Greek Mathematical Works, Volume I: Thales to Euclid

Ivor Thomas, translator

Publisher:

Harvard University Press

Publication Date:

1939

Number of Pages:

511

Format:

Hardcover

Series:

Loeb Classical Library

Price:

26.00

ISBN:

9780674993693

Category:

Sourcebook

BLL Rating:

BLL*

The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries.

MAA Review
Table of Contents

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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
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
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