Geometry by Its History

作者：Alexander Ostermann, Gerhard Wanner
出版：Springer, 2012
内容：Part I Classical Geometry   Part II Analytic Geometry

开始漫谈：发帖前书目查重，在论坛搜索Geometry，看到Algebraic Geometry、Differential Geometry之类的近世几何学书籍甚夥，而经典欧式几何与解析几何类书则鲜矣。诚然，几何学的研究内容与方法在与时嬗进，但欧几的美与魅力亦必万世永辉！——我相信古希腊人研究几何，不仅是实用之需，更是对美学与信仰的追求。随着代数方法的极大成功，几何方法早已式微，体现在当代数学教育上更是分明。后来，只是在竞赛中邂逅那些简洁优美的几何线条，或偶然得知某定理有对应的几何直观，经典几何大体已被我们封存于记忆深处而渐蒙尘埃。一别已阔，曷其有佸！
       欧几里得在两千多年前的巅峰之作《几何原本》是数学中的不朽经典，对后世影响极巨，仅在《原理》一书中即可显见牛顿对其的师法。然而《原本》及诸如阿波罗尼奥斯的《圆锥曲线论》，笛卡尔的《几何学》之类的原著，当今忙于应试的学生却少有品读。此书作者有感于此，书中命题证明多注引出处，使读者得览经典之胜义，兼可源清发展脉络。作者序言：

Geometry, so named at least since Plato’s times, is the oldest branch of mathematics. It contains many beautiful results, elegant ideas and surprising connections, to which many great thinkers have contributed through the centuries. Among these are Thales, Pythagoras, Euclid, Apollonius, Archimedes, Ptolemy, Pappus, the Arabs, Regiomontanus, Copernicus, Vi`ete, Kepler, Descartes, Newton, the Bernoullis, Euler, Monge, Poncelet and Steiner. In this book, we study geometry from the texts of these masters as closely as we judge useful and roughly in historic order, in accordance with the famous maxim of Niels Henrik Abel, “I learned from the masters and not from the pupils”. This explains “by Its History” in the title, without aiming at a complete history of the subject.  

       那么，不妨与作者一起，对初等几何做一次回顾之旅吧！如晤故人，亲切可喜~