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 арсвро?' the next power after 
the fourth [SvvapoSvvapLs = ж 4 ), i.e. ж 5 , the Egyptians called 
‘ the first undescribed ’ {dXoyos тгрштоу) or the ‘ fifth number ’; 
the sixth, ж 6 , they apparently (like Diophantus) called the 
cube-cube; but with them the seventh, ж 7 , was the 1 second 
undescribed ’ or the £ seventh number ’, the eighth (ж*) was the 
‘ quadruple square ’ (тетратгХу SvrapLs), the ninth (ж 9 ) the 
‘ extended cube ’ (kv(3os egeXLKros). 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 {Hurray pa тсог траста poor равуратш 
or Тетра/Зс/ЗХог). The arithmetical portion contains, besides 
excerpts from Nicomachus and Euclid, a paraphrase of Dio 
phantus, Book I, which Tannery published in his edition of 
Diophantus 1 ; 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 Dio 
phantus. 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. ’¿кв. = ¿квеспъ, гетр. = 
тетраусоикгрб^, аигв. = avrOeai?, &c.); the result is to make 
the work almost as easy to follow as it is in our notation. 
Another work of Planudes is called Фуфофорса кат’ ’IrSovs, 
or Arithmetic after the Indian method, and was edited as Das 
1 Diophantus, vol. ii, pp. 78-122, 
2 Notices et extraits, xvii, 1858, ¡эр. 362-533. 
3 Diophantus, vol. ii, pp. 125-255.