A history of Greek mathematics - Wilbourhall.org

WORKS
44 ( J
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 V, 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 (fieOopLov) between number and aliquot parts,
says thus Diophantus in the Moriastica .... for he describes
'
as " parts " the progression without limit in the direction of
The Moriastica may be a separate work
but
less than the unit '.
by Diophantus giving rules for reckoning with fractions ;
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 remaining
seven, which, partly as a consequence, were first forgotten
and then lost (cf. the case of Apollonius's Conies, 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 Fakhra,
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,
1523.2 Q g