## Formulas and theorems in pure mathematics |

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Page 244

1198 The diameter bisects all chords parallel to the

— (Ellipse. Fig. 1195.) — By projection from the circle (1088) QV=VQ'. (Hyperbola

.) By (1189.) 1199 Cor. 1. — The

1198 The diameter bisects all chords parallel to the

**tangent**at its extremity. Proof.— (Ellipse. Fig. 1195.) — By projection from the circle (1088) QV=VQ'. (Hyperbola

.) By (1189.) 1199 Cor. 1. — The

**tangents**at the extremities of any chord meet ...Page 256

1282 If the

is 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 ...

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 ...

Page 793

For these are the conditions of perpendicularity to the normals of the

planes at xyz and x'y'z respectively. There are three exceptional cases in which

the ratios X : fi : v have more than one set of values ; namely — 5787 I- — When <

p„ ...

For these are the conditions of perpendicularity to the normals of the

**tangent**planes at xyz and x'y'z respectively. There are three exceptional cases in which

the ratios X : fi : v have more than one set of values ; namely — 5787 I- — When <

p„ ...

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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