The accidental weight is created by the natural weight.

The accidental weight increases in the sides of the angled cord as much as the axle of that angle, in which the weight is sustained, diminishes.

Let the angled cord be c t d; and the axle of its angle is the line r t, which ends at the angle where the weight o is sustained.

The weight o, which was 2 upon the cords that were equal to their axle, a t and b t, having diminished that axle, or perpendicular, by half its length, when the fronts of the cords have descended to c, d, the axle is at r t, half of a t; then the weight 2 of o is made 4 at c, d: and thus subdividing that axle successively by half. Which division is an infinite diminution of the axle; and consequently there would follow an infinite multiplication of weight upon the hypotenuses of such axles.

If the cord that is joined to the ends of the shaft has its straightness tangent to the straightness of the shaft, it is impossible to tie another cord to suspend that shaft without an angle being caused. Let d e be the shaft; d b e is the cord fixed at the ends of that shaft d e; a b is the cord tied to the cord d b e; b is the angle which, by necessity of the weight of the shaft, is made by that cord which before was tangent to that shaft.

Every heavy body weighs along the line of its motion, whether violent or natural or natural-violent, and curvilinear as well as rectilinear.

The support loads itself entirely with the weight joined to it, which descends straight down upon that weight, for what is said in the margin of the opposite face; and in such calculations of weights one has to work with the arms 2 r and 2.4. The lever 2 r is terminated at the right-angled junction with the appendage a r, and the counter-lever 2 and 4 is terminated at the right-angled junction at the appendage 4 and 4, that is the appendage of the weight.

The heaviest part of bodies makes itself the guide of their motion.

The central line of the motion of bodies passes through the centre of the heaviest part and through the centre of the lightest and through the centre of gravity of the whole body that moves.

Here the potential lever d b is double to its potential counter-lever b c; whence it follows that one pound placed on the appendage d n is equal in power to 6 pounds placed on the half-real appendage c a, and 6 other pounds of power are joined at b. Therefore the cord a e b, for one pound placed at d n, feels a power of 12 pounds.

The 8, which sustained the appendage a p, having arrived from p at o, has become 7 at that appendage; which 7 divides in half at the appendage o n, which comes to remain.

Never will the greater arm of the balance o m and o n be double one to the other, unless their appendages n a and m p are parallel; which is impossible, since these appendages concur in the creation of the angle p, unless indeed those lines were in contact, for then the angle would be consumed together with the arms of that balance.

By what is said in the penultimate, the arm o n is less than double the arm o m; for which reason its appendage n a feels more than half the weight p. Which 'more' will have such proportion with the whole weight p as the shortfall of the greater arm o n from becoming double to o m has with the whole arm. And all that 'more' is accidental weight.