## Formulas and theorems in pure mathematics |

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Page 268

Itf(x)

continuous functions between the same limits ; then f (x)

of x between a and b. Yor f (x) must change sign somewhere between the

assigned limits ...

Itf(x)

**vanishes**when x — a, and also when x = 6, and if f(x) and f (x) arecontinuous functions between the same limits ; then f (x)

**vanishes**for some valueof x between a and b. Yor f (x) must change sign somewhere between the

assigned limits ...

Page 286

1607 If «* = 0, v = 0, w = 0 be a number of homogeneous equations of

dimensions m,n,p in the same number of variables x, y, z; then J (uvw)

and if the dimensions are equal Jx, Jt, Jz also

yuy + zu, ...

1607 If «* = 0, v = 0, w = 0 be a number of homogeneous equations of

dimensions m,n,p in the same number of variables x, y, z; then J (uvw)

**vanishes**,and if the dimensions are equal Jx, Jt, Jz also

**vanish**. Prook. — By (1624), xux +yuy + zu, ...

Page 289

See (1652). 1635 If a quantic, u=f(x,y,z...), involving n variables can be expressed

as a function of the second degree in Xlf Xjj ... X.-1. where the latter are linear

functions of the variables, the discriminant

, ...

See (1652). 1635 If a quantic, u=f(x,y,z...), involving n variables can be expressed

as a function of the second degree in Xlf Xjj ... X.-1. where the latter are linear

functions of the variables, the discriminant

**vanishes**. Proof.— Let u = <j>X] + ^XtX, ...

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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