BOOK II.

13 or 169 square

236. EXERCISES.

What is the content, in square feet and inches, of a room whose sides are 42 ft. 5 inch. and 31 ft. 9 inch.? and supposing the piece from

which its carpet is taken to be three quarters of a yard in breadth, what length of it must be cut off?—Answer, The content is 1346 square feet 105 square inches, and the length of carpet required is 598 feet 6⁵/₉ inches.

The sides of a rectangular field are 253 yards and a quarter of a mile; how many acres does it contain?—Answer, 23.

What is the difference between 18 square miles, and a square of 18 miles long, or 18 miles square?—Answer, 306 square miles.

237. It is by this rule that the measure in (215) is deduced from that in (214); for it is evident that twelve inches being a foot, the square foot is 12 × 12 or 144 square inches, and so on. In a similar way it may be shewn that the content in cubic inches of a cube, or parallelepiped,¹³ may be found by multiplying together the number of inches in those three sides which meet in a point. Thus, a cube of 6 inches contains 6 × 6 × 6, or 216 cubic inches; a chest whose sides are 6, 8, and 5 feet, contains 6 × 8 × 5, or 240 cubic feet. By this rule the measure in (216) was deduced from that in (214).

SECTION II. RULE OF THREE .

238. Suppose it required to find what 156 yards will cost, if 22 yards cost 17s. 4d. This quantity, reduced to pence, is 208d.; and if 22 yards cost 208d., each yard costs ²⁰⁸/₂₂d. But 156 yards cost 156 times the price of one yard, and therefore cost

Again, if 25½ French francs be 20 shillings sterling, how many francs are in £20. 15? Since 25½ francs are 20 shillings, twice the number of francs must be twice the number of shillings; that is, 51 francs are 40

shillings, and one shilling is the fortieth part of 51 francs, or ⁵¹/₄₀ francs. But £20 15s. contain 415 shillings (219); and since 1 shilling is ⁵¹/₄₀ francs, 415 shillings is

239. Such