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

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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 |

### Common terms and phrases

algebraic angle approach arranged asymptotes base becomes called chance chord circle coefficients common computation conjugate constant convergent coordinates corresponding curve decimal derivative determine diameter difference distance divided division draw drawn ellipse equal equation evident Examples expansion expression factors figure Find four fraction function geometric progression give given graph greater hence hyperbola identity imaginary increases indefinitely indicated infinite infinity instance integers intersections length less limit locus logarithm loge means method multiplying negative obtained occur original parallel perpendicular places polynomial positive powers preceding principles quadratic quantity ratio relation represented respectively result roots sides simplified slope solution solve square straight line success tables taken taking tangent Theorem things throw tion trace true unit variable vertical write written x-axis zero

### Popular passages

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...