94 
PYTHAGOREAN ARITHMETIC 
((3) The ¿Trdvdrj/xa {‘bloom’) of Thymaridas. 
Thymaridas of Paros, an ancient Pythagorean already 
mentioned (p. 69), was the author of a rule for solving a 
certain set of n simultaneous simple equations connecting n 
unknown quantities. The rule was evidently well known, for 
it was called by the special name of kndvOppa, the ‘ flower ’ or 
‘bloom’ of Thymaridas. 1 (The term kirdvOppa is not, how 
ever, confined to the particular proposition now in question; 
Iamblichus speaks of errai/Oppara of the Introductio arith 
metica, ‘arithmetical kirai/dijpaTa’ and kiTavOrjpara of par 
ticular numbers.) The rule is stated in general terms and no 
symbols are used, but the content is pure algebra. The known 
or determined quantities {¿»pLcrpevor) are distinguished from 
the undetermined or unknown {dopia-jov), the term for the 
latter being the very word used by Diophantus in the expres 
sion irXyOos povdScov dopuTTov, ‘ an undefined or undetermined 
number of units’, by which he describes his dpiQpoy or un 
known quantity (= x). The rule is very obscurely worded, 
but it states in effect that, if we have the following n equa 
tions connecting n unknown quantities x, x x , x 2 . . . x n _ x , 
namely 
X + x x + x 2 +... + x n _ x = s, 
x + x x = a x , 
x + x 2 = a 2 
x T x n _ x — a n _ x , 
the solution is given by 
(cq + a 2 + ... + j) — s 
X ~ n— 2 
Iamblichus, our informant on this subject, goes on to show 
that other types of equations can be reduced to this, so that 
the rule does not ‘ leave us in the lurch ’ in those cases either. 2 
He gives as an instance the indeterminate problem represented 
by the following three linear equations between four unknown 
quantities: 
x + y = a {z + u), 
x + z = h (u + y), 
x + u= c(y + z). 
1 Iambi, in Nicorn., p. 62. 18 sq. 
2 lb., p. 68. 16.