BOOK II.

Then, since a e is twice a b, or twice ⁷/₂ inches, it is 7 inches. And since a f is four times a c, or four times ⁹/₄ inches, it is 9 inches. Therefore, the whole rectangle a e f g contains, by (234), 7 × 9 or 63 square inches. But the rectangle a e f g contains 8 rectangles, all of the same figure as a b c d; and therefore a b c d is one-eighth part of a e f g, and contains ⁶³/₈ square inches. But ⁶³/₈ is made by multiplying ⁹/₄ and ⁷/₂ together (118). From this and the last article it appears, that, whether the sides of a rectangle be a whole or a fractional number of inches, the number of square inches in its surface is the product of the numbers of inches in its sides. The square itself is a rectangle whose sides are all equal, and therefore the number of square inches which a square contains is found by multiplying the number of inches in its side by itself. For example, a square whose side is 13 inches in length contains 13