TRANSLATIONS AND EDITIONS 
455 
unfortunately spoiled by corrections made, especially in Books 
I, II, from some manuscript of the ‘ Planudean ’ class ; where 
this is the case recourse must be had to Yat. gr. 191 which 
was copied from it before it had suffered the general alteration 
referred to : these are the first two of the manuscripts used by 
Tannery in his definitive edition of the Greek text (Teubner, 
1893, 1895). 
Other editors can only be shortly enumerated. In 1585 
Simon Stevin published a French version of the first four 
Books, based on Xylander. Albert Girard added the fifth and 
sixth Books, the complete edition appearing’ in 1625. German 
translations were brought out by Otto Schulz in 1822 and by 
G. Wertheim in 1890. Poselger translated the fragment on 
Polygonal Numbers in 1810. All these translations depended 
on the text of Bachet. 
A reproduction of Diophantus in modern notation with 
introduction and notes by the present writer (second edition 
1910) is based on the text of Tannery and may claim to be the 
most complete and up-to-date edition. 
My account of the Arithmetica of Diophantus will be most 
conveniently arranged under three main headings (1) the 
notation and definitions, (2) the principal methods employed, 
so far as they can be generally stated, (3) the nature of the 
contents, including the assumed Porisms, with indications of 
the devices by which the problems are solved. 
Notation and definitions. 
In his work Die Algebra der Griechen Nesselmann distin 
guishes three stages in the evolution of algebra. (1) The 
first stage he calls £ Rhetorical Algebra 5 or reckoning by 
means of complete words. The characteristic of this stage 
is the absolute want of all symbols, the whole of the calcula 
tion being carried on by means of complete words and forming- 
in fact continuous prose. This first stage is represented by 
such writers as Iamblichus, all Arabian and Persian algebraists, 
and the oldest Italian algebraists and their followers, including 
Regiomontanus. (2) The second stage Nesselmann calls the 
‘ Syncopated Algebra essentially like the first as regards