The Wheel on the Thinnest Axle; a Loaded Roller
Why a thinner pole eases a wheel's turning, with a weighted cylinder resting in its support
Three linked notes on the mechanics of wheels and axles. Leonardo states that among wheels of equal diameter the one on the thinnest pole turns most easily — the wheel whose pole-diameter divides more times into its own diameter. A drawn cylinder rests in the notch of a block with a weight hanging from it: he corrects a false reckoning, since pole and counterweight together weigh 200 pounds, a quarter of which (50) will move the 200. A closing note explains that a pole weighing 100 pounds loads its support a n m o p with that full force, working against the ease of turning.
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The wheel eased by the thinnest axle
Among wheels of equal diameter the one carried on the thinnest pole moves most easily. Put another way, the wheel of easier movement is the one whose pole-diameter enters more times into the diameter of the wheel itself.
A false reckoning of the loaded cylinder
The drawn cylinder, treated as all pole and weighing 100 pounds, is set in the recess of its support. Leonardo calls the reckoning false: pole and counterweight together weigh 200 pounds, and since a quarter of 200 is 50, only 50 pounds will move the 200, referring the reader to the fifth proposition of the first book.
The pole's weight bearing on its support
If the wheel above were the head of a pole weighing 100 pounds by itself, that weight rests and loads upon its support a n m o p with a force of 100 pounds. This is no different from someone pressing down with a hundred-pound weight against the pole, wholly opposing the ease with which the pole is turned.