Analysis of Greek mathematical documents

• 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
• Project Status: Completed (Fiscal Year 2018)
• Budget Amount: ¥8,320,000 (Direct Cost: ¥6,400,000、Indirect Cost: ¥1,920,000); Fiscal Year 2017: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000); Fiscal Year 2016: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000); Fiscal Year 2015: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000); Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
• Keywords: ユークリッド / エウクレイデス / 構文解析 / 『原論』 / ギリシャ数学 / 古典ギリシャ語 / 依存文法 / ギリシャ数学史

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.

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．

Research Products

• [Int'l Joint Research] American University in Cairo(エジプト)
• [Journal Article] Re-examination of the different origins of the arithmetical books of Euclid's Elements (2019)
  • Author(s): Ken Saito
  • Journal Title: Historia Mathematica Volume: 印刷中
• [Journal Article] ギリシャ語数学文献構文解析における文法の定義および解析作業の現況 (2018)
  • Author(s): 斎藤憲
  • Journal Title: 津田塾大学数学・計算機科学研究所報 Volume: 39 Pages: 184-190
  • Open Access
• [Presentation] エウクレイデス『原論』全文の構文解析の進行状況 (2018)
  • Author(s): 斎藤憲
  • Organizer: 日本数学会秋季総合分科会
• [Presentation] エウクレイデス『原論』全文の構文解析 (2016)
  • Author(s): 斎藤憲
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 関西大学千里山キャンパス
• [Presentation] Analisi sintattiche del testo degli Elementi di Euclide (2015)
  • Author(s): Ken Saito
  • Organizer: XIV Convegno (Societa italiana di storia delle matematiche)
  • Place of Presentation: Dipartimento di Matematica e Informatica, Universita degli studi di Palermo （イタリア，パレルモ）
  • Year and Date: 2015-11-13
• [Presentation] エウクレイデス『原論』の用語・語法の分析によって追加部分を判別する試み (2015)
  • Author(s): 斎藤憲
  • Organizer: 第26会数学史シンポジウム（津田塾大学数学・計算機科学研究所）
  • Place of Presentation: 津田塾大学（東京都小平市）
  • Year and Date: 2015-10-11