## A Treatise on Elementary and Higher AlgebraReprint of the original, first published in 1859. |

### Contents

DEFINITIONS AND NOTATION | 1 |

Vinculum Parenthesis etc Coefficients | 8 |

SECTION IV | 17 |

Product of a Polynomial and a Monomial | 24 |

Polynomial Products 86 | 54 |

SECTION V | 62 |

Division of Polynomials | 68 |

Horners Synthetic Division | 87 |

Method of finding any Power of a Polynomial | 279 |

Roots of Monomials | 286 |

Roots of Polynomials | 297 |

SECTION XII | 315 |

Multiplication and Division of Surds 821 | 321 |

Method of Freeing any Algebraic Expression from Surds 826 | 330 |

SECTION XII | 337 |

Algebraic and Transcendental Equations 888 | 353 |

Appendix to Multiplication and Division | 120 |

Prime and Composite Numbers | 128 |

Method of finding Prime Numbers 185 | 141 |

Rule for finding the Least Common Multiple | 150 |

Reduced to their Lowest Terms | 157 |

Addition of Fractions | 163 |

Division of Fractions | 169 |

Progressions | 175 |

SECTION IX | 182 |

Inversion | 188 |

Ex æquali in Inverse Proportion | 196 |

Method of finding any Term of a Proportion from the other Terms 203 | 203 |

Terms | 207 |

Abridged ProportionsHarmonical Proportions and Progressions | 215 |

Of the Characters 0 and and their Uses | 225 |

Application of the Principle to Examples 280 | 254 |

SECTION X | 269 |

Particular Methods of Solution illustrated by Examples | 362 |

Appendix to Simple Equations 888 | 388 |

SECTION XIV | 394 |

Questions giving rise to Quadratic Equations | 415 |

SECTION XV | 428 |

To the Reversion of Scries | 435 |

Illustration by Examples | 441 |

SECTION XVI | 454 |

SECTION XVII | 462 |

Solution of Biquadratic Equations | 469 |

Descartes Theorem | 481 |

SECTION XIX | 494 |

New and General Method of Developing the Roots of Equations | 512 |

SOLUTION OF EXPONENTIAL EQUATIONS | 521 |

SECTION XXI | 535 |

SECTION XXII | 544 |

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### Common terms and phrases

according adding arithmetical arranged ascending powers becomes called changed clear clearly coefficients common compound consequently contains correct corresponding course cube denominator denote derived difference divide dividend division divisor easily easy equal evident exact EXAMPLES exponent expressed extract factors follows fourth fraction function given equation gives greater greatest common divisor Hence imaginary inequality integer kind less limits logarithm manner mean method multiplier nearly negative roots numbers or quantities observing obtained places positive positive roots preceding prime proceed progression proportion proposed question quotient ratio real roots reduced remainder represent result rule satisfied second term shown signs similar simple solution square root stand substitution subtract successive suppose surds taken thence tion unit unknown letter variation write