A history of Greek mathematics - Wilbourhall.org

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458 DIOPHANTUS OF ALEXANDRIA
Signs for the powers of the unknown and their reciprocals.
The powers of the unknown, corresponding to our x 2 , x ?J . . . x
are defined and denoted as follows
6 ,
x 2 is Svvctfjus and is denoted by A Y ,
x ?> „ kv/3os „ „ „ K Y ,
X 4 ,, BvvajxoSvvajjLLS „ „ A A,
x 5 „ SvvctfioKvPos „ „ AK
,
x G „ KvfioKvffos „ „ „ K K.
Beyond the sixth power Diophantus does not go. It should
be noted that, while the terms from Kvfios onwards may be
used for the powers of any ordinary known number as well as
for the powers of the unknown, Svuafii? is restricted to the
square of the unknown
;
wherever a particular square number
is spoken of, the term is reTpdyoovos dptOfio?. The term
SwanoSyvajiis occurs once in another author, namely in the
Metrica of Heron, 1 where it is used for the fourth power of
the side of a triangle.
Diophantus has also terms and signs for the reciprocals of
the various powers of the unknown, i.e. for 1/x, l/x 2 ....
As an aliquot part was ordinarily denoted by the corresponding
numeral sign with an accent, e.g. /= J> ia!= tt> Diophantus
has a mark appended to the symbols for x, x 2 . . . to denote the
reciprocals; this, which is used for aliquot parts as well, is
printed by Tannery thus, *. With Diophantus then
dpiOjxoa-Tou, denoted by ?*, is
equivalent to l/x,
SwafiocrTOv, „ A „ „ 1 / x 2 ,
and so on.
The coefficient of the term in x, x 2 ... or l/x, l/x 2 ... is
expressed by the ordinary numeral immediately following,
e.g. AK Y /c