## Formulas and theorems in pure mathematics |

### From inside the book

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Page 212

perpendicular to the line of centres which divides the distance between the

centres into segments, the difference of whose squares is equal to the difference

of the squares of ...

**Radical Axis**. 984 Definition. — The**radical axis**of two circles is thatperpendicular to the line of centres which divides the distance between the

centres into segments, the difference of whose squares is equal to the difference

of the squares of ...

Page 214

990 Also PX : PN = the cosine of the angle at which the circle of radius PX cuts

the

touches two fixed circles has its radius in a constant ratio to the distance of its

centre ...

990 Also PX : PN = the cosine of the angle at which the circle of radius PX cuts

the

**radical axis**. This angle is therefore constant. 991 Cor. — A circle whichtouches two fixed circles has its radius in a constant ratio to the distance of its

centre ...

Page 224

1049 Gergonne's method of describing the circles which touch three given circles

. Take Pjr, one of the four

to the given circles, centres A, B, C (1016). From 0, the

1049 Gergonne's method of describing the circles which touch three given circles

. Take Pjr, one of the four

**axes**of similitude, and find its poles a, /3, y with respectto the given circles, centres A, B, C (1016). From 0, the

**radical**centre, draw ...### What people are saying - Write a review

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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