## Formulas and theorems in pure mathematics |

### From inside the book

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Page 58

See (97 and 98). The greatest coefficient in the expansion of (a-\-b-\-c-\- to m

terms)", n being an integer, is 140 rn — .Jy .t notation of (95) where qm+k = n.

Obtained by making the denominator in (138) as small aa possible.

See (97 and 98). The greatest coefficient in the expansion of (a-\-b-\-c-\- to m

terms)", n being an integer, is 140 rn — .Jy .t notation of (95) where qm+k = n.

Obtained by making the denominator in (138) as small aa possible.

**LOGARITHMS**.Page 59

That is — The

number divided by the

taken to any the same base at pleasure. 146 log6 a = T-t-7. Put c=a in (145).

That is — The

**logarithm**of a number to any base is equal to the**logarithm**of thenumber divided by the

**logarithm**of the base, the two last named**logarithms**beingtaken to any the same base at pleasure. 146 log6 a = T-t-7. Put c=a in (145).

Page 404

By differentiating the

O p + 1 when fi = oo , = -0577215,664901,532860,60 ... (Euler). All other values

of +(x), when * is a commensurable quantity, may be made to depend upon the ...

By differentiating the

**logarithm**of (2293). 2744 CoR.^(l) = log/i-l— J.-!- ... — i_, , &O p + 1 when fi = oo , = -0577215,664901,532860,60 ... (Euler). All other values

of +(x), when * is a commensurable quantity, may be made to depend upon the ...

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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