Practical Algebra (revised) Prepared for the Use of the Midshipmen at the United States Naval Academy1910 - Algebra - 191 pages |
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Practical Algebra (Revised) Prepared for the Use of the Midshipmen at the ... Stimson Joseph Brown,Paul Capron No preview available - 2016 |
Practical Algebra (Revised): Prepared for the Use of the Midshipmen at the ... Stimson J. Brown No preview available - 2016 |
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a+bi abscissa angle asymptotes Binomial Theorem called chance of success chord circle computation conjugate constant convergent coordinates corresponding cubic function curve degree diameter difference divergent series divided draw ellipse equa evident Examples expression factors figure Find the equation Find the value function geometric progression give given number given point graph hence hyperbola identity imaginary infinite infinity instance integers intersections limiting tangent linear loga logarithm loge mantissa multiplying negative number number of terms parabola parallel partial fractions permutations perpendicular polynomial power-series proper fraction quadratic quadratic equation quotient real numbers real root region of convergence represented result rithms root of f(x)=0 simplified slope solution solve square root straight line surds synthetic division T₁ Theorem tion trace triangle undetermined coefficients value of f(x variable vertical vertical limiting x-axis x₁ x²+1 y-axis y-intercept y=mx+b y₁
Popular passages
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 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 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 157 - ... the coefficients of like powers of x in the two series are equal.
Page 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...
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 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