n S, t o, m, r, 98 a, 63 63, X y

let the wh[eels …]

The weights attached to the hanging ends of the level cord, which rests upon two different wheels, (will have between them the same proportion as the diameters of the said wheels have,) will always perform the same office between them as if they were suspended over a single wheel.

If the large wheel has its semidiameter m r 6 times greater than the semidiameter of the small wheel t o, and thereby shows that the weight X can be 6 times less than y, it then also has the line of retention n r 6 times that of the small wheel S t; whence it is proven that there is no variation.

a, n 20, 1, h g m b, f

I ask you which motion is rendered more difficult: that which is made along the line n m, or that which is made along the line h m.

If you wish to move the beam a b (noting that the mover which moves the beam along the line of its length has of that beam as many different weights as there are different lines of its obliquities): but as regards the contact, or dragging, of the friction, it will be the less difficult the more it is along a more perpendicular line, because it is clearly shown that friction made along the level line is much more difficult than that made along the perpendicular line, as is demonstrated in the next-to-last [proposition] of the 5th. But the beam's own weight burdens the cord that pulls it along that perpendicular line more than it did along the level line. Whence it is concluded that pulling the beam along the level line is easier than along any other line, as is shown by the line h m; because along that line you have, at the start of the motion, the friction of the level beam and yet not its weight. In the middle of the motion it lightens, because it loads onto a. 4

[continues at the right]

4 I do not mean, however, that it lightens on the cord, but on the plane. But as much as it lightens at b, so much it loads at h, in such a way that the level cord is always burdened only by the friction of the beam, and not by its weight. But the cord that pulls obliquely — the more it pulls, the more the friction is wanting to it and the more it is loaded with the beam's weight; so that, at the last, the whole beam rests entirely upon the cord that moves it.