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| Introduction | |
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| Arithmetic | |
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| Calculating with Natural Numbers | |
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| Introduction of Numbers in the Schools | |
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| The Fundamental Laws of Reckoning | |
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| The Logical Foundations of Operations with Integers | |
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| Practice in Calculating with Integers | |
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| The First Extension of the Notion of Number | |
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| Negative Numbers | |
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| Fractions | |
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| Irrational Numbers | |
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| Concerning Special Properties of Integers | |
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| Complex Numbers | |
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| Ordinary Complex Numbers | |
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| Higher Complex Numbers, especially Quaternions | |
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| Quaternion Multiplication--Rotation and Expansion | |
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| Complex Numbers in School Instruction | |
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| Concerning the Modern Development and the General Structure of Mathematics | |
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| Algebra | |
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| Real Equations with Real Unknowns | |
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| Equations with one parameter | |
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| Equations with two parameters | |
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| Equations with three parameters [lambda], [mu], [nu] | |
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| Equations in the field of complex quantities | |
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| The fundamental theorem of algebra | |
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| Equations with a complex parameter | |
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| The "pure" equation | |
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| The dihedral equation | |
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| The tetrahedral, the octahedral, and the icosahedral equations | |
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| Continuation: Setting up the Normal Equation | |
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| Concerning the Solution of the Normal Equations | |
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| Uniformization of the Normal Irrationalities by Means of Transcendental Functions | |
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| Solution in Terms of Radicals | |
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| Reduction of Genral Equations to Normal Equations | |
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| Analysis | |
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| Logarithmic and Exponential Functions | |
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| Systematic Account of Algebraic Analysis | |
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| The Historical Development of the Theory | |
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| The Theory of Logarithms in the Schools | |
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| The Standpoint of Function Theory | |
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| The Goniometric Functions | |
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| Theory of the Goniometric Functions | |
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| Trigonometric Tables | |
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| Purely Trigonometric Tables | |
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| Logarithmic--Trigonometric Tables | |
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| Applications of Goniometric Functions | |
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| Trigonometry, in particular, spherical trigonometry | |
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| Theory of small oscillations, especially those of the pendulum | |
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| Representation of periodic functions by means of series of goniometric functions (trigonometric series) | |
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| Concerning Infinitesimal Calculus Proper | |
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| General Considerations in Infinitesimal Calculus | |
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| Taylors Theorem | |
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| Historical and Pedagogical Considerations | |
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| Supplement | |
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| Transcendence of the Numbers e and [pi] | |
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| The Theory of Assemblages | |
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| The Power of an Assemblage | |
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| Arrangement of the Elements of an Assemblage | |
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| Index of Names | |
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| Index of Contents | |