Here account is taken of the natural weight and not of the force, because force has no weight; but the natural weight lies in the straight appendages [the vertical hangings].

4 5 1

a d e - c - f. When the perpendicular that falls into the angle supporting the weight cannot divide the angle, it is a manifest sign that only one cord is the supporter of that weight, and the other counts for nothing.

4 n 1 - r - 3 4 1. Such proportion is from weight to weight as is from triangle to triangle, and such proportion is from triangle to triangle as is from base to base.

When from the equidistant [horizontal] line two lines descend meeting at the angle that suspends the weight, the perpendicular that divides that angle will fall. Then the weight will be divided among the two cords of that suspension, and between these loads there will be the same proportion as that of the two angles generated by the aforesaid division of the first angle. As, if from the horizontal line a e there descend the two lines a c and e c, meeting to compose the angle c, from which the weight f is suspended, and there falls the perpendicular d c that divides that angle into two other angles a c d and d c e, I say that the cords will receive the aforesaid weight in the same proportion as that which the two aforesaid angles have between them, and as the proportion of the quantities of the two triangles between them. And the perpendicular that divides the angle of such a triangle will always divide the suspended gravity into two equal parts, because it passes through the centre of that gravity.