Movement & Weight
The Four Accidental Powers
Force with material movement and weight with percussion are the four accidental powers in which all the works of mortals have their being and their end.
— Leonardo da Vinci
Overview
This is Leonardo's physics. Long before Newton formalized the laws of motion, Leonardo was investigating force, inertia, momentum, and the relationship between weight and movement with an intensity that fills thousands of notebook pages — over 41,000 words survive on this subject alone.
His approach was experimental and observational. He studied falling bodies, the flight of projectiles, the behavior of weights on balances, the compression of air, and the transmission of force through water. He challenged the ancient authorities directly, identifying errors in classical mechanics and proposing corrections based on his own experiments.
These writings sit at the intersection of art and engineering. Leonardo needed to understand how bodies move in order to paint them convincingly, and how forces work in order to design his machines.
First Principles
How to begin studying motion
Speak first of the movement then of the weight because it is produced by the movement, then of the force which proceeds from the weight and the movement, then of the percussion which springs from the weight the movement and often from the force.
C.A. 155 v. b
The action of a pole drawn through still water resembles that of running water against a stationary pole.
C.A. 79 r. c
Nothing that can be moved is more powerful in its simple movement than its mover.
C.A. 91 v. b
That second observation — that pulling a pole through still water is the same as water flowing past a fixed pole — is a statement of relative motion. Galileo would formalize this principle a century later. Leonardo saw it from watching boats. -D
Where the Ancients Were Wrong
Leonardo identifies errors in classical mechanics
The science of weights is led into error by its practice, and in many instances this is not in harmony with this science nor is it possible to bring it into harmony; and this is caused by the poles of the balances by means of which the science of such weights is formed, which poles according to the ancient philosophers were placed by nature as poles of a mathematical line and in some cases in mathematical points, and these points and lines are devoid of substance whereas practice makes them possessed of substance, since necessity so constrains as needful to support the weight of these balances together with the weights which are reckoned upon them.
I have found that the ancients were in error in their reckoning of weights, and that this error has arisen because in a considerable part of their science they have made use of poles which had substance and in a considerable part of mathematical poles, that is such as exist in the mind or are without substance; which errors I set down here below.
C.A. 93 v. b
This is a remarkable passage. Leonardo is saying: the ancient scientists assumed perfect, frictionless, dimensionless balance points — mathematical abstractions. But real balances have real thickness, real weight, real friction. The theory breaks down in practice because the theory ignores physical reality. This is the empirical method in action, a century before Francis Bacon would formally describe it. -D
On Air and Resistance
How bodies move through air
In equal movements made in equal time the mover will always have more power than the thing which is moved. And the mover will be so much the more powerful than the thing moved in proportion as the movement of this thing moved exceeds the length of movement of its mover.
But observe, O reader, that in this case you must take count of the air which becomes so much the more condensed in front of the thing moved as this thing moved is of greater speed; for this air is capable of being condensed in an infinite degree.
C.A.
Among movable things of the same gravity that one will have the slower movement of which the front that cleaves the air takes up more space; and so conversely as it occupies less air, not however extending itself in such a degree of thinness as to cause its weight to fail, for where there is no weight there is no local movement through the air.
C.A.
Leonardo is describing air resistance and drag — that a wider object moves slower through air because it has to push more air out of the way. He also recognizes that air compresses in front of fast-moving objects. This is the seed of aerodynamics, written by a man who was simultaneously trying to build a flying machine. -D
The Arrow and the Bow
How projectiles work
And this we see with an arrow from a bow when its point is resting against wood, for though the cord drive it with all the force of the bow it only penetrates the wood a very little distance, but does the contrary if it has some movement. Some say that the arrow in moving propels a wave of air in front of itself, and that this wave by means of its movement prevents the course of the arrow from being impeded. This is incorrect however because everything which is moved exhausts and impedes its mover. The air therefore which passes in waves in front of the arrow does so because of the movement of this arrow, and it lends little or no help of movement to its mover, which has to be moved by the same mover, but rather checks and shortens the movement of the thing moved.
C.A.
Leonardo is debunking the ancient antiperistasis theory — the idea that air pushed aside by a moving object circled around and pushed it from behind. He correctly identifies that air resistance slows the arrow, it doesn't help it. This was a live debate in medieval physics, and Leonardo got it right through observation rather than speculation. -D
This is the second-largest body of text in Leonardo's notebooks after the water writings. It's dense, technical, and occasionally brilliant. He gets some things right that wouldn't be formally proven for centuries (like the relationship between air resistance and speed), and some things wrong. But the method — experiment over authority — is consistently modern. -D