## Formulas and theorems in pure mathematics |

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Page 144

The determinant 6i «2 6, is equivalent to aj>i — (hbx, and is called a determinant

of the second order. A determinant of the third order is Oj at a8 = ^(ftgCj— 6sci) +

a2(6sc1— 61cg) + as(61cil-6,Ci)- &i bt bt Cl Cj Cg Another

...

The determinant 6i «2 6, is equivalent to aj>i — (hbx, and is called a determinant

of the second order. A determinant of the third order is Oj at a8 = ^(ftgCj— 6sci) +

a2(6sc1— 61cg) + as(61cil-6,Ci)- &i bt bt Cl Cj Cg Another

**notation**is 2 ± aybtcs...

Page 266

An abbreviated

operation of multiplication, it will be requisite, in transferring the operation to

differentiation, to change all such indices to suffixes when the abbreviated

An abbreviated

**notation**is dx, d^, d^, d^.^, &c. Since dxXdx = rf* in the symbolicoperation of multiplication, it will be requisite, in transferring the operation to

differentiation, to change all such indices to suffixes when the abbreviated

**notation**is ...Page 267

such reasons I have introduced the shorter

pages. ( All such abbreviated forms of differential coefficients as y'y'y" ' . . . or y y y.

.., though convenient in practice, are incomplete expressions, because the ...

such reasons I have introduced the shorter

**notation**experimentally in thesepages. ( All such abbreviated forms of differential coefficients as y'y'y" ' . . . or y y y.

.., though convenient in practice, are incomplete expressions, because 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