Elements of Algebra by Leonhard Euler
Elements of Algebra - Table of Contents
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 Impossible or 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
What You Will Learn in Elements of Algebra
"An Introduction to the Elements of Algebra, Designed for the Use of Those who are Acquainted only with the First Principles of Arithmetic" by "Leonhard Euler" is a foundational mathematics text that has influenced generations of students and educators. The book offers a clear and systematic approach to "algebra", starting with basic arithmetic and gradually advancing to more complex topics. Euler emphasizes "conceptual understanding", ensuring learners grasp the reasoning behind each method rather than relying solely on memorization.
The book is filled with practical examples and exercises designed to develop strong "problem-solving" skills. Euler’s logical structure guides readers step by step, making it accessible to beginners while still valuable for advanced learners. Each chapter reinforces prior knowledge, helping students build confidence and a solid foundation in "foundational mathematics".
Even today, "Elements of Algebra" remains relevant for its clarity, structure, and pedagogical approach. It highlights "algebraic principles" in a way that is both timeless and practical, bridging historical methods with modern learning needs. Euler’s work is celebrated not just for its mathematical content but for its enduring influence on how algebra is taught and understood around the world.
Book Details & Specifications
Title:
Elements of Algebra by Leonhard Euler
Publisher:
Printed by Hilliard and Metcalf
Year:
1821
Pages:
238
Type:
PDF
Language:
English
ISBN-10 #:
150890118X
ISBN-13 #:
978-1508901181
License:
Public Domain Work
Amazon:
Amazon
About the Author: Leonhard Euler
The author
Leonhard Euler
, a Swiss mathematician (1707–1783), is one of history’s greatest minds in "mathematics". Known for his contributions to "algebra, calculus, number theory, and notation", Euler made complex concepts simple and accessible. He worked in St. Petersburg and Berlin, producing hundreds of papers and books, shaping modern mathematics. His book "“Elements of Algebra”" (1770) is a classic, systematic guide to "algebra". It covers basic operations, "equations, polynomials, and number theory", emphasizing understanding over memorization. Euler’s clear, logical style and practical examples make it a landmark text, still influential in teaching mathematics today.
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