Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/213

 I would not have you, Salviatus, measure our wits by the scale of yours: you, who use to be continually busied about the sublimest contemplations, esteem those notions frivolous and below you, which we think matters worthy of our profoundest thoughts: yet sometimes for our satisfaction do not disdain to stoop so low as to give way a little to our curiosity. As to the refutation of the last argument, taken from the extrusions of the diurnal vertigo, far less than what hath been said, would have given me satisfaction: and yet the things superfluously spoken, seemed to me so ingenious, that they have been so far from wearying my fancy, as that they have, by reason of their novelty, entertained me all along with so great delight, that I know not how to desire greater: Therefore, if you have any other speculation to add, produce it, for I, as to my own particular, shall gladly hearken to it.

I have always taken great delight in those things which I have had the fortune to discover, and next to that, which is my chief content, I find great pleasure in imparting them to some friends, that apprehendeth and seemeth to like them: Now, in regard you are one of these, slacking a little the reins of my ambition, which is much pleased when I shew my self more perspicacious, than some other that hath the reputation of a sharp sight, I will for a full and true measure of the past dispute, produce another fallacy of the Sectators of Ptolomey and Aristotle, which I take from the argument alledged.

See how greedily I wait to hear it.

We have hitherto over-passed, and granted to Ptolomey, as an effect indubitable, that the extrusion of the stone proceeding from the velocity of the wheel turn'd round upon its centre, the cause of the said extrusion encreaseth in proportion, as the velocity of the vertigo (or whirling) is augmented: from whence it was inferred, that the velocity of the Earth's vertigo being very much greater than that of any machin whatsoever, that we can make to turn round artificially; the extrusion of stones, of animals, &c. would consequently be far more violent. Now, I observe that there is a great fallacy in this discourse, in that we do compare these velocities indifferently and absolutely to one another. It's true, that if I compare the velocities of the same wheel, or of two wheels equal to each other, that which shall be more swiftly turn'd round, shall extrude the stone with greater violence; and the velocity encreasing, the cause of the projection shall likewise encrease: but when the velocity is augmented, not by encreasing the velocity in the same wheel, which would be by causing it to make a greater number of revolutions in equal times; but by encreasing the diameter, and making the wheel greater, so as that the conversion taking up the same time in the lesser wheel,