## Formulas and theorems in pure mathematics |

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Page 54

If n be

and therefore universally true ; because the form of an algebraical product is not

altered by changing the letters involved into fractional or

If n be

**negative**the expansion reduces to ... (1) is true when m and n are integers,and therefore universally true ; because the form of an algebraical product is not

altered by changing the letters involved into fractional or

**negative**quantities.Page 116

413 If all the terms of an even order are of one sign, and all the rest are of another

sign, there is no

root. 415 If all the indices are even, and all the 116 THEORY OF EQUATIONS.

413 If all the terms of an even order are of one sign, and all the rest are of another

sign, there is no

**negative**root. 414 Thus z*— x' + x'— 3 + 1 = 0 has no**negative**root. 415 If all the indices are even, and all the 116 THEORY OF EQUATIONS.

Page 703

A curve is reckoned convex or concave towards the axis of as according as yy^ is

positive or

exists where the tangent has a limiting position, and therefore where yx takes a ...

A curve is reckoned convex or concave towards the axis of as according as yy^ is

positive or

**negative**. POINTS OF INFLEXION. 5175 -4 point of inflexion (Pig. 96)exists where the tangent has a limiting position, and therefore where yx takes a ...

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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