Among the last-mentioned race geometry mado no actual progress, though many of the works of the Greek writers were translated, and Euclid among the rest. There are several Arabic versions, the most perfect of which is that of Othman of Damascus, who augmented the usual imperfect translations by means of a Greek manuscript which he saw at Rome. D'llerbelot (at tho words Aklides and ()elides) states that the Orientals believe Euclid to have been a native of Tyre, and also that they frequently gave his name to the eidetic° which he taught. The same author gives the names of the Arabio versions, one of which, that of Nasir eddin, the most celebrated of all, was printed at the Medicean press at Rome in 1594. The astronomer Thabet ben Korrah was one of the translators, or rather, perhaps, revised the translation of Honein ben Ishak, who died A.D. 873. There is a manuscript In the Bodleian Library, purporting to be the transla tion of the latter edited by the former.
The first translation of Euclid Into Latin, of which tho date can be tolerably well fixed, is that of Atheism), or Adelard; a monk of Bath, who lived under Henry I. (about A.D. 1150). We have given [Can es:We) a summary of authorities to show that Campanus, supposed to be another translator of Euclid, lived after this period; but we are inclined to believe that this translation (so called) of Campanus (printed 1482), is in fact that of Atbelard, with a commcutary by Campanus.
There is a considerable number of Greek manuscripts of the Ele , manta, for which see Febricius and Heilbronner. There is no account of the manuscripts which they consulted by the earlier Latin trans later, (from the Greek), nor by Gregory. It appears however that several, if not many, of the manuscripts arc entitled ElocXEsSou CPTOIXEICCY /30Am is ?K IVY Oecoros crilyoucruoy, front which it was inferred that the compilation of the elements was the work of Theon, from the mate rials left by Euclid. It is certain that Tbeon, in his commentary on the Almageet, speaks of his edition (te800es) of Euclid, and mentions that the part of the last proposition which relates to the sectors was added by himself. On looking at that proposition, it is found that the demonstration relative to the sectors comes after the 57rEp Act Beitat,' with which Euclid usually ends his propositions. And Alexander, the commentator on Aristotle, who lived before Theon, calls that the 'fourth' proposition of the tenth book which is the fifth' in all the manuscripts. We can then distinctly trace the band of Theon as a commentator, and may suspect that he performed the duty of a revis ing editor to the work of Euclid as it now appears; but there is not the smallest reason to suppose that Theon actually digested the work into the form which it now has. These remarks relative to the claims of Theon were first made by Sir Henry Savile, who opened the chair of geometry which he founded at Oxford by thirteen lectures on the fundamental parts of the first book of Euclid, which were delivered in 1620, and published in 1621.
We now give a short summary of the early editions of Euclid, which have appeared in Greek or Latin. It is unnecessary to specify the common editions of Simsou, Playfair, &a, which confine them selves to the first six books, and the eleventh and twelfth, and are generally known.
L Editions of the whole of Euclid's works :-1. An imperfect Latin edition, by Bartholomew Zamberti, Venice, 1505. 2. A Latin edition, printed at Basel, marked Bullet° apud Johannem Hervagium,' 1537, 1546, and 1558. 3. Greek edition, with Scholia, Basel, 1539. But the principal edition of all the works of Euclid is that published by the Oxford press in 1703, under the care of David Gregory, then Savilian professor.
IL Greek editions of the Elements only :-1. An edition curl Simonis Gryntei, Basel, 1530. 2. Another, with the commentary of Proclue, 'Batlike) apud Johannem Hervaglum,' 1533. 3. Greek and Italian, by Angeli Cajaui, Rome, 1545. 4. At Strasburg, 1559. 5. Greek and Latin, with Scholia, by Conrad Dasypoditre, Strasburg, 1564.
III. Latin editions of the Elements only :-1. That of Campanua, the first Euclid printed, Ratdolt, Venice, 1482. 2. A reprint of the preceding, marked Vincenthe, anno e:ilutis 1491.' 3. An edition con taining the text and comment of Campanue, from the Arabio ; also the text and comment of Zamberti, from the Greek ; Paris, Henry Stephens, 1505 ; and again in 1516. This edition is very commodious for a general comparisoo of the Greek and Arabic. 4. Edition of Lucas de Burge, Venice, 1509, according to Murhard, and 1489 according to Heilbrooner. who appears to be the authority for the existence of this edition, and is doubted (with reason, we think) by Harles, in hie Fabri clue. 5. Edition of Stephen Gracilie, Paris, 1557, 1573, and 1578. The first edition of Clavius is that of Rome, 1574; of Commandine, Pesaro, 1572. [Ctaysus ; Coalman:1m.] IV. Earliest editions of the Elements in modern tongues :-English The Elements of Geometry of the most antient philosopher Euclid of Megara, &c.,' by H. Billingsley, with a preface by John Dee, London, 1570, and again in 1661. French-. Les quioza livres dee El6thents, &c., &e., Par D. Henrion, Mathematicum, First edition, Paris, 1565 ( ?); second, 1623, with various others. According to Fabriciva there was an edition by Peter Forcadel, in 1565. Get-man-`Die sechs ersten Bucher, ike.; by William Holtzman!), Augsburg, 1562. Scheubelius bad previously given the 7th, 8th, and 9th books in 1555. Italian ' Euclid° Megarense Philosophe, &c.,' per Nicole Tartalea, Venice, 1543. Dutch-' De see erste boecken Euclidis, &c.,' dor Jan Pieterazoon Dou, Amsterdam, 1603 (or 1606). Swedish-' De sex Forsta, by Marten Stromer, Upset, 1753. Spanish-By Joseph Saragoza, Valentin, 1673. Murhard (compared with Fabricius) is the authority foe all of these, except the first.