命题顺序与文本逻辑:比林斯利英译欧几里得《原本》双版第十四卷成因分析

Propositional Sequence and Textual Logic: An Analysis of the Double Edition of Book XIV in Billingsley’s English Translation of The Elements of Euclid

1570年比林斯利英译欧几里得《原本》(简称比氏《原本》)集文艺复兴时期欧几里得《原本》研究之大成,收录了双版第十四卷:14A和14B。14A源自赞伯蒂《原本》,保持4道基本命题顺序,呈现以基本命题为核心的文本原貌。14B源自坎帕努斯《原本》和弗鲁萨特斯《原本》,优先考虑完善4道基本命题逻辑结构的完备性,在原基本命题之间插入2道必要的增补命题,改变基本命题的顺序,并扩展12道衍生命题。比氏《原本》双版第十四卷的两种命题顺序反映出两种主旨迥异的文本逻辑,揭示出命题顺序中蕴含的文本逻辑是欧几里得《原本》公理化体系的基石。

In 1570, Billingsley’s English translation of Elements of Euclid epitomized Numerous studies of Euclidean, it is unique and contains two editions of the XIV books: 14 A and 14 B.14 A is derived from Zamberti’s translation, which maintains 9 propositions: 4 basic propositions and their supplement.It keeps the original sequence and takes the basic proposition as the core of logic.14 B is derived from Campanus’ and Flussates’. It gives priority to improving the completeness of the logical structure of the 4 basic propositions in XIV, inserting necessary supplementary propositions between the original basic propositions, changing the sequence of the basic propositions, and further adding subsequent content.The two propositional sequences in the XIV reflect two textual logics with different themes, showing that the textual logic contained in the propositional sequence is the cornerstone of the axiomization of the system of Elements of Euclid.