The question of weights on inclined planes
Why equal weights on equal arms differ once they rest on unequal slopes
Under the heading 'Question of weights,' Leonardo asks whether equal weights hung on equal balance arms, equidistant from the fulcrum, must always prove equal, and answers no. A double inclined plane (labelled b a c, with weights of 4 balanced over a pulley) shows that of two equal weights the one on the steeper slope shows less: because line a L is twice as oblique as a h, the 4 hung at b loses 2 and keeps 2. A square divided by its two diagonals (labelled n, m o) defines the 'middle obliquity', the diameter of the square, at which a weight would lose exactly half; and he traces how the remaining load rests on the perpendicular pendants b r, c n versus the oblique ones a n, c n.
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Equal weights differ once they rest on unequal slopes
Of equal weights, the one on the more oblique site shows itself of lesser weight. Since line a L is twice as oblique as a h, the 4 sustained at b loses 2 and only 2 of its heaviness remains.
The diagonal of the square as the 'middle obliquity'
A weight would lose exactly half its heaviness only on a middle obliquity, that is, the diameter of the square formed by two straight sides, as shown in the square n m divided by its diagonals below.
Load shared by perpendicular and oblique pendants
Because this obliquity receives the weight of 4 as one, the line a h receives its 4 with a weight of one, and the remainder rests upon the pendants a r and a n (or b r and c n); yet the perpendicular cords b r, c n bear a different weight than the oblique ones a n, c n.