17 17

18 - 4 - n a m - r n o // The support a n will bend toward m and will do the same office with the beam m n as [if] it were placed at a r. - Provided the foot is well fixed. If the support a n is a sustainer of 4 pounds, it suffers a force for 24, because n is the fulcrum of o a, the lever a n being 6 times longer than o n, its counter-lever. Therefore, a having 4 pounds, o has 24 and the fulcrum n feels 28.

23 - 4 - o p - 8 - n m // The manner of the position that the support n o holds with its weight upon it makes n sustain a weight of 8 pounds, and it sustains 64 on account of the weight [multiplied] by itself of the support, because the eight spaces multiply by themselves, as is shown in the ninth [book] On the simple and compound rod. Then it has 16 on account of the 2 pounds of the beam at o which, m n entering 8 times into n o, the 2 at o stand equal with 16 at m.

19 - a - b c

General rule to know a beam tied at its end by a cord, which is pulled from a single place and raised upright, and to be able to tell, in all the degrees of its raising, of how much weight it is to its mover. // Motion made through acute angles.

S t u x y z K - p g r - 9 1 2 3 4 5 6 - a b c m n o e // The circular line r g is the intersection above the other circles of the middle of each line similar to r S and of the levers such as a g.

S t u x y z K - p g r - 9 1 2 3 4 5 6 - a b c m n o e // The circular line r g is the intersection above the other circles of the middle of each line similar to r S and of the levers such as a g.

: o m - 242 n - f 100 // If the line m n enters 50 times into the whole length of the beam, and the beam weighing 4 weights, the head o weighs 2, and 100 weights must be in the counterweight f to stand equal with 2 at o. // That line, which departs from the foot of the rod and is produced at equal angles upon the cord that lies between the puller and the end of the rod pulled, will be the true length of the lever and moves the rod from its position. // As much as the line, which departs at equal angles from the cord that stretches between the end of the rod pulled and the hands of the puller, enters in length into the rod pulled, so much more force does the puller need than the weight of the head of that rod.