Solving problems by algebra in late antiquity: New evidence from an unpublished fragment of Theon’s commentary on the Almagest Jean Christianidis Ioanna Skoura University of Athens University of Athens Dpt. of History & Philosophy of Science Dpt. of History & Philosophy of Science Centre Alexandre Koyré, Paris iskoura3@gmail.com ichrist@phs.uoa.gr I. Introduction Theon of Alexandria wrote in the second half of the fourth century AD a full-scale ἵὁmmeὀtary ὁὀ ἢtὁlemy’s Almagest. Of this commentary, originally composed in thirteen books, corresponding to the books of the Almagest itself, most parts have been preserved. What is lost is the entire book XI, while, with regard to book V and the last books of the work there are lacunae in the transmitted text. Furthermore book VII and portions of other books are preserved only in a late Byzantine recension. As Adolph Rome has explained, in the prolegomena to his edition (Rome 1931, xxi ff.), the direἵt maὀusἵript traditiὁὀ ὁf Theὁὀ’s commentary has three branches: one is formed by the early ninth century manuscript Laur. Plut. 28.18, “le maὀusἵrit le plus fidèle” as Rὁme says (1λγ1, xxiii), and it is available only for books I–IV, already published by him (1936; 1943), and VI; a second ἴraὀἵh traὀsmits alsὁ a ‘geὀuiὀe’ text, possibly not coinciding with the one of the first branch, whose sole testimony for books VIII–X and XII–XIII (and of these, only partially) is Vat. gr. 1087; and a third branch is formed by a group of manuscripts – among which are Vat. gr. 198, Marc. gr. 310, Norimb. Cent. V, app. 8 – that carry the text of the aforementioned Byzantine recension; the printed version of the last manuscript is the Basel edition of 1538. 1 On the other hand, it is also known that at some time – most likely in Late Antiquity, but, at any rate, not later than the first half of the ninth century – portions of Theὁὀ’s main text were copied in some manuscripts in the margins of the Almagest. These portions have been transmitted as scholia appended to the text of the Almagest either in 1 Claudii Ptolemaei Magnae Constructionis id est Perfectae caelestium motuum pertractationis lib. XIII. Theonis Alexandrini in eosdem commentariorum lib. XI. Basileae, Apud Joannem Vvalderum, an. MDXXXVIII. SCIAMVS 14 (2013), 41-57