Analysis of Greek mathematical documents

2018 Fiscal Year Final Research Report

• Project/Area Number: 26282066
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Partial Multi-year Fund
• Section: 一般
• Research Field: Sociology/History of science and technology
• Research Institution: Yokkaichi University (2018); Osaka Prefecture University (2014-2017)
• Principal Investigator: Saito Ken 四日市大学, 関孝和数学研究所, 研究員 (10221988)
• Project Period (FY): 2014-04-01 – 2019-03-31
• Keywords: ユークリッド / エウクレイデス / 構文解析 / 『原論』

Outline of Final Research Achievements

We have embarked on the project of making syntactic analysis of the whole text of Euclid's Elements hoping that its result would be helpful in identifying the propositions and arguments of different origins such as later interpolation. We have developed a computer program which helps the user to perform the analysis according to the grammar modeled after Tesniere's (NB : accent grave is not accepted in this format) dependency grammar. We have completed the analysis of all the sentences of Books I-IV and Book VI of the Elements. The result is registered in xml file. A tool which would enable research of a specific word and/or grammatical structure without the knowledge of xml file is still under development.

Free Research Field

数学史

Academic Significance and Societal Importance of the Research Achievements

ギリシャ数学文献，とりわけ最も広く読まれた『原論』は，その成立以降，多くの注釈や編集を経てきたことが確実であるにもかかわらず，伝来の中世写本の内容が無批判に原著者エウクレイデスの記述と受け取られてきた．本研究で開発した構文解析支援プログラムによって，後世の編集に由来する部分を特定するための，主観的でない議論が展開できることが期待される．また，この手法は，基本的にはすべての古典文献に応用可能であり，古典研究が新たな分析手段を獲得する可能性を持つ．