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I'm searching for a good edition of Philosophiae Naturalis Principia Mathematica of Isaac Newton in English. Which edition of the Principia can you suggest me? If it's possible, cheap and similar to original with the original proofs of Isaac Newton.

I'm sorry for my poor English, I'm just learning it.

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    $\begingroup$ I would recommend you skip it entirely. $\endgroup$ – Asaf Karagila Mar 28 '18 at 23:49
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    $\begingroup$ It's not what you asked but is related (and interesting): Arnold's Newton's principia read 300 years later $\endgroup$ – Billy Rubina Mar 29 '18 at 5:27
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    $\begingroup$ @Asaf Can you elaborate why? $\endgroup$ – lcv Mar 29 '18 at 9:01
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    $\begingroup$ @lcv: There's often this feeling—especially by amateur or beginning mathematicians—of "reading the masters". But mathematics is not philosophy. Nor it is physics. It is different from anything else. It's not new points of view vs. old ones, or ultimately personal opinions. In mathematics, it's the same material, chewed and regurgitated from modern points of view, in modern language. Reading "classics" should be done, but only after you have the knowledge from the modern point of view. For historical perspective. Not in order to learn from it. $\endgroup$ – Asaf Karagila Mar 29 '18 at 9:07
  • $\begingroup$ @AsafKaragila : What makes you think that gmorkk is trying to learn mathematics from the Principia? I interpreted gmorkk as saying that he's just learning English. Also the Principia contains a lot of physics, not just mathematics. $\endgroup$ – Timothy Chow Mar 29 '18 at 15:44
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The difficulty is not in the language that Newton uses, but in the incredibly original viewpoint that he takes. Get a good translation, by all means, but you'll also need the help of a good guide.

One of the best such guides I ever found was S. Chandrasekhar's fantastic "Newton's Principia for the Common Reader", Oxford University Press, 1995. (Don't be fooled by the title, though, apparently Chandrasekhar had a much higher opinion of the 'common reader' than is warranted by the available evidence.)

It doesn't cover the entire Principia, but mainly the parts that lead to Newton's results on gravity. What Chandrasekhar does is explain Newton's propositions, translate them into modern notation/language and show you a 'modern' proof, and then, with that knowledge of what is going on, he goes back to Newton's argument and shows the reader how Newton's approach works. Along the way, he comments on how Newton's ideas harked back to Euclid and, at the same time, anticipated concepts in mechanics that would not be developed until many years later.

It's an amazing, edifying work by one of the greatest astrophysicists of the 20th century.

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    $\begingroup$ Rather than say “with that knowledge of what is going on”, it would be helpful to say “with that idea of what might have gone on”. See G.E. Smith’s review for some of Chandrasekhar’s erroneous corrections of Newton at adsabs.harvard.edu/full/1996JHA....27..353S $\endgroup$ – Matt F. Mar 28 '18 at 20:10
  • $\begingroup$ @MattF.: Thanks. I'll have a look at this reference. It has been a few years since I went through Chandrasekhar's book, but I remember it as a very enlightening experience. $\endgroup$ – Robert Bryant Mar 28 '18 at 20:37
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    $\begingroup$ Chaddrasekhar is not "an edition of Newton". It is only his own digest and only of the first volume. $\endgroup$ – Alexandre Eremenko Mar 28 '18 at 21:47
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I would recommend this 1999 version by Cohen & Whitman:

The Principia: The Authoritative Translation and Guide: Mathematical Principles of Natural Philosophy

This edition has comments that help you understand the original. It is also quite cheap.

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    $\begingroup$ This is an excellent edition indeed, the best that I know. With very detailed and professional commentaries on everything. $\endgroup$ – Alexandre Eremenko Mar 28 '18 at 21:49
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Here is a free copy offered by its author, (edit: the translator, Ian Bruce),

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    $\begingroup$ Ah, for a moment I thought the free copy was offered by Newton himself. $\endgroup$ – Lucia Mar 28 '18 at 17:51
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This 2003 edition by Densmore & Donahue has the following book review

Makes the great adventure of Principia available not only to modern scholars of history of science, but also to nonspecialist undergraduate students of humanities. It moves carefully from Newton's definitions and axioms through the essential propositions, as Newton himself identified them, to the establishment of universal gravitation and elliptical orbits. The guidebook unfolds what is implicit in Newton's words as he himself would have filled in the steps and completes the argument in ways that are authentic and not anachronistic, exactly following Newton's thinking rather than substituting tools of modern calculus or the formulations of modern physics. It is Newton in his own terms. This is a wonderful book. ―Richard S. Westfall

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