EPIGRAMS IN THE GREEK ANTHOLOGY 443 
tions of this type with the same number of unknown quantities 
which was given by Thymaridas, an early Pythagorean, and 
was called the knavOyixa, ‘ flower ’ or ‘ bloom’ of Thymaridas 
(see voi. i, pp. 94-6). (3) Six more are problems of the usual 
type about the filling and emptying of vessels by pipes; e.g. 
(xiv. 130) one pipe fills the vessel in one day, a second in two 
and a third in three ; how long will all three running together 
take to fill it? Another about brickmakers (xiv, 136) is of 
the same sort. 
Indeterminate equations of the first degree. 
The Anthology contains (4) two indeterminate equations of 
the first degree which can be solved in positive integers in an 
infinite number of ways (xiv. 48, 144) ; the first is a distribu 
tion of apples, 3ìc in number, into parts satisfying the equation 
x — 3y = y, where y is not less than 2; the second leads to 
three equations connecting four unknown quantities : 
x + y = X 1 + y 1 , 
x = 2 y v 
«i = 3 y, 
the general solution of which is x — 4/c, y = k, x 1 = 3 k, 
y l = 2k. These very equations, which, however, are made 
determinate by assuming that x + y — x l + y 1 — 100, are solved 
in Dioph. I. 12. 
Enough has been said to show that Diophantus was not 
the inventor of Algebra. Nor was he the first to solve inde 
terminate problems of the second degree. 
Indeterminate equations of second degree before 
Diophantus. 
Take first the problem (Dioph. II. 8) of dividing a square 
number into two squares, or of finding a right-angled triangle 
with sides in rational numbers. We have already seen that 
Pythagoras is credited with the discovery of a general formula 
for finding such triangles, namely, 
«■+{*(**-1)} 2 = {f(* 2 +l)} 2 >