WORKS 
449 
« 
Six Books only of the former and a fragment of the latter 
survive. 
Allusions in the Arithmetica imply the existence of 
(3) A collection of propositions under the title of Porisms; 
in three propositions (3, 5, 16) of Book Y, Diophantus quotes 
as known certain propositions in the Theory of Numbers, 
prefixing to the statement of them the words ‘ We have it in 
the Porisms that.. 
A scholium on a passage of Iamblichus, where Iamblichus 
cites a dictum of certain Pythagoreans about the unit being 
the dividing line (fj.e66pi.ov) between number and aliquot parts, 
says ‘ thus Diophantus in the Moriastica .... for he describes 
as “parts” the progression without limit in the direction of 
less than the unit ’. The Moriastica may be a separate work 
by Diophantus giving rules for reckoning with fractions; but 
I do not feel sure that the reference may not simply be to the 
definitions at the beginning of the Arithmetica. 
\ 
The Arithmetica. 
The seven lost Books and their place. 
None of the manuscripts which we possess contain more 
than six Books of the Arithmetica, the only variations being 
that some few divide the six Books into seven, while one or 
two give the fragment on Polygonal Numbers as VIII. The 
missing Books were evidently lost at a very early date. 
Tannery suggests that Hypatia’s commentary extended only 
to the first six Books, and that she left untouched the remain 
ing seven, which, partly as a consequence, were first forgotten 
and then lost (cf. the case of Apollonius’s Conics, where the 
only Books which have survived in Greek, I-IV, are those 
on which Eutocius commented). There is no sign that even 
the Arabians ever possessed the missing Books. The Fakhrl, 
an algebraical treatise by Abu Bekr Muh. b. al-Hasan al- 
Karkhi (d. about 1029), contains a collection of problems in 
determinate and indeterminate analysis which not only show 
that their author had deeply studied Diophantus but in many 
cases are taken direct from the Arithmetica, sometimes with 
a change in constants; in the fourth section of the work, 
1623.2 Q g*