## Formulas and theorems in pure mathematics |

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Page 244

1198 The

— (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 ...

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 250

Draw the

1238 Cor. 2.— Hence, the

tangent at P. If QVbe a semi-chord parallel to the tangent at P, 1239 QVi = 4!PS.

Draw the

**diameter**7? IF. QW= WP; therefore QR = RO (VI. 2). Similarly Q'R' = KO.1238 Cor. 2.— Hence, the

**diameter**through P bisects all chords parallel to thetangent at P. If QVbe a semi-chord parallel to the tangent at P, 1239 QVi = 4!PS.

Page 252

The triangle SRr is always similar to the isosceles triangle 1252 To find the axes

and centre of a given central conic. (i.) Draw a right line through the centres of

two parallel chords. This line is a

found ...

The triangle SRr is always similar to the isosceles triangle 1252 To find the axes

and centre of a given central conic. (i.) Draw a right line through the centres of

two parallel chords. This line is a

**diameter**, by (1198) ; and two**diameters**sofound ...

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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