Weights on wheels and the fall of heavy bodies
Motion, the inclined path, and gravity toward the centre of the world
This double opening is a dense study in the physics of weights, wheels, and descent. On 121v Leonardo argues that a moving body is never swifter than its mover and analyses how a weight resting on the rim of a wheel is directed either toward the centre of the world or toward the wheel's own centre; on 120r he states that all unhindered heavy bodies run to the lowest place, compares descent in water to a river's oblique flow, and treats the ease of descending versus the difficulty of climbing an incline (labels m s, n r, s f). A closing note challenges the philosophers who hold that a weight gains heaviness as it nears the centre of the world. Numerous small lettered diagrams accompany the arguments.
On this page
The descent of a weight between two wheels
Leonardo argues that the weight b cannot descend from its place because the line a c is much shorter than the line a b c. The line a c spans the gap between the supports of the greater wheel and of the smaller, while a b c runs from the pole of the greater wheel through the point of contact o of the two wheels to the weight's centre and on to the contact c.
A body is never faster than its mover
A series of aphorisms on motion and weight: the moving body is never swifter than its mover, and its greatest speed comes at the moment of separation. A weight on the rim of a wheel weighs by its crosswise distance from the wheel's centre; supported above the contact point it is directed to the wheel's centre rather than to the centre of the world.
Heavy bodies seek the lowest place; descent in water and a river's flow
The universe has nothing lower than its centre, and every unhindered heavy body runs to the lowest parts; there are three orthogonal motions. Leonardo then poses the case in which the natural descent of a weight within water is of motion equal to the oblique motion of the river.
Easy to descend, hard to climb: the inclined path
Where it is easier to descend, there it is harder to climb. The obliquity m s equals that of n r, and s f equals r n, so the ease and power of the descent m s f equal the difficulty of the ascent n r a. Hence things equal among themselves do not overcome one another.
A body driven from its place by the water
A lettered diagram with the note that here d is driven out of c by the water. A companion figure shows a body a driven out of f by the wind, illustrating how a moving medium displaces a body.
Proportion, position, and a challenge to the philosophers
The proportion of space n o to space o c equals, by reason of position, the proportion of the weight of body c to that of body a. Leonardo finds weight a heavier though it is higher, contrary to the philosophers who claim a body gains heaviness as it nears the centre of the world; experience, he says, gives greater motion than before.