Intro
Preface
Translator's Introduction
0.1 The Lehrbuch Project
0.2 Doing Algebra with Classes
0.3 From Boole to Boolean Algebra
References
Contents
1 Numbers
1.1 The Mathematical Sciences
1.2 Numbers in General
1.3 What Makes Counting Possible?
1.4 When Do We Count?
1.5 The Emergence or Construction of the Natural Numbers
1.6 The Appellation of a Number
1.7 The Concept of Multiplicity
1.8 Numbers as Measures of Numerousness
1.9 Numbers as Rules
1.10 The General Purpose of Numbers
1.11 Cardinal and Ordinal Numbers

1.12 Independence of Numbers from the Ordering Imposed by the Counting Process
1.13 A Single Axiom
1.14 A Fundamental Proposition
1.15 Calculation: Expressions
1.16 Relations: Equations and Inequalities
1.17 Propositions About Equations
1.18 More on Equations
1.19 Ambiguous Expressions
1.20 Logical Subordination
1.21 Substitution
1.22 Parentheses
1.23 Literal and Numerical Numbers
1.24 Use of Letters Justified: Principles of Nomenclature
1.25 Use of Letters: Motivations and Benefits
1.26 Analytic and Synthetic Equations
1.27 Theorems, Rules

1.28 Constant and Variable Numbers, Functions
1.29 Conclusion
References
2 The Three Direct Operations
2.1 Independent Treatment of Addition: Concepts and Terminology
2.2 First Law of Addition
2.3 Second Law of Addition
2.4 The Two Laws Combined
2.5 Addendum on Inequalities
2.6 Recursive Treatment of Addition: Number and Sum
2.7 The Associative Law for Trinomials
2.8 The Associative Law for Polynomials
2.9 The Commutative Law for Binomials
2.10 The Commutative Law for Polynomials
2.11 Independent Treatment of Multiplication: Basic Concepts

2.12 The Commutative Law of Multiplication
2.13 The Associative Law of Multiplication
2.14 Combination and Extension of the Two Laws
2.15 Expanded Definition of Product
Dirichlet's Proof of the Fundamental Theorem
2.16 The Distributive Laws
2.17 Extension of the Distributive Laws
Multiplying Out and Factoring
2.18 Fusion of the Distributive Laws in the Rule for Multiplying Polynomials
2.19 Toward an Alternative Treatment of the Foregoing
2.20 Additional Properties of Inequalities
2.21 Recursive Treatment of Multiplication: Concept and Laws

2.22 Another Proof of the Fundamental Theorem
2.23 Independent Treatment of Elevation: Potentiation and Exponentiation
2.24 Laws Governing These Operations
the Iteration Law
2.25 The Second Law
2.26 The Third Law
2.27 Addendum on Inequalities
2.28 Recursive Treatment of Elevation
2.29 Review
Iteration
References
3 The Four Inverse Operations
3.1 Introduction
Inversion
3.2 Inversion of Univocal Operations: Subtraction
3.3 Division
3.4 Roots and Logarithms
3.5 Overview of the Operations, Expressions, and Operands
3.6 The Transposition Rules