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Codex Forster II — 094v

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© Victoria and Albert Museum, London

Tre ruote (l'ultima dentata) che ne muovono altre minori, con:

2 - a b c 2 - 2; 2 r - n m 1; m 4 4

Tutte le rote di sotto che si pongano intorno alla rota m, sono d'una medesima difficultà al contrappeso che move essa rota m, e sieno situate dove si voglino, pure che sieno equidistanti al centro della rota che le move.

Perché il perpendiculare di r è più propinquo la metà al polo n che non è m, r vole 2 tanti più peso che m a volere stare pari.

Ma guarda che questa regola non ti ingannassi nel calculare i pesi, perché la rota che solo adopera co' sua pesi intorno a' sua poli in se medesima semplice, fa altro effetto che quella che adopera ne' sua stremi contra altre rote, ferme sopra altri poli, come nel settimo delle mia matematiche si dimostra; 41

Three wheels (the last one toothed) driving other smaller ones, with:

2 - a b c 2 - 2; 2 r - n m 1; m 4 4

All the wheels below that are placed around wheel m are of one and the same difficulty for the counterweight that moves that wheel m, wherever they be situated, provided they are equidistant from the center of the wheel that moves them.

Because the perpendicular of r is by half nearer to the pole n than m is, r requires twice as much weight as m in order to stand level.

But take care that this rule does not deceive you in calculating the weights, for the wheel that acts only with its weights around its own poles, simple in itself, produces a different effect from one that acts at its extremities against other wheels fixed on other poles, as is shown in the seventh [book] of my mathematics; 41

A counterweight turning a train of wheels

Wheels set equidistant around a toothed wheel m; r needs twice m's weight to balance

Physics & Mechanics Machines & Devices

Three linked wheels are drawn, the largest toothed and labelled m, with a hanging counterweight. The note argues that all the smaller wheels set around m offer the same resistance to the counterweight turning m, provided they are equidistant from its center; because r's perpendicular lies half as far from pole n, r requires twice m's weight to balance. Leonardo warns that a wheel acting alone on its own pole behaves differently from one meshing at its rim against wheels on other poles, referring to the seventh book of his 'mathematics.'

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Equidistant wheels and the doubled weight at r

All the wheels placed around wheel m offer the same difficulty to the counterweight that moves m, wherever situated, so long as they are equidistant from the center that moves them. Because r's perpendicular is half as near to pole n as m's, r requires twice as much weight as m to stand level.

Toothed wheel m with counterweight

The lowest of the three drawn wheels is toothed and labelled m, carrying a hanging counterweight at its rim. It illustrates the warning that a simple wheel acting on its own pole produces a different effect from one that meshes at its extremities against other wheels fixed on other poles.

Reader's Edition — described with AI from the e-Leo transcription.