## Formulas and theorems in pure mathematics |

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Page 200

937

three straight lines, and three

through the

...

937

**Given**in position any three of the following nine data — viz., three points,three straight lines, and three

**circles**, — it is required to describe a**circle**passingthrough the

**given**points and touching the**given**lines or**circles**. The following five...

Page 201

There are two more in which the

construction is quite analogous, 0 taking the place of A. 941 IV.

A, B and the

C, ...

There are two more in which the

**circle**AG lies within the described**circle**. Theconstruction is quite analogous, 0 taking the place of A. 941 IV.

**Given**two pointsA, B and the

**circle**CD. Draw any**circle**through A, B, cutting the required**circle**inC, ...

Page 220

1027 Also, the points in which any

inverse points for the

last. 1028 Problem. —

...

1027 Also, the points in which any

**circle**of the system cuts the central axis areinverse points for the

**circle**whose centre is I and radius 8. [Proof.— Similar to thelast. 1028 Problem. —

**Given**two**circles**of a coaxal system, to describe a**circle**of...

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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