II. On some remarkable relations which obtain among the roots of the four squares into which a number may be divided, as compared with the corresponding roots of certain other numbers

Abstract

The first property of numbers mentioned in this paper is best illustrated by an example— 13 2 = 169 15 2 = 225. These odd numbers may be divided into 4 squares, and the roots may be so arranged that they will have this relation to each other: the middle roots will be the same, and the exterior roots will be, the one 2 more, the other 2 less than the corresponding roots of the other. Putting the roots below the number and comparing them, the result is obvious.