Euler

Leonhard Euler, The Elements of Algebra (Vollständige Anleitung zur Algebra)

English table of contents

German table of contents

Part I. “Containing the Analysis of Determinate Quantities.”

Section I. “Of the different Methods of calculating Simple Quantities.”

Section II. “Of the different Methods of calculating Compound Quantities.”

Section III. “Of Ratios and Proportions.”

Section IV. “Of Algebraic Equations, and the Resolution of Them.”

Part II. “Containing the Analysis of Indeterminate Quantities.”

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Part I. “Containing the Analysis of Determinate Quantities.”

Section I. “Of the different Methods of calculating Simple Quantities.”

Part I. Section I. Chapter 1. "Mathematics in general."

Part I. Section I. Chapter 2. "Explanation of the Signs + Plus and - Minus."

Part I. Section I. Chapter 3. "Of the Multiplication of Simple Quantities."

Part I. Section I. Chapter 4. "Of the Nature of whole Numbers, or Integers, with respect to their Factors."

Part I. Section I. Chapter 5. "Of the Division of Simple Quantities."

Part I. Section I. Chapter 6. "Of the Properties of Integers, with respect to their Divisors."

Part I. Section I. Chapter 7. "Of Fractions in general."

Part I. Section I. Chapter 8. "Of the Properties of Fractions."

Part I. Section I. Chapter 9. "Of the Addition and Subtraction of Fractions."

Part I. Section I. Chapter 10. "Of the Multiplication and Division of Fractions."

Part I. Section I. Chapter 11. "Of Square Numbers."

Part I. Section I. Chapter 12. "Of Square Roots, and of Irrational Numbers resulting from them."

Part I. Section I. Chapter 13. "Of Impossible, or Imaginary Quantities, which arise from the same source."

Part I. Section I. Chapter 14. "Of Cubic Numbers."

Part I. Section I. Chapter 15. "Of Cube Roots, and of Irrational Numbers resulting from them."

Part I. Section I. Chapter 16. "Of Powers in general."

Part I. Section I. Chapter 17. "Of the Calculation of Powers."

Part I. Section I. Chapter 18. "Of Roots, with relation to Powers in general."

Part I. Section I. Chapter 19. "Of the Method of representing Irrational Numbers by Fractional Exponents."

Part I. Section I. Chapter 20. "Of the different Methods of Calculation, and of their mutual Connection."

Part I. Section I. Chapter 21. "Of Logarithms in general."

Part I. Section I. Chapter 22. "Of the Logarithmic Tables now in use."

Part I. Section I. Chapter 23. "Of the Method of expressing Logarithms."

Section II. “Of the different Methods of calculating Compound Quantities.”

Part I. Section II. Chapter 1. "Of the Addition of Compound Quantities."

Part I. Section II. Chapter 2. "Of the Subtraction of Compound Quantities."

Part I. Section II. Chapter 3. "Of the Multiplication of Simple Quantities."

Part I. Section II. Chapter 4. "Of the Division of Compound Quantities."

Part I. Section II. Chapter 5. "Of the Resolution of Fractions into Infinite Series."

Part I. Section II. Chapter 6. "Of the Squares of Compound Quantities."

Part I. Section II. Chapter 7. "Of the Extraction of Roots applied to Compound Quantities."

Part I. Section II. Chapter 8. "Of the Calculation of Irrational Quantities."

Part I. Section II. Chapter 9. "Of Cubes, and of the Extraction of Cube Roots."

Part I. Section II. Chapter 10. "Of the higher Powers of Compound Quantities."

Part I. Section II. Chapter 11. "Of the Transposition of the Letters, on which the demonstration of the preceding Rule is founded."

Part I. Section II. Chapter 12. "Of the Expression of Irrational Powers by Infinite Series."

Part I. Section II. Chapter 13. "Of the Resolution of Negative Powers."

Section III. “Of Ratios and Proportions.”

Part I. Section III. Chapter 1. "Of Arithmetical Ratio, or of the Difference between two Numbers."

Part I. Section III. Chapter 2. "Of Arithmetical Proportion."

Part I. Section III. Chapter 3. "Of Arithmetical Progressions."

Part I. Section III. Chapter 4. "Of the Summation of Arithmetical Progressions."

Part I. Section III. Chapter 5. "Of Figurate, or Polygonal Numbers."

Part I. Section III. Chapter 6. "Of Geometrical Ratio."

Part I. Section III. Chapter 7. "Of the Greatest Common Divisor of two given Numbers."

Part I. Section III. Chapter 8. "Of Geometrical Proportions."

Part I. Section III. Chapter 9. "Observations on the Rules of Proportion and their Utility."

Part I. Section III. Chapter 10. "Of Compound Relations."

Part I. Section III. Chapter 11. "Of Geometrical Progressions."

Part I. Section III. Chapter 12. "Of Infinite Decimal Fractions."

Part I. Section III. Chapter 13. "Of the Calculation of Interest."

Section IV. “Of Algebraic Equations, and the Resolution of Them.”

Part I. Section IV. Chapter 1. "Of the Solution of Problems in General."

Part I. Section IV. Chapter 2. "Of the Resolution of Simple Equations, or Equations of the First Degree."

Part I. Section IV. Chapter 3. "Of the Solution of Questions relating to the preceding Chapter."

Part I. Section IV. Chapter 4. "Of the Resolution of two or more Equations of the First Degree."

Part I. Section IV. Chapter 5. "Of the Resolution of Pure Quadratic Equations."

Part I. Section IV. Chapter 6. "Of the Resolution of Mixed Equations of the Second Degree."

Part I. Section IV. Chapter 7. "Of the Extraction of the Roots of Polygon Numbers."

Part I. Section IV. Chapter 8. "Of the Extraction of the Square Roots of Binomials."

Part I. Section IV. Chapter 9. "Of the Nature of Equations of the Second Degree."

Part I. Section IV. Chapter 10. "Of Pure Equations of the Third Degree."

Part I. Section IV. Chapter 11. "Of the Resolution of Complete Equations of the Third Degree."

Part I. Section IV. Chapter 12. "Of the Rule of Cardano, or of Scipione del Ferro."

Part I. Section IV. Chapter 13. "Of the Resolution of Equations of the Fourth Degree."

Part I. Section IV. Chapter 14. "Of the Rule of Bombelli, for reducing the Resolution of Equations of the Fourth Degree to that of Equations of the Third Degree."

Part I. Section IV. Chapter 15. "Of a new Method of resolving Equations of the Fourth Degree."

Part I. Section IV. Chapter 16. "Of the Resolution of Equations by Approximation."

Part II. “Containing the Analysis of Indeterminate Quantities.”

Part II. Chapter 1. "Of the Resolution of Equations of the First Degree, which contain more than one unknown Quantity."

Part II. Chapter 2. "Of the Rule which is called Regula Coeci, for determining, by means of two Equations, three or more Unknown Quantities."

Part II. Chapter 3. "Of Compound Indeterminate Equations, in which one of the Unknown Quantities does not exceed the First Degree."

Part II. Chapter 4. "Of the Method of rendering Surd Quantities of the form √(𝑎+𝑏𝑥+c𝑥𝑥) rational."

Part II. Chapter 5. "Of the Cases in which the Formula 𝑎+𝑏𝑥+𝑐𝑥𝑥 can never become a Square."

Part II. Chapter 6. "Of the Cases in Integer Numbers, in which the Formula 𝑎𝑥𝑥+𝑏 becomes a Square."

Part II. Chapter 7. "Of a particular Method, by which the Formula 𝑎𝑛𝑛+1 becomes a Square in Integers."

Part II. Chapter 8. "Of the Method of rendering the Irrational Formula √(𝑎+𝑏𝑥+𝑐𝑥𝑥+𝑑𝑥³) Rational."

Part II. Chapter 9. "Of the Method of rendering rational the incommensurable Formula √(𝑎+𝑏𝑥+𝑐𝑥𝑥+𝑑𝑥³+𝑒𝑥⁴)."

Part II. Chapter 10. "Of the Method of rendering rational the irrational Formula ∛(𝑎+𝑏𝑥+𝑐𝑥𝑥+𝑑𝑥³)"

Part II. Chapter 11. "Of the Resolution of the Formula 𝑎𝑥𝑥+𝑏𝑥𝑦+𝑐𝑦𝑦 into its Factors."

Part II. Chapter 12. "Of the Transformation of the Formula 𝑎𝑥𝑥+𝑐𝑦𝑦 into Squares and higher Powers."

Part II. Chapter 13. "Of some Expressions of the Form 𝑎𝑥⁴+𝑏𝑦⁴, which are not reducible to Squares."

Part II. Chapter 14. "Solution of some Questions that belong to this Part of Algebra."

Part II. Chapter 15. "Solutions of some Questions in which Cubes are required."

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Joseph Louis de Lagrange. Additions aux éléments d’algèbre d’Euler. Analyse indéterminée.

English translation PDF

French text PDF

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Editions

1. Leonhard Euler. Vollständige Anleitung zur Algebra. Mit den Zusätzen von Joseph Louis Lagrange. Herausgegeben von Heinrich Weber. B. G. Teubner. Leipzig and Berlin. 1911. Leonhardi Euleri Opera omnia. Series prima. Opera mathematica. Volumen primum.
   • Springer
2. Leonhard Euler. Vollständige Anleitung zur Algebra. Kayserlichen Akademie der Wissenschaften. St. Petersburg. 1771.
   • ETH-Bibliothek Zürich
   • Bayerische Staatsbibliothek. Münchener DigitalisierungsZentrum (MDZ)
3. Leonhard Euler. Vollständige Anleitung zur Algebra. Zweyter Theil. Von Auflösung algebraischer Gleichungen und der unbestimmten Analytic. Kays. Acad. der Wissenschaften. St. Petersburg. 1770.
   • Deutsches Textarchiv
4. Leonhard Euler. Élémens d’algèbre par M. Léonard Euler, traduits de l’allemand, avec des notes et des additions. Tome Premier. De l’analyse déterminée. Translated by Jean Bernoulli. Chez Jean-Marie Bruyset, Pere & Fils. Lyon. 1774.
   • BnF Gallica
5. Leonhard Euler. Élémens d’algèbre par M. Léonard Euler, traduits de l’allemand, avec des notes et des additions. Tome Second. De l’analyse indéterminée. Translated by Jean Bernoulli. Chez Jean-Marie Bruyset, Pere & Fils. Lyon. 1774.
   • BnF Gallica
6. Leonhard Euler. Elements of Algebra. Translated by Rev. John Hewlett. Third Edition. Longmans, Hurst, Rees, Orme, and Co. London. 1822.
   • Archive.org
7. Leonard Euler, Elements of Algebra, Translated by Rev. John Hewlett. (Reprinted from Elements of Algebra, Fifth Edition, Longman, Orme, and Co., London, 1840.) With an Introduction by Clifford Truesdell. Springer. 1972.
   • Springer
8. Leonhard Euler. Elements of Algebra. Translated by Rev. John Hewlett. Third Edition. Cambridge Library Collection - Mathematics. Cambridge University Press. 2009.
   • Cambridge University Press
9. Scott L. Hecht. Transcription in Microsoft Word of Hewlett’s translation. 2015.
   • Archive.org
   • Amazon.com
10. Ian Bruce. Euler’s Algebra. New translation from the German. 2016.
    • Ian Bruce. 17centurymaths.com
11. Christian Siebeneicher. Leonhard Euler. Einleitung zur Rechen-Kunst. https://www.math.uni-bielefeld.de/~sieben/Rechnen.html