(H/B) GREEK MATHEMATICAL WORKS (VOLUME I)

Παρουσίαση

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. (From the publisher)

Περιεχόμενα

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-
(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 incommemurables
(iv) Method of exhaustion
(v) Regular solids
(c) The Data
(d) The Porisms
(e) The Conies
(f) The Surface Loci
(g) The Optics
(h) A Pre-Eudoxan Theory of Proportion
(i) The Golden Section