A history of Greek mathematics - Wilbourhall.org

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546 COMMENTATORS AND BYZANTINES
and that Anatolius's account, which was different and more
succinct, was dedicated to Diophantus (this enables us to
determine Diophantus's date approximately). He also notes
the difference between the Diophantine and Egyptian names
for the successive powers of dpiOfjios : the next power after
the fourth (Svvafj.o8vvaiJ.is = x^), i.e. x 5 , the Egyptians called
'
the first undescribed ' (aXoyos irpcoros) or the ' fifth number '
the sixth, x 6 , they apparently (like Diophantus) called the
cube -cube ; but with them the seventh, x 1 , was the second
'
undescribed ' or the ' seventh number ', the eighth (x*) was the
'
quadruple square ' (reTpairXfj Swa/its), the ninth (x d ) the
'extended cube' (kv&os k^tXiKros). Tannery conjectures that
all these remarks were taken direct from an old commentary
on Diophantus now lost, probably Hypatia's.
Georgius Pachymeres (1242-1310) was the author of a
work on the Quadrivium (SvvTayjia rcov Tea-crdpcov fiaOrj/jLarcou
or TerpafiifiXov). The arithmetical portion contains, besides
excerpts from Nicomachus and Euclid, a paraphrase of
Diophantus,
Book I, which Tannery published in his edition of
Diophantus l ;
the musical section with part of the preface was
published by Vincent, 2 and some fragments from Book IV by
Martin in his edition of the Astronomy of Theon of Smyrna.
Maximus Planudes, a monk from Nicomedia, was the
envoy of the Emperor Andronicus II at Venice in the year
1297, and lived probably from about 1260 to 1310. He
wrote scholia on the first two Books of Diophantus, which
are extant and are included in Tannery's edition of Diophantus.
3 They contain nothing of particular interest except
a number of conspectuses of the working-out of problems of
Diophantus written in Diophantus's own notation but with
steps in separate lines, and with abbreviations on the left of
words indicating the operations (e.g. €k0. = e/c^eo-ij, rerp. =
TeTpayodvio-fios,