The accidental weight is created by the natural weight.

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

Let c t d be the angled cord; and the upright 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 when the cords a t and b t were equal to their upright, once that upright (or perpendicular) has been diminished by half its length, when the fronts of the cords have descended to c, d and the upright r t is half of a t, then the weight 2 of o is made 4 in c, d: and so on, subdividing that upright successively by half. This division is an infinite diminution of the upright; and consequently an infinite multiplication of weight would follow on the hypotenuses of such uprights.

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

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

The support is fully loaded with the weight joined to it, which descends straight over that weight, as is said in the margin of the opposite side; and in such calculations of weights one must work with the arms 2 r and 2-4. The lever 2 r is terminated at the right-angled junction with the pendant a r, and the counter-lever 2-4 is terminated at the right-angled junction at the pendant 4-4, that is the pendant 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, 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 sextuple its potential counter-lever b c; whence it follows that one libra placed at the pendant d n is equal in power to 6 libre placed at the semi-real pendant c a, and 6 further libre of power are joined at b. Therefore the cord a e b, for one libra placed at d n, feels a power of 12 libre.

The 8, which sustained the pendant a p, having come from p to o, has returned to 7 at that pendant, which 7 divides by half at the pendant o n, which comes to remain.

Never will the greater arm of the balance, o m and o n, be double one another, unless their pendants n a and m p are parallel; which is impossible, since those pendants concur in the creation of the angle p, unless 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 proposition, the arm o n is less than double the arm o m; wherefore its pendant n a feels more than half of the weight p. This 'more' will have the same proportion to the whole weight p as the shortfall of the greater arm o n from becoming double o m has with the whole arm. And all that 'more' is accidental weight.