The Principia : Mathematical Principles of Natural Philosophy

Media:	Paperback
Author:	Isaac Newton, I. Bernard Cohen, Anne Whitman
Publisher:	University of California Press
Release date:	01 July, 1999
List price:	~~$45.00~~
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The Principia : Mathematical Principles of Natural Philosophy

Average rating: Stars

Wonderful overview, somewhat overwhelming.

This is a wonderful reference, but frankly, it was overwhelming for me. Let's just say that while the first two sections of this book were clear, informative, meticulously and thoroughly footnoted and annotated, the last section-- the actual translation-- proved beyond my abilities. I'd HIGHLY recommend a college-level geometry course before attempting to read the actual translation of Newton's revolutionary work.

Frankly, the combination of archaic verbiage (Cohen kept a number of obsolescent terms in translating from the original Latin), combined with a predominately narrative style (reading in an entire paragraph what can in modern mathematical symbology be articulated in a single line) combined with my lack of working analytic geometry enabled me to follow this seminal work conceptually, but not in detail. Other reviwers have suggested that a working knowledge of calculus and Newtonian physics is required. I disagree. To follow Newton's proofs in detail, it is Euclidean geometry that is required. Newton's Principia CONCEPTUALLY utilizes calculus, but the proofs themselves are Euclidean with the concept of "infinitisimally small" added to the equation. I have single- and multi-variable calculus, linear algebra, differential equations (first-, second-order, and partial), and graduate-level statistics under my belt. Junior high school geometry is insufficient to understand his work. So far, I am studying tensors, differential geometry/exterior calculus with respect to gravitation physics without too much difficuly. Geometry!

Otherwise, this book was wonderful. Section One is a thoroughly researched historical background. Social setting, scientific thought at the time, the controversies of the times, historical perspective, insights into Newton himself. Wonderfully referenced and annotated.

Section Two is a clear "How to Read" section-- discussing section by section of the Principia what the main concepts and issues are, even critiquing Newton's flaws and obvious attempts to fill in gaps or alter data when existing data were insufficient to his theories! Cohen even guides us step-by-step through some of the more important proofs in the Principia-- proofs that for the most part I followed, except for certain geometric assumptions that I had to assume were true.

My fascination has always been relativity... which I am working on understanding now. When finished, I may read a college-level text in analytic geometry, then come back to this. But I was impressed by the sheer breadth of conceptual material Newton covered. Certainly entitling his last book of The Principia "The System of the World" was justified.

The Principia : Mathematical Principles of Natural Philosophy - Isaac Newton, I. Bernard Cohen, Anne Whitman

A Masterful Translation

When not using this book as a reference, I often use it to exercise. Seriously, the translation from the original Latin has finally paid off. This book is an important part of science and history. One can get into the thought processes of Newton with this book. Having read other translations, I must say that this one is by far the best.

Isaac Newton, I. Bernard Cohen, Anne Whitman - The Principia : Mathematical Principles of Natural Philosophy

now there is a good english edition!

[...]
It was very difficult to grasp in Latin (I've had a try on it),
not that much easy in the Motte facsimile translation (I can assure it), and the Cajori-Motte edition was only half modernized and otherwise flawed.

This edition, sponsored by I.B. Cohen (the Latin editor) gives us a fresh, modern English translation of the text, and -almost as thick- a guide to using and reading this all-important book, which is not -as everybody is aware- an easy reader. One word of caution: Newton was, of course, (pace Leibnitz) the discoverer of calculus, but he doesn't use it here, but "more geometrico"
rigorous proofs, much in the style of that other genius of all ages, Archimedes. If you need help grasping the contents and impact of this work, then you must get some book like DENSMORE, D., Newton's Principia: The Central Argument (other auxiliary books are commented in the Guide potion of the book I'm reviewing).

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