A train of fifteen wheels and pinions multiplying by twenty
Each 200-tooth wheel drives a 10-spindle pinion, so the last wheel's speed reaches the powers of 20
A geared train runs across the top of the sheet: fifteen wheels of 200 teeth each meshing with pinions of 10 spindles, so every wheel turns 20 times for each turn of the one before it. Leonardo tabulates the resulting motion as a column of numbers rising from 1 to 20, 400, 8000 and on up to 1,638,400,000,000,000,000, each figure twenty times the last, and notes that a point on the rim of the last wheel n travels 3 and 1/7 braccia per turn because its diameter is one braccio. He observes that no material movement could match the velocity of that final rim, yet remarks the scheme would fail in practice through the gears catching fire from friction, whether under water or out of it. A small drawing of the wheel-and-pinion assembly sits at lower right.
On this page
Train of fifteen wheels and pinions, m to n
Fifteen wheels of 200 teeth each drive pinions of 10 spindles, so each wheel turns 20 times for one turn of its predecessor, running from the first wheel m to the last wheel n. Because the last wheel's diameter is one braccio, a point on its rim travels 3 and 1/7 braccia per turn. The geared row is drawn across the top and again at lower right.
Multiply each result by twenty: the powers of 20
The motion is tabulated as a column of numbers, each twenty times the one above: 1, 20, 400, 8000, 160000 and so on to 1,638,400,000,000,000,000. The instruction is to multiply every result by 20, following the 200-to-10 ratio of wheel to pinion.
No motion so swift as the compounded rim
No material or evident movement would be of such velocity that it could be likened to the part of the wheel moved by the motion of many other wheels. The note also warns the scheme would have no effect in practice because the gearing would catch fire from friction.