## Formulas and theorems in pure mathematics |

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Page 82

a geometrical progression which converges; therefore the given series

converges. 245 The series of which — ^ r- is the general term is to (log n)p

convergent if p be greater than

By (243), (244).

a geometrical progression which converges; therefore the given series

converges. 245 The series of which — ^ r- is the general term is to (log n)p

convergent if p be greater than

**unity**, and divergent if p be not greater than**unity**.By (243), (244).

Page 389

Jo \i+r a+y> 2620 Hog (1— 2a cos x+a*) dx = 0, when a is equal to, or less than,

log 2 (1— cos a) = log 4 + 2 log sin Jz. (ii.) a < 1. By integrating (2922) from 0 to *.

Jo \i+r a+y> 2620 Hog (1— 2a cos x+a*) dx = 0, when a is equal to, or less than,

**unity**; but is equal to 2n log a, when a ...**unity**. Proof. — (i.) a=l. By (2635), sincelog 2 (1— cos a) = log 4 + 2 log sin Jz. (ii.) a < 1. By integrating (2922) from 0 to *.

Page 649

But the points of intersection of each pair are real, and are identical with the

points which are obtained by substituting

and drawing the six lines accordingly. Proof. — Let the coordinates of the four

points ...

But the points of intersection of each pair are real, and are identical with the

points which are obtained by substituting

**unity**for \/ — l in the given coordinates,and drawing the six lines accordingly. Proof. — Let the coordinates of the four

points ...

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### Contents

Introduction The C G S System of Units | 1 |

VHI Common and Hyperbolic Logarithms of | 7 |

QUANT1C8 1620 | 30 |

Copyright | |

108 other sections not shown

### Common terms and phrases

becomes Binomial Theorem bisect changes of sign chord circumscribing circle columns conic conjugate constant continued fraction convergent cosec cosine curve denoted determinant diameter divided eliminant ellipse equal equate coefficients expand factors figure formula function given circle given ratio Hence hyperbola imaginary roots infinite inscribed circle integer integral intersect inverse points limits logarithm method Multiply negative nine-point circle notation obtained orthogonally pair parabola parallel partial fractions perpendicular plane positive powers Proof Proof.—By Proof.—In Proof.—Let Proof.—The quantic quantities quotient radical axis radius respect result right angle rows Rule sides similar triangles Similarly sine singular solution solution squares substituting successive tangent Taylor's theorem theorem tion transformed triangle ABC unity vanishes variables zero