Propositions on force, mass, space, and time in motion
Six numbered rules relating a moving power to the weight moved, the distance, and the time
The page sets out a series of numbered propositions on how a moving power relates to the body it moves, the distance covered, and the time taken. Leonardo argues that halving the body lets the same power carry it twice the distance in equal time, but cautions that such proportions do not always hold, since a diminished force might fail to move the body at all. A closing proposition states that two separate forces joined together move the two bodies joined together the same distance, because the same proportion is always preserved. The sheet is written entirely in text, with numbered markers in the margin and no diagram.
On this page
Halving the body doubles the distance for the same power
First: if a power moves a body through a certain space in a certain time, the same power will move half of that body, in the same time, twice that space. The second and third propositions vary the same relation by trading distance against time and against weight.
Limits of the rule: a lessened force may not move at all
Leonardo warns that it does not follow that a power will move double the weight in double the time twice the space, nor that half the force will move the same body half the space, because such a diminished force might be unable to move the body at all.
United forces keep the same proportion
If two separate forces move two separate bodies, the same forces united will move the two bodies joined together the same distance in the same time, because the same proportion always remains.
