The Geometry of Rene Descartes Paperback – 17 Mar 2003
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From the Back Cover
This is an unabridged republication of the definitive English translation of one of the very greatest classics of science. Originally published in 1637, it has been characterized as "the greatest single step ever made in the progress of the exact sciences" (John Stuart Mill); as a book which "remade geometry and made modern geometry possible" (Eric Temple Bell). It "revolutionized the entire conception of the object of mathematical science" (J. Hadamard).With this volume Descartes founded modern analytical geometry. Reducing geometry to algebra and analysis and, conversely, showing that analysis may be translated into geometry, it opened the way for modern mathematics. Descartes was the first to classify curves systematically and to demonstrate algebraic solution of geometric curves. His geometric interpretation of negative quantities led to later concepts of continuity and the theory of function. The third book contains important contributions to the theory of equations.This edition contains the entire definitive Smith-Latham translation of Descartes' three books: Problems the Construction of which Requires Only Straight Lines and Circles; On the Nature of Curved Lines; and On the Construction of Solid and Supersolid Problems. Interleaved page by page with the translation is a complete facsimile of the 1637 French text, together with all Descartes' original illustrations; 248 footnotes explain the text and add further bibliography.
Translated by David E. Smith and Marcia L. Latham.
About the Author
Ren? Descartes, known as the Father of Modern Philosophy and inventor of Cartesian coordinates, was a seventeenth century French philosopher, mathematician, and writer. Descartes made significant contributions to the fields of philosophy and mathematics, and was a proponent of rationalism, believing strongly in fact and deductive reasoning. Working in both French and Latin, he wrote many mathematical and philosophical works including The World, Discourse on a Method, Meditations on First Philosophy, and Passions of the Soul. He is perhaps best known for originating the statement I think, therefore I am. --This text refers to the Hardcover edition.
Most helpful customer reviews on Amazon.com
His mathematics is kind of obsolete; but, that's disappointing! His ideas of coordinate geometry were obsolete as of the writing of his own book. He realized the two dimensional grid idea only after thinking about going to three dimensions, and he was thinking about solving three dimensional curves, not just plotting third degree equations. And it's the solving of mathematical problems by means of properties of curves that led him to analytic geometry.
Most non-mathematician students get a little geometry in high school and that's it. This is generally plane geometry. Even this plane geometry is watered down compared to what the Greeks did. There's none of the geometric algebra. The greeks solved equations and did basic arithmetic operations by means of this geometric algebra. This is Rene Descartes starting point including finding roots of sqaree roots. The Greeks derived conics from trying to solve the three Delian problems - trisecting an angle, duplicating a cube, and squaring the circle. They came up with various curves and studied them to a certain extent. Rene Descartes solves and goes far beyond what the Greeks did there. His invention of analytic geometry evolved out of solving these problems. Rene Descartes little book here solves the past, and heralds the future.
Descartes uses lines to find intersections of these special curves. These intersections are roots of equations. Descartes basically generalizes the old Greek geometric algebra of finding roots to higher curves. He finds correspondences to properties of the theory of equations and solving these problems - of what's a linear curve, what's a space curve and so on. We're talking about spirals(Archimedes favorite curve), quadratrixes, conchoids, and cissoids.
His treatments of systems of equations are also far ahead of what the average community college degree student will see. And he relates it to his theory of curves as well.
There's new constructions, insights on almost every page.
The Dover book I bought and looks like everyone else has bought in the 20th and 21st centuries uses scholarly commentary from an Eugene Smith. And that's a good thing. Without the footnotes explaining things, one couldn't solve anything, much less see where/when Rene ever actually discovered analytic geometry. He also seems to reference some obscure late 1600 work commentary that gets into all the findings of Descartes more than this little book - elliptic and hyperbolic concoids and other geometric theorems. I need to learn French and buy that gem in a haystack book. That sounds like a great book.
Reading this, and having read Galileo's "Two new Systems" book, there was plenty more that the Greeks could have done geometrically; but, they did not. It's proof that there was a dark ages(there's dark ages denyers, just like moon landing denyers)
More interesting is if you read a modern text analyzing DeCartes to see where he struggled. Such as with complex roots.
Yes there are way better instructional texts.
My one issue with this book, well two actually is the facsimile of the orginal could be better. And each page faces each other, so you can see the translation and the original. One thing they did not do is copy the diagrams from the original. It is minor, but I like working the problems, and I wish they had them in the translation as well. It would help with the alignment and make it a bit more user friendly.
For the price it is a bargain.
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