Murby's Excelsior Arithmetic, for All Schools and Colleges, Μέρος 2

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Σελίδα 204 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Σελίδα 204 - Subtract the square thus found from the said period, and to the remainder annex the two figures of the next following period for a dividend. Double the root above mentioned for a divisor, and find how often it is contained in the said dividend, exclusive of its right-hand figure ; and set that quotient figure both in the quotient and divisor.
Σελίδα 230 - Suppose that a"= n, then x is called the logarithm of n to the base a : thus the logarithm of a number to a given base is the index of the power to which the base must be raised to be equal to the number.
Σελίδα 251 - Nothing is more proverbially uncertain than the duration of human life when the maxim is applied to an individual, but there are few things less subject to fluctuation than the average duration of life in a multitude of individuals.
Σελίδα 231 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Σελίδα 227 - Dahir's request was a seemingly modest one: one grain of wheat on the first square of a chessboard, two on the second, four on the third, and so on.
Σελίδα 231 - Then by definition we have ef" =m, and a» = n. Dividing, we have a? ~ » = — . Whence x — y is the logarithm of — . Q. K . ». 123. Prop. 3. The logarithm of a power of a number is the logarithm of the number multiplied by the index of the power. DEM. — Let a be the base, and x the logarithm of m.
Σελίδα 169 - A ship's company take a prize of $4440, which they agree to divide among them according to their pay and the time they have been on board. Now the officers and midshipmen have been on board 6 months, and the sailors 3 months; the officers have $12 per month, the midshipmen $8, and the sailors $6 per month ; moreover, there are 4 officers, 12 midshipmen, and 100 sailors.
Σελίδα 208 - The roots of most powers may be found by the square and cube root only : thus, the biquadrate, or 4th root, is the square root of the square root ; the 6th root is the cube root of the square root; the 8th root is the square root of the 4th root ; the 9th root is the cube root of the cube root, &c.
Σελίδα 204 - RULE. — Divide the given number into periods of two figures each, by setting a point over the place of units, another over the place of hundreds, and so on, over every second figure, both to the left hand in integers, and to the right in decimals.

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