# Elements of Algebra

Springer Science & Business Media, Dec 6, 2012 - Mathematics - 595 pages
""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

 Leonard Euler Supreme Geometer by C Truesdell 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 Copyright