## Formulas and theorems in pure mathematics |

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Page 118

sign, there is at least one less than the same number of

the cubic equation z* + 4a; — 7 = 0, there must be two

equation as8— 1 = 0 there are, for certain, four

sign, there is at least one less than the same number of

**imaginary roots**. Thus, inthe cubic equation z* + 4a; — 7 = 0, there must be two

**imaginary roots**. And in theequation as8— 1 = 0 there are, for certain, four

**imaginary roots**. 423 If an even ...Page 129

In the former case, there will be one real and two

case, three real roots. BIQUADRATIC EQUATIONS. 492 Descartes' Solution. —

To solve the equation x* + qa* + rx + s = 0 (i.) the term in 3? having been

removed ...

In the former case, there will be one real and two

**imaginary roots**; in the lattercase, three real roots. BIQUADRATIC EQUATIONS. 492 Descartes' Solution. —

To solve the equation x* + qa* + rx + s = 0 (i.) the term in 3? having been

removed ...

Page 682

4944 The expression (4943) is the last term of the equation whose roots are the

squares of the differences of the roots of the cubic in k, and when it is positive, the

cubic in k has two

4944 The expression (4943) is the last term of the equation whose roots are the

squares of the differences of the roots of the cubic in k, and when it is positive, the

cubic in k has two

**imaginary roots**; when it is negative, three real roots ; and ...### What people are saying - Write a review

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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