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Kepler's Area Law in the Principia: Filling in some details in Newton's proof of Prop. 1

Michael Nauenberg
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Abstract

During the past 25 years there has been a controversy regarding the adequacy of Newton's proof of Prop. 1 in Book 1 of the {\it Principia}. This proposition is of central importance because its proof of Kepler's area law allowed Newton to introduce a geometric measure for time to solve problems in orbital dynamics in the {\it Principia}. It is shown here that the critics of Prop. 1 have misunderstood Newton's fundamental limit argument by neglecting to consider the justification for this limit which he gave in Lemma 3. We clarify the proof of Prop. 1 by filling in some details left out by Newton which show that his proof of this proposition was adequate and well grounded.

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Michael Nauenberg. 2001-12-05. Kepler's Area Law in the Principia: Filling in some details in Newton's proof of Prop. 1. https://arxiv.org/abs/math/0112048

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