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Greek Mathematical Works: From Thales to Euclid v. 1 : Selections - I. Thomas

Greek Mathematical Works: From Thales to Euclid v. 1

Selections

By: I. Thomas (Translator)

Hardcover Published: 1st July 1989
ISBN: 9780674993693
Number Of Pages: 576

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The wonderful achievement of Greek mathematics is here illustrated in two volumes of selected mathematical works. Volume I contains: The divisions of mathematics; mathematics in Greek education; calculation; arithmetical notation and operations, including square root and cube root; Pythagorean arithmetic, including properties of numbers; square root of 2; proportion and means; algebraic equations; Proclus; Thales; Pythagorean geometry; Democritus; Hippocrates of Chios; duplicating the cube and squaring the circle; trisecting angles; Theaetetus; Plato; Eudoxus of Cnidus (pyramid, cone, etc.); Aristotle (the infinite, the lever); Euclid.

Volume II ("Loeb Classical Library no. 362") contains: Aristarchus (distances of sun and moon); Archimedes (cylinder, sphere, cubic equations; conoids; spheroids; spiral; expression of large numbers; mechanics; hydrostatics); Eratosthenes (measurement of the earth); Apollonius (conic sections and other works); later development of geometry; trigonometry (including Ptolemy's table of sines); mensuration: Heron of Alexandria; algebra: Diophantus (determinate and indeterminate equations); the revival of geometry: Pappus.

Introductory
Mathematics and its divisions
Origin of the name
The Pythagorean quadrivium
Plato's scheme
Logistic
Later classification
Mathematics in Greek Education
Practical calculation
Enumeration by fingers
The abacus
Arithmetical Notation And The Chief Arithmetical Operations
English notes and examples
Division
Extraction of the square root
Extraction of the cube root
Pythagorean Arithmetic
First principles
Classification of numbers
Perfect numbers
Figured numbers
General
Triangular numbers
Oblong and square numbers
Polygonal numbers
Gnomons of polygonal numbers
Some properties of numbers
The " sieve " of Eratosthenes
Divisibility of squares
A theorem about cube numbers
A property of the pythmen
Irrationality of the square root of 2
The theory of proportion and means
Arithmetic, geometric and harmonic means
Seven other means
Pappus's equations between means
Plato on means between two squares or two cubes
A theorem of Archytas
Algebraic equations
Side and diameter-numbers
The " bloom " of Thymaridas
Proclus's Summary
Thales
Pythagorean Geometry
General
Sum of the angles of a triangle
" Pythagoras's theorem "
The application of areas
The irrational
The five regular solids
Democritus
Hippocrates Of Chios
General
Quadrature of lunes
Two mean proportionals
Special Problems
Duplication of the Cube
General
Solutions given by Eutocius
" Plato "
Heron
Diocles
Menaechmus : solution by conies
Archytas : solution in three dimensions
Eratosthenes
Nicomedes : the Conchoid 2. Squaring of the Circle
General
Approximation by polygons
Antiphon
Bryson
Archimedes
Solutions by higher curves
General
The Quadratrix 3. Trisection of an Angle
Types of geometrical problems
Solution by means of a verging
Direct solutions by means of conies
Zeno Of Elea
Theaetetus
General
The five regular solids
The irrational
Plato
General
Philosophy of mathematics
The diorismos in the Meno
The nuptial number
Generation of numbers
Eudoxus of Cnidos
Theory of proportion
Volume of pyramid and cone
Theory of concentric spheres
Aristotle#151
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780674993693
ISBN-10: 0674993691
Series: Loeb Classical Library : Book 1
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 576
Published: 1st July 1989
Publisher: HARVARD UNIV PR
Country of Publication: US
Dimensions (cm): 17.15 x 12.07  x 2.54
Weight (kg): 0.36
Edition Number: 335

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