Produced by Marius Masi, Bryan Ness and the Online Distributed Proofreading Team at http://www.pgdp.net (This file was produced from images generously made available by The Internet Archive) Transcriber's notes: (1) Numbers following letters (without space) like C2 were originally printed in subscript. Letter subscripts are preceded by an underscore, like C_n. (2) Characters following a carat (^) were originally printed in superscript. (3) [root] stands for the root symbol; [alpha], [beta], etc. for greek letters. [Illustration: _Aristippus Philosophus Socraticus, nausragio cum ejectus ad Rhodiensium litus animadvertisses Geometrica Schemata descripta, exclamavisse ad comites ita dicitur_, Bene Speremus, Hominum enim vestigia video. _Vitruv. Architect lib. 6. Prief_. delin MBurghers sculptUniv. Oxon.] PIONEERS OF PROGRESS MEN OF SCIENCE EDITED BY S. CHAPMAN, M.A., D.SC., F.R.S. ARCHIMEDES BY SIR THOMAS HEATH K.C.B., K.C.V.O., F.R.S.; SC.D., CAMB. HON. D.SC., OXFORD [Greek: Dos moi pou sto, kai kino ten gen] LONDON: SOCIETY FOR PROMOTING CHRISTIAN KNOWLEDGE NEW YORK: THE MACMILLAN CO. 1920 CONTENTS. CHAP. PAGE I. ARCHIMEDES 1 II. GREEK GEOMETRY TO ARCHIMEDES 7 III. THE WORKS OF ARCHIMEDES 24 IV. GEOMETRY IN ARCHIMEDES 29 V. THE SANDRECKONER 45 VI. MECHANICS 50 VII. HYDROSTATICS 53 BIBLIOGRAPHY 57 CHRONOLOGY 58 CHAPTER I. ARCHIMEDES. If the ordinary person were asked to say off-hand what he knew of Archimedes, he would probably, at the most, be able to quote one or other of the well-known stories about him: how, after discovering the solution of some problem in the bath, he was so overjoyed that he ran naked to his house, shouting [Greek: eureka, eureka] (or, as we might say, "I've got it, I've got it"); or how he said "Give me a place to stand on and I will move the earth"; or again how he was killed, at the capture of Syracuse in the Second Punic War, by a Roman soldier who resented being told to get away from a diagram drawn on the ground which he was studying. And it is to be feared that few who are not experts in the history of mathematics have any acquaintance with the details of the original discoveries in mathematics of the greatest mathematician of antiquity, perhaps the greatest mathematical genius that the world has ever seen. History and tradition know Archimedes almost exclusively as the inventor of a number of ingenious mechanical appliances, things which naturally appeal more to the popular imagination than the subtleties of pure mathematics.