Trochilike

Trochilike is that mathematical art which demonstrates the properties of all circular motions, simple and compound. And because the fruit of it, commonly received, is in wheels, it has the name Trochilike, as one might say, Wheel Art. By this art a wheel may be given which shall turn once about in any assigned time. Two wheels may be given whose turnings about in one and the same time (or in equal times) shall have to one another any appointed proportion. By wheels a straight line may be described; likewise a spiral line in a plane, conic section lines, and other irregular lines may be drawn at pleasure. These and such like are principal conclusions of this art, and help forward many pleasant and profitable mechanical works:

Sawmills.

Mills that saw great and very long deal boards, with no man standing by. Such I have seen in Germany, and in the city of Prague, in the kingdom of Bohemia; coining mills, hand mills for grinding corn; and all manner of mills and wheelwork, moved by wind, smoke, water, weight, spring, man or beast. Take up in your hand Agricola's On the Nature of Metals, and then you shall perceive, in all mines, how great need there is of wheelwork. By wheels strange and incredible works are done, as will appear hereafter in other arts. A wonderful example of further possibility and of present benefit was seen in my time in a certain instrument: which its inventor and artificer had formerly sold for twenty talents of gold, and which had then, by misfortune, suffered some injury and hurt. One Ianellus of Cremona mended it, and presented it to Emperor Charles the Fifth. Hieronymus Cardanus can be my witness that in it there was one wheel which moved, and that at such a rate that in 7000 years only its own period would be completed. A thing almost incredible; but how far I keep within my bounds, very many men yet alive can tell.

Trochilike is the mathematical art that shows the properties of all circular motions, simple and compound. Because its fruit, as people commonly receive it, is in wheels, it takes the name Trochilike: what you might call wheel art. With this art you can set a wheel to make one full turn in any given time. You can also set two wheels so that their turns in the same time, or in equal times, stand in any proportion you choose. With wheels you can describe a straight line. You can also draw a spiral line on a flat plane, conic section lines, and other irregular lines, as you please. These and similar results are the main conclusions of this art, and they bring forward many pleasant and profitable mechanical works:

(Saw mills.)

Such as mills that saw great and very long deal boards, with no one standing by. I have seen such in Germany, and in the city of Prague, in the kingdom of Bohemia: coining mills, hand mills for grinding grain, and all manner of mills and wheelwork, driven by wind, smoke, water, weight, springs, people, or animals. Take Agricola's On the Nature of Metals in hand and you will see, in every mine, how great the need for wheelwork is. With wheels, strange and incredible works are done, as will appear in other arts later. A wonderful example of still greater possibility, and of present use, appeared in my time in a certain instrument. Its inventor and craftsman had sold it earlier for twenty talents of gold, and it had then suffered injury and damage by misfortune. Ianellus of Cremona repaired it and presented it to Emperor Charles V. Hieronymus Cardanus can be my witness that in it there was one wheel which turned at such a rate that in 7000 years only it would complete its own period. That is almost incredible. How much further it goes, I keep within my bounds: very many men, still alive, can tell.