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

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1910 - 191 páginas
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Página 16 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. , M , ,• , . logi — = log
Página 16 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 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.
Página 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.
Página 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.
Página 157 - ... the coefficients of like powers of x in the two series are equal.
Página 78 - Thus 3 and — 4 are roots ; and since x = -~ , we have -. and - 2 •"* ~ as roots of the original equation. IX. OF THE DEPRESSION OF EQUATIONS. 121. In the present Chapter we shall shew how the solution .of an equation may be made to depend upon the solution of an equation of lower degree, in certain cases where known relations subsist among the roots; this process is called the depression of equations. 122. When two equations have a root or roots in common, it is required to determine the root...
Página 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.
Página 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.
Página 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

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