What weight is. Weight, in itself, is properly earth and water mixed together; and although air and fire are not separated from these, because they are without weight they are not named.

1; 2; 3; 5; 6; 7; 8; 9 — i h g f e d c b a. Each has the ninth part. Take one away from the head and the next-to-last will have 2/9, and the opposite end unloads itself. And I do not extend further, because this subtle matter must be seen more subtly and well considered.

If the cord that transversely pulls the suspended body is joined at a right angle to the lower end of the cord that sustains the weight, you will find that the weight which moves has the same proportion to the weight which is moved as the width between the perpendiculars of the ends of the motion has to the straight length of the cord that sustains the weight.

c a — f d — n b — 1 4. a n is the cord that sustains, n f is the one that has pulled the weight transversely, and n is the right angle made at the junction of the two cords. Now I find that the weight which was at b is drawn by weight 1 to n, and that the perpendiculars of the ends of the motion b n — that is a b, c n — are apart from one another by a measure that goes four times into the sustaining cord, that is a n. Therefore the weight 1 that moves will go four times into the weight n that is moved.

d — c e r a — m — f b. The reason is that when the weight is at cord a b, the whole weight b is in a and f feels none of it; and when the weight is at d c, the whole weight will be in d and a is entirely deprived of it. We hold that each midpoint shares equally in the equal ends, and m is found at the middle of the line a c; and if, when the weight was at b, a felt it all, so likewise does d when the weight is at c; and being at the middle, r sustains half the weight; being perpendicular over the quarter of the motion, a quarter of weight b will be the weight that b brings to r.