History of Greek Mathematics

Little Heath Thomas

Description

Whilst the greatest effort has been made to ensure the quality of this text, due to the historical nature of this content, in some rare cases there may be minor issues with legibility. The idea may seem quixotic, but it is nevertheless the author's confident hope that this book will give a fresh interest to the story of Greek mathematics in the eyes both of mathematicians and of classical scholars. For the mathematician the important consideration is that the foundations of mathematics and a great portion of its content are Greek. The Greeks laid down the first principles, invented the methods ab init'io, and fixed the terminology. Mathematics in short is a Greek science, whatever new developments modern analysis has brought or may bring.

Sujets

• Sciences et techniques
• Geometry

Informations

• Publié par: Forgotten Books
• Date de parution: 27 novembre 2019
• Nombre de lectures: 0
• EAN13: 9780243654277
• Langue: English
• Poids de l'ouvrage: 11 Mo

Extrait

i ea may seem but it is nevertheless th e author s confident hope that this book will give a fresh interes to the story of ree mathematics in the eyes both of mathematicians and of classical scholars the mathematician the important consideration is that the foundations of mathematics and a great portion of its content are reek The reeks laid down the rst principles invented the methods andfixed the terminology athematics in short is a reek science whatever new developments modern analysis has brought or bring Th e interest of the subj ect for the classical scholar is no doubt of a if eren kind reek athematics reveals an important aspect of the reek genius of which the student of reek culture is apt to lose sight ost people when they think of the reek gen us naturally call to mind its master pieces in literature and art with their notes of beauty truth freedom and humanism the reek with his insatiable desi re to know the true meaning of every hing in the uni verse to be able to give a rational explanation of it was j ust as irresistibly driven to natural sci nce mathematics and exact reasoning in general or logic This austere side of the reek genius found perhaps its most complete expression in ristotle ristotle would however no means admi that mathematics was d vorced fro aesthetic he could conceive he said of nothing more beautiful than the obj ects of mathe maties Plato delighted in geometry and in the wonders of numbers said the inscription over the door of the cademy uc id was a no less typical reek Indeed seeing that so much of is mathematics

vi P R C it is arguable that if one would understand the ree genius fully it would be a good plan to begin with their geometry The story of reek mathematics has been written before James did a great service by the publication in of his a scholarly and useful work which has held its own and has been quoted with respect and appreciation by authorities the history of mathematics in all parts of the wor d the ate when he wrote however had necessarily to rely upon the wor s of the pioneers ankel l man and orit Cantorfirst edition ect has beenince then the subj ve ry greatly advanced new texts have been published portant new docume ts have been discovered and researches by scholars and mathematicians in di erent countries have throw light on many obscure points I t is therefore high time for the complete story to be rewritten It is true that in recent years a number of attractive histories of mathematics have been published ngland and merica but these have only dealt with reek mathematics as part of the larger sub ect and in consequence the writers have been precluded by considerations of alone from presenting the work of the reeks in su cient detail same remark applies to the erman histories of mathe maties even to the great work of orit Cantor who treats of the history of reek mathematics in about pages of vol i hile no one would wish to disparage so great a monument of indefatigable research it was inevitable that a book on such a scale would in time prove to be inadequate and to need correction in details and the later unfortu ately failed to ta e sufficient account of the new materials which have become avai able since thefirst edition the light The best history of reek athematics which exists at present is undoubtedly that of ino oria under the title second edition

R E A E vii Ulrico ilano Professor oria arran es his aterial infion u ve ooks clidean geometry on olden of ree k eometry uclid to pollo ius on app ied mathematics including astronomy optics on th e il ve r of reek eometry on arithmetic of the reeks ithin the separate ooks the arrangement is ch ronologic l under the names of persons or school s I enti on these details because they raise the question whether in a history of this kin i s best to follow chronological order or to arrange the material according to subj ects and if the latter in what sense of the ord subj ect and within hat limits Professor oria ays his arrange ment is a compromise between arrangement according to subj ects and a strict a herence to chronolo ical o der each of which plans has advantages and disadvanta es of its own In this book I have adopted a new arrangement mainly according to subj ects th e nature of which and th e reasons for w ich will be made clear by an illustration Take the case of a famou s problem which plays a great part in the h istory of reek geometry the oubling of the cube or its equivalent thefin ing e proportionof two mean proportionals in contin between two i ven straight lines n er a chronolo ical arrangement th s problem comes up afresh on the occasion of each ne w solution it is obviou s that if all the recorded solutions are collected together it is m ch easier to see the relation s amounting in some cases to s bstantial identity between the and to get a comprehensive V the historyiew of of the problem have therefore dealt with this problem in a separate section of th e chapter devoted to pecial Problems and I have followed the same course with the other famous problems of sq ar ng the circle and trisecting any angle imil r considerations arise with regar to certain well efiects s ned subj sec ions ch as conic It wo ld be to interrupt the account of solution of the problem of mean proportionals or er to

viii R EE A consider the way in which he may have iscovered the conic sect ons and their f ndamental properties It see s to me much better to ive the complete story of th e orig n and velopment of the eometry of th e coni c sections in one place and this has been done in the chapter on conic sections associated with the name of pollonius of Perga imilarly a chap er has been evoted to algebra in connex on with iophantus and another to trigonometry un er ipparchus enelaus Ptolemy the same time the outstand n personalities of uclid and rchime es demand chapters to themselves uclid the author of th e incomparable wrote almost all the other branches of mathematics known in his day rchi work all original and set forth in treatises which are models of scientific exposition style wasform and perfect in even wider in its range of subj ects The imperishable and unique monuments of the genius of these two men must be detached from their surroundi gs and seen as a whole if we would appreciate to the full the pre eminent place which they occupy and ill hold for all time in the history of science The arrangement which I have adopted necessitates as does any other order of exposition a certain amo t of repetition and cross references but only in this way can the necess ry unity be given to the whole narrative other point sho l be mentioned It i s a defect in the xisting histories that while th ey state enerally th e contents of and th e main propositions proved in the g e t treat ses of rchimedes and pollonius they make little attempt to describe the procedure by which the res lts are obtained I have therefore taken pains in the ost significant cases to show the course of the argument in suf cient detail to enable a competen t mathematician to rasp th e method used to apply it if he i l to other similar investigations The work was be un in the bulk of it was ritten as a distraction during thefirst three years of the

P R C war the hideous course of which seemed day by day to en orce the profou truth conveyed in the answer of Plato to th e elians hen they consulte him on the problem set them by the racle namely that of uplicating the cube he replied It must be supposed that the god specially wished this problem solved but that h e would have the reeks desist from war and ickedness and cultivate the uses so that their passions being assuaged by ph losophy and mathematics they might live in innocent utually helpful inte rcourse with one another Tru y reece and her foundations are uilt below the tide of war ased on the cryst lline sea thoug t and its eternity T

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