The Reasons of Motive Forces

Book One,

pounds with the said axle E, they would require no more effort to pull than 50 pounds would at axle C. Likewise, the weight rises 8 times as much at axle C as it would if it were at axle E; so that a single man will exert as much force pulling a burden with this machine as eight men would do if each had an axle C. But also, if the eight men take one hour to lift their weight, the single man will take eight hours to lift his.

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THEOREM XVI.

The multiplication of motive forces is so great that Archimedes Archimedes of Syracuse (c. 287–212 BC), the Greek mathematician who famously claimed that with a long enough lever and a place to stand, he could move the world. said that if he had known where to support a machine, he would have moved the earth. Truly, the power of toothed wheels Gears with interlocking teeth used to transmit and multiply force. can be imagined to increase unto infinity, as I will demonstrate here by a machine—even though it cannot be put into practical use, for no burdens so great exist to be moved, and even if they did, one could not make the machine strong enough to support such a heavy load.

Let there be a wheel marked A, which shall have 96 teeth, and will be turned by a pinion A small gear (B) that meshes with a larger wheel (A) to create a mechanical advantage. B, which shall have 8 teeth; thus the said pinion will make 12 turns for every one turn of wheel A. Next, let there be on the axle of the said pinion a wheel C, also with 96 teeth, moved by another pinion D, also with 8 teeth; thus the said pinion D will also make 12 turns for every one turn of wheel C, so that the said pinion D will make 12 times 12 turns—which is 144—for every one turn of wheel A. Next, let there be another similar pinion E and a third wheel F with the same number of teeth; it will be necessary for the said pinion E to make 1,728 turns for every one turn of wheel A. After this, the pinion of the fourth wheel, marked G, will make 20,736 turns for every one turn of the said wheel A. Then pinion H will make 248,832 turns, and pinion L will make 2,985,984 turns for every one turn of the aforementioned wheel A.

The result is such that if a man turns the handle original: "manuevelle" — a crank or winch handle used to provide the initial manual input to the machine. 10,000 times every day, he would spend 298 and a half days just to make the said wheel A turn once. Likewise, if one places as many pounds of weight on the axle of wheel A as the number of turns the handle must make to complete one turn of wheel A, all this great burden will be equally balanced by a single pound hanging from the handle N. Thus, each wheel that is added will increase the force 12 times over, and with this addition of wheels, one could go unto infinity, following the proposition of Archimedes.