Diophane ̄s of Nikaia (85 – 60 BCE)
Compiled a six-book epitome of C D’ translation of Mago’s agricultural
work, dedicated to Deiotaros, tetrarch of Galatia; cf. V, RR 1.1.8–10. The popular
epitome eventually superseded the original translation; Varro treats it as well-known ca 55
BCE (1.9.7). A collection of “paradoxes” was also ascribed to Diophane ̄s (Pho ̄tios Bibl.
163), though it may be the case that these were simply items culled from his agricultural
work.
Ed.: Speranza (1971) 75–119.
RE 5.1 (1903) 1049 (#9), M. Wellmann, S.6 (1935) 27, W. Kroll; 18.3 (1949) 1137–1166 (§22, 1159), K.
Ziegler; KP 2.85, H.G. Gundel.
Philip Thibodeau
Diophantos (Geog.) (325 – 150 BCE)
A K notes that Diophantos wrote about the north-lands; scraps
are preserved in the scholia to Apollo ̄nios of Rhodes and in S B, s.v.
Abioi and Libustinoi.
FGrHist 805.
PTK
Diophantos of Alexandria (ca 250 CE)
Greek mathematician, author of a sizeable and influential algebraic treatise, the Arithme ̄tika.
A small fragment of a treatise on polygonal numbers is also attributed to him. Diophantos
lived in Alexandria, the main scientific center of antiquity. Not mentioned before the 4th c.,
he is thought to have lived in the 3rd, and the Dionusios addressed in the introduction to
the Arithme ̄tika may have been Saint Dionusios of Alexandria (d. ca 264 CE). An arithmetical
epigram from the Anthologia Graeca (14.126), retracing some events of his life (marriage at
33, birth of his son at 38, death of his son four years before his own at 84), seems
contrived.
The Arithme ̄tika has not been preserved in its entirety; only ten of its 13 books (biblia) have
been transmitted, at different times and in a different form. Six in Greek (numbered 1–6)
reached Europe in the 15th c. Four more, in a 9th c. Arabic translation, (numbered 4–7)
were discovered in 1968; since this latter numbering turned out to be correct, the last three
Greek books must follow them, probably as Books 8–10, while Books 11–13, still missing,
must be considered lost. The Arabic version (originally covering Books 1–7) is notably more
prolix than the extant Greek text, for it completes computations and verifies that solutions
indeed fulfill the equations. Certainly Greek in origin, it must be the commentary (hupom-
ne ̄ma) which the Souda Y-166 (as emended by Tannery 1895: 36) attributed to H, the
daughter of T A.
In the introduction, Diophantos provides general instructions regarding treating equa-
tions, and he defines relevant symbols, with signs for the unknown and its powers, as well
as for a few operations, the first known algebraic symbolism. Like its late medieval succes-
sors, Diophantos’ symbolism originated in scribal abbreviations of commonly repeated
words. Then Diophantos proceeds with the problems (some 250 survive). In Book 1, the
problems are of the familiar kind seen by the student in school and solved, with an early
form of algebra, by applying identities already in use in Mesopotamia; but Diophantos
DIOPHANTOS OF ALEXANDRIA