Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/102

From Wikisource
Jump to navigation Jump to search
This page has been validated.
56
Mathematical Principles
Book I

founded on a falſe ſuppoſition. For thoſe ultimate ratio's with which quantities vaniſh, are not truly the ratio's of ultimate quantities, but limits towards which the ratio's of quantities, decreasing without limit, do always converge; and to which they approach nearer than by any given difference, but never go beyond, nor in effect attain to, till the quantities are diminiſhed in infinitum. This thing will appear more evident in quantities infinitely great. If two quantities, whoſe difference is given, be augmented in infinitum, the ultimate ratio of these quantities will be given, to wit, the ratio of equality; but it does not from thence follow, that the ultimate or greateſt quantities themſelves, whoſe ratio that is, will be given. Therefore if in what follows, for the ſake of being more eaſily understood, I ſhould happen to mention quantities as leaſt, or evaneſcent, or ultimate; you are not to ſuppoſe that quantities of any determinate magnitude are meant, but ſuch as are conceiv'd to be always diminiſhed without end.