The Works of Archimedes

by Archimedes; Heath, Sir Thomas

• ISBN13: 9780486420844
• ISBN10: 0486420841
• Format: Paperback
• Copyright: 2002-04-16
• Publisher: Dover Publications

Summary

The complete works of antiquity's great geometer appear here in a highly accessible English translation by a distinguished scholar. Remarkable for his range of thought and his mastery of treatment, Archimedes addressed such topics as the famous problems of the ratio of the areas of a cylinder and an inscribed sphere; the measurement of a circle; the properties of conoids, spheroids, and spirals; and the quadrature of the parabola. This edition offers an informative introduction with many valuable insights into the ancient mathematician's life and thought as well as the views of his contemporaries. Modern mathematicians, physicists, science historians, and logicians will find this volume a source of timeless fascination. Unabridged reprint of the classic 1897 edition, with supplement of 1912.

Table of Contents

Introduction
Archimedes	xv
Manuscripts and Principal Editions---Order of Composition---Dialect---Lost Works	xxiii
Relation of Archimedes to his Predecessors	xxxix
Use of traditional geometrical methods	xl
Earlier discoveries affecting quadrature and cubature	xlvii
Conic Sections	lii
Surfaces of the second degree	liv
Two mean proportionals in continued proportion	lxvii
Arithmetic in Archimedes	lxviii
Greek numeral system	lxix
Addition and subtraction	lxxi
Multiplication	lxxii
Division	lxxiii
Extraction of the square root	lxxiv
Early investigations of surds or incommensurables	lxxvii
Archimedes' approximations to √3	lxxx
Archimedes' approximations to the square roots of large numbers which are not complete squares	lxxxiv
Note on alternative hypotheses with regard to the approximations to √3	xc
On the problems known as NeyΣeiΣ	c
Neευσεισ referred to by Archimedes	c
Mechanical constructions: the conchoid of Nicomedes	cv
Pappus' solution of the νευσισ referred to in Props. 8, 9 On Spirals	cvii
The problem of the two mean proportionals	cx
The trisection of an angle	cxi
On certain plane νευσεισ	cxiii
Cubic Equations	cxxiii
Anticipations by Archimedes of the Intergral Calculus	cxlii
The Terminology of Archimedes	clv
THE WORKS OF ARCHIMEDES
On the Sphere and Cylinder, Book I	1	(55)
On the Sphere and Cylinder, Book II	56	(35)
Measurement of A Circle	91	(8)
On Conoids and Spheroids	99	(52)
On Spirals	151	(38)
On The Equilibrium of Planes, Book I	189	(14)
On the Equilibrium of Planes, Book II	203	(18)
The Sand-Reckoner	221	(12)
Quadrature of the Parabola	233	(20)
On Floating Bodies, Book I	253	(10)
On Floating Bodies, Book II	263	(38)
Book of Lemmas	301	(18)
The Cattle-Problem	319	(7)
Supplement---The Method of Archimedes	326