## Elements of Algebra""This is a facsimile reprint of John Hewlett's 1840 translation of Euler's Algebra and Lagrange's Additions thereto. Most of Euler's contribution is elementary, nothing more advanced than solving quartic equations, but worth having in order to appreciate his leisurely and effective style--would that more great mathematicians wrote so well and to such pedagogic effect. However, one third of the book is his lucid treatment of questions in number theory, and it is this material that drew Lagrange's comments. Here for the first time are the rigorous treatments of continued fractions and ""Pell's. |

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### Contents

vii | |

Excerpt from the Memoir of the Life and Character of Euler by Francis | xl |

Horner Esq M P | liii |

Containing the Analysis of Determinate Quantities SECTION I | 1 |

Explanation of the signs + plus and minus | 3 |

Of the Multiplication of Simple Quantities | 6 |

Of the Nature of whole Numbers or Integers with respect to their Factors | 10 |

Of the Division of Simple Quantities | 13 |

Of the Squares of Compound Quantities | 97 |

Of the Extraction of Roots applied to Com | 100 |

Of the Transposition of the Letters on which | 115 |

Of the Resolution of Negative Powers | 123 |

Of Arithmetical Proportion | 129 |

Of Geometrical Ratio | 146 |

Of Geometrical Proportions | 152 |

SECTION IV | 186 |

Of the Properties of Integers with respect to their Divisors | 16 |

Of Fractions in general | 20 |

Of the Properties of Fractions | 24 |

Of the Addition and Subtraction of Fractions | 27 |

Of the Multiplication and Division of Fractions | 30 |

Of Square Numbers | 36 |

Of Square Roots and of Irrational Numbers re sulting from them | 38 |

Of Impossible or Imaginary Quantities which arise from the same source | 42 |

Of Cubic Numbers | 45 |

Of Cube Roots and of Irrational Numbers re sulting from them | 46 |

Of Powers in general | 48 |

Of the Calculation of Powers | 52 |

Of Roots with relation to Powers in general | 54 |

Of the Method of representing Irrational Num bers by Fractional Exponents | 56 |

Of the different Methods of Calculation and of their Mutual Connexion | 60 |

Of Logarithms in general | 63 |

Of the Logarithmic Tables now in use | 66 |

Of the Method of expressing Logarithms | 69 |

Elements of Algebra lv | 74 |

SECTION II | 76 |

Of the Subtraction of Compound Quantities | 78 |

Of the Multiplication of Compound Quantities | 79 |

Of the Division of Compound Quantities | 84 |

Of the Resolution of Fractions into Infinite Series | 89 |

Of the Solution of Questions relating to the pre | 194 |

Of the Resolution of two or more Equations | 206 |

Second Degree | 222 |

Of the Extraction of Square Roots of Binomials | 234 |

Of the Nature of Equations of the Second Degree | 244 |

Of the Resolution of Complete Equations | 253 |

XIV Of the Rule of Bombelli for reducing the | 272 |

PART II | 299 |

Of the Rule which is called Regula Caeci for | 312 |

Of the Cases in which the Formula a + ba + ca | 322 |

Of the Cases in Integer Numbers in which | 335 |

Of a particular Method by which the Formula | 342 |

Of the Method of rendering the Irrational Formula | 351 |

Of the Method of rendering rational the Incommen | 368 |

Of the Method of rendering rational the irrational | 379 |

Of the Transformation of the Formula awcy? | 396 |

Solution of some Questions that belong to this | 405 |

Solutions of some Questions in which Cubes | 449 |

Advertisement | 463 |

Of the Resolution in Integer Numbers of Equa | 530 |

A direct and general Method for finding | 537 |

Of Double and Triple Equalities | 547 |

Of the Manner of finding Algebraic Functions | 583 |

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### Common terms and phrases

Algebra already arithmetical progression become a square bers biquadrate calculation called CHAPTER coefficient common divisor consequently consider contains continued fraction crowns cube root DANIEL BERNOULLI decimal fraction denominator determine difference divided dividend divisible equal equation EULER evident example exponent expressed factors farther formula fourth geometrical progression given number gives greater number greatest common divisor Hence infinite number integer numbers irrational JOHN BERNOULLI last term lastly LEONARD EULER less let us suppose letters likewise logarithm manner mathematics method multiplied negative number of terms numbers sought observed obtain perceive positive numbers preceding prime numbers proposed question quotient ratio reduced remainder represented resolve result rule second term shew solution square number square root substitute subtract tion transform unity unknown quantity whence wherefore whole numbers