The Pell equation, by Edward Everett Whitford.

8

THE PELL EQUATION

that from
3
2'
we have
3 -1 17
2 2+ 3.2 -12'
and
17 -1 577
12 2.17 12 408'
where 3, 2; 17, 12; and 577, 408 are solutions of
2- 2y2 = 1.
Baudhayana1 sometimes used for l-3 the approximation 26/15, for he gave for the area of a circle the rule
which which would have this meaning,
(13d ) 1 d2,r
Here ir is evidently set equal to 3, as in the early writings
of all oriental nations. Therefore
132
3 ~ -2.4,
152
and
- 26
15k
Baudhayana also knew the more exact value2
2 1 1.3 3+35 3552'
which value, 1351/780, was probably obtained by the
1S. Giinther, op. cit., p. 41. M. Cantor, "Vorlesungen fiber der
Geschichte der Mathematik," vol. I, 2d ed., p. 548, Leipzig, 1894.
2 S. Gunther, loc. cit.