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Cover courtesy of Harvard University Press
LCL · Greek
Greek Mathematical Works, Volume I: Thales to Euclid
Greek mathematics in extracts, from the earliest geometry to the late commentators, with the Greek set against a facing translation.
The Edition
- Original language
- Greek
- Translated by
- Ivor Thomas
Publication
- Publisher
- Harvard University Press
- Series volume
- 335
- Date published
- 1939-01-01
- Print status
- In print
The Physical Book
- Binding
- Hardcover
- Dust jacket
- Yes
- Total pages
- 576 pages
- ISBN-13
- 9780674993693
Reference
- Read online
- Read Here
- Publisher page
- View at publisher
Contents
- I. Introductory
- (a) Mathematics and its divisions
- (i) Origin of the name
- (ii) The Pythagorean quadrivium
- (iii) Plato’s scheme
- (iv) Logistic
- (v) Later classification
- (b) Mathematics in Greek education
- (c) Practical calculation
- (i) Enumeration by fingers
- (ii) 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
- (i) General
- (ii) Triangular numbers
- (iii) Oblong and square numbers
- (iv) Polygonal numbers
- (v) Gnomons of polygonal numbers
- (e) Some properties of numbers
- (i) The “sieve” of Eratosthenes
- (ii) Divisibility of squares
- (iii) A theorem about cube numbers
- (iv) A property of the pythmen
- (f) Irrationality of the square root of 2
- (g)The theory of proportion and means
- (i) Arithmetic, geometric and harmonic means
- (ii) Seven other means
- (iii) Pappus’s equations between means
- (iv) Plato on means between two squares or two cubes
- (v) A theorem of Archytas
- (h) Algebraic equations
- (i) Side- and diameter-numbers
- (ii) The “bloom” of Thymaridas
- IV. Proclus’s Summary
- 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
- (i) “Plato”
- (ii) Heron
- (iii) Diocles
- (iv) Menaechmus: solution by conics
- (v) Archytas: solution in three dimensions
- (vi) Eratosthenes
- (vii) Nicomedes: the Conchoid
- 2. Squaring of the Circle
- (a) General
- b) Approximation by polygons
- (i) Antiphon
- (ii) Bryson
- (iii) Archimedes
- c) Solutions by higher curves
- (i) General
- (ii) 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
- (i) Principle of the lever
- (ii) Parallelogram of velocities
- XV. Euclid
- (a) General
- b) The Elements
- (i) Foundations
- (ii) Theory of proportion
- (iii) Theory of incommensurables
- (iv) Method of exhaustion
- (v) 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