s
expressions of his proper character as a deity of vegetation; F. A.
Voigt in Roscher's _Lexikon der Mythologie_; L. Preller, _Griechische
Mythologie_ (4th ed. by C. Robert); F. Lenormant (s.v. "Bacchus") in
Daremberg and Saglio's _Dictionnaire des antiquites_; O. Kern in
Pauly-Wissowa's _Realencyclopadie_ (with list of cult titles); W.
Pater, _Greek Studies_ (1895); E. Rohde, _Psyche_, ii., who finds the
origin of the Hellenic belief in the immortality of the soul in the
"enthusiastic" rites of the Thracian Dionysus, which lifted persons
out of themselves, and exalted them to a fancied equality with the
gods; O. Gruppe, _Griechische Mythologie und Religionsgeschichte_, ii.
(1907), who considers Boeotia, not Thrace, to have been the original
home of Dionysus; P. Foucart, "Le Culte de Dionysos en Attique" in
_Memoires de l'Institut national de France_, xxxvii. (1906), who finds
the prototype of Dionysus in Egypt. _The Great Dionysiak Myth_
(1877-1878) by R. Brown contains a wealth of material, but is weak in
scholarship. For a striking survival of Dionysiac rites in Thrace
(Bizye), see Dawkins, in _J.H.S._ (1906), p. 191.

DIOPHANTUS, of Alexandria, Greek algebraist, probably flourished about
the middle of the 3rd century. Not that this date rests on positive
evidence. But it seems a fair inference from a passage of Michael
Psellus (_Diophantus_, ed. P. Tannery, ii. p. 38) that he was not later
than Anatolius, bishop of Laodicea from A.D. 270, while he is not quoted
by Nicomachus (fl. c. A.D. 100), nor by Theon of Smyrna (c. A.D. 130),
nor does Greek arithmetic as represented by these authors and by
Iamblichus (end of 3rd century) show any trace of his influence, facts
which can only be accounted for by his being later than those
arithmeticians at least who would have been capable of understanding him
fully. On the other hand he is quoted by Theon of Alexandria (who
observed an eclipse at Alexandria in A.D. 365); and his work was the
subject of a commentary by Theon's daughter Hypatia (d. 415). The
_Arithmetica_, the greatest treatise on which the fame of Diophantus
rests, purports to be in thirteen Books, but none of the Greek MSS.
which have survived contain more than six (though one has the same text
in seven Books). They contain, however, a fragment of a separate tract
on _Polygonal Numbers_. The missing books were apparently lost early,
for there is no reason to suppose that