## Formulas and theorems in pure mathematics |

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Page 227

1065 If Ti,. o, be the quadratic expressions in (1063) for two

u represent a third

points u will also be harmonically conjugate with every

« ...

1065 If Ti,. o, be the quadratic expressions in (1063) for two

**pairs**of points, and ifu 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 228

Let p, p'\ q, q'; r, r'\ s, s be the distances of the

centre. In the anharmonic ratio of any fonr of the points, for instance {pq'rs},

substitute p = k*-i-p', q = k'-r-q, Ac, and the result is the anharmomo ratio j^'grV}.

1070 Any ...

Let p, p'\ q, q'; r, r'\ s, s be the distances of the

**pairs**of inverse points from thecentre. In the anharmonic ratio of any fonr of the points, for instance {pq'rs},

substitute p = k*-i-p', q = k'-r-q, Ac, and the result is the anharmomo ratio j^'grV}.

1070 Any ...

Page 649

The other

intersection of each

obtained by substituting unity for \/ — l in the given coordinates, and drawing the

six lines ...

The other

**pairs**of lines PQ, BS and PB, QS are imaginary. But the points ofintersection of each

**pair**are real, and are identical with the points which areobtained by substituting unity for \/ — l in the given coordinates, and drawing the

six lines ...

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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