enunciations in their present order. So completely was this notion received, that editions of Euclid, 60 called, contained only enunciations ; all that contained demonstrations were said to be Euclid with the commentary of Theon, Campanus, Zam- bertus, or some other. Also, when the enunciations were given in Greek and Latin, and the demon- strations in Latin only, this was said to constitute an edition of Euclid in the original Greek, which has occasioned a host of bibliographical errors. We have already seen that Theon did edit Euclid, and that manuscripts have described this editorship in a manner calculated to lead to the mistake: tut Proclus, who not only describes Euclid as rci fiaKaKwrepou SeiKvifieua to7s %jj.ttpo<tQ^u eis dvc- yKTovs dTToSei'l^ts dvayayuv, and comments on the very demonstrations which we now have, as on those of Euclid, is an unanswerable witness ; the order of the propositions themselves, connected as it is with the mode of demonstration, is another ; and finally, Theon himself, in stating, as before noted, that a particular part of a certain demonstra- tion is his own, states as distinctly that the rest is not. Sir Henry Savile (the founder of the Savilian chairs at Oxford), in the lectures[1] on Euclid with which he opened his own chair of geometry before he resigned it to Briggs (who is said to have taken up the course where his founder left off, at book i. prop. 9), notes that much discussion had taken place on the subject, and gives three opinions. The first, that of quidam stulti et perridiculi, above discussed : the second, that of Peter Ramus, who held the whole to be absolutely due to Theon, propositions as well as demonstrations, false, quis negatl the third, that of Buteo of Dauphiny, a geometer of merit, who attributes the whole to Euclid, quae opinio aut vera est, aut veritati eerie jiroxima. It is not useless to remind the classical student of these things : the middle ages may be called the "ages of faith " in their views of criticism. Whatever was written was received without exa- mination ; and the endorsement of an obscure scho- liast, which was perhaps the mere whim of a tran- scriber, was allowed to rank with the clearest as- sertions of the commentators and scholars who had before them more works, now lost, written by the contemporaries of the author in question, than there were letters in the stupid sentence which was allowed to overbalance their testimony. From such practices we are now, it may well be hoped, finally delivered : but the time is not yet come when refutation of " the scholiast " may be safely abandoned.
All the works that have been attributed to Euclid are as follows:
1. Srotxf'a, the Elements, in 13 books, with a 14th and 15th added by Hypsicles.
2. AeSojueca, the Data, which has a preface by Marinas of Naples.
3. Eia-aywyiii 'ApfjLoviic^, a Treatise on Music; and 4. KaraTOfiil Kavovos, the Division of the Scale : one of these works, most likely the former, must be rejected. Proclus says that Euclid wrote Kara. fiovaiKrv (TToix^iwcreis.
5. ^aipSfiem, the Appearances (of the heavens). Pappus mentions them.
6. 'OiTTiKd, on Optics ; and 7. KaroTrrpiKd, on Catoptrics. Proclus mentions both.
The preceding works are in existence ; the fol- lowing are either lost, or do not remain in the original Greek.
8. liepX Aiaipeffewv fiiSKlov, On Divisions. Pro- clus (I. c.) There is a translation from the Arabic, with the name of Mohammed of Bagdad attached, which has been suspected of being a translation of the book of Euclid : of this we shall see more.
9. KauiKuv Pi§la S', Four hooks on Conic Sec- tions. Pappus (lib. vii. praef.) affirms that Euclid wrote four books on conies, which Apollonius en- larged, adding four others. Archimedes refers to ilie elements of conic sections in a manner which shews that he could not be mentioning the new work of his contemporary Apollonius (which it is most likely he never saw). Euclid may possibly have written on conic sections ; but it is impossible that the first four books of Apollonius (see his life) can have been those of Euclid.
10. Tlopi(Tp.dTu>v ^L^Kiay' , Three boohs of Porisms. These are mentioned by Proclus and by Pappus (/. c), the latter of whom gives a description which is so corrupt as to be unintelligible.
11. ToTvtav 'ETTtTreSwi/ fii§ia j8', Two hooks on Plane Loci. Pappus mentions these, but not Eu- tocius, as Fabricius affirms. {Comment, in Apoll. lib. i. lemm.)
12. ToTTwi/ irpos 'ETTKpdvetav Pt€la 0, men- tioned by Pappus. What these Toitoi irpos 'Ettl- (pdveiav, or Loci ad Siiperfidem, were, neither Pappus nor Eutocius inform us ; the latter says they derive their name from their own tSiOTTjs, which there is no reason to doubt. We suspect that the books and the meaning of the title were as much lost in the time of Eutocius as now.
13. riept ^^vBapiccv, On Fallacies. On this work Proclus says, " He gave methods of clear judgment (Sioport/cTjs (ppovfin^ws) the possession of which enables us to exercise those who are begin- ning geometry in the detection of false reasonings, and to keep them free from delusion. And the book which gives us this preparation is called ^GvZapiiav, in which he enumerates the species of fallacies, and exercises the mental faculty on each species by all manner of theorems. He places truth side by side with falsehood, and connects the confutation of falsehood with experience." It thus appears that Euclid did not intend his Ele- ments to be studied without any preparation, but tliat he had himself prepared a treatise on fallacious reasoning, to precede, or at least to accompany, the Elements. The loss of this book is much to be regretted, particularly on account of the explana- tions of the course adopted in the Elements which it cannot but have contained.
We now proceed to some bibliographical account of the writings of Euclid. In every case in which we do not mention the source of information, it is to be presumed that we take it from the edition itself.
The first, or editio princeps, of the Elamenis is that printed by Erhard Ratdolt at Venice in 1482, Ijlack letter, folio. It is the Latin of the fifteen books of the Elements, from Adelard, with the commentary of Campanus following the demon- strations. It has no title, but, after a short intro- duction by the printer, opens thus : "Preclarissimus liber elementorum Euclidis perspicacissimi : in artem geometric incipit qua foelicissime : Punctus est cujus ps nn est," &c. Ratdolt states in the
introduction that the difficulty of printing diagrams
- ↑ Praelectiones tresdecim in principium elementorum Euclidis; Oxonii habitae M.DC.XX. Oxoniae, 1621.
