Kepler ’ s Area Law in the Principia : Filling in some details in Newton ’ s proof of Prop . 1 .
نویسنده
چکیده
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 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 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. Rigor merely sanctions the conquests of sound intuition, Jacques Hadamard
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