## Formulas and theorems in pure mathematics |

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Page 235

When the axes are equal, or BC=AC, the ellipse becomes a circle, and the

the orthogonal projection of a circle or rectangular

When the axes are equal, or BC=AC, the ellipse becomes a circle, and the

**hyperbola**becomes rectangular or a equilateral. 1158 Any ellipse or**hyperbola**isthe orthogonal projection of a circle or rectangular

**hyperbola**respectively. Proof.Page 245

Let PN, DN be the ordinates at the extremities of conjugate diameters, and PT the

tangent at P. Let the ordinates at N and R in the ellipse, but at T and 0 in the

Let PN, DN be the ordinates at the extremities of conjugate diameters, and PT the

tangent at P. Let the ordinates at N and R in the ellipse, but at T and 0 in the

**hyperbola**, meet the auxiliary circle in p and d ; then 1205 CN=dR, CR=pN. Proof.Page 599

THE

— By (4273) and (4050). Here x = OK, y = PK. Equations of the tangent at P, (x, y)

. 4388 xy'+*y = ?(**+*>*)□ 4389 y — mx+Vm (a8+62)- 4390 m = — —2L x 4391 ...

THE

**HYPERBOLA**REFERRED TO THE ASYMPTOTES. 4387 xy=\{a*+V). Proof.— By (4273) and (4050). Here x = OK, y = PK. Equations of the tangent at P, (x, y)

. 4388 xy'+*y = ?(**+*>*)□ 4389 y — mx+Vm (a8+62)- 4390 m = — —2L x 4391 ...

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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