## Formulas and theorems in pure mathematics |

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Page xxiii

A right line parallel to the sido of a

and conversely. VI. 3 and A. ... A right-angled

perpendicular from the right angle upon the hypotenuse into

itself. VI.

A right line parallel to the sido of a

**triangle**cuts the othor sides proportionally ;and conversely. VI. 3 and A. ... A right-angled

**triangle**is divided by theperpendicular from the right angle upon the hypotenuse into

**triangles similar**toitself. VI.

Page 217

OQ" ; therefore, by

constant, therefore the Incus of 1" is the circle whose diameter is OQ". 1013

Example. — The inversion of a polygon produces a figure bounded by circular

arcs which ...

OQ" ; therefore, by

**similar triangles**, I OPQ = OQP, a right angle ; and OQ' isconstant, therefore the Incus of 1" is the circle whose diameter is OQ". 1013

Example. — The inversion of a polygon produces a figure bounded by circular

arcs which ...

Page 253

(ii.) By the

i.) (iii.) By the

(ii.) ; and PE = AC (1179). 1260 In the parabola, the chord of curvature at P.

(ii.) By the

**similar triangles**PHU, PFC (III. 31), we have PU.PF=CP.PH= 2CJy, by (i.) (iii.) By the

**similar triangles**PIU, PFE (1168), we have PI.PE = PU.PF = 2CV, by(ii.) ; and PE = AC (1179). 1260 In the parabola, the chord of curvature at 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