《数学史(英文珍藏版·原书第3版)》配有翻译成中文的前言和目录,采用特种纸双色印刷,主要包含小学、中学以及大学所涉及的数学内容的历史。本书将数学史按照年代顺序划分成若干时期,每一时期介绍多个专题。本书的前半部分内容是讲述公元前直到17世纪末微积分发明为止的这一时期的历史,后半部分内容则介绍18世纪至20世纪的数学发展。详细内容可参考中文目录。
《数学史(英文珍藏版·原书第3版)》适合所有对数学的来龙去脉感兴趣的读者。正在学习数学的学生通过本书可以更深入地了解数学的发展过程。教师不仅可以使用本书讲解专门的数学史课程,而且可以在其他和数学相关的课程中使用本书的内容。
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."