Customer Reviews

The Geometry of Rene Descartes (Dover Books on Mathematics)

5 star:		(3)
4 star:		(2)
3 star:		(0)
2 star:		(0)
1 star:		(1)

 

 

Using the locii problems investigated by Apollonius, Descartes employs the rules of his "method" in this treatise on geometry. By approaching geometrical problems with algebraic processes and vice versa, he manages to create point coordinate geometry. This work drastically changed the way in which we view conic sections as well as the very process of analytic inquiry. The math is mostly straightforward and more familiar to the reader than the works of the ancient mathematicians. It is not neccesary to have studied much previous mathematical works to gain a basic comprehension of Descartes' solutions. Attempting at most times to maintain the simple and straighforward presentation advocated by his method, Descartes will give you most of the basics that you need to understand the rest of the work. However, close concentration must be paid for the math to mean anything. It is easy to skip a step in a proof and find yourself completely lost. Given the proper patience, this work is invaluable for anyone who wants to see the origins of our method of thought today. Fascinating both as a mathematical treatise and as a perfect trial run for anyone wanting to follow the cartesian method of learning.

This book contains a facsimile of the original version which runs nearly page for page with the English version. This is a true mathematical masterpiece. This was the supposed beginning of analytical Geometry(although it is now known that this was not true). It's a great book to work through that should be accessable to a high school student with some Geometry background. A Fantastic Book!

This is a cheaply printed book with unquestionable value for any mathematician or liberal arts major. It has facing-page French with an English translation (which is fairly strict and literal), with great diagrams. It's difficult to read, and that's okay, because when other mathematicians at the time read it they thought it was impossible and that Descartes was insane.

Descartes, apart from this edition, is brilliant and worth the time to study.

This book is a bad choice for anyone not familiar with Euclidian and Apollonian geometry. Period. If you're not, you should find some commentary on Cartesian geometry instead of tackling this monster head-on.

Descartes' Geometrie, published in 1637, is possibly the second most influential book in the history of mathematics, after Euclid's Elements. In it, Descartes introduces analytic geometry, that is, the connection between geometry and algebra, in order to use algebra to solve geometric locus problems. The book's influence is reflected in the fact that Descartes' notation is far closer to the notation used today than anyone else's from that period (for example, Fermat or Viete). But it is not a book for someone who is not already knowledgeable. As Descartes himself wrote, (as translated and quoted in a footnote on page 10), "In my previous writings I have tried to make my meaning clear to everybody; but I doubt if this treatise will be read by anyone not familiar with the books on geometry, so I have thought it superfluous to repeat demonstrations contained in them." The 17th century mathematicians who read La Geometrie found it difficult, both because it was in French and because of its uncompromising exposition. Thus the book only became understood after the publication in 1649 of a Latin translation with commentaries by Frans van Schooten.

For the modern reader the book is a fascinating record of the state of mathematics in the early 17th century, and the format, with Descartes' 17th century French (readily readable to someone with some knowledge of modern French) opposite the reliable English translation, is very helpful for understanding what Descartes does in the book. How can it not have five stars?

This is a great read both historically and for the student of math.

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.

The problems discussed in this book are very remote from our
present day geometry. The English translation uses a smaller font
than the French original, which makes the book even harder to read.