N. B. The following questions are left without any answers, that the Schol ar may operate and prove each question.

19. WHAT Will 11 yards of flannel, at 2s6 per yard, come to ? OPERATION.

PROOF.

20. WHAT Will 13 lb. of cotton cost, at 384 per lb?

21. WHAT Will 183 yards of ribbon come to, at 8d. per yard?

THE

SCHOLAR'S ARITHMETIC.

SECTION III.

Rules ocsasionally useful to men in particular callings and pursuits of life.

§ 1. Involution.

INVOLUTION, or the raising of powers is the multiplying of any given number into itself continually, a certain number of times. The quantities in this way produced, are called POWERS of the given number. Thus,

4X416 is the 2d. power, or square of 4. 4X4X464 is the 3d. power, or cube of 4.

42 -43

4X4X4X4 256 is the 4th. power, or biquadrate of 4-44

The given number, (4) is called the first power; and the small figure, which points out the order of the power, is called the Index or the Exponent.

§ 2. Evolution.

EVOLUTION, or the extraction of roots, is the operation by which we find any root of any given number.

THE root is a number whose continual multiplication into itself produces the power, and is denominated the square, cube, biquadrate, or 2d, 3d, 4th, root, &c. accordingly as it is, when raised to the 2d, 3d, 4th, &c. power, equal to that power. Thus, 4 is the square root of 16, because 4X416. 4 also is the cube root of 64, because 4X 4X4 64; and 3 is the square root of 9, and 12 is the square root of 144, and the cube root of 1728, because 12X 12X12 1728, and so on.