Odometer and pedometer: machines that measure distance
A cart-wheel that counts miles and a step-counter driven by the walker's thigh
Two columns of text and several geared devices set out instruments for measuring how far one has travelled. The first column describes an odometer: a cart-wheel of known circumference drives a train of toothed wheels so that after exactly one mile a wheel drops a small stone into a resonant vessel, sounding each mile like a clock striking the hour. The second column describes a pedometer strapped to a man or horse, whose lever is struck by the thigh at every pace and advances a 60-tooth wheel by one tooth. The reasoning is built on a worked calculation of a circle's diameter from its circumference using 3 and 1/7 (pi) and the rule of three.
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Odometer: the cart-wheel that measures a mile
The cart-wheel turns through 10 braccia at each revolution. Its motion is geared down through a train (labelled f, m, n) so that the wheel m, which has 300 teeth, advances by a single tooth per turn of the road-wheel. When m has made one full revolution the cart has run exactly one mile, and a spoke marks off each mile.
Finding a circle's diameter with 3 1/7 and the rule of three
To find any diameter, Leonardo multiplies it by 3 and 1/7 of itself to recover the circumference; a diameter of 7 gives a circumference of 22. He then sets a proportion by the rule of three: if 22 of circle gives 7 of diameter, what does 10 of circle give? Working it yields a diameter of 3 and 4/22 braccia for the 10-braccia wheel.
Sounding each mile with a falling stone
Rather than merely displaying the count, one wheel (f) makes the mile audible: at each mile it lets a little stone fall into a vessel shaped to receive sound, so the ear hears a distinct strike. The pointing wheel n marks the miles as the small hand of a clock marks its hours.
Pedometer: the lever g that counts each pace
In the second device (labelled f, a, b, c, g) a lever g is struck against the thigh of the man or horse at every step, advancing one tooth of the toothed wheel a while the pawl f prevents it running back. Wheel a has 60 teeth, so it completes one full turn every 60 paces.
