Hypatia's Work on Apollonius' Conics

References

In the 10th century Suda Lexicon, Hesychius' 6th century material was summarized: "She wrote a commentary on Diophantus, the Canon of Astronomy and a commentary on the conics of Apollonius".

From The Primary Souces for the Life and Work of Hypatia of Alexandria, by Michael A.B. Deakin

The most ambitious attempt to recover what traces of Hypatia's influence still remain in extant mathematical writing is Knorr's (op. cit. supra); this endeavour has been criticised by Cameron (op. cit. supra). In particular, Knorr suggests that traces of Hypatia's hand may be found in other parts of Theon's Commentary on the Almagest, and also in the surviving text of Apollonius' Conics.

From Hypatia's Mathematics: A Review of Recent Studies, by Edith Prentice Mendez

"She wrote. . .a commentary on the Conics of Apollonius." In addition to Hypatia, Pappus, Serenus, and Eutocius in the Greek tradition wrote on the Conics. Eutocius' new edition of Books I - IV became standard in the West. The first seven books, based on Eutocius and an older edition, were translated into Arabic and edited by the Banu Musa; only the eighth was lost completely [52, xvi-xviii]. The lemmas in Pappus's Collection refer to all eight books and reconstructions of Apollonius' last book have been attempted, beginning with a medieval one in Arabic by ibn al-Haytham. Hogendijk concludes that Book VIII contained geometric constructions which solved problems concerning conics. [18, 43-47].

The commentary by Eutocius does not credit Hypatia, or name any earlier commentator except Pappus, but Knorr, seeing style characteristics of textual symmetry which are reminiscent of the commentaries on Books III and IV of the Almagest, thinks it possible that some of the work of Eutocius could have come from Hypatia [24, 765-770]. Cameron and Long, without any text to ground their assertion, dismiss Hypatia's work with the comment, "like her work on Diophantus, Hypatia's commentary on Apollonius mainly consisted of simple exegesis" [4, 49].

Hypatia's work on Apollonius' Conics

Discussion of the above
p. 182-191 on Apollonius' Conics from Fauvel and Gray's The History of Mathematics, A Reader.
Discuss p. 185 definitions 1 thru 4 in depth.
Homework p. 190 Book II: Proposition 29.
Go over this proof at the begining of the next class.