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Index
Cover
Title Page
Copyright
Contents
Introduction
Euclid
Selections from Euclid’s Elements
Book I: Basic Geometry—Definitions, Postulates, Common Notions; and Proposition 47, (leading up to the Pythagorean Theorem)
Book V: The Eudoxian Theory of Proportion—Definitions & Propositions
Book VII: Elementary Number Theory—Definitions & Propositions
Book IX: Proposition 20: The Infinitude of Prime Numbers
Book IX: Proposition 36: Even Perfect Numbers
Book X: Commensurable and Incommensurable Magnitudes
Archimedes
Selections from The Works of Archimedes
On the Sphere and Cylinder, Books I and II
Measurement of a Circle
The Sand Reckoner
The Methods
Diophantus
Selections from Diophantus of Alexandria, A Study in the History of Greek Algebra
Book II Problems 8–35
Book III Problems 5–21
Book V Problems 1–29
René Descartes
The Geometry of Rene Descartes
Isaac Newton
Selections from Principia
On First and Last Ratios of Quantities
Leonhard Euler
On the sums of series of reciprocals (De summis serierum reciprocarum)
The Seven Bridges of Konigsberg
Proof that Every Integer is A Sum of Four Squares
Pierre Simon Laplace
A Philosophical Essay on Probabilities
Jean Baptiste Joseph Fourier
Selection from The Analytical Theory of Heat
Chapter III: Propagation of Heat in an Infinite Rectangular Solid (The Fourier series)
Carl Friedrich Gauss
Selections from Disquisitiones Arithmeticae (Arithmetic Disquisitions)
Section III Residues of Powers
Section IV Congruences of the Second Degree
Augustin-Louis Cauchy
Selections from Oeuvres complètes d’Augustin Cauchy Résumé des leçons données à l’École Royale Polytechnique sur le calcul infinitésimal (1823), series 2, vol. 4
Lessons 3–4 on differential calculus
Lessons 21–24 on the integral
Nikolai Ivanovich Lobachevsky
Geometrical Researches on the Theory of Parallels
János Bolyai
The Science of Absolute Space
Évariste Galois
On the conditions that an equation be soluble by radicals
Of the primitive equations which are soluble by radicals
On Groups and Equations and Abelian Integrals
George Boole
An Investigation of the Laws of Thought
Bernhard Riemann
On the Representability of a Function by Means of a Trigonometric Series (Ueber die Darstellbarkeit eine Function durch einer trigonometrische Reihe)
On the Hypotheses which lie at the Bases of Geometry (Ueber die Hypothesen, welche der Geometrie zu Grunde liegen)
On the Number of Prime Numbers Less than a Given Quantity (Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse)
Karl Weierstrass
Selected Chapters on the Theory of Functions, Lecture Given in Berlin in 1886, with the Inaugural Academic Speech, Berlin 1857
§ 7 Gleichmässige Stetigkeit (Uniform Continuity)
Richard Dedekind
Essays on the Theory of Numbers
Georg Cantor
Selections from Contributions to the Founding of the Theory of Transfinite Numbers
Articles I and II
Henri Lebesgue
Selections from Integrale, Longeur, Aire (Intergral, Length, Area)
Preliminaries and Integral
Kurt Gödel
On Formally Undecidable Propositions of Principia Mathematica and Related Systems
Alan Turing
On computable numbers with an application to the Entscheidungsproblem, Proceedings of the London Mathematical Society
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