Conics, Books I-III, by Apollonius of Perga

[this web page last updated 14 June 2005]

Apollonius of Perga

Conics, Books I-III

Translation by R. Catesby Taliaferro
Diagrams by William H. Donahue
Introduction by Harvey Flaumenhaft

Dana Densmore, Editor

7" x 10", 322 pages, diagrams, index and bibliography
Publication date 1998.

Also available in a deluxe set with Conics IV.

10% Discount
for Online Purchases

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, and Newton. Reading the Conics is an unparalleled adventure into the highest reaches of human intellectual achievement.

Ý A surprise bestseller for the Green Lion, now in its second printing!

This is a completely new edition of Taliaferro's translation of the first three books of Apollonius's Conics, with all new diagrams. It is the only English translation of these books other than Heath's out-of-print version which is a modernized retelling rather than a true translation.

Conics Books I--III were formerly included in Volume 11 of the Encyclopædia Britannica's Great Books of the Western World, but the work is no longer included in that series and has been out of print.

We made many corrections to the old edition's text, translation, and notes. The book features all new diagrams, an index, a bibliography, and an introductory essay by Harvey Flaumenhaft. Design and layout make it easy to read and work with, with diagrams repeated on every spread, adequate space for notes, and high quality paper to prevent show-through.

from the reviews

"...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
Mathematical Reviews,
Issue 2000d

"[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."

An Introduction to the History of Science

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 wellóeither way, whether to understand the past in its own terms or to understand the present as a deliberate transformation of the pastówe need to study Apollonius."

Apollonius of Perga was probably 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 best known for this treatise on conic sections.

Links to selections from the book, showing typesetting and layout in PDF format (This requires Adobe Acrobat Reader; Click here to download Acrobat PDF reader.)

View the first definitions and propositions of Book I.
View Proposition 54 of Book I.

Pp. xliii + 284. 7x10"

New! Now available in a deluxe set with Conics IV.

Sewn Softcover: List price $23.95 ISBN: 1-888009-05-5.

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Library Binding: List price $42.00 ISBN: 1-888009-04-7

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