## Formulas and theorems in pure mathematics |

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the aid of the Trigonometrical tables. 490 The roots of the cubic will be n cos o, n

cos ($ ir+o), n cos ($tt— a). 491 Observe that, according as -j- + ^ is positive or ...

**Equate coefficients**in the two equations ; the result ia a must now be found withthe aid of the Trigonometrical tables. 490 The roots of the cubic will be n cos o, n

cos ($ ir+o), n cos ($tt— a). 491 Observe that, according as -j- + ^ is positive or ...

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1527 Rule I.— Assume f (x) = A+Bx+Cx8 + &c. Differ- entiate both sides of the

equation. Then expand f'(x) by some known theorem, and

the two results to determine A, B, C, fyc. -•coo i? • -i , 1 a» . 1.3*» , 1.3.5** , . 1528

Ex.

1527 Rule I.— Assume f (x) = A+Bx+Cx8 + &c. Differ- entiate both sides of the

equation. Then expand f'(x) by some known theorem, and

**equate coefficients**inthe two results to determine A, B, C, fyc. -•coo i? • -i , 1 a» . 1.3*» , 1.3.5** , . 1528

Ex.

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Expand each term of the result by the Binomial Theorem, and

of like powers of 6 in tbe two expansions. STIRLING'S THEOREM. 1546 4>(x+h)-

<f> (*) = ftf (X) + A,h {f (*+A)-f (*)} •where At„ = (— l)"-B2.-r- [2n_ and ^2n+1 = 0.

Expand each term of the result by the Binomial Theorem, and

**equate coefficients**of like powers of 6 in tbe two expansions. STIRLING'S THEOREM. 1546 4>(x+h)-

<f> (*) = ftf (X) + A,h {f (*+A)-f (*)} •where At„ = (— l)"-B2.-r- [2n_ and ^2n+1 = 0.

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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