more from Isaac Newton

Single Idea 18082

[catalogued under 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits]

Full Idea

Quantities and the ratios of quantities, which in any finite time converge continually to equality, and, before the end of that time approach nearer to one another by any given difference become ultimately equal.

Gist of Idea

Quantities and ratios which continually converge will eventually become equal


Isaac Newton (Principia Mathematica [1687], Lemma 1), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.2

Book Reference

Kitcher,Philip: 'The Nature of Mathematical Knowledge' [OUP 1984], p.238

A Reaction

Kitcher observes that, although Newton relies on infinitesimals, this quotation expresses something close to the later idea of a 'limit'.