When one reads Newton's Principia Mathematica, one is immediately aware of the complexity of the synthetic geometry that he uses to prove his propositions. This I understand because all of the necessary calculus is being described in geometric language. Fortunately for us lesser mortals, the mathematician-astrophysicist Chandrasekhar has written a book that rephrases Newton's arguments in the language of modern-day calculus. However, if we stick to Newton's way of doing things, how can we improve the rigor of his synthetic-geometric arguments?
On the geometric arguments used in Newton's *Principia Mathematica Naturalis Philosophae*
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calculus
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math-history
proof-writing
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0Maybe you could give some examples from Newton? Synthetic descriptions of plane geometry after Hilbert have been pretty successful, also for non-Euclidean planar, but I'm not sure how that helps you. – 2012-10-21