## Formulas and theorems in pure mathematics |

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Page 253

The circle of curvature is the circle which passes through three coincident points

on the curve at P. 1256 Any

curvature at P. 1257 Through Q draw BQ' parallel to PH, meeting the tangent at ...

The circle of curvature is the circle which passes through three coincident points

on the curve at P. 1256 Any

**chord**PH of the circle of curvature is called a**chord**ofcurvature at P. 1257 Through Q draw BQ' parallel to PH, meeting the tangent at ...

Page 254

1260 In the parabola, the

axis, and the one drawn through the focus, are each equal to 4SP, the parameter

of the diameter at P (1241). Proof.— By (1258). The

1260 In the parabola, the

**chord**of curvature at P (Fig. 1259) drawn parallel to theaxis, and the one drawn through the focus, are each equal to 4SP, the parameter

of the diameter at P (1241). Proof.— By (1258). The

**chord**parallel to the axis ...Page 655

Eliminate B from the equations of the two tangents (4790). 4796 The

FQ and the line CE all intersect in the same point on B. Proof.— The equations of

PQ', P'Q are, by (4789), /i/i'Łą (ft-?') B-M = 0, and, by addition and subtraction, ...

Eliminate B from the equations of the two tangents (4790). 4796 The

**chords**PQ',FQ and the line CE all intersect in the same point on B. Proof.— The equations of

PQ', P'Q are, by (4789), /i/i'Łą (ft-?') B-M = 0, and, by addition and subtraction, ...

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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