Publisher Description

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.

Author Biography

Ivor Thomas (1905–1993; later surnamed Bulmer-Thomas) was a journalist, scholar, and Member of Parliament.

Table of 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 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 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- (i) " Plato " (ii) Heron (iii) Diocles (iv) Menaechmus : solution by conies (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 conies 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#151

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