## Formulas and theorems in pure mathematics |

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Page 220

1025 There is a

D' for common points, and the circles of one species intersect all the circles of the

1025 There is a

**conjugate**system of circles having B, R for limiting points, and D,D' for common points, and the circles of one species intersect all the circles of the

**conjugate**system of the other species orthogonally (1005). Thus, in figures (1) ...Page 227

1065 If Ti,. o, be the quadratic expressions in (1063) for two pairs of points, and if

u represent a third pair harmonically

points u will also be harmonically

« ...

1065 If Ti,. o, be the quadratic expressions in (1063) for two pairs of points, and if

u represent a third pair harmonically

**conjugate**with », and «„ then the pair ofpoints u will also be harmonically

**conjugate**with every pair given by the equation« ...

Page 256

1282 If the tangent at P meets any pair of

is constant and equal to OB*. Pkoof. — Let CA, CB (Figs. 1205) be the

radii, the figures being deformed through any angle. By similar triangles, PT ...

1282 If the tangent at P meets any pair of

**conjugate**diameters in T, T, then PT.PTis constant and equal to OB*. Pkoof. — Let CA, CB (Figs. 1205) be the

**conjugate**radii, the figures being deformed through any angle. By similar triangles, PT ...

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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