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For a long time, the self-contained nature of Newton's Principia has intrigued me. At a glance, it looks as if Euclid's Elements would be the only required reading for understanding his arguments. But it's still pretty tough going. Are there any lesser-known works from his time or before his time (I'm not looking for something to explain him to me, I want to read him and understand his arguments from first principles, the way he wrote them) that might have been obvious points of reference for people at the time he published, that simply haven't survived the way Euclid has?

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A lot of the content of Newton's Principia was in response to the physical theories espoused by Descartes, so Descartes would be a good place to start. –  Unreasonable Sin Jan 17 '12 at 18:39
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Debes intellegere linguam latinam, amice care! –  Georges Elencwajg Jan 17 '12 at 22:55
    
gratias i opus iustus unus magis latinam discere. –  ixtmixilix Jan 18 '12 at 19:47
    
You might be interested in Spivak's book Physics for Mathematicians which discusses some passages from the Principia. (I know that's not what you want, but you still might like this book.) –  littleO Dec 31 '13 at 6:55
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up vote 4 down vote accepted

Pappus.

Newton knew the book of Pappus and other books of ancient Greeks. In his last years he even believed that the Greeks had a knowledge that did not survived, according to some statements in the book of Pappus.

from Hellenica.

Superficially, it looks like Newton knew his works on geometry very thoroughly, or could guess most of what was in it. Newton does mention Pappus a bit. And besides all that, the diagrams in Pappus and the diagrams in the Principia just look similar.

Which is what made me look for the connection. I happened to be browsing through Book IV of Pappus's works, the section dealing with plane geometry and thought, "wow, that sure looks a lot like Newton's stuff."

But no, Newton avidly read Pappus, according to a paper linking Newton to Pappus:

Newton belonged to a mathematical community in which the distinction between theorems and problems was articulated according to criteria sanctioned by the venerated Greek tradition. Most notably in the work of the late Hellenistic compiler Pappus entitled Mathematical Collection which appeared in 1588 in Latin translation Newton – who avidly read this dusty work – could find a distinction between ‘theorematic and problematic analysis’. In the 7th book of the Collection there was a description of works (mostly lost and no longer available to early modern mathematicians) which – according to Pappus – had to do with a heuristic method followed by the ancient geometers. The opening of the seventh book is often quoted. It is an obscure passage whose decoding was top in the agenda of early modern European mathematicians, convinced as they were that here lay hidden the key to the method of discovery of the ancients. Given the importance this passage had for Newton, it is worth quoting at length:

(long quote by Pappus follows; pdf here)

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You should start with Euclid's Elements, then Apollonius' Conics' and Archimedes' Works. All these works have been edited by T.L.Heath. Kepler and Galileo would follow. Some first year physics and mathematics texts would help. And lab work in first year college physics course to appreciate the experimental philosophy. Watch all 52 episodes of The Mechanical Universe.

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See Newton Revisited: An excursion in Euclidean geometry

by Greg Markowsky

http://arxiv.org/abs/0910.4807

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