The Pell equation, by Edward Everett Whitford.

CONTENTS.
PAGE
Origin of the name Pell Equation................. 1
D efinition..................................... 3
Relation to square root approximation............ 4
The most ancient Hindu solutions................ 6
The most ancient Greek solutions................ 9
Theon of Smyrna............................... 13
A rchim edes.................................... 15
Heron of Alexandria............................ 21
D iophantus.................................... 22
The H indus.................................... 26
The Arabs..................................... 39
Europeans before Fermat........................ 41
Fermat, Brouncker and Wallis.................. 46
E u ler......................................... 59
Relation to the general indeterminate equation of the
second degree................................ 64
L agrange...................................... 71
Relation to the theory of quadratic forms......... 76
Gauss...................................... 77
Dirichlet...................................... 79
Relation to circle division....................... 88
Relation to elliptic functions..................... 91
Relation to units of a quadratic domain........... 92
Relation to hyperbolic functions.................. 93
Classes of fundamental solutions................. 93
Tables of solutions............................. 95
Table of the fundamental solutions of the equations
x2- Ay2 = = 1 from A = 1,501 to A = 1,700... 102
Bibliography................................. 113
Appendix A, table of continued fractions for JIA
from A = 1,501 to A = 2,012.................. 162
Index of names............................. 191
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