Commandine's first edition of the fifteen books, with commentaries, Pisauri, 1572, fol. (Fabr., Murhard); tiie fifteen books of Christopher Clavius, with com- mentary, and Candalla's sixteenth book annexed, Korae, 1574, fol. (Fabr., Murhard); thirteen books, by Ambrosiiw Rhodius, Witteberg, 1609, 8vo. ( Fabr., Murh.) ; thirteen books by the Jesuit Claude Richard, Antwerp, 1645, folio (Murh.) ; twelve books by Horsley, Oxford, 1802. We have not thought it necessary to swell this article with the various reprints of these and the old Latin editions, nor with editions which, though called Elements of Euclid, have the demonstrations given in the edi- tor's own manner, as those of Maurolycus, Barrow, Cotes, &c., &c., nor with the editions contained in ancient courses of mathematics, such as those of Herigonius, Dechales, Schott, &c., &c., which ge- nerally gave a tolerably complete edition of the Elements. Commandine and Clavius are the pro- genitors of a large school of editors, among whom Robert Simson stands conspicuous.
We now proceed to English translations. We find in Tanner {Bibl. Brit. I lib. p. 149) the fol- lowing short statement : " Candish, Richardus, patria SufFolciensis, in linguam patriam transtulit Euclidis geometriara, lib. xv. Claruit[1] a.d. mdlvi. Bal. par. post. p. 111." Richard Candish is men- tioned elsewhere as a translator, but we are confi- dent that his translation was never published. Before 1570, all that had been published in Eng- lish was Robert Recorders PcUhway to Knowledge, 1551, containing enunciations only of the first four books, not in Euclid's order. Recorde considers demonstration to be the work of Theon. In 1570 appeared Henry Biilingsley's translation of the fif- teen books, with Candalla's sixteenth, London, folio. This book has a long preface by John Dee, the magician, whose picture is at the beginning : 60 that it has often been taken for Dee's transla- tion ; but he himself, in a list of his own works, ascribes it to Billingsley. The latter was a rich citizen, and was mayor (with knighthood) in 1591. We always had doubts whether he was the real translator, imagining that Dee had done the drud- gery at least. On looking into Anthony Wood's account of Billingsley {^Aih. Occon. in verb.) we find it stated (and also how the information was ob- tained) that he studied three years at Oxford be- fore he was apprenticed to a haberdasher, and there made acquaintance with an "eminent mathema- tician" called Whytehead, an Augustine friar. When the friar was "put to his shifts" by the dissolution of the monasteries, Billingsley received and maintained him, and learnt mathematics from hira. "When Whytehead died, he gave his scho- lar all his mathematical observations that he had made and collected, together with his notes on Euclid's Elements." This was the foundation of the translation, on which we have only to say that it was certainly made from the Greek, and not from any of the Arab ico- Latin versions, and is, for the time, a very good one. It was reprinted, Lon- don, folio, 1661. Billingsley died in 1606, at a great age.
Edmund Scarburgh (Oxford, folio, 1705) trans- lated six books, with copious annotations. We omit detailed mention of Whiston's translation of Tacquet, of Keill, Cunn, Stone, and other editors, whose editions have not much to do with the pro gress of opinion about the Elements.
Dr. Robert Simson published the first six, and eleventh and twelfth books, in two separate quarto editions. (Latin, Glasgow, 1 756. English, London, 1756.) The translation of the Data was added to the first octavo edition (called 2nd edition), Glas- gow, 1762 : other matters unconnected with Euclid have been added to the numerous succeeding edi- tions. With the exception of the editorial fancy about the perfect restoration of Euclid, there is lit- tle to object to in this celebrated edition. It might indeed have been expected that some notice would have been taken of various points on which Euclid has evidently fallen short of that formality of rigour which is tacitly claimed for him. We prefer this edition very much to many which have been fasliioned upon it, particularly to those which have introduced algebraical symbols into the de- monstrations in such a manner as to confuse geo- metrical demonstration with algebraical operation. Simson was first translated into German by J. A. Matthias, Magdeburgh, "1799, 8vo.
Professor John Playfair's Elements of Geometry contains the first six books of Euclid ; but the so- lid geometry is supplied from other sources. The first edition is of Edinburgh, 1795, octavo. This is a valuable edition, and the treatment of the fifth book, in particular, is much simplified by the aban- donment of Euclid's notation, though his definition and method are retained.
EucliiCs Elements of Plane Geometry, by John Walker, London, 1827, is a collection containing very excellent materials and valuable thoughts, but it is hardly an edition of EucHd.
We ought perhaps to mention W. Halifax, whose English Euclid Schweiger puts down as printed eight times in London, between 1685 and 1752. But we never met with it, and cannot find it in any sale[2] catalogue, nor in any English enumeration of editors. The Diagrams of Euclid's Elements by the Rev. W. Taylor, York, 1828, 8vo. size (part i. containing the first book; we do not know of any more), is a collection of lettered diagrams stamped in relief, for the use of the blind.
The earliest German print of Euclid is an edition by Scheubel or Scheybl, who published the seventh, eighth, and ninth books, Augsburgh, 1555, 4to. (Fabr. from his own copy) ; the first six books by W. Holtzmann, better known as Xylander, were published at Basle, 1562, folio (Fabr., Murhard, Kastner). In French we have Errard, nine books, Paris, 1598, 8vo. (Fabr.) ; fifteen books by Hen- rion, Paris, 1615 ((Fabr.), 1623 (Murh.), about 1 627 (necessary inference from the preface of the fifth edition, of 1649, in our possession). It is a close translation, with a comment. In Dutch, six books by J. Petersz Don, Leyden, 1 606 (Fabr.), 1608 (Murh.). Dou was translated into German, Amsterdam, 1634, 8vo. Also an anonymous trans- ladon of Clavius, 1663 (Murh.). In Italian, Tar- taglia's edition, Venice, 1543 and 1565. (Murh., Fabr.) In Spanish, by Joseph Saragoza, Valentia 1673, 4to. (Murh.) In Swedish, the first six books, by Martin Stromer, Upsal, 1753. (Murh.)
The remaining writings of Euclid are of small interest compared with the Elements, and a shorter account of them will be sufficient.
