A Dictionary of Greek and Roman biography and mythology. By various writers. Ed. by William Smith. Illustrated by numerous engravings on wood.

i70 EUCLEIDES. EUCLEIDES.
enunciations in their present order. So completely The preceding works are in existence; the fol.
was this notion received, that editions of Euclid, lowing are either lost, or do not remain in the
so called, contained only enunciations; all that original Greek.
contained demonstrations were said to be Euclid 8. Hiepl AtaLpeaecov'8Aov, On Divisions. Prowith the commentary of Theon, Campanus, Zam- clus (1. c.) There is a translation from the Arabic,
bertus, or some other. Also, when the enunciations with the name of Mohammed of Bagdad attached,
were given in Greek and Latin, and the demon- which has been suspected of being a translation of
strations in Latin only, this was said to constitute the book of Euclid: of this we shall see more.
an edition of Euclid in the original Greek, which 9. KWVoKOcV,BlAkla 8', Four books on Conic Sechas occasioned a host of bibliographical errors. We tions. Pappus (lib. vii. prae/:) affirms that Euclid
have already seen that Theon did edit Euclid, and wrote four books on conics, which Apollonius enthat manuscripts have described this editorship larged, adding four others. Archimedes refers to
in a manner calculated to lead to the mistake: the elements of conic sections in a manner which
but Proclus, who not only describes Euclid as da shews that he could not be mentioning the new
UCahaaicJrepov 8ettcvrSCeva'ro?s`urpoaooev elrs dve- work of his contemporary Apollonius (which it is
e'YKUTovs &CrooeteSLS dvayCaycv, and comments on most likely he never saw). Euclid may possibly
the very demonstrations which we now have, as have written on conic sections; but it is impossible
on those of Euclid, is an unanswerable witness; that the first four books of APOLLONIUS (see his
the order of the propositions themselves, connected life) can have been those of Euclid.
as it is with the mode of demonstration, is another; 10. IHoptatocdowv jBt3Aa y', Thlree booksofPorisms.
and finally, Theon himself, in stating, as before These are mentioned by Proclus and by Pappus
noted, that a particular part of a certain demonstra- (1. c.), the latter of whom gives a description which
tion is his own, states as distinctly that the rest is is so corrupt as to be unintelligible.
not. Sir Henry Savile (the founder of the Savilian 11. Tor'v'ETrL7re&ov fA'a', Two books on
chairs at Oxford), in the lectures* on Euclid with Plane Loci. Pappus mentions these, but not Euwhich he opened his own chair of geometry before tocius, as Fabricius affirms. (Commaent. in Apoll.
he resigned it to Briggs (who is said to have taken lib. i. lemnr.)
up the course where his founder left off, at book i. 12. Tchrwv 7rpos'EIrLcpveLav re kaa /', menprop. 9), notes that much discussion had taken tioned by Pappus. What these TdIroL 7rpbs'ErLplace on the subject, and gives three opinions. pavera'v, or Loci ad Superficiem, were, neither
The first. that of quidam stulti et perridiculi, above Pappus nor Eutocius inform us; the latter says
discussed: the second, that of Peter Ramus, who they derive their name from their own i8IT7)s,
held the whole to be absolutely due to Theon, which there is no reason to doubt. We suspect
propositions as well as demonstrations, false, quis that the books and the meaning of the title were
negat? the third,: that of Buteo of Dauphiny, a as much lost in the time of Eutocius as now.
geometer of merit, who attributes the whole to 13. nlepl TevSapoev, On Fallacies. On this
Euclid, quae opinio act vera est, ant veritati certe work Proclus says, "He gave methods of clear
proxima. It is not useless to remind the classical judgment (Btopar'ucjrs povfrcewts) the possession of
student of these things:: the middle ages may be which enables us to exercise those who are begincalled the "ages of faith" in their views of criticism. ning geometry in the detection of false reasonings,
Whatever was written was received without exa- and to keep them free from delusion. And the
mination; and the endorsement of an obscure scho- book which gives us this preparation is called
liast, which was perhaps the mere whim of a tran-'evsapiwv, in which he enumerates the species of
scriber, was allowed to rank with the clearest as- fallacies, and exercises the mental faculty on each
sertions of the commentators and scholars who had species by all manner of theorems. He places
before them more works, now lost, written by the truth side by side with falsehood, and connects
contemporaries of' the author in question, than the confutation of falsehood with experience." It
there were letters in the stupid sentence which thus appears that Euclid did not intend his Elewas allowed to overbalance their testimony. From ments to be studied without any preparation, but
such practices we are now, it may well be hoped, that he had himself prepared a treatise on fallacious
finally delivered: but the time is not yet come reasoning, to precede, or at'least to accompany, the
when refutation of " the scholiast " may be safely Elements. The loss of this book is much to be
abandoned. regretted, particularly on account of the explanaAll the works that have been attributed to tions of the course adopted'in the Elements which
Euclid are as follows: it cannot but have contained.
1. VoTXE'a, the Elements, in 13 books, with a We now proceed to some bibliographical account
14th and 15th added by Hi'PSICLES.' of the writings of-Euclid. In every case in which
2. Aeso/eva, the Data,'which has a preface by we do not mention the source of information, it is
Mlarinus of Naples. to be presumed that we take it from the edition
3. Eiaaoyaw?'Aptxoetcm4, a Treatise on Aiztsic; itself.
and 4. Kar'aTop7) Kaovos, the Division'of the Scale: The first, or editio princeps, of the Elements is
one of these works, most likely the former, must that printed by Erhard Ratdolt at Venice in 1482,
be rejected. Proclus says that Euclid wrote KaTa black letter, folio. It is: the Latin of the fifteen
pooarK?'v o'rolxeLaorels. books of the Elements, from Adelard, with thde
5. clawdpeva, the Appearances (of the heavens). commentary of Campanus following the demon-:
Pappus mentions them. strations. It has no title, but, after a short intro6.'OrsKiad, on Optics; and 7. Ka'o7rv'plKd, on duction by the printer, opens thus: "Preclarissimus
Catoptrics. Proclus mentions both.' liber elementorum Euclidis perspicacissimi: in
artem geometrie incipit qua foelicissime: Punctus:i'Praelectiones tresdecimn inprincipiunm elementorum est cujus ps nii est," &c. Ratdolt states in the:
Euclidis; Oxonii habitae M.DC.XX. Oxoniae, 1621. introduction that the difficulty of printing diagrams