《數學史(英文珍藏版·原書第3版)》配有翻譯成中文的前言和目錄,采用特種紙雙色印刷,主要包含小學、中學以及大學所涉及的數學內容的歷史。本書將數學史按照年代順序劃分成若干時期,每一時期介紹多個專題。本書的前半部分內容是講述公元前直到17世紀末微積分發明為止的這一時期的歷史,后半部分內容則介紹18世紀至20世紀的數學發展。詳細內容可參考中文目錄。
《數學史(英文珍藏版·原書第3版)》適合所有對數學的來龍去脈感興趣的讀者。正在學習數學的學生通過本書可以更深入地了解數學的發展過程。教師不僅可以使用本書講解專門的數學史課程,而且可以在其他和數學相關的課程中使用本書的內容。
Pappus's Book 7,then,is a companion to the Domain of Analysis,which itself consists of several geometric treatises,all written many centuries before Pappus.These works,Apollonius's Conics and six other books(all but one lost),Euclid's Data and two other lost works,and single works(both lost)by Aristaeus and Eratosthenes,even though the last-named au thor is not mentioned in Pappus's introduction,provided the Greek mathematician with the tools necessary to solve problems by analysis.For example,to deal with problems that result in conic sections,one needs to be familiar with Apollonius's work.To deal with problems solvable by"Euclidean"methods,the material in the Data is essential.Pappus's work does not include the Domain of Analysis itself.It is designed only to be read along with these treatises.Therefore,it includes a general introduction to most of the individual books along with a large collection of lemmas that are intended to help the reader work through the actual texts.Pappus evidently decided that the texts themselves were too difficult for most readers of his day to understand as they stood.The teaching tradition had been weakened through the centuries,and there were few,like Pappus,who could appreciate these several-hundred-year-old works.Pappus's goal was to increase the numbers who could understand the mathematics in these classical works by helping his readers through the steps where the authors wrote"clearly...!"He also included various supplementary results as well as additional cases and alternative proofs.Among these additional remarks is the generalization of the three-and four-line locus problems discussed by Apollonius.Pappus noted that in that problem itself the locus is a conic section.But,he says,if there are more than four lines,the loci are as yet unknown; that is,"their origins and properties are not yet known."He was disappointed that no one had given the construction of these curves that satisfy the five-and six-line locus.The problem in these cases is,given five(six)straight lines,to find the locus of a point such that the rectangular parallelepiped contained by the lines drawn at given angles to three of these lines has a given ratio to the rectangular parallelepiped contained by the remaining two lines and some given line(remaining three lines).Pappus noted that one can even generalize the problem further to more than six lines,but in that case,"one can no longer say ‘the ratio is given between some figure contained by four of them to some figure contained by the remainder'since no figure can be contained in more than three dimensions."Nevertheless,according to Pappus,one can express this ratio of products by compounding the ratios that individual lines have to one another,so that one can in fact consider the problem for any number of lines.But,Pappus omplained,"(geometers)have by no means solved(the multi-line locus problem)to the extent that the curve can be recognized....The men who study these matters are not of the same quality as the ancients and the best writers.Seeing that all geometers are occupied with the first principles of mathematics...and being ashamed to pursue such topics myself,I have proved propositions of much greater importance and utility."