Gain and loss of friction on different slopes
Diagrams and curves marking how a dragged weight's friction and load vary with the incline
Several lettered figures, including a graduated quarter-circle used as a protractor, accompany Leonardo's continued study of friction and load on inclined paths. He argues that a weight's burden on its mover and its friction arise at opposite positions, so that as one grows the other diminishes, though not in the same proportion. Curves such as b h and lines such as m n and a f are said to mark the degrees of gain and loss of friction. He closes by distinguishing the natural weight a body gives to several supports from an added 'accidental' weight that may exceed or fall short of it.
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Load and friction arise at opposite positions on the mover
The birth of a weight upon its mover is always caused at a position opposite to that where its friction arises. As regards mover n, the body a gives it no weight, since that weight presses only on the horizontal where it rests, and the mover is tired only by the whole friction, a quarter of its heaviness. Mover m, by contrast, feels none of that friction but carries the whole natural weight.
The curve b h marks the degrees of gain and loss of friction
This figure shows the degrees of the gain and loss of the friction of bodies dragged over different obliquities of position; these degrees are marked on the curve b h.
Line m n: weight and friction vary inversely but not in proportion
On the line m n are shown the degrees of the gain or loss of the weight in the power of its mover. As much as the weight is lacking to its mover, its friction increases, and as friction is lacking, the weight increases; but these increases and diminutions are not in proportion with one another, since they are not measured by the same nature.
Natural and accidental weight on several supports (line a f)
All the degrees of friction are to be taken upon the line a f, since friction follows the nature of the dragged weight. Every body suspended from several supports gives them its natural weight and, beyond it, an accidental weight that often exceeds and is often exceeded by the natural.