Notebook on Mechanics and Natural Philosophy

· The ball that always approaches the return original: "rendita"; here Leonardo likely means the "return" to a state of rest or the point of impact at the end of its path of its motion
always as much as the motion along the return, nor along the movement
· purely stated concerning the motion, which should be said of the weight of the

A geometric diagram featuring a semicircle oriented with its curved edge at the top. A horizontal baseline forms the diameter, with a central vertical axis extending from the bottom center point, labeled 'C'. Several horizontal chords are drawn parallel to the diameter. Numerous radiating lines originate from point 'C', intersecting the horizontal lines and the outer arc at various points. These intersection points are labeled with letters, including A, B, D, E, F, G, H, I. Below the central point 'C', there is a small, separate circle containing the letter 't'.

· The movement that is made through the middle of the circle without returning to the curve of the circle, and for this reason it is said: as much as the weight is to its return, because here the motion occurs by a shorter original: "più brieve" way. As much as it will be of it Leonardo frequently repeats "fia d' essa" (it will be of it) as a shorthand for establishing mathematical proportions between different variables. through the straightness of the movement, the motion returns in that length of the movement of the weight; it will be of it, it will be of it, the motion while it will be of it, the weight will be of it, the motion must, must state the weight in the motion; it will be of the motion, it will be of the motion, it must state the weight while the movement will be of it, while the motion will be of that movement of the weight, and of the motion it will be of that movement, it will be of it, as much as that movement will be of it, while the motion will be of that movement of the weight and of the motion while it will be of that movement, it will be of it, the motion while the weight of the motion will be of it, the motion while the motion will be of that movement, it will be of that movement of the weight, while the motion will be of that movement of the weight, of the motion, of the motion, it will be of that movement of the weight, while the motion will be of that movement of the weight, of the motion, of the motion, while the motion will be of that movement of the weight and while it will be of that movement of the motion, while it will be of it, the motion must, must state the weight of the motion while it will be of that movement of the motion, it will be of that movement of the weight, while the motion will be of that movement of the weight, while the motion must, must state the weight of the motion while it will be of that movement of the motion, it will be of that movement of the weight, while the motion will be of that movement of the weight, of the motion, while it will be of that movement of the motion.

This repetitive section represents Leonardo's attempt to work out a formula for proportions. He is essentially saying that the relationship between the weight and the distance moved is constant, trying to find the exact linguistic phrasing for a mathematical law of mechanics.