希腊化数学和应用数学领域理性精神的发展

亚历山大里亚的学术活动与应用实践领域紧密结合在一起。这种希腊化特征具有促进应用实践技术领域理性意识的成长和理性推测领域的理论发明向观察一实验视界靠拢的双重意义。欧几里得思想体系对于从希腊古典时期的数学理性向近代以来科学理性的范式转换，在很大程度上起到中枢作用。托勒密对由柏拉图发起的以数学原理“拯救现象”的传统起到无可替代的中继环节作用。此外，应用数学的发展还与力学、光学等应用科学和营造技术等实践技术紧密联系在一起，从而达到了与近代科学革命相隔近千年之久的古代科学巅峰。

The Development of the Rational Spirit in Hellenistic Theoretical and Applied Mathematics

The academic activities in mathematics in Alexandria were closely linked with those in the applied practi- cal domain. This Hellenistic characteristic was of double significance ： On the one hand, the link could promote the growth of rational consciousness in the technical domain;while in the field where rational speculation was valued highly, the inclination for theoretical inventions was turning to that for observation and experiment. Euclid＇ s ideological system was pivotal to the paradigm shift from classical Greek mathematical reason to modern scientific reason. Ptolemy played an irreplaceable intermediate role in the tradition started by Plato of ＂saving the phenomena＂ with mathematical principles. Besides, the development of Hellenistic applied mathematics was also closely linked with such applied sciences as mechanics and optics, and with such practical techniques as building technique, etc. , and hence arriving on the peak of ancient science, which was nearly one thousand years earlier than the Scientific Revolution.