## Formulas and theorems in pure mathematics |

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Page 62

P»-i+P»-a _ p The true value of the

a»P»-i +/>»-» in which a'H is the complete quotient or value of the

P»-i+P»-a _ p The true value of the

**continued fraction**will be expressed 163 F =a»P»-i +/>»-» in which a'H is the complete quotient or value of the

**continued****fraction**commencing with an. 164 P»q»-i— p.-i9» = ±1 alternately, by (162).Page 64

174 F is incommensurable when the components are all proper fractions and

infinite in number. ... 180 If in the

always; then, by (168), P» = bi + bibi+b1b1b3+ ... to n terms, and qn = pn+l. 181 If

...

174 F is incommensurable when the components are all proper fractions and

infinite in number. ... 180 If in the

**continued fraction**V (167), we have an = bn + 1always; then, by (168), P» = bi + bibi+b1b1b3+ ... to n terms, and qn = pn+l. 181 If

...

Page 65

Vn is equal to a

and w+lth components being J_ vx p— ig. [Proved by Induction. V ' V-l + X* vH-\-

cv 184 The sign of x may be changed in either of the statements in (182) or ...

Vn is equal to a

**continued fraction**7(167), with n+1 components, the first, second,and w+lth components being J_ vx p— ig. [Proved by Induction. V ' V-l + X* vH-\-

cv 184 The sign of x may be changed in either of the statements in (182) or ...

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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