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 >