Elements of Algebra

Review\n"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" equation, and of quadratic forms. The combination of Euler's and Lagrange's tests, of experimental and theoretical research in Weil's description, is justly celebrated by the editors of Euler's Opera omnia, who print the two together, and it is good to see this classic back in print in English. Every library without much Euler should at least have this volume. It is accompanied by an excerpt of Horner's memoir on the life of Euler, and a eulogy by Truesdell, with a useful bibliography." -- MATHEMATICAL REVIEWS\nI. Containing the Analysis of Determinate Quantities.- Section I. Of the Different Methods of calculating Simple Quantities.- Chap. I. Of Mathematics in general.- II. Explanation of the signs + plus and - minus.- III. Of the Multiplication of Simple Quantities.- IV. Of the Nature of whole Numbers, or Integers, with respect to their Factors.- V. Of the Division of Simple Quantities.- VI. Of the Properties of Integers, with respect to their Divisors.- VII. Of Fractions in general.- VIII. Of the Properties of Fractions.- IX. Of the Addition and Subtraction of Fractions.- X. Of the Multiplication and Division of Fractions.- XI. Of Square Numbers.- XII. Of Square Roots, and of Irrational Numbers resulting from them.- XIII. Of Impossible, or Imaginary Quantities, which arise from the same source.- XIV. Of Cubic Numbers.- XV. Of Cube Roots, and of Irrational Numbers resulting from them.- XVI. Of Powers in general.- XVII. Of the Calculation of Powers.- XVIII. Of Roots, with relation to Powers in general.- XIX. Of the Method of representing Irrational Numbers by Fractional Exponents.- XX. Of the different Methods of Calculation, and of their Mutual Connexion.- XXI. Of Logarithms in general.- XXII. Of the Logarithmic Tables now in use.- XXIII. Of the Method of expressing Logarithms.- Section II. Of the different Methods of calculating Compound Quantities.- Chap. 1. Of the Addition of Compound Quantities.- II. Of the Subtraction of Compound Quantities.- III. Of the Multiplication of Compound Quantities.- IV. Of the Division of Compound Quantities.- V. Of the Resolution of Fractions into Infinite Series.- VI. Of the Squares of Compound Quantities.- Chap. VII. Of the Extraction of Roots applied to Compound Quantities.- VIII. Of the Calculation of Irrational Quantities.- IX. Of Cubes, and of the Extraction of Cube Roots.- X. Of the higher Powers of Compound Quantities.- XI. Of the Transposition of the Letters, on which the demonstration of the preceding Rule is founded.- XII. Of the Expression of Irrational Powers by Infinite Series.- XIII. Of the Resolution of Negative Powers.- Section III. Of Ratios and Proportions.- Chap. I. Of Arithmetical Ratio, or of the Difference between two Numbers.- II. Of Arithmetical Proportion.- III. Of Arithmetical Progressions.- IV. Of the Summation of Arithmetical Progressions.- V. Of Figurate, or Polygonal Numbers.- VI. Of Geometrical Ratio.- VII. Of the greatest Common Divisor of two given Numbers.- VIII. Of Geometrical Proportions.- IX. Observations on the Rules of Proportion and their Utility.- X. Of Compound Relations.- XI. Of Geometrical Progressions.- XII. Of Infinite Decimal Fractions.- XIII. Of the Calculation of Interest.- Section IV. Of Algebraic Equations, and of the Resolution of those Equations.- Chap. I Of the Solution of Problems in General.- II. Of the Resolution of S