Conics Books I-IV

by Apollonius of Perga, Catesby R. Taliaferro (Translator), Michael N. Fried (Translator)

A single volume that replaces the previous two-volume edition, Conics Books I-III and Conics Book IV, both by Apollonius of Perga.

Genres: Mathematics, Science, Nonfiction

413 pages, Paperback

First published January 1, 201

About the author

born circa 240 BC
died circa 190 BC

https://en.wikipedia.org/wiki/Apollon...

Reviews

[Orhan Pelinkovic · Rating 4 out of 5]

Conics, or conic sections, are when taking cross-sections of a cone or when a plane intersects a cone. Now depending on a different angle a particular cone is intersected we uncover various curved shapes and figures, such as circles, ellipses, parabolas, and hyperbolas. Understanding the properties of various conic sections enable us to better comprehend the quantifiable things of nature. Essentially, space-time as we know it is curved, planets revolve in an elliptical orbit, and the DNA, the fundamental component of life, spirals into a coil-shaped structure. Hence, there is more curvature in nature than the uncommon straight lines and sharp edges. Nevertheless, Apollonius utilizes Euclidean geometry to demonstrate his propositions of the conic sections, thus, employing man-made geometry to demonstrate a more nature-like geometry.

The Conics: Books I-IV (c.200BCE) were written in Alexandria, Egypt by a Greek geometrician and astronomer Apollonius of Perga (c.240BCE–190BCE). The English translation I have read is impeccable and the layout of the pages with numerous geometrical illustrations and expressions leave enough room for notes.

This is a wonderful book and I look forward to reading next La Géométrie (1637) in which Rene Descartes interprets Euclid's and Apollonius' geometrical language and theorems only to translate them into easier to follow algebraic expressions.

[Tyler · Rating 5 out of 5]

I took a break from reading for a little bit, but when I returned 5 or so months later, I found that I could recall most propositions from the first two books. Remarkably, On Conics sticks with you, and reading mathematical propositions is like riding a bicycle, you never really forget.

All jokes aside, this is a terribly difficult book if you are really trying to understand it well. And in my opinion, Friedman's Book IV translation was leagues better than Taliaferro's. The edition of Taliaferro I have is in the 'Great Books' edition, editor in chief Mortimer J. Adler. Don't get this one. Absolutely riddled with errors starting in book two and onward, and it actually interfered with me understanding the material tremendously.

I do have to say, though, it is very well constructed. The entire thing is well done, and Apollonius' logic does lapse at times. To such an extent that Eutocius' commentary is literally necessary to understanding certain propositions in book III and Friedman's commentary is necessary to understanding a proposition in IV (LOL!). As you can see, mathematical logic is improved upon as time goes on, with errors happening as they may. This document is not easy, and is a signal of great intelligence if you can push through it. Remarkably, if you have the capacity to understand everything presented well, you can pretty much get through most mathematical/logical proofs published today. It prepares you for rigorous, thorough thinking. And it shows you how it all comes together.

The first three books are about the harmonic ratio (I. 34), the fourth book is just a solidification of many of the proofs in the first and second through reductio ad absurdum.

The three and four line locus commentaries are among the best explication of the material I've ever seen, it's too bad Taliaferro's brilliance is masked by his and Adler's inability to notice simple clerical errors along the way. In spite of this, the first three books reads almost like Apollonius set out to prove the harmonic ratio works externally, then prove it works inversely, then with a conjunction of various proofs from Books I and II he proceeds to define certain proportional ratios of a hyperbola do NOT change no matter where or how the slice of the three-dimensional figure is procured.

A wonderful book, prepare to rack your brain :) At times, very intense, almost Archimedean. I'm going to read the other books as well.

[Jackson Snyder · Rating 4 out of 5]

So many cool ideas in this book. The propositions are difficult but that’s not his fault, that’s just how conics are. This book is laid out in such a comprehensive way that makes it clear Apollonius cared about the reader and wanted to ensure they were given the tools to do conics themselves. Great stuff, wish I understood it better.

[Brody Moran · Rating 4 out of 5]

It’s only really good if you’re into math history. But Apollonius goes hard.