Apollonius of Perga: Treatise on Conic Sections

by Apollonius of Perga, Thomas Little Heath

Despite being generally unknown to the greats of contemporary mathematics, Apollonius’s Conics is said by Chasles to contain ‘the most interesting properties of conics’. Written by one of the great pioneers of geometry, this scarce text contains a comprehensive account of the mathematics of conics, and as such constitutes a valuable to addition to the libraries of serious mathematicians and historians alike. Apollonius of Perga was a Greek geometer and astronomer, most famous for his work pertaining to conic sections and whose methodology and terminology influenced such intellectual giants as Ptolemy, Johannes Kepler, Francesco Maurolico, Isaac Newton, and René Descartes. This rare text is proudly republished here with an introductory biography of the author.

Genres: Classics, Mathematics, Science, Nonfiction, Philosophy

424 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

[Saranya ⋆☕︎ ˖ [hibernating]]

I need to ace in this

[David Sarkies · Rating 3 out of 5]

More Ancient Greek Maths
28 June 2025

I remember a section in my maths book from year 12 called Conic Sections, and that was the chapter that was after calculus, so it my mind at the time, anything that comes after calculus must be hard. Of course, years later, I discovered why conic sections came after calculus and that was because calculus is the maths behind measuring curves and integral calculus involves obtaining the area of a curved shape. So yeah, I now understand why conic sections came after calculus.

Mind you, while this work involves dealing with cones (or conics, which I suspect means pertaining to cones, or conic shapes) it has nothing to do with calculus. The reason behind this is because calculus didn’t exist (and wouldn’t exist until Isaac Newton, though the Arabs were probably playing around with something). What this work does, and is similar to a lot of the other works that was in the volume on Ancient Greek maths is that is uses ratios to measure sections of cones, and how to work out these measurements.

So, the guy who wrote this book actually wrote it in response to another book on cones, and when he sent it to somebody to review it, they thought that he was simply being a smartarse, namely because the person whom he was criticising happened to be an expert in his field. I would say it would sort of like Stephen Hawking (the late) publishing a paper, and me coming along and correcting it (though, to be honest, in the age of the internet we have a lot of people doing just that). Though, a part of publishing a paper is actually sending it to a group of people to review your paper and is part and parcel of getting a paper published because, well, that is what a peer-reviewed article is all about.

Also, as some academics have suggested, people citing your paper is the academic equivalent of likes (well not really, more like sharing your content) but as my Dad pointed out one of the easiest ways to get lots and lots of citations is to write rubbish. Mind you, writing crap with the intention of getting citations probably won’t do all that much for your academic career, but then again we also live in an age where people post stuff on line with in intention of creating controversy and becoming incredibly famous because of that. It’s sort of like Libs of Tik Tok – she is basically posting rage bait because she knows that it boosts her profile. Mind you, the last time I posted rage bait was loudly declaring to the film society that 2001 A Space Odyssey was the most boring piece of crap I have ever watched in my life. I was excommunicated, though twenty-five years later I still hold to that opinion.

So, I’ve spoken about rage-bait, Libs of Tik Tok, and 2001 A Space Odyssey and little about this book. Well, that’s probably because there isn’t all that much to say about this book. It’s basically 200 pages of proofs regarding cones. Then again, I wish I could sit down and write 200 pages of proofs (or other things because as much as I like maths, writing proofs is sort of a little beyond me – and the proofs that are worth anything are really really hard). Then again, it’s basically like the nobility from the early modern era, who had so much time on their hands that they ended up studying stuff. Well, not all of them, but some of them did. This was no doubt the same thing in the Ancient World, though we should remember that the Eastern Mediterranean was actually much more philosophically and scientifically astute – the Romans to the west were just a bunch of boys playing soldiers.