
the sea rests upon the part of the bed: and as water possesses gravity 
when out of its element it ought to weigh down and press upon the 
things that rest on its bed. But we see the contrary, for there the sea- 
weed and grass that grows in these depths are not bent or crushed 
upon the bottom but cleave it directly as though they were growing 
within the air. 

So we arrive at the conclusion that all the elements, though they are 
without weight in their own sphere, possess weight away from their 



sphere, that is away towards the sky, but not away towards the centre 
of the earth; because if it proceeds away towards this centre it finds 
an element heavier than itself, with its thinnest and lightest part touch- 
ing an element lighter than itself, and the heavier part of the element 
is so placed as to be near the element that is heavier than itself. 

How water when transformed becomes changed into wind which is 
so much drier as the process of transformation is more complete. 

How wind is generated by the coagulation of the water within the 
air, for the air hastens to where there is a lack of it, and so it flees from 
where it is in excess. How the air has a greater volume where there is 
more wind, because the air there is thicker. 

How the winds are strongest in the moist seasons, and more so in 
the rains than in clear weather. How great winds proceed from the 
mountains that are covered with snow; and to this the sailors bear wit- 
ness for they experience it every day. And this is brought about 
through the fact of the snow becoming dissolved in the air, and being 
dissolved in very fine particles; hence philosophers say that there are 
dry land vapours; as to which I have nothing to say. 

How the wind, proceeding from the cloud, is not exhaled in a circle 
through every line away from the cloud, because it acquires more 
weight than the air through which it passes, and so of necessity is bent 
to the ground as are all the things that are heavier than the air, and it 
rambles through it, driven by that which follows, which is created 
behind it, or by the impetus it has acquired from its past movement. 

Leic. 26 v. 

That water may have tenacity and cohesion together is quite clearly 
shown in small quantities of water, where the drop, in the process of 
separating itself from the rest, before it falls becomes as elongated as 
possible, until the weight of the drop renders the tenacity by which 
it is suspended so thin that this tenacity, overcome by the excessive 
weight, suddenly yields and breaks and becomes separated from the 
aforesaid drop, and returns upwards contrary to the natural course of 
its gravity, nor does it move from there any more until it is again 
driven down by the weight which has been reformed. From this prop- 
osition two conclusions follow, of which the first is that the drop has 
cohesion and nerve-structure in common with the water with which 



it is joined; secondly that the water drawn by force breaks its co- 
hesion, and the part that extends to the break is drawn up by the 
remainder in the same manner as is the iron by the magnet. The same 
is seen with water passing through a filter, for the greater weight of 
the water that is outside the vessel draws back the lesser weight of the 
water which this filter holds back curved within the vessel. 

One may offer a proof of the tenacity of water and set it out in 
proportion, thus: — if a drop of water of two grains is supported by 
water of the volume of half a drop by how much will a pound be sup- 
ported? And in this way we shall arrive near the truth. The sand 
weighs more than the water; and if there be left within the air in 
continuous line a quantity of sand and a quantity of water, separated 
from the sand but of the same weight as the sand, without doubt the 
movement of the sand will be slower than that of the water; and this 
comes about because the lower part of the water draws down the 
water that is joined to it above, and consequently it makes itself all 
one body and weighs all together upon the air, which opens below to 
give it place. This does not happen however with the sand, for in itself 
it is all separated and loose, and the whole of the amount falls with 
the same speed that one of its grains would, as they are all equal. So 
that we may conclude that the continuous descent of the water as it 
falls through the air proceeds with the speed that its weight requires, 
because it is a united and continuous quantity; and the sand of the 
same weight which descends from the same position of the water only 
proceeds with as much speed as is required by the weight of one of 
its medium-sized grains, for those that are larger descend more swiftly 
than those of medium size, and the less descend more slowly. 

For if water has in itself adhesiveness and a tendency to unite, the 
water that is poured from a siphon, being surrounded by air, does not 
draw itself after that of the siphon; and experience shows us that un- 
less the outlet of the water of the siphon is lower than its entrance into 
the pipe, the water that continues below its outlet from the pipe will 
never draw itself after that of the vessel. If in the descent of the water 
within the air the water above, which drives it downwards, does not 
descend there with the same speed or a greater, that below will divide 
itself from that above, if it is swifter. 

How the water that descends through the air breaks because the 



air through which it passes divides it. How the water which is di- 
vided as it descends continuously through the air has a medium of 
spray, which extends from one divided part to the other, and binds 
them up together. How all the volume of the water which descends 
through the air in continuous quantities, is constrained to descend 
with equal movement, because where it made itself swifter it would 
separate itself from the part that was slower, and where it made itself 
slower it would be doubled and multiplied by the part that was 
swifter. How as great a weight of water is displaced as the weight of 
the thing that is supported by this water. How in the same slant, the 
water will make itself so much slower in its movement as it is lower 
upon its bed. How water made to gyrate in swift movement in a 
vessel by the hands of him who is whirling it round becomes extremely 
concave at the centre. 

Of the great difference there is when water is whirled in a vessel, 
according to whether the hand is held near to the centre of this vessel 
or near the larger circle of the surface of the water. How the hand 
drawn frequently across the vessel up and down produces strange 
movements and surfaces of different heights. What water does when 
made to gyrate in an oval vessel. What water does when made to gyrate 
in a vessel with corners. What water does in a vessel that is struck 
from below. What water does in a vessel that is struck at the side. 
What water does in a vessel when the spot is struck on which it is 

Of the music of water falling into its vessel. Leic. 27 r. 

How nothing evaporates except by means of moisture, which after 
having been evaporated preserves in itself the nature of the body in 
which it was infused. How the rumbling produced by the earthquake 
in the body of the earth proceeds from the destruction of places, torn 
open by force by the winds which continually strike upon the beds of 
their great caverns or lakes, covered and shut in within the earth. 

But the tempest of the sea, snatched from its shores and borne far 
over the sea will be turned back, and especially if there is great depth 
there; and this happens because during a storm the wave of the sea 
does not penetrate to its great depths; and if it should chance to reach 
there it changes its movement. The water of the sea during a storm 



makes a great movement on its bed in a different direction from that 
of its surface. 

The dams of rivers if not of too great width may be made in this 
manner: a stake such as pile-drivers use should be fixed every three 
braccia, as big as possible and the bigger the better; and their tops 
should be of uniform height. On these a log of the shape of a beam 
should be fastened very firmly; next long trunks with all their 
branches should be taken and laid upon the aforesaid beam, and they 
should be fastened to it by using one of the branches as a hook; and 
this process should be repeated as often as possible, placing the branches 
towards the coming of the water; and they should then be loaded with 
shingle and stones; and after the first flood it is left grounded. But 
remember to fix the branches so that they are raised up and make 
them fall with the others. And if the river should be narrow you set 
the beam across from one bank to the other and fix it well; and set 
the aforesaid branches to lean upon it fastened with their natural hooks. 
The beam here is only for the purpose of holding the heads of the logs 
so that they do not drop down; and the branches which stand against 
the course of the river laden with stones, are not allowed to push this 
beam or bend its direction because it is held by their natural hooks, 
and their buried branches do not allow them to move or to tear away 
the said hooks. 

How the diverting of rivers ought to be carried on when the water 
has completely lost the fury of its current, that is when it shows itself 
tired. How with a small dam a river may be diverted by aiding and 
increasing the line where it shows that it wishes to turn of itself. 

How a river may be diverted by a few stones if one understands the 
line of its current; and this movement may be made in the aforesaid 
line of the water. How the dams of the river should never be formed 
by placing stakes in deep places but in the more shallow places. How 
the dams of the rivers when formed of masonry ought to be con- 
structed in the deepest parts of the rivers, so that they may be less in 
the power of the water which undermines them. How the dams of the 
rivers ought to be made in the fields away from the rivers and then 
the said river be directed against them. How the bridges ought also 
to be made in the fields in that part where it is afterwards intended 
to direct the river. Leic. 27 v. 



The ramifications of the springs of water are all joined together in 
this earth, as are those of the blood in other animals; and they are in 
continual revolution, and thus vivified they are perpetually wear- 
ing away the places in which they move, both those within the earth 
and those on the surface of it; and the rivers universally pour out 
much more water now than formerly: for which reason the surface of 
the sea is somewhat lowered towards the centre of the world as it has 
had to fill up the vacuum caused by this increase in these springs; of 
which I shall speak presently. The heat of the fire generated within 
the body of the earth warms the waters which are pent up within it 
in the great caverns and other hollow places; and this heat causes 
these waters to boil and pass into vapour and raise themselves up to 
the roofs of the said caverns, and penetrate through the crevices in the 
mountains up to their greatest height, where coming upon the cold it 
is suddenly changed into water, as one sees happen in a retort, and 
goes falling down again and forming the beginnings of rivers which 
are afterwards seen descending from them. But when the great frosts 
drive back the heat towards the centre of the world, this heat becomes 
more powerful and causes a greater vaporisation of the aforesaid water; 
and this vapour heating the caverns round which it moves in circles 
cannot form itself into water as it usually does : as is seen in the mak- 
ing of aqua vitae, for unless the vapour of the wine passed through 
fresh water it would not change into aqua vitae, but would go back 
and become at last so much condensed as to break down every obstacle. 
We may say the same of water heated in the bowels of the earth, 
which not finding in its passage places of such freshness as harmonises 
with it, does not form itself into water as formerly, but condenses 
and hardens like fire multiplied and condensed within a mortar, 
which becomes harder and more powerful than the substance that con- 
tains it, and so unless it be suddenly dissolved in smoke it instantly 
hurls itself forward, breaking and destroying whatever opposes its 
growth. It is the same with the aforesaid steam from the water, for it 
bursts forth within the bowels of the earth in divers places; ranging 
about and roaring with great tumult until it reaches the surface; and 
with a mighty earthquake makes whole regions tremble, and often 
makes mountains fall in ruin, and lays waste cities and lands in divers 
parts, and with a mighty hurricane bursts its way forth through the 



cracks in the earth which it has made; and so by thus escaping it con- 
sumes its own might. The wind is formed by the water in the air 
through the processes of the dissolving and the formation of clouds; 
that is that when the cloud is dissolved it becomes changed into air 
and increases in its bulk fitfully and irregularly, since the process of 
its dissolution does not work uniformly; because the cloud is in itself 
of varying thinness and density, consequently the part that is thinnest 
is dissolved most rapidly, and the thick part offers most resistance to 
this process: this therefore is the cause why the movement of this 
wind does not proceed uniformly. 

And when the cloud is created it also generates wind, since every 
movement is created from excess or scarcity; therefore in the creation 
of the cloud it attracts to itself the surrounding air, and so becomes 
condensed, because the damp air was drawn from the warm into the 
cold region which lies above the clouds; consequently as it has to make 
water from air which was at first swollen by it, it is necessary for a 
great quantity of air to rush together in order to create the cloud; 
and since it cannot make a vacuum, the air rushes in to fill up with 
itself the space that has been left by the [former] air, which was first 
condensed and then transformed into a dense cloud. In this circum- 
stance the wind rushes through the air, and does not touch the earth, 
except on the summits of the high mountains; it cannot draw the air 
from the earth, because there would then be a vacuum between the 
earth and the cloud; and it draws but little air through the traverse 
and draws it more abundantly through every line. I have already had 
an opportunity of observing this process; and on one occasion above 
Milan, over in the direction of Lake Maggiore, I saw a cloud shaped 
like a huge mountain, made up of banks of fire, because the rays of 
the sun which was then setting red on the horizon had dyed it with 
their colour. 

This great cloud drew to itself all the little clouds which were round 
about it. And the great cloud remained stationary, and it retained the 
light of the sun on its apex for an hour and a half after sunset, so 
enormous was its size. And about two hours after night had fallen 
there arose a stupendous storm of wind. 

And this, as it became closed up, caused the air which was pent up 
within it, being compressed by the condensation of the cloud, to burst 



through and escape by the weakest part, rushing through the air with 
incessant tumult, acting in the same way as a sponge when squeezed 
by the hand underneath the water, for the water with which it is 
soaked escapes between the ringers of the hand that squeezes it, and 
rushes swiftly through the other water. So it is with the cloud, driven 
back and compressed by the cold that clothes it round, driving away 
the air with its own impetus, and striking it through the other air, 
until the heat that is mingled with the moisture of the cloud that has 
drawn it to so great a height flies back towards the centre of the cloud, 
escaping the cold which is its contrary, and having approached towards 
the centre becomes powerful, and consequently takes fire and makes 
a sudden emission of damp steam, which surrounds it and creates a 
furious wind that moves with the fire thrown out by the increasing 
pressure of the steam; and thus fire is expelled from the cloud as is 
the flame from the mortar, by the wind increasing behind it; and so 
this flame compressed by the cloud issues forth, and spreads through 
the air, with the more radiance in proportion as the fire of which it 
is formed is more concentrated and of greater heat: and this is the 
thunderbolt which afterwards ruins and smashes in pieces whatever 
opposes its destined course. 

I have already seen fire created under the water with the movement 
of a wheel which whirled its arms; and it will do the same at any 
depth however great. 

If the river be turned at the upheaval of the earthquake, it will no 
longer run forwards but will return into the body of the earth, as does 
the river Euphrates; and let this serve for any of those at Bologna 
who lament over their rivers. Leic. 28 r. 

That water will rise higher with its wave than the common surface 
of the water of the lake, when it is nearer the spot at which it falls 
into the lake. When the waters from different parts meet together in 
a hole that is in the bed of the river this water will be bored through 
as far as the entrance of the hole, and the cavity so made will be filled 
with air as far as the bed of the water. 

The revolving movement cannot be continued strictly below the 
water unless this revolving mass of water has air in the middle of it. 
That water will form a sudden hollow in its bank of earth which 



strikes within equal angles at any object that projects from this bank. 
The rain that parts from the cloud does not all fall on the earth: this 
is clue to its friction with the air that it penetrates, because in the 
course of this friction it becomes consumed either altogether or in great 
part and pours itself into the above-mentioned air; and often one sees 
the clouds descend towards the earth and immediately become cut 
short in the manner of a horse's tail and remain invisible; and they 
are changed into wind. Leic. 28 v. 

Where the straight course of the water is impeded, there sudden 
depth will be produced. This occurs because when the course of the 
water is impeded it is making percussion against an obstacle that im- 
pedes it, and because no movable thing can immediately end and 
consume its impetus, but it must be retained by the body which it pene- 
trates; and also it does not end in this immediately after the percus- 
sion, seeing that every percussion is made upon the surfaces of the 
bodies which are struck; therefore, the penetration of movable things 
within their objects is a consequence born after their percussion, in 
which the impetus of the movement is consumed. 

The penetration of the movable things within their objects will be 
of as much less length than their reflex movement made in the same 
space of the falling movement, as the thing penetrated is thicker than 
the medium, where this reflex movement is made. Now the water 
when its straight movement is impeded strikes the object that impedes 
it, and immediately, not being able to penetrate it, is reflected at almost 
equal angles; after which percussion it divides and escapes by different 
lines from the spot where it struck; of these that which raises itself 
in the air acquires weight, and falls back and penetrates the other 
water as a heavy thing; after which it strikes and consumes the bed 
of the river; but in the process of penetration it is struck by the water 
which flows beneath its surface, and from stage to stage is driven back 
in threefold movement towards the place where it first struck. 

There are three positions of the movement that the water makes on 
being reflected from its percussion within the water penetrated by it: 
the first movement is towards the bed of the water; the second is to- 
wards the place where the water is moving; the third is whirling 
movement after the manner of a screw, boring continually the bank 



and the bed on which it rubs, and always gathering fresh force from 
the water that follows in succession, thrown back from the bank, 
which descends upon it from the air, and resubmerges it anew with 
itself at the bottom. 

Here then is a percussion, and the movable thing after having struck 
the object remains in the position where it was when it made the per- 
cussion; and the object struck follows the same line and extent of the 
course of which the striker was deprived. This happens because in this 
instance the weights are equal in size, weight and substance, and to the 
weight of the movable thing has been joined the power of the impetus 
of which the object was deprived, and it only rested with its natural 
weight; this is so, because no impetus is consumed immediately, and 
because the body that strikes is accustomed to make the reflex move- 
ment when it finds an object that offers resistance; but here reflex 
movement is not produced, because the object immediately flies away, 
bearing with it the power and impetus of its striker; and because 
always the movable thing, which does not attach itself to its object, is 
accustomed to finish the remainder of its destined movement in the 
reflex movement, which starts immediately it has finished its percus- 
sion. Here they do not become fixed, because they are of spherical 
body and of equal substance. It does not advance farther because it has 
exhausted its impetus in its percussion, and has given it to the object 
struck; it does not spring back, for it has nothing to serve as a founda- 
tion for its spring, after the manner of a man who wishes to jump 
from a board which is placed on the pavement on top of several pieces 
of a beam which has been sawn up; for as he gathers impetus for the 
leap, this impetus communicates itself to and unites with the board 
which flies away as though upon wheels; and he who would fain leap 
deprived of the impetus of the leap, is left in the same position in 
which he was when he formed the intention of leaping; so that from 
this we may conclude that the impetus can be immediately separated 
from the body where it was created and pour itself into the object 
which it has struck. 

But if the body struck be lighter than its striker, the length of the 
movement destined for this striker will be as much shorter as the 
impetus which is divided from it, attaching itself to the body struck, is 
diminished. That is, if the body struck was a pound and the striker 



two pounds, I affirm that the percussion will take away half the im- 
petus and the movement of its striker, and the body struck having 
only half the power of impetus will take a medium course, but so 
much more than that made by the striker which follows it as it is 
lighter than it, and there is less resistance of air; excepting the power 
of the resistance of the air which is measured by drawing the same 
movable thing with double power; and if the movements are not of 
double length, that which is lacking has been taken away from them 
by the resistance of the air, which may be said to resist in the same 
proportion as the aforesaid movable thing is lacking in movement 
when driven by double the power there was at first. And if the object 
struck was much lighter than the striker, the air will offer much 
resistance to the movement of the body struck. And if the body struck 
is double the body that strikes it, its movement will be in the sub- 
duplicate ratio of the reflex movement of its striker. And if the bodies 
which strike are equal and similar and of equal movement and power, 
then their reflex movements will be equal in length and power. But if 
the movement of similar and equal bodies be unequal then their reflex 
movement will be unequal. Leic. 29 r. 




It often happens that when one wind meets another at an obtuse 
angle, these same winds circle round together and twine themselves 
together into the shape of a huge column, and becoming thus con- 
densed the air acquires weight. I once saw such a hollow column 
assume the shape of a man above the sand of the sea shore, where 
these winds were ranging round together and digging stones of a con- 
siderable size from this hollow, and carrying sand and seaweed through 
the air for the space of a mile and dropping them in the water, whirl- 
ing them round and transforming them to a dense column which 
formed dark thick clouds at its upper extremity; and beyond the sum- 
mits of the mountains these clouds were scattered and followed the 
direct course of the wind when it was no longer impeded by the 



\0f the movement of water] 

That thing is lower which is nearer to the centre of the earth; there- 
fore that will be higher which is more remote from this centre. 

Every quantity of water will move towards its lower extremity; and 
where these extremities are of equal height, this water will not in itself 
have any movement. 

Here it is proved by these two propositions that the waters of the 
seas which are contingent will never of themselves have movement; 
and how of necessity they are of spherical surface. 

Therefore water that moves of itself has one of its extremities lower 
than the others; and that which does not move is of the same height 
in its extremities. 

A corollary follows which says that water does not move of itself 
unless it descends. Leic. 30 v. 

The variety of the positions and rates of speed of the waters within 
their rivers is caused by the variety of the slant of their bed. The 
variety of the slant of the beds of rivers is caused by the variety of the 
swiftness of the current of the waters. 

Water of itself does not move unless the slant of the bed draws it to 
itself: what therefore was the cause of this slant of the bed different 
from its first general slant? For I allow myself to understand that the 
movements more or less of the waters in the rivers were caused only 
by the greater and less slants of the beds, as I have set forth above. 

And if the first bed of the river was formed with uniform width, 
slant and straightness, what was the cause of the varying of such con- 
ditions as regards the bed? For it is here shown that the water which 
moves above them must of necessity be of uniform current. The mat- 
ter which makes the water of the rivers turbid is that which after 
being carried some distance settles upon their beds, and raises them, 
and changes the slant of the bed; and in this way it causes the varia- 
tion in the courses of the waters. And from this we conclude that the 
water is the cause of the variation of its bed, and that the bed then of 
necessity changes the courses of the waters in greater or less speed; 
which variety of courses is then the most powerful cause of varying 
.ill the bed of its river; and so it is concluded: — The bed of the rivers 
is varied by the matter that the course of the water deposits there; 



and the variety in the course of the waters is further varied by the 
irregularity in the bed of the river. 

A drop of water that falls in a place of uniform density and smooth- 
ness will splash in such a way that the edges of its mark will be at an 
equal distance from its circumference; and so conversely if it should 
not fall in a level place. Leic. 33 r. 

The centres of the sphericity of water are two: the one is of the 
universal watery sphere, the other of the particular. 

That of the universal is that which serves for all the waters that are 
without movement, which are in themselves in great quantity such as 
canals, ditches, ponds, fountains, wells, stagnant rivers, lakes, marshes, 
swamps and seas; for these although of different depth in themselves 
have the boundaries of their surfaces equidistant from the centre of 
the world, as are the lakes situated at the tops of high mountains, as 
above Pietra Pana and the lake of the Sybil at Norcia, and all the 
lakes which form the sources of great rivers, as the Ticino from Lake 
Maggiore; the Adda from Lake Como; the Mincio from Lake Garda; 
and the Rhine from Lake Constance and Coire, and from the lake 
of Lucerne; and as Trigon which passes through Africa Minor, which 
carries with it the water of three swamps at different altitudes one after 
another: of which the highest is Munace, the middle one is Pallas and 
the lowest is Triton. Again, the Nile has its source in three very high 
lakes in Ethiopia: it runs to the north and discharges itself into the 
Egyptian sea with a course of four thousand miles, and its shortest 
and most direct line which is known measures three thousand miles; 
it issues forth from the Mountains of the Moon from divers and 
unknown beginnings; and comes upon the said lakes high above the 
watery sphere at an altitude of about four thousand braccia, that is 
a mile and a third, in order to allow for the Nile falling a braccio in 
every mile. And the Rhone issues from the lake of Geneva and flows 
first west then south with a course of four hundred miles, and empties 
its waters in the Mediterranean sea. 

The centre of a particular sphere of water is that which occurs in the 
tiniest particles of dew, which are seen in perfect roundness clustering 
upon the leaves of the plants on which it falls; it is of such lightness 
that it does not flatten itself upon the spot on which it rests, and it 



is almost supported by the atmosphere that surrounds it, so that it does 
not itself exert any pressure or form any foundation; and for this 
reason its surface is drawn to itself equally from every side with equal 
force; and so each part runs to meet another with equal force, and they 
become magnets one of another, with the result that of necessity each 
becomes of perfect roundness, forming its centre therefore in the 
middle at an equal distance from each point of its surface, and being 
pulled asunder equally by each part of its gravity, always placing itself 
in the middle between opposite parts of equal weight. But as the 
weight of this particle of water comes to be increased, the centre of 
the curved surface immediately emerges from this portion of water, 
and makes its way towards the centre of the common sphere of the 
water; and the more the weight of this drop increases the nearer the 
centre of the said curve approaches towards the centre of the earth. 

Leic. 34 v. 

I have seen in the case of two small canals each of a breadth of two 
braccia, which serve as a line of demarcation between the road and the 
estates, how their waters clashed together with unequal force, and then 
united, and bent at a right angle, and passed underneath a small bridge 
by this road and continued their course. But what I want to refer to in 
them is the fact that they formed there a flow and ebb, with a height of 
a quarter of a braccio, caused, now by one, now by the other canal, as 
will be stated. The first canal, being the more powerful, subdued the 
onrush of the water of the opposite canal, and by adding to it from the 
opposite direction caused it to swell up; and then the water coming 
above this from the swollen river, rose up in such a way as to acquire 
so much weight from the more sluggish water that it overcame the 
impetus and power of the water which at first was more powerful, and 
so drove it back with great fury; and consequently the victor, re- 
doubling the impetus of its movement, entered with an undulation 
extending over more than a hundred feet into the more powerful 
canal, which at that time retarded and held up such of its waters as 
were at the boundary of the conquering wave. And from this wave 
upwards the river massed together so much water that after the end 
of the aforesaid impetus of the wave, these waters gained the victory 
and drove back the first waters; and so they continued in succession, 



without ever retarding the movement of that third canal in which they 
were united under the aforesaid bridge. 

For this canal had four different movements, of which the first and 
second were with greater or less current, and the others according as it 
varied from the right to the left bank. The variation from the greater 
to the less current occurred when one of the streams of water made 
itself victor over the other, for as this other is turned back together 
with that which drives it an abundance of water is created under the 
bridge. The fall of the water under this bridge took place when the 
one stream of water which conquered the other had almost consumed 
its impetus and the opposing stream was left with its force already 
exhausted; the water under the bridge was then extremely low. The 
changing across of the current from the right to the left bank occurred 
when the water on the right or the left was victor, that is when the 
water on the right was victor the current struck against the left bank, 
and when the current in the canal on the left was victor it struck upon 
the right bank underneath the aforesaid bridge. 

And if this ebb and flow created within so small a quantity of water 
has a variation of a quarter of a braccio, what will it be in the great 
channels of the seas which are shut in between the islands and the 
mainland ? 

It will be so much the more in proportion as its waters are greater. 

Leic. 35 r. 


The wave of water created by the wind is slower than the wind that 
moves it, and swifter than the current of the water that produces the 
wind; of this there is an example in the waves of the meadows. 

The wave of the water created by the descent of the rivers is slower 
than the current of the water that produces it; and this happens because 
the wave in such rivers is formed from the bottom of this river, or 
from its sides, and it stands as firm as is the firmness of the object that 
produces it, while the water, which continually forms itself into a wave, 
is continually escaping from this wave. 

There are many occasions when the wave of the water and that of 
the wind have the same course; and many occasions when they are 
contrary, intersecting at right angles or often at acute angles. 



The movement of the falling wave penetrates into the movement of 
the wave recoiling. The wave of the water in a circular vessel runs 
from the edge to the centre and is then bent back from the centre 
to the edge and from the edge to the centre; and so it continues in 

The wave of a triangular vessel, or a vessel with sides, has not uni- 
formity of time, because its sides and angles are not equidistant from 
the centre of the vessel. 

The circle of the wave made by an object in running water will be 
oval in shape. Leic. 36 v.