The Reasons of Motive Forces

Book One

A detailed technical engraving shows a vertical mechanical hoist system designed for heavy lifting. The entire apparatus sits within a tall, narrow wooden frame made of thick vertical beams and multiple horizontal cross-axles. In the upper-left quadrant, a man in seventeenth-century attire, including a doublet, breeches, and a hat, stands on a wooden platform. He pushes a horizontal lever attached to the topmost axle to begin the mechanical process. The machine functions through a complex gear train of ten horizontal axles. It uses a series of large gear wheels and small pinions to achieve significant mechanical advantage. Key components of the gear sequence are labeled with letters. E is a large gear wheel on the fourth axle from the top. G is a gear wheel on the fifth axle. F is a gear wheel on the sixth axle. D is a gear wheel on the seventh axle. C is a gear wheel on the eighth axle. B is a small pinion gear on the ninth axle that drives the final wheel. A is a large, spoked gear wheel on the tenth and lowest axle. This lowest axle serves as a winding drum or capstan. A thick rope coils around this drum and descends into a dark, excavated pit. At the end of the rope, a large, heavy boulder is secured by a harness and hook, being lifted from the ground. The terrain surrounding the machine is rocky and uneven.

THEOREM XVI.

The multiplication of motive forces is so great that Archimedes Archimedes of Syracuse (c. 287–212 BC) was a Greek mathematician. He 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 These are gears with interlocking teeth used to transmit and increase 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...