K(i5ov troix^iuv fit§ia te', Rome, 1545, 8vo., printed by Antonius Bladus Asulanus, containing enimciations only, without demonstrations or dia- grams, edited by Angelas Cujanus, and dedicated to Antonius Altovitus. We happen to possess a little volume agreeing in every particular with this description, except only that it is in Italian, being " I quindici libri degli elementi di Euclide, di Greco tradotti in lingua Thoscana." Here is another in- stance in which the editor believed he had given the whole of Euclid in giving the enunciations. From this edition another Greek text, Florence, 1 545, was invented by another mistake. All the Greek and Latin editions which Fabricius, Mur- hard, &c., attribute to Dasj^podius (Conrad Rauch- fuss), only give the enunciations in Greek. The same may be said of Scheubel's edition of tha first six books (Basle, folio, 1550), which nevertheless professes in the title-page to give Eudid, Gr. Lat. There is an anonymous complete Greek and Latin text, London, printed by William Jones, lb"20, Avhich has ihhieen books in the title-page, but contains only six in all copies that we have seen : it is attributed to the celebrated mathematician Rriggs.
The Oxford edition, folio, 1703, published by David Gregory, with the title Eu«:AeiSou to aw^o- /jLeva, took its rise in the collection of manuscripts bequeathed by Sir Henry Savile to the University, and was a part of Dr. Edward Beniard's plan (see his life in the Penny Cyclopaedia) for a large republication of the Greek geometers. His inten- tion was, that the first four volumes should contain Euclid, ApoUonius, Archimedes, Pappus, and Heron ; and, by an undesigned coincidence, the University has actually published the first three volumes in the order intended : we hope Pappus and Heron will be edited in time. In this Oxford text a large addi- tional supply of manuscripts was consulted, but various readings are not given. It contains all the leputed works of Euclid, the Latin work of Mo- hammed of Bagdad, above mentioned as attributed by some to Euclid, and a Latin fragment De Levi et Ponderoso, which is wholly unworthy of notice, but which some had given to Euclid. The Latin of this edition is mostly from Commandine, with the help of Henry Savile 's papers, which seem to liave nearly amounted to a complete version. As an edition of the whole of Euclid's works, this stands alone, there being no other in Greek. Peyrard, who examined it with every desire to find errors of the press, produced only at the rate of ten for each book of the Elements.
The Paris edition was produced under singular circumstances. It is Greek, Latin, and French, in 3 vols. 4to. Paris, 1814-16-18, and it contains fifteen books of the Elements and the Data ; for, though professing to give a complete edition of Euclid, Peyrard would not admit anything else to be genuine. F. Peyrard had published a translation of some books of Euclid in 1804, and a complete translation of Archimedes. It was his in- tention to publish the texts of Euclid, ApoUonius, and Archimedes ; and beginning to examine the manuscripts of Euclid in the Royal Library at Paris, 23 in number, he found one, marked No. 190, which had the appearance of being written in the ninth century, and which seemed more complete and trustworthy than any single known manu- script. This document was part of the plunder sent from Rome to Paris by Napoleon, and had belonged to the Vatican Library. When restitu- tion was enforced by the allied armies in 1815, a special pennission was given to Peyrard to retain this manuscript till he had finished the edition on which he was then engaged, and of which one vo- lume had already appeared. Peyrard was a wor- shipper of this manuscript. No. 190, and had a con- tempt for all previous editions of Euclid. He gives at the end of each volume a comparison of the Paris edition with the Oxford, specifying what has been derived from the Vatican manuscript, and making a selection from the various readings of the other 22 manuscripts which were before him. This edition is therefore very valuable ; but it is veiy incorrectly printed: and the editor's strictures upon his predecessors seem to us to require the support of better scholarship than he could bring to bear upon the subject. (See the Dublin Review^ No. 22, Nov. 1841, p. 341, &c.)
The Berlin edition, Greek only, one volume in two parts, octavo, Berlin, 1 826, is the work of E. F. August, and contains the thirteen books of the Elements, with various readings from Peymrd, and from three additional manuscripts at Munich (making altogether about 35 manuscripts consulted by the four editors). To the scholar who wants one edition of the Elements, we should decidedly recommend this, as bringing together all that has been done for the text of Euclid's greatest work.
We mention here, out of its place, The Elements of Euclid with dissertations, by James Williamson, B.D. 2 vols. 4to., Oxford, 1781, and London, 1788. This is an English translation of thirteen books, made in the closest manner from the Oxford edi- tion, being Euclid word for word, with the addi- tional words required by the English idiom given in Italics. This edition is valuable, and not very scarce : the dissertations may be read with profit by a modern algebraist, if it be true that equal and opposite errors destroy one another.
Camerer and Hauber published the first six books in Greek and Latin, with good notes, Ber- lin, 8vo. 1824.
We believe we have mentioned all the Greek texts of the Elements ; the liberal supply with which the bibliographers have furnished the world, and which Fabricius and others have perpetuated, is, as we have no doubt, a series of mistakes arising for the most part out of the belief about Euclid the enunciator and Theon the demonstrator, which we have described. Of Latin editions, which must have a slight notice, we have the six books by Orontius Finoeus, Paiis, 1536, folio (Fabr., Murhard) ; the same by Joachim Camerarius, Leipsic, 1549, 8vo (Fabr., Murhard); the fifteen books by Steph. Gracilis, Paris, 1557, 4to. (Fabr., who calls it Gr. Lat., Murhard); the fifteen books of Franc, de Foix de Candale(Flussa8 Candalla), who adds a sixteenth, Paris, 1566, folio, and promises a seventeenth and eighteenth, which he gave in a subsequent edition,
Paris, 1578, folio (Fabr., Murhard) ; Frederic
classical bibliographers are trustworthy as to writers with whom a scholar is more conversant than with Euclid. It is much that a Fabricius should enter upon Euclid or Archimedes at all, and he may well be excused for simply copying from bibliographical lists. But the mathematical bibliographers, Heilbronner, Murhard, &c., are inexcusable for copying from, and perpetuating, the almost unavoidable mistakes of Fabricius.
