All that we have left is a portion of a work entitled, Τῶν κατὰ μαθηματικὴν χρησίμων εἰς τὴν τοῦ Πλάτωνος ἀνάγνωσιν. The portion which now exists is in two books, one on arithmetic, and one on music : there was a third on astronomy, and a fourth περὶ τῆς ἐν κόσμῳ ἁρμονίας. The work on arithmetic is of the same character as that of NICOMACHUS; and as both these writers name Thrasyllus, and neither names the other, it may be supposed that the two were nearly contemporary. The book on music is on the simplest application of arithmetic.

Of these there are at least two sets, the second first printed by Buhle, in his edition, as emendatiora. Grotius is of opinion that the first are not the work of Theon, but of several hands : this he infers from their containing repetitions and contradictions, which is not a very safe pretmise for the conclusion. Kuster (Suidas, s. v.) attributes them, without reason given, rather to Theon the sophist. That they are unworthy of the astronomer, is true enough; but rejections made on such a ground are dangerous things. These scholia were printed in the Aldine * This Aldine edition, Venice, 1409, folio, is not a separate work, but part of what is frequently catalogued as Scriptores Astronomici Veteres, containing Julius Firmicus, Manilius, &c. as well as Aratus. edition of Aratus, in that of Valder's collection [PTOLEMAEUS, p. 573], in Morell's edition, Paris, 1559, 4to., in Fell's, Oxford, 1672, 8vo. and also in Buhle's. Halma, in his edition (Gr. Fr.) Paris, 1822, 4to, has given selections, which his critics have asserted to be very ill chosen. (Hoffman, Lexic. Bibliogr. vol. i. p. 233).

Of the manner in which Theon is asserted to have edited Euclid we have already said enough. [EUCLEIDES, pp. 63, b, 69, b>, 70, a.]

This is the great work of Theon, the commentary on the addressed to his son Epiphanius. But the Almagest has thirteen books, while Theon's commentary is marked as having only eleven. The commentary on the third book has not come down to us with the name of Theon, but with that of Nicolas Cabacillas; and those on the tenth and eleventh books are joined together. The commentary on the later books is obviously mutilated by time; for a circumstance connected with that on the fifth book, see PAPPUS. On this commentary, Delambre (who has given a full account of it, Hist. Astron. Ane. vol. ii. pp. 550-616) passes the following judgment : " Theon commences by announcing that he will not follow the example of ordinary commentators, who show themselves very learned on passages which offer no difficulty, and are silent upon all which would give trouble to understand or to explain. He has not always kept this promise; I have often referred for information, and I have only found Ptolemy's words faithfully copied or slightly modified. It is a paraphrase which may give some explanation of methods, but which really presents nothing which a little attention would not find in the text, none of those lost traditions, which must then have existed at the Observatory of Alexandria, nothing new upon the instruments or the method of using them. Theon seems to know no one but Ptolemy and to have read nothing but the Syntaxis ....... This commentary is not what could have been made then, nor even what could have been made now."

We have mentioned in the article PTOLEMAEUS all the editions of the commentary which accompany those of the text. The only separate edition (if it be right so to call it) is that of Halma, forming a continuation of the four volumes already mentioned in PTOLEMAEUS. It includes only the commentary on the first and second books (Gr. Fr.) in two volumes, quarto, Paris, 1821 and 1822.

Knowledge of this work is very recent, and as it involves a work of Ptolemy himself which we have not mentioned in its place, a few words of explanation will be necessary. It was long known that certain unpublished tables (as they were called) of Theon existed in manuscript : and there is in Fabricius and others a frequent confusion of these tables with the chronological table presently mentioned. Not but what accurate information might have been found. Kuster, speaking of an emendation of Suidas, who attributes to Theon a work εἰς τὸν Πτολεμαίου πρόχειρον κανόνα, says that Theon wrote a commentary on the canon of Ptolemy, which canon existed in manuscript in the Imperial library. Delambre found a manuscript in the Royal Library at Paris, which he has described (Hist. Astr. Anc. vol. ii. p. 616) under the head Θέωνος Ἀλεξανδρέως κάνονες πρόχειροι. Tables manuelles de Thén d'Alexandrie. This work was afterwards published by Halma, but under the title , in three parts, Paris, 1822, 1823, 1825, 4to. Having only very recently seen this last work, we have only as recently known that there is a distinct work of Ptolemy himself, the κάνονες πρόχειροι. Ptolemy's part is addressed to Syrus; Theon's to his son Epiphanius. The contents are, prolegomena, tables or latitude and longitude, and a collection of astronomical tables, somewhat more extensive than those in the syntaxis. The prolegomena are separately headed; one set is given to Ptolemy, another to Theon. But the tables themselves are headed Πτολεμαίου Θέωνος, καὶ Ὑπατίας πρόχειροι κάνονες. Dodwell had previously printed a fragment of the prolegomena in his , Oxford, 1684, 8vo.

The continuation of the regal canon [PTOLEMAEUS, p. 572] down to his own time is attributed to Theon. In the manual tables it is carried down to the fall of the Eastern empire with the heading Πτολεμαίου, Θέωνος, κ. τ. λ. A very full dissertation on this canon is to be found in an anonymous work " Observationes in Theonis Fastos Graecos priores." Amsterdam 1735, quarto.

The list of works attributed to Theon of Alexandria by Suidas is Μαθηματικά, Ἀριθμητικά, Περὶ σημείων καὶ σκοπῆς ὀρνέων καὶ τῆς τῶν κοπάκων φωνῆς, Περὶ τῆς τοῦ κυνὸς ἐπιτολῆς, Περὶ τῆς τοῦ Νείλου ἀναβάσεως, Εἰς τὸν Πτολεμαίου πρόχειρον κανόνα, εἰς τὸν μικρὸν Ἁστρολάβον ὑπόμνημα. In the last, Fabricius proposes to read ἀστρολόγον, taking the work to be a commentary on the collection of minor writers, which went by the name of the lesser Syntaxis.