Selections Illustrating the History of Greek Mathematics

by Thomas, Ivor

• ISBN13: 9780674993990
• ISBN10: 0674993993
• Format: Hardcover
• Copyright: 1968-06-01
• Publisher: Loeb Classical Library

Summary

The wonderful achievement of Greek mathematics is here illustrated in two volumes of selected mathematical works. Volume I (Loeb Classical Library no. 335) 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); Aristotle (the infinite, the lever); Euclid. Volume II 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

Aristarchus Of Samos

General

Distances of the sun and moon

Continued fractions (?)

Archimedes

General

Surface and volume of the cylinder and sphere

Solution of a cubic equation

Conoids and spheroids-

Preface

Two lemmas

Volume of a segment of a paraboloid of revolution

The spiral of Archimedes-

Definitions

Fundamental property

A verging

Property of the subtangent

Semi-regular solids

System of expressing large numbers

Indeterminate analysis : the Cattle Problem

Mechanics : centres of gravity-

Postulates

Principle of the lever

Centre of gravity of a parallelogram

Mechanical method in geometry

Hydrostatics-

Postulates

Surface of fluid at rest

Solid immersed in a fluid

Stability of a paraboloid of revolution

Eratosthenes-

General

On means

The Platonicus

Measurement of the earth

Apollonius of Perga-

The conic sections-

Relation to previous works

Scope of the work

Definitions

Construction of the sections

Fundamental properties

Transition to new diameter

Other works-

General

On the Cutting-off of a Ratio

On the Cutting-off of an Area

On Determinate Section

On Tangencies

On Plane Loci

On Vergings

On the dodecahedron and the icosahedron

Principles of mathematics

On the Cochlias

On unordered irrationals

Measurement of a circle

Continued multiplications

On the Burning Mirror

Later Developments In Geometry-+

Classification of curves

Attempts to prove the parallel postulate

General

Posidonius and Geminus

Ptolemy

Proclus

Isoperimetric figures

Division of zodiac circle into 360 parts: Hypsicles

Handbooks-

Cleomedes

Theon of Smyrna

Trigonometry

Hipparchus and Menelaus

Ptolemy

General

Table of sines

Introduction

sin 18 degree and sin 36 degree

sin sup 2 theta + cos sup 2 theta =1

Ptolemy's theorem

sin ( theta - phi ) = sin theta cos phi -cos theta sin phi

Sin sup 2 1/2 theta = 1/2(l -COS theta )

cos ( theta + phi ) = cos theta cos phi -sin theta sin phi

Method of interpolation

The table

Menelaus's theorem-

Lemmas

Mensuration : Heron Op Alexandria-

Definitions

Measurement of areas and volumes-

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