Monsignor de' Pazzi. Ser Antonio Pacini.

2-f-4-28-2 16-bmna-2-b, it being fixed. / The potential arm f b feels 3, and the patient arm a b resists in a as 2, and the 3 of f remains 2; and this 2 will always be maintained until the cord that pulls is deprived of the lever's arm. That lever will be consumed when the line of the cord that pulls is on the same line as the friction of the cord pulled, that is, on the line enclosed between the surface of the thing pulled and the surface of the plane over which that thing is dragged. / f b, the lever, is 2/3 of the counter-lever a b. Therefore 3 in f resists 2 in a. And because the descent of a is along a perpendicular line, and f, although it follows it along an oblique line, is not therefore, if it were of the same length, of the same power as that a; but by being nearer the center of the revolvable (circle), it is 1/3 more powerful, as was demonstrated by the first (proposition); whence to that f with power of 3 there is resisted in a which has power of 2.

rb-ca-22

4 2 / a descends downward and weighs downward b, and by the adversary that is founded upon the things already concluded, it says by the ninth of the second that the weight a, being at a, would descend if the line b r did not sustain it, and that the lever b c is equal to the counter-lever a c by the definition of the circle. Therefore the whole weight of a is sustained in such a position by the lever b, and by the sixth of the ninth, equal things do not overcome one another. Therefore a and b do not move from their position by cause of one another; whence if the weight a, which is 2, is sustained by the 2 which is the power of b, whoever moves b will move a; and b, by what is said in the ninth of the second, being moved along the level-lying line b r, weighs by a quarter of its whole, that is 2. Therefore 1/2 moves 2 with an equal arm. This is impossible by the tenth of the first, which says that in equal time the mover is more powerful than its movable; wherefore a will not be raised on high except by a power greater than itself, because equal power only resists its descent, and the greater draws it along with itself. Therefore if that which is in a is in b, b will not move toward r unless a rises with power greater than 2.

* All the members of the instruments that are employed in the motion of any heavy body, if they be of equal motion with the motion of that heavy body, will be loaded with the whole aforesaid gravity. / And all those members of the instruments that, at the motion of that heavy body, are of slower motion, will feel of that gravity so much less as they are of slower motion. / * And so conversely they will be loaded with so much greater weight than the gravity raised by them, as they are faster than that gravity.

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10 10 10 10-mn-1000001 / * That motion which in equal ti[me] ...

10 100 - b a / As much as, in equal time, the mover is faster than its movable, so much greater will be its power than that movable. / And by as much as the mover is slower than the movable, so much less will be its power. / When the motion of the mover is equal to the motion of its movable, then the power of that mover will be equal to the power of that movable.