## Formulas and theorems in pure mathematics |

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Page 204

20), and therefore

Again, / MGB = MED (IIT. 22) = OCT), (III. 21), by the circle circumscribing OECD.

Therefore MO is parallel to OC, and therefore

CA ...

20), and therefore

**bisects**OB. Similarly OC and OA are bisected at N and L.Again, / MGB = MED (IIT. 22) = OCT), (III. 21), by the circle circumscribing OECD.

Therefore MO is parallel to OC, and therefore

**bisects**BO. Similarly H and K**bisect**CA ...

Page 248

(1.29,6) 1226 The tangents at the extremities of a focal chord PQ, intersect at right

angles in the directrix. Proof. — (i.) They intersect in the directrix, as in (1169). (ii.)

They

(1.29,6) 1226 The tangents at the extremities of a focal chord PQ, intersect at right

angles in the directrix. Proof. — (i.) They intersect in the directrix, as in (1169). (ii.)

They

**bisect**the angles SZM, SZM' (1224), and therefore include a right angle.Page 250

Hence, the diameter through P

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

fundamental equation of the parabola, eqnation (1229) being the most important

...

Hence, the diameter through P

**bisects**all chords parallel to the tangent at P. IfQVbe a semi-chord parallel to the tangent at P, 1239 QVi = 4!PS.PV. This is the

fundamental equation of the parabola, eqnation (1229) being the most important

...

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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