## Formulas and theorems in pure mathematics |

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Page 232

Additional Theorems. 1094 The sum of the

P from n equidistant points on a circle whose centre is 0 and radius r = n(r*-{-

OP1). Proof.— Sum the values of PB>, PC, &c., given in (819), and apply (803).

Additional Theorems. 1094 The sum of the

**squares**of the distances of any pointP from n equidistant points on a circle whose centre is 0 and radius r = n(r*-{-

OP1). Proof.— Sum the values of PB>, PC, &c., given in (819), and apply (803).

Page 906

multiples of : C.2. non-pentagonal th : J.31. numbor of integers primo to n in nl = <

t> (n) : L.57. odd: A.l, : and primo to all

LM.15 : sol. by ell. functions, Mo. 63. perfect : C.81 : N.79. polygonal, Fermat's th.

multiples of : C.2. non-pentagonal th : J.31. numbor of integers primo to n in nl = <

t> (n) : L.57. odd: A.l, : and primo to all

**squares**, C.67. Pollian equation : prA.49 :LM.15 : sol. by ell. functions, Mo. 63. perfect : C.81 : N.79. polygonal, Fermat's th.

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2

asq.: E.17. 4

diff. of two to be a sq. : Mem.18. 2 sums of 8 sqs. into 8 sqs. : Me. 78. a sum of 4 ...

2

**squares**whose sum is a sq. : E.20 : N.50. 3**squares**, the sum of every two beingasq.: E.17. 4

**squares**, the sum of every two being a sq. : E.16. 3 nos., the sum ordiff. of two to be a sq. : Mem.18. 2 sums of 8 sqs. into 8 sqs. : Me. 78. a sum of 4 ...

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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