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Ideas for '', 'On the Essence of Human Freedom' and 'Principia Mathematica'

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2 ideas

6. Mathematics / A. Nature of Mathematics / 2. Geometry

18079	Newton developed a kinematic approach to geometry [Newton, by Kitcher]
	Full Idea: The reduction of the problems of tangents, normals, curvature, maxima and minima were effected by Newton's kinematic approach to geometry.
	From: report of Isaac Newton (Principia Mathematica [1687]) by Philip Kitcher - The Nature of Mathematical Knowledge 10.1
	A reaction: This approach apparently contrasts with that of Leibniz.

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits

18082	Quantities and ratios which continually converge will eventually become equal [Newton]
	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.
	From: Isaac Newton (Principia Mathematica [1687], Lemma 1), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.2
	A reaction: Kitcher observes that, although Newton relies on infinitesimals, this quotation expresses something close to the later idea of a 'limit'.