# Greek Mathematics

# XXIII. Algebra: Diophantus

## (a) General

## Anthol. Palat. xiv. 126, The Greek Anthology, ed. Paton (L.C.L.) v. 92–93

Οὕτός τοι Διόφαντον ἔχει τάφος· ἆ μέγα θαῦμα· καὶ τάφος ἐκ τέχνης μέτρα βίοιο λέγει. ἕκτην κουρίζειν βιότου θεὸς ὤπασε μοίρην· δωδεκάτην δ᾿ ἐπιθείς, μῆλα πόρεν χνοάειν· τῇ δ᾿ ἄφ᾿ ἐφ᾿ ἑβδομάτῃ τὸ γαμήλιον ἥψατο φέγγος, ἐκ δὲ γάμων πέμπτῳ παῖδ᾿ ἐπένευσεν ἔτει. αἰαῖ, τηλύγετον δειλὸν τέκος, ἥμισυ πατρὸς τοῦδε καὶ ἡ κρυερὸς μέτρον ἑλὼν βιότου. πένθος δ᾿ αὖ πισύρεσσι παρηγορέων ἐνιαυτοῖς τῇδε πόσου σοφίῃ τέρμ᾿ ἐπέρησε βίου.

# Algebra : Diophantus

# XXIII. Algebra: Diophantus

## (a) General

## Palatine Anthology^{a} xiv. 126, The Greek Anthology, ed. Paton (L.C.L.) v. 92–93

This tomb holds Diophantus. Ah, what a marvel! And the tomb tells scientifically the measure of his life. God vouchsafed that he should be a boy for the sixth part of his life; when a twelfth was added, his cheeks acquired a beard; He kindled for him the light of marriage after a seventh, and in the fifth year after his marriage He granted him a son. Alas! late-begotten and miserable child, when he had reached the measure of half his father’s life, the chill grave took him. After consoling his grief by this science of numbers for four years, he reached the end of his life.^{b}

^{a}There are in the Anthology 46 epigrams which are algebraical problems. Most of them (xiv. 116–146) were collected by Metrodorus, a grammarian who lived about a.d. 500, but their origin is obviously much earlier and many belong to a type described by Plato and the scholiast to the Charmides (v. vol. i. pp. 16, 20). Diophantus’s surviving works and ancillary material are admirably edited by Tannery in two volumes of the Teubner series (Leipzig, 1895). There is a French translation by Paul Ver Eecke, Diophante d’Alexandre (Bruges, 1926). The history of Greek algebra as a whole is well treated by G. F. Nesselmann, Die Algebra der Griechen, and by T. L. Heath, Diophantus of Alexandria: A Study in the History of Greek Algebra, 2nd ed. 1910.^{b}If x was his age at death, then1/6x+1/12x+1/7x+5+1/2x+4=x, whencex=84.