On Friction: Level, Sloping, and Calculated
Friction equal in both directions on the level, unequal on a slope, and reckoned in fractions of weight
Continuing his study 'On friction,' Leonardo distinguishes three cases with accompanying diagrams: a dense body on a horizontal plane, whose friction resists motion equally to right and left; the same body on an oblique plane, where difficulty gained pushing one way exactly equals the ease lost the other way; and a 'calculation of frictions' on a quadrant, assigning each position a fraction of the weight's natural gravity. He tabulates the resistances as a quarter, an eighth, and a sixteenth, until the last point resists with nothing because its friction has been used up in the descent.
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On the level, friction is symmetric
A dense body rubbed upon a flat dense surface, placed in the position of equality (the level), meets as much difficulty of friction moving to the right as moving to the left.
On a slope, difficulty and ease trade off
But if the dense body is rubbed toward the upper part of the oblique site, the motion is made as much more difficult than the level motion as the contrary motion is easier; thus difficulty increases on one side exactly as much as it diminishes on the other.
Calculation of the frictions
The weight n gives resistance equal to a quarter of its natural gravity, m an eighth, o a sixteenth, and p none, having consumed its friction. Said better: n resists by a quarter of its natural weight, m by half a quarter, o by a quarter of that quarter, and p with nothing, since that last quarter is used up in the motion from o to p.