490 
DIOPHANTUS OF ALEXANDRIA 
(v) Systems oi* equations apparently indeterminate but 
really reduced, by arbitrary assumptions, to deter 
minate equations of the first degree. 
I. 14. xy — on(x + oj). [Value of y arbitrarily assumed.] 
II. 3*. xy — on(x + y), and xy = on{x — y)’. 
II. 1*. (cf. I. 31). x 2 + y 2 = m{x + y). 
ì II. 2*, (cf. I. 34). x 2 ~y 2 = on{x — y). j \x assumed = 2y.] 
II. 4*. (cf. I. 32). x 2 + y 2 = m{x — y). 
II. 5*. (cf. I. 33). x 2 — y 2 — on{x + y). ) 
II. 7*. x 2 — y 2 = m{x — y) + cl, [Dioph. assumes x — y— 2.] 
/ T 11 11 11 
I. 22. x x+ -z = y V + — x — z— - z+ -y. 
on p on on p n 
[Value of y assumed.] 
T 11 11 11 
1. 23. x— —x-\—w = y y + — x = z « H—y 
on q on on p n 
— w — -0. [Value of y assumed.] 
1.24. X + — (y + z) = y + - {z + x) = z + - (x + y). ■ 
on oi ' p 
[Value of y + z assumed.] 
{ L 25> x +^(y + z + w ) = y+ l -(z + w + x) 
oi 
= 0 + ~ (w + X + y) = w + ~ {x + y + z). 
[Value of y + z + w assumed.] 
11.17*. (cf. I. 22). x— (^x +a) + + c^ 
= y- Q,y +b ) + (s“ + “) = *-(|* +c ) + (s» +i )- 
[Ratio of x to y assumed.]