The Mathematical Principles of Natural Philosophy, Book I: Of the Motion of Bodies
Book I
OF THE MOTION OF BODIES.
SECTION I.
Of the method of first and last ratios of quantities, by the help whereof we demonstrate the propositions that follow.
Lemma I
Quantities, and the ratios of quantities, which in any finite time converge continually to equality, and before the end of that time approach nearer the one to the other than by any given difference, become ultimately equal.
If you deny it, suppose them to be ultimately unequal, and let D be their ultimate difference. Therefore they cannot approach nearer to equality than by that given difference D; which is against the supposition.