CHAPTER FOUR
APOLLONIUS' PROEMS AND EUTOCIUS' COMMENTARY
IV 1 The Proems of Apollonius' Conica
Four of the eight books of Apollonius of Perga's Conica are extant in Greek, together with a Commentary by Eutocius of Ascalon. 122 Apollonius is a great mathematician, admired but also criticized by Pappus, who has also preserved information about the books of the Conica lost in Greek and about other lost works, both in the Collectio and in the Commentary on Elements X. 123 The final version of the Conica (in instalments) presumably has to be dated not too long after 200 BCE. Of great interest in our present context are Apollonius' proems to the individual books; these are in the form of letters to the dedicatees: Eudemus, the first teacher of the Epicurean philosopher Philonides,124 for books 1-111, a certain Attalus for books IV-VII (and VIII, I presume) after Eudemus' death. 125
122 Ed. Heiberg (1891-3), including Eutocius' Commentary (for which see Ch. IV 2). Books V-VII are extant in Arabic (book VIII being lost), and are now acccessible in Toomer (1990) which replaces Halleius (1710); note that Toomer's remark at (1990) l.vii that Halleius failed to print the Arabic text is a slip. The Conica belongs with the domain of Analysis, see above Ch. II. On their mathematical contents see Heath (1921) 2.154-75, Toomer (1970) 181-8, and Toomer (1990) l.xiv-v and xxviii-xxxiv esp. for books V-VII. For Apollo nius' dates see Toomer (1970) 179-80 and (1990) l.xi-xii: his son and messen ger was an adult, and Philonides is allowed to see the work (proem to book II; see below). 123 Reprinted from Hultsch (1876-8)-including the mathematical lem mas on the extant books-and Woepke (1856) at Heiberg (1891-3) 2.102-66, together with fragments cited from Eutocius' Commentaries on Archimedes, from Philoponus, Prod us, Hypsicles (i.e. Elem. XIV), Marin us, Ptolemy, Hippolytus, Ptolemaeus Chennus, and the Fragmentum Bobiense. The section derived from Woepke (1856) at 2.120-4 Heiberg should be corrected on the basis of Thomson ( 1930). 124 Pap. Here. 1044 Fr. 25.4-5, see Gallo (1980) 33 and 36. 125 The proems to books I-II and IV-VII are translated and discussed by Heath (1896) lviii-lxxxvi, i.e. those to books I-II and IV are translated from Heiberg's Greek text, that to book V from Nix's Latin (1889), and those to books VI-VII from Halleius' Latin ( 171 0). I have consulted Heath's transl. for books II and IV, that of Toomer ( 1990) for the proems to books V-VIII, as well as Toomer's new translation of the proem to book I at ( 1990) l.xiv-xv. On the APOLLONIUS AND EUTOCIUS 37
In the introduction to book I (1.2-4 Heiberg) he writes to Eudemus that he sends him the revised version of this book, and that the others will follow as soon as they have been revised too. Drafts of books I-VIII already exist: the work was written at the request of the geometer Naucrates when this colleague was staying with Apollonius at Alexandria, and Apollonius (or so he claims) hurriedly (!) jotted down a preliminary version of the whole treatise in eight books and gave this to his friend, who had to leave Alexandria. This remark about an earlier dedicatee (?) and to hurried composition sounds a bit like a topos, but this is by the way. Copies of this preliminary version of books I and II had since also been given to other friends. Eudemus should therefore not be surprised when encountering versions different from the present corrected and polished, i.e. an authorized edition. The preliminary version therefore cannot have been very rudimentary. Revision must have been a matter of style, of adding prefaces, etc. Apollonius then meticulously informs Eudemus (and so the general public) beforehand about the contents of the whole treatise. Books I to IV deal with the elementary instruction; next, the contents of each book are announced and summarized (m::ptEXEt ... 'tO 7tponov [scil., ~t~A.iov], ... 'tO Se{m:pov, etc.) The first book deals with matters that have been already treated by others (no names given), but according to the author it does so in a fuller and more general i.e. systematic way. Nevertheless, what we have here is a reference to the history of the subject. The specific utility (yEvtK'i)v l((lt avayK:aiav xpciav) of the contents of book II is emphasized. Book III contains a great number of theorems which are useful (xpflcrq.ta) for the synthesis of solid loci etc. 126 Most of these are new, that is to say have been found by Apollonius himself, or so he claims. Greek mathematicians are not averse to the idea of progress! Euclid's treatment of a specific issue, for instance, is said to be both incomplete and unsystematic-an affirmation which produced an interesting controversy.127 The contents of book IV, he tells us, are for the most part original. final section of the proem to book I see Friderici (1911) 43-4. 126 Cf. above, n. 26 and text thereto; below, p. 123, complementary note 26. 127 Cf. above n. 19, below text ton. 131, and n. 139 and text thereto. Toomer (1970) 180 and 186-7 argues that Apollonius in books I-IV for the most part systematized the findings of his predecessors, among whom Archimedes (whom he fails to mention by name in the preface to book I). So this part of his work would be of the same nature as most of Euclid's Elements.