## Formulas and theorems in pure mathematics |

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Page 734

For by projecting the equal lines upon AB, we get NL = BN' and BN = N'L',

therefore BL = BL' — NN = a

Make lea = d and X = b. Then B1 coincides with D, P with C, and P1 with C.

Replace VC, ...

For by projecting the equal lines upon AB, we get NL = BN' and BN = N'L',

therefore BL = BL' — NN = a

**constant**, by (5402). 5409 Case V.— (Fig. 142.)Make lea = d and X = b. Then B1 coincides with D, P with C, and P1 with C.

Replace VC, ...

Page 736

Then, if the angle POB be kept

POB (Euc. m. 21), will also be

B describes the other. If the bar PO carries a plane along with it, every point in ...

Then, if the angle POB be kept

**constant**by the tie-bar PB, PQB, being one half ofPOB (Euc. m. 21), will also be

**constant**, and therefore, while P describes one line,B describes the other. If the bar PO carries a plane along with it, every point in ...

Page 900

pd

E.19. * quadratic for ym, giving the directions : 5810. of two homofocal quadrics :

L.45. of quartic surfaces : C.59 : L.76. of ruled surfaces : C 78. spherical : C.362 ...

pd

**constant**along it : 5836. projected from an umbilic into con- focal Cartesians :E.19. * quadratic for ym, giving the directions : 5810. of two homofocal quadrics :

L.45. of quartic surfaces : C.59 : L.76. of ruled surfaces : C 78. spherical : C.362 ...

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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