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Codex Forster II — 124r

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© Victoria and Albert Museum, London

Ruote di carro, con:

S a t n

Se le rote saranno di pari altezza, il carro si moverà con certa qualità di forza. Ma se scambi le 2 dirieto in rote di più altezza, esso1 si moverà con più facilità. Ma se alle prime rote tu scambiassi quelle rote dinanzi in rote di più bassezza, in modo che medesimamente le rote dinanzi fussino basse e quelle dirieto alte, il primo moto si farà più difficile e più faticoso.

a t sia il centro delle rote equali, S t sia il centro delle rote sproporzionate crescendo quelle dirieto, che fa il moto facile; a n siano i centri delle rote abbassando quelle là dinanzi. E tanto fia più faticoso l'un moto che l'altro, quanto la maggiore cresce più che la prima, e quanto la minore diminuisce più che la prima.

Cart wheels, with:

S a t n

If the wheels are of equal height, the cart will move with a certain quality of force. But if you change the two rear ones for wheels of greater height, it will move more easily. But if, from those first wheels, you change the front wheels for wheels of lesser height, so that likewise the front wheels are low and the rear ones high, that first motion will become more difficult and more laborious.

Let a t be the centre of the equal wheels; let S t be the centre of the disproportionate wheels, enlarging the rear ones, which makes the motion easy; let a n be the centres when lowering those in front. And the one motion will be more laborious than the other by as much as the larger grows beyond the first, and as much as the smaller diminishes below the first.

Cart wheels and the ease of hauling

How unequal front and rear wheel heights change the effort of motion

Physics & Mechanics Machines & Devices

A cart is drawn schematically as two wheels on a common ground line, their centres labelled t and S (A). Leonardo reasons that with wheels of equal height the cart moves with a fixed force, but raising the two rear wheels makes it move more easily, while lowering the front wheels makes the motion harder and more laborious. He fixes the geometry with the letters a, t, S and n: a t marks the centres of equal wheels, S t the centres when the rear ones are enlarged, and a n the centres when the front ones are lowered.

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Wheel height and the effort of hauling

With equal wheels the cart moves with a certain force; enlarging the two rear wheels eases the motion, while lowering the front wheels makes it more laborious. Let a t be the centres of the equal wheels, S t the centres with enlarged rear wheels (easy motion), and a n the centres when the front wheels are lowered; the difference in effort grows as the larger wheel exceeds and the smaller falls short of the original.

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