## Formulas and theorems in pure mathematics |

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Page 65

185 Also, if any of these series are

fractions become infinite. 186 To find the value of a continued fraction with

recurring quotients. Let the continued fraction be x = — — — where y _ c/n+i «i+...

+ «.

185 Also, if any of these series are

**convergent**and infinite, the continuedfractions become infinite. 186 To find the value of a continued fraction with

recurring quotients. Let the continued fraction be x = — — — where y _ c/n+i «i+...

+ «.

Page 70

multiple of that number, and let the mth

then the 2mth

210). 198 F°r example, in approximating to ^/29 above, there are five recurring ...

multiple of that number, and let the mth

**convergent**to s/Q, be represented by Fm ;then the 2mth

**convergent**is given by the formula FlM = A [ Fn + |L \ by (203) and (210). 198 F°r example, in approximating to ^/29 above, there are five recurring ...

Page 97

is

is

and divergent if y— a— /3 is zero. (239 v.) Let the hypergeometrical series (291)

...

is

**convergent**if a: is < 1, and divergent if x is > 1 ; (239 ii.) and if a = 1, the seriesis

**convergent**if y — a— /3 is positive, divergent if y— o— /3 is negative, (239 iv.)and divergent if y— a— /3 is zero. (239 v.) Let the hypergeometrical series (291)

...

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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