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A Short History of Greek Mathematics Dear Reader, This book was referenced in one of the 185 issues of 'The Builder' Magazine which was published between January 1915 and May 1930. To celebrate the centennial of this publication, the Pictoumasons website presents a complete set of indexed issues of the magazine. As far as the editor was able to, books which were suggested to the reader have been searched for on the internet and included in 'The Builder' library.' This is a book that was preserved for generations on library shelves before it was carefully scanned by one of several organizations as part of a project to make the world's books discoverable online. Wherever possible, the source and original scanner identification has been retained. Only blank pages have been removed and this header- page added. The original book has survived long enough for the copyright to expire and the book to enter the public domain. 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Please do not assume that a book's appearance in 'The Builder' library means it can be used in any manner anywhere in the world. Copyright infringement liability can be quite severe. The Webmaster fllTES SCI ENTIA VEfllTAS - A SHORT HISTORY OF GREEK MATHEMATICS. l1onbon: C. J. CLAY AND SON, CAMBRIDGE UNIVERSITY PRESS WABEHOUSE, AVE MARIA LANE• ClmlJribgt: DEIGHTON, BELL, AND CO. J,tip)ig:• F. A. BROCKHAUS. A SHORT HISTORY OF GREEK MATHEMATICS BY JAMES GOW, M.A. FELLOW OF TRINITY COLLEGE, CAMBRIDGE. IIClp' EVK~dB11 T&f d,p~d,P.f"OS 'YftIJp.n-peW, WS TO rpWTO" (JEwfY1IJLCIIp.Cl8E", .qpeTO TO" EVK~Elm,,,· T£ aI P.O& 'Ir~~O" 'tTTCI& TClVrCl p4J1(Ja",OJ1T&; /CCll 0 Eti/C~dB'71S TO" 'lrCliBCI /CCI~~(TClS· Bos, ItP'71, CliJTri TP'WfJO~O", nmB.q BE;: ClVrtl, i~ w" p.fUl8UE&, ICEpBa.(",e,,,. STOBABUS, FWr. IV. p. 205. EDITED FOR THE SYNDICS OF THE UNIVERSITY PRESS. CAMBRIDGE: AT THE UNIVERSITY PRESS. 1884 €amlJdbp: PRINTED BY C. J. CLAY, M.A. AND SON, AT THE UNIVERSITY PRESS. Q .-_1.1 ifc.?,'/·,~·· l r ... t PREFACE. THE history of Greek mathematics is, for the most part, only the history of such mathematics as are learnt daily in all our public schools. And very singular it is that, though England is the only European country which still retains Euclid as its teacher of elementary geometry, and though Cambridge, at least, has, for more than a century, required from all candidates for any degree as much Greek and mathe- matics together as should make this book intelligible and interesting, yet no Englishman has been at the pains of writing, or even of translating, such a treatise. If it was not wanted, as it ought to have been, by our classical professors and our mathematicians, it would have served at any rate to quicken, with some human interest, the melancholy labours of our schoolboys. The work, as usual, has been left to Germany and even to France, and it has been done there with more than usual excellence. It demanded a combination of learning, scholarship and common sense which we used, absurdly enough, to regard as peculiarly English. If anyone still cherishes this patriotic delusion, I would advise him to look at the works of Nessel- mann, Bretschneider, Hankel, Hultsch, Heiberg and Cantor, Of, again, of Montucla, Delambre and Chasles, which are so frequently cited in the following pages. To match them we can show only an ill-arranged treatise of Dean Peacock, many brilliant but scattered articles of Prof. De Morgan, and three essays by Dr Allman. I have treated all these writers with VI PREFACE. freedom and have myself added matter which is not to be found in any of them, but they strike me still with humiliation such as a classical scholar feels when he edits a text which Bentley has edited before him. My own book represents part of a collection of notes which I have for many years been making with a view to a general history of. the great city of Alexandria. The fact that the history of Alexandrian mathematics begins with the Elements of Euclid and closes with the Algebra of Diophantus, both of which are founded on the discoveries of several pre- ceding centuries, made it necessary that I should extend my inquiries over the whole field of Greek mathematics. In this way, the materials for an account of the Alexandrian Mathematical School grew to exceed the reasonable limits of a chapter, and I have thought it desirable to publish them as a separate essay. I shall treat the Literary School with the same fulness. As a history of Alexandria ought to be interesting to most people, I took especial. pains that my treatment of the Mathematical School, which was the oldest, the most con- spicuous and the longest-lived of them all, should not be excessively technical. I have tried to put my account of it generally in such a form as should be useful and attractive to readers of various tastes. As a matter of fact, mathematicians will here find some account of every extant Greek mathe- matical book and a great number of pretty proofs translated from the ipsissima verba of the ancients. Greek scholars will find nomenclature and all manner of arithmetical symbols more fully treated than in any other work. A student of history, who cares little for Greek or mathematics in par- ticular, but who likes to watch how things grow, will be able to extract from these pages a notion of the whole history of mathematical science down to Newton's time, and will find PREFACE. Vll some very curious questions raised which it is his especial duty to answer. It was impossible to satisfy the requirements of all readers, but eacb will perhaps be willing to concede something to the claims of the others, and wherever a subject is introduced but inadequately treated, I have at least given references to sources of fuller information, if any such exist to my knowledge. As the whole book is an endeavour to compromise between conflicting claims, I have allowed myself, with the same intent, some inconsistency in two details. In the first place, I have not drawn a strict line between pure and mixed mathematics, but have given an account of the Phaenomena and Optics of Euclid and the mechanical books of Aristotle and Archimedes, while I have omitted any summary of Ptolemy's astronomical theories. The former are books which are little known, which are short, whicb came in my way and which are almost purely deductive. A com- plete history of Greek astronomy is tolerably common, is long, is founded for the most part on non-mathematical writers and would consist largely of a history of astronomical observations. In the second place, I have tried to write proper names (following indeed Smith's Dictionary of Greek and Boman Biography) in a way which should generally indicate the Greek form and pronunciation without offending the ordinary eye. I have always -written c for" and final -us for -oe, I have generally not Latinized names ending in -to», because it is sometimes inconvenient and the Latin usage was inconsistent with itself; for instance, it retained Conon but altered Plaion. I have left in their English form, the names of well-known writers. Thus the reader will find Plato, Aristotle and Euclid side by side with Heron, Nicoteles and N eocleides. If I must offend somebody, I would soonest offend a pedant. The complete MS. of this book left my hands last January and the whole edition has been printed off, sheet by sheet, viii at various intervals" since that time. I have therefore been unable to correct any errors or omissions which I observed too late or to incorporate new matter which appeared after the sheet to which it was relevant had gone to press. The chief notices which I wish to insert are given in the Addenda which immediately follow this preface. My work, dreary as it has often been, has been enlivened by one constant pleasure, the interest and unselfish assistance of many friends. Two of them, in particular, deserve recogni- tion very near the title-page. The first is Mr F. T. Swanwick, late scholar of Trinity College, Cambridge, and now Mathemati- cal Lecturer in the Owens College. He has, with incredible care and patience, read through the whole book from page 66, has made a hundred valuable suggestions and has saved me a hundred times from myself. The other is Mr Joseph Jacobs, late scholar of St John's College, Cambridge, whose' wide intellectual interests and unsurpassed knowledge of bibliography have made the book far more useful and entertaining than it otherwise would have been.
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