- G. J. Toomer
- and Reviel Netz
Diophantus of *Alexandria (1) (date uncertain, between 150 bce and ce 280), mathematician, wrote an algebraic work on indeterminate equations, Ἀριθμητικά, in thirteen books, of which six survive in Greek and four more in Arabic. The latter are numbered, and then to go through every step of finding a single solution, in rational but not necessarily integer numbers. The method for finding more solutions is only implied by the example given. This procedure, using specific numbers, puts Diophantus in a tradition going back ultimately to Babylonian mathematics (see Heron), and may perhaps be compared to the use of particular diagrams for the sake of general arguments in Greek geometry (see mathematics). He does not recognize negative or irrational numbers as solutions. Books 1–3 contain linear or quadratic indeterminate equations, many of them simultaneous. Beginning with book 4 cubes and higher powers are found. The solutions often demonstrate great ingenuity. A small treatise by Diophantus on polygonal numbers is preserved and may be authentic, but a work on porisms to which he refers and which may be his own is lost.