- I. Introductory
- A. Mathematics and Its Divisions
- 1. Origin of the Name
- 2. The Pythagorean Quadrivium
- 3. Plato’s Scheme
- 4. Logistic
- 5. Later Classification
- B. Mathematics in Greek Education
- C. Practical Calculation
- 1. Enumeration by Fingers
- 2. The Abacus
- A. Mathematics and Its Divisions
- II. Arithmetical Notation and the Chief Arithmetical Operations
- A. English Notes and Examples
- B. Division
- C. Extraction of the Square Root
- D. Extraction of the Cube Root
- III. Pythagorean Arithmetic
- A. First Principles
- B. Classification of Numbers
- C. Perfect Numbers
- D. Figured Numbers
- 1. General
- 2. Triangular Numbers
- 3. Oblong and Square Numbers
- 4. Polygonal Numbers
- 5. Gnomons of Polygonal Numbers
- E. Some Properties of Numbers
- 1. The “Sieve” of Eratosthenes
- 2. Divisibility of Squares
- 3. A Theorem about Cube Numbers
- 4. A Property of the Pythmen
- F. Irrationality of the Square Root of 2
- G. The Theory of Proportion and Means
- 1. Arithmetic, Geometric and Harmonic Means
- 2. Seven Other Means
- 3. Pappus’s Equations between Means
- 4. Plato on Means between Two Squares or Two Cubes
- 5. A Theorem of Archytas
- H. Algebraic Equations
- 1. Side- and Diameter-Numbers
- 2. The “Bloom” of Thymaridas
- IV. Proclus’s Summary
- V. Thales
- VI. Pythagorean Geometry
- A. General
- B. Sum of the Angles of a Triangle
- C. “Pythagoras’s Theorem”
- D. The Application of Areas
- E. The Irrational
- F. The Five Regular Solids
- VII. Democritus
- VIII. Hippocrates of Chios
- A. General
- B. Quadrature of Lunes
- C. Two Mean Proportionals
- IX. Special Problems
- 1. Duplication of the Cube
- A. General
- B. Solutions Given by Eutocius
- 1. “Plato”
- 2. Heron
- 3. Diocles
- 4. Menaechmus: Solution by Conics
- 5. Archytas: Solution in Three Dimensions
- 6. Eratosthenes
- 7. Nicomedes: The Conchoid
- 2. Squaring of the Circle
- A. General
- B. Approximation by Polygons
- 1. Antiphon
- 2. Bryson
- 3. Archimedes
- C. Solutions by Higher Curves
- 1. General
- 2. The Quadratrix
- 3. Trisection of an Angle
- A. Types of Geometrical Problems
- B. Solution by Means of a Verging
- C. Direct Solutions by Means of Conics
- 1. Duplication of the Cube
- X. Zeno of Elea
- XI. Theaetetus
- A. General
- B. The Five Regular Solids
- C. The Irrational
- XII. Plato
- A. General
- B. Philosophy of Mathematics
- C. The Diorismos in the Meno
- D. The Nuptial Number
- E. Generation of Numbers
- XIII. Eudoxus of Cnidos
- A. Theory of Proportion
- B. Volume of Pyramid and Cone
- C. Theory of Concentric Spheres
- XIV. Aristotle
- A. First Principles
- B. The Infinite
- C. Proof Differing from Euclid’s
- D. Mechanics
- 1. Principle of the Lever
- 2. Parallelogram of Velocities
- XV. Euclid
- A. General
- B. The Elements
- 1. Foundations
- 2. Theory of Proportion
- 3. Theory of Incommensurables
- 4. Method of Exhaustion
- 5. Regular Solids
- C. The Data
- D. The Porisms
- E. The Conics
- F. The Surface Loci
- G. The Optics
- H. A Pre-Eudoxan Theory of Proportion
- I. The Golden Section
LOEB CLASSICAL LIBRARY
Loeb Classical Library 335
Greek Mathematical Works, Volume I: Thales to Euclid
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Book Details
HARDCOVER
$24.00 • £15.95 • €19.50
ISBN 9780674993693
Publication: January 1939
576 pages
4-1/4 x 6-3/8 inches
mathematical examples
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