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

56 founded on a fale uppoition. For thoe ultimate ratio's with which quantities vanih, 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 diminihed in infinitum. This thing will appear more evident in quantities infinitely great. If two quantities, whoe 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 greatet quantities themelves, whoe ratio that is, will be given. Therefore if in what follows, for the ake of being more eaily understood, I hould happen to mention quantities as leat, or evanecent, or ultimate; you are not to uppoe that quantities of any determinate magnitude are meant, but uch as are conceiv'd to be always diminihed without end.