Practical Algebra (revised) Prepared for the Use of the Midshipmen at the United States Naval Academy

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United States Naval Institute, 1910 - Algebra - 191 pages
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Page 16 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 16 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. , M , ,• , . logi — = log
Page 19 - Let N be a number whose integral part contains n digits ; then ff—. lQ(>ll)-hl lection . . ' . log N— (n - 1 ) + a fraction. Hence the characteristic is n — 1 ; that is, the characteristic of the logarithm of a number greater than unity is less by one than the number of digits in its integral part, and i& positive.
Page 20 - The characteristic of a number less than 1 is found by subtracting from 9 the number of ciphers between the decimal point and the first significant digit, and writing — 10 after the result.
Page 90 - ... therefore 1 being the trigonometrical tangent of the angle made by the line with the axis of a;, this angle must be 45, and the ordinate at the origin is 2.
Page 4 - In practice, the quotient of two complex numbers is usually found by multiplying both numerator and denominator by the conjugate of the denominator: o + ib _ a + ib c — id _ ac + bd be — ad . , . , n ^Md " F+ld
Page 56 - ... number of combinations of n things r at a time is the same as the number of combinations of n things n — r at a time ; This result is frequently useful in enabling us to abridge arithmetical work.
Page 23 - The cologarithm of a number is found by subtracting each figure of the logarithm from 9, except the last figure, which is subtracted from 10; then append — 10.
Page 53 - The various orders in which a number of things can be arranged are called their permutations. Thus...
Page 110 - ... in a few cases, to be hereafter pointed out, where oblique axes may be more advantageously employed. PROBLEM I. (8.) To find the equation of a straight line passing through a given point. Let us denote the coordinates of the given point by x...

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