NOTATION AND DEFINITIONS 459
When there are units in addition, the units are indicated by
° o
the abbreviation M ; thus K' a A Y ty s e M (3 corresponds to
i» 3 +13ic 2 +5ic+2. .
The sign (A) for minus and its meaning.
For subtraction alone is assign used. The full term for
wanting is Aas opposed to vnap^is, a forthcoming,
which denotes a 'positive term. The symbol used to indicate
a wanting, corresponding to our sign for minus, is A, whicli
is described in the text as a ‘-v/r turned downwards and
truncated ’ (W eXXnrh kutco vevov). The description is evidently
interpolated, and it is now certain that the sign has nothing
to do with \fs. Nor is it confined to Diophantus, for it appears
in practically the same form in Heron’s Metrical where in one
place the reading of the manuscript is govdScov 08 T l'8',
74— jtp In the manuscripts of Diophantus, when the sign
is resolved by writing the full word instead of it, it is
generally resolved into Aen/rei, the dative of XeL\jns, but in
other places the symbol is used instead of parts of the verb
XuneLv, namely Xlttcov or Aen/my and once even Xincocri;
sometimes Aeiyfsei in the manuscripts is followed by the
accusative, which shows that in these cases the sign was
wrongly resolved. It is therefore a question whether Dio
phantus himself ever used the dative Xeir/su for minus at all.
The use is certainly foreign to classical Greek. Ptolemy has
in two places Xu\frav and Auirovaav respectively followed,
properly, by the accusative, and in one case he has to dub
Tfjs FA Xu(f)6ev vnb rov dnb rfjs ZT (where the meaning is
ZT 2 — TA 2 ). Hence Heron would probably have written a
participle where the T occurs in the expression quoted above,
say govdScov 08 XfL\fracrd>v reacrapaKOuSf Karov. On the whole,
therefore, it is probable that in Diophantus, and wherever else
it occurred, A is a compendium for the root of the verb XuirtLv,
in fact a A with I placed in the middle (cf. A, an abbreviation
for rdXavTov). This is the hypothesis which I put forward
in 1885, and it seems to be confirmed by the fresh evidence
now available as shown above.
1 Heron, Metrica, p. 156. 8, 10.
