Greek Mathematical Works Thales to Euclid

by Ivor, Thomas

• ISBN13: 9780674993693
• ISBN10: 0674993691
• Format: Hardcover
• Copyright: 1980-06-01
• Publisher: Loeb Classical Library

Summary

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.

Table of Contents

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

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