The first Greek edition of the Data is Eu/cAcfSou hi^ojxfva^ Sec, by Claudius Hardy, Pans, 1625, 4to., Gr. Lat, with the preface of Marinus prefixed. Murhard speaks of a second edition, Paris, 1695, 4to. Dasypodius had previously published them in Latin, Strasburg, 1570. (Fabr.) We have al- ready spoken of Zamberti's Latin, and of the Greek of Gregory and Peyrard. There is also Euclidis Datorum Liber by Horsley, Oxford, 1803, 8vo.
The Phaenomena is an astronomical work, con- taining 25 geometrical propositions on the doctrine of the sphere. Pappus {h. y. praef.) refers to the second proposition of this work of Euclid, and the second proposition of the book which has come down to us contains the matter of the refer- ence. We have referred to the Latin of Zamberti and the Greek of Gregory. Dasypodius gave an edition (Gr. Lat., so said ; but we suppose with only the enunciations Greek), Strasburg, 1571, 4to. (?) (Weidler), and another appeared (Lat.) by Joseph Anria, with the comment of Maurolycus, Rome, 1591, 4to. (Lalande and Weidler.) The book is also in Mersenne's Synopsis, Paris, 1644, 4to. (Weidler.) Lalande names it {Bill. Astron. p. 188) as part of a very ill-described astronomical collec- tion, in 3 vols. Paris, 1626, 16mo.
Of the two works on music, the Harmonies and the Division of tlie Canon (or scale), it is unlikely that Euclid should have been the author of both. The former is a very dry description of the inter- minable musical nomenclature of the Greeks, and of their modes. It is called Aristoxenean [Aris- TOXKNUs] : it does not contain any discussion of the proper ultimate authority in musical matters, though it does, in its wearisome enumeration, adopt some of those intervals which Aristoxenus retjiined, and the Pythagoreans rejected. The style and matter of this treatise, we strongly sus- pect, belong to a later period than that of Euclid. The second treatise is an arithmetical description and demonstration of the mode of dividing the scale. Gregory is inclined to think this treatise cannot be Euclid's, and one of his reasons is that Ptolemy does not mention it ; another, that the theory followed in it is such as is rarely, if ever, mentioned before the time of Ptolemy. If Euclid did write either of these treatises, we are satisfied it must have been the second. Both are contained in Gregory (Gr. Lat.) as already noted ; in the collection of Greek musical authors by Meiboraius (Gr. Lat.), Amsterdam, 1652, 4to.; and in a sepa- rate edition (also Gr. Lat.) by J. Pena, Paris, 1537, 4to. (Fabr.), 1557 (Schweiger). Possevinus has also a corrected Latin edition of the lirst in his liM. Set. Colon. 1657. Forcadel translated one treatise into French, Paris, 1566, 8vo. (Schweiger.)
The book on Optics treats, in 61 propositions, on the simplest geometrical characteristics of vision and perspective : the Catoptrics have 31 proposi- tions on the law of reflexion as exemplified in plane and spherical mirrors. We have referred to tlie Gr. Lat. of Gregory and the Latin of Zam- berti ; there is also the edition of J. Pena (Gr. Lat.), Paris, 1557, 4to. (Fabr.) ; that of Dasypo- dius (Latin only, we suppose, with Greek enuncia- tions), Strasburg, 1557, 4to. (Fabr.) ; a reprint of the Latin of Pena, Leyden, 1599, 4to. (Fabr.) ; and some other reprint, Leipsic, 1607. (Fabr.) There is a French translation by Rol. Freart Mans, L6')3, 4 to. ; and an Italian one by Egnatic Dan.ti, Florence, 1573, 4to. (Schweiger.)
(Proclus; Pappus; August edcif.; Fahric. Bihl.
Graec. vol. iv. p. 44, &c. ; Gregory, Praef. edit,
cit. ; Murhard, Bibl. Afath. ; Zamberti, ed. cit.;
Savile, Praelect. in EucL ; Heilbronner, IJist.
Matlies. Univ. ; Schweiger, Handb. der Classisch.
Bihl. ; Peyrard, ed. cit., &c. &c. : all editions to
which a reference is not added having been ac-
tually consulted.)
EUCLEIDES (Εὐκλείδης), historical. 1. One of the leaders of the body of colonists from Zancle who founded Himera. (Thucyd. vi. 5.)
2. One of the sons of Hippocrates, tyrant of Gela. It was in suppressing a revolt of the Geloans against Eucleides and his brother, which broke out on the death of Hippocrates, that Gelon managed to get the sovereignty into his own hands, B.c.491. (Herod, vii. 155.)
3. One of the Thirty Tyrants at Athens. (Xen. Hell. ii. 3. § 2.)
4. The archon eponymus for the year b. c. 403. His archonship is memorable for the restoration, with some modifications, of the old laws of Solon and Draco. These were inscribed on the stoa poe- cile in the so-called Ionian alphabet, which was then first brought into use at Athens for public documents. ( Andoc. de Myst. p. 1 1 ; Plut. Arist. 1.) Athenaeus (i. p. 3, a.) mentions an Athenian of this name who was famous as a collector of books. Whether he was the same person as the archon, or not, does not appear.
5. The brother of Cleomenes III. king of Sparta. He commanded a division of the forces of the lat- ter at the battle of Sellasia, B. c. 223, and by his unskilful tactics in a great degree brought about the defeat of the Lacedaemonians. He fell with the whole of the wing which he commanded. (Polyb. ii. 65, 67, 68 ; Plut. Philop. p. 358, Arat. p. 1046, Cleom. pp. 809, 818.) [C. P. M.]
EUCLEIDES (Εὐκλείδης), a native of Megara, or, according to some less probable accounts, of Gela. He was one of the chief of the disciples of Socrates, but before becoming such, he had studied the doctrines, and especially the dialectics, of the Eleatics. Socrates on one occasion reproved him for his fondness for subtle and captious disputes. (Diog. Laert. ii. 30.) On the death of Socrates (B.C. 399), Eucleides, with most of the other pupils of that philosopher, took refuge in Megara, and there established a school which distinguished it- self chiefly by the cultivation of dialectics. The doctrines of the Eleatics formed the basis of his philosophical system. With these he blended the ethical and dialectical principles of Socrates. The Eleatic dogma, that there is one universal, un- changeable existence, he viewed in a moral aspect, calling this one existence the Good., but giving it also other names (as Reason, Intelligence, &.c.), perhaps for the purpose of explaining how the real, though one, appeared to be many. He rejected demonstration, attacking not so much the premises assumed as the conclusions drawn, and also reason- ing from analogy. He is said to have been a man of a somewhat indolent and procrastinating dispo- sition. He was the author of six dialogues, none of which, however, have come down to us. He has frequently been erroneously confounded with the mathematician of the same name. The school which he founded was called sometimes the Mega- ric, sometimes the Dialectic or Eristic. (Diog. Lal'rt. ii. 106—108 ; Cic. Acad. ii. 42 ; Plut. de Fratr. Avi. 18.) LC P. M.]
