Weights on Two Inclined Planes and the Proportion of Slopes
How a weight's effective force falls to a fraction of its natural weight on a slope
A pulley carries two weights resting on inclined planes: the weight q, by the right angle at e, keeps only two-thirds of its natural three pounds (a power of two pounds), while p keeps only one pound, so one pound stands against two. Leonardo then analyses how the two obliquities d a and d c differ, d a exceeding d c by two and a half times, a double-sesquialteral proportion against the weights' simple double proportion, so that the gravities 'change nature.' A second sketch of a pulley holding a rod adds that, because a c is half the lever c b, one pound at c yields a power of two pounds.
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Effective weight of q and p on their slopes
The weight q, by the right angle n upon d f at e, weighs two-thirds of its natural three pounds, remaining a power of two pounds; p likewise keeps only one pound by m at right angles on h d at g. So one pound stands against two.
Double-sesquialteral proportion of the obliquities
The obliquities d a and d c are not in the same ratio as the weights: d a exceeds d c, receiving it two and a half times, giving a double-sesquialteral proportion, whereas the weights were in simple double proportion. Thus the excess of the greater obliquity over the lesser is one and a half.
A pulley, a rod, and the half-lever a c
In a second figure a pulley supports a rod: c is the pole or centre of the turning point, and because a c is half the lever c b, one pound at c gives a power of two pounds.