Friction on the inclined plane
Two triangle diagrams working out the fifth-part rule for sliding weights
A long note, written upside down, studies friction on inclined planes, illustrated by two right-triangle diagrams that carry small weights on their slopes, lettered a, b, c, d, f, m, n, r. Leonardo reasons that a weight of five pounds bears four parts along the line b n and pushes one at n, and, taking friction as a quarter of a weight, divides the weight by five to fix the slope at which it just begins to slide. He then gives a geometric construction: divide the line a d into five equal parts, mark the point f at the end of the first, draw the line f r and set the obliquity r a, placing the weight m upon it.
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The fifth part that begins the slide
The weight m of five pounds has four parts felt along the line b n while one part pushes at n. Taking friction as equal to a quarter of a weight, the note reasons that when the slope lets the weight gain a fifth of its natural gravity, that fifth stands against the four remaining parts, which cannot move but only resist, and so the body is at the point of sliding.
Construction: dividing line a d into five parts
To set the critical slope, divide the line a d into five equal parts and mark the point f at the end of the first. Then draw the line f r, form the obliquity r a and place the weight m upon it, giving the inclined plane at which sliding just begins.