Elements of Algebra by Leonhard Euler

SECTION I — METHODS OF CALCULATING SIMPLE QUANTITIES

• 1. Of Mathematics in General
• 2. Explanation of the Signs “+” (Plus) and “–” (Minus)
• 3. Of the Multiplication of Simple Quantities
• 4. Of the Nature of Whole Numbers or Integers, with Respect to Their Factors
• 5. Of the Division of Simple Quantities
• 6. Of the Properties of Integers with Respect to Their Divisors
• 7. Of Fractions in General
• 8. Of the Properties of Fractions
• 9. Of the Addition and Subtraction of Fractions
• 10. Of the Multiplication and Division of Fractions
• 11. Of Square Numbers
• 12. Of Square Roots, and of Irrational Numbers Resulting from Them
• 13. Of Imaginary Quantities, Which Arise from the Same Source
• 14. Of Cubic Numbers
• 15. Of Cube Roots, and of Irrational Numbers Resulting from Them
• 16. Of Powers in General
• 17. Of the Calculation of Powers
• 18. Of Roots with Relation to Powers in General
• 19. Of the Method of Representing Irrational Numbers by Fractional Exponents
• 20. Of the Different Methods of Calculation, and of Their Mutual Connection

SECTION II — METHODS OF CALCULATING COMPOUND QUANTITIES

• 1. Of the Addition of Compound Quantities
• 2. Of the Subtraction of Compound Quantities
• 3. Of the Multiplication of Compound Quantities
• 4. Of the Division of Compound Quantities
• 5. Of the Resolution of Fractions into Infinite Series
• 6. Of the Squares of Compound Quantities
• 7. Of the Extraction of Roots Applied to Compound Quantities

SECTION III — RATIOS AND PROPORTIONS

• 1. Of Arithmetical Ratio, or of the Difference Between Two Numbers
• 2. Of Arithmetical Proportion
• 3. Of Arithmetical Progressions
• 4. Of the Summation of Arithmetical Progressions
• 5. Of Geometrical Ratio
• 6. Of the Greatest Common Divisor of Two Given Numbers
• 7. Of Geometrical Proportions
• 8. Observations on the Rules of Proportion and Their Utility
• 9. Of Compound Ratios
• 10. Of Geometrical Progressions
• 11. Of Infinite Decimal Fractions

SECTION IV — ALGEBRAIC EQUATIONS, AND THE RESOLUTION OF THOSE EQUATIONS

• 1. Of the Solution of Problems in General
• 2. Of the Resolution of Simple Equations, or Equations of the First Degree
• 3. Of the Solution of Questions Relating to the Preceding Chapter
• 4. Of the Resolution of Two or More Equations of the First Degree
• 5. Of the Resolution of Pure Quadratic Equations
• 6. Of the Resolution of Mixed Equations of the Second Degree
• 7. Of the Mixture of Equations of the Second Degree
• 8. Questions for Practice
• 9. New Demonstrations of the Fundamental Propositions of the Fifth Book of Euclid’s Elements