Conics: Books I-IV
Apollonius of Perga
Books I-III translated by R. Catesby Taliaferro
Book IV translated by Michael N. Fried
Diagrams by William H. Donahue
7" x 10", 413 pages, diagrams, index and bibliography
Publication date July 2013.
For pricing and ordering information, see the ordering section below.
About this edition
For many years, only the first three books of the Conics were available in English translation. This situation was partly remedied in 1990 by the appearance of a translation of Books V-VII (from the Arabic); however, Book IV remained untranslated until Green Lion Press brought it out as a separate volume in 2002.
We have now at last restored Book IV to its rightful place, along with the other books whose Greek text has survived, in a single attractively priced volume, available in sewn softcover and hardcover library editions.
The translation of Books I-III is the same revised Taliaferro translation that was published separately by Green Lion Press in 1998 and subsequent editions. For the convenience of those who wish to continue to use the older edition, the pagination of that edition has been preserved in the present combined edition. A number of typographical errors in the older edition have been corrected. Harvey Flaumenhaft's fine introductory essay has been retained.
The translation of Book IV, by Michael N. Fried, is a newly laid out version of the text published by Green Lion Press in 2002. This book has a separate introduction by Fried and extensive explanatory footnotes.
About Apollonius and the Conics
Apollonius of Perga was born about 262 B.C.E. in Perga, on the southern coast of what is now Turkey. He flourished in Alexandria in the second half of the third century. He is known for this treatise on conic sections, as well as his correspondance with Archimedes.
The Conics of Apollonius (3rd Century BCE) is the culmination of the brilliant geometrical tradition of ancient Greece. With astonishing virtuosity, and with a storyteller's flair for thematic development, Apollonius leads the reader through the mysteries of these intriguing curved lines, treated as objects of pure mathematics. His work in turn provided a basis for the very differently conceived investigations of modern mathematicians and scientists such as Viète, Descartes, Kepler, Pascal, and Newton. Reading the Conics is an unparalleled adventure into the highest reaches of human intellectual achievement.
- For the first time: Conics I-IV in a single volume
- The only English translation of these four books from the Greek
- Comprehensive index for all four books.
- Includes introductory essays by Harvey Flaumenhaft and Michael N. Fried.
... One can therefore only welcome the appearance of the present translation of the first three books of Apollonius's Conics, which is based on Taliaferro's translation. Although the editors have occasionally reworked Taliaferro's English to a more readable style, they have shunned Heath's error of attempting to "improve" Apollonius's exposition, in which [Heath] combined as many as five propositions into one. Even when it is not a case of tampering as flagrant as this, the advantage of the present translation over that of Heath is marked. The following sample of the statement of Conics 1, 32 must suffice here.
Heath: If a straight line be drawn through the extremity of the diameter of any conic section parallel to the ordinates of that diameter, the straight line will touch the conic, and no other straight line can fall between it and the conic.
Taliaferro/Donahue: If a straight line is drawn through the vertex of a section of a cone, parallel to an ordinate, it touches the section and in the place between the section of the cone and the straight line another straight line will not fall.
Comparison with the Greek reveals the latter translation to be superior in all respects in which they differ, including the absence of modern algebraic symbolism.
[Diagrams] have been executed with the reader in mind to maintain the simplicity and clarity of those in Commandino's Renaissance edition, but redrawn when necessary to avoid, for example, every diameter appearing to be an axis. They have also redone certain diagrams in perspective, and the result is quite useful. Another welcome feature for the reader interested in the mathematics or the history is that some of the more helpful parts of Eutocius's commentary on the Conics have been translated and reprinted as footnotes on the relevant pages.
— J. L. Berggren
[Apollonius's Conics] is one of the greatest scientific books of antiquity.
[Apollonius was a] giant, not simply as compared with men of antiquity, but even with men of all times. ... [T]he ingenuity that enabled him to discover so much with imperfect tools [i.e., lacking the arts of analytic and projective geometry] is truly admirable...such achievements pass our imagination, they are almost weird.
— George Sarton,
from An Introduction to the History of Science and A History of Science
If we want to read for ourselves authors like Kepler and Newton, or if we want to understand the significance of the Cartesian mathematics that has shaped the world we live in and shapes our minds as well — either way, whether to understand the past in its own terms or to understand the present as a deliberate transformation of the past — we need to study Apollonius.
— Harvey Flaumenhaft
Dean, St. John's College, Annapolis
Below are links to PDF versions of the first definitions and propositions of Book I and Proposition 54 of Book I. Part of Michael Fried's introduction to Book IV is also available.
You may need to open these PDF documents in Adobe Reader or an equivalent program.
- First definitions and propositions of Book I
- Proposition 54 of Book I
- Excerpt of Michael Fried's Introduction to Book IV