Doctoral Dissertation Research: The Medieval Latin Transmission of the Menelaus Theorem

博士论文研究：墨涅拉俄斯定理的中世纪拉丁语传播

• 批准号: 1027200
• 负责人: Steven Livesey
• 金额: $ 1.38万
• 依托单位: University of Oklahoma Norman Campus
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-01 至 2012-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1027200&HistoricalAwards=false
• 关键词: Doctoral; Dissertation; Research; Medieval; Latin

The Menelaus theorem is a mathematical result from Antiquity that has to do with arcs on the surface of a sphere. It played an important role in Ptolemaic astronomy and astrology as well as in the mathematical theory of proportions. While the ancient and medieval Islamic history of the theorem has been told, the theorem's history in the medieval West has not. Moreover, many of the medieval texts central to this history still exist only in manuscript copies. The researcher is currently working on a dissertation to provide that history.The plan of research for writing the history sketched above includes examining Latin texts that contain the theorem (or relate to it in some way) in order to determine who read it and their reasons for doing so, and thereby locate its place in the history of medieval astronomy and mathematics. To fulfill these goals, the researcher will consult the extensive resources on the history of medieval texts at the Institut de Recherche et d'Histoire des Textes (IRHT) in Paris. In addition, he will utilize the IRHT's large collection of reproductions of manuscripts and consult many of the actual manuscripts that contain the texts on the Menelaus theorem in libraries in Paris, London, Cambridge, Oxford, and the Vatican. The intellectual merit of the project is mainly that it will add to our understanding of the history of medieval mathematics by providing a better account of the role that Menelaus theorem played in medieval theories of proportion, especially the theory of compound ratios, which became one of the most powerful mathematical tools of the last three centuries of the Middle Ages. This dissertation will also examine the history of this fundamental theorem in medieval astronomy, focusing on the scholars who used it and how it fared when easier alternatives were introduced at the end of the Middle Ages. A potential broader impact of the project will result from the researcher's plan to include in his dissertation editions of many medieval texts. Doing so will thereby provide resources for future historians.

墨涅拉俄斯定理是古代的一个数学结果，与球面上的弧有关。 它在托勒密的天文学和占星术以及比例的数学理论中发挥了重要作用。 虽然古代和中世纪的伊斯兰历史的定理已经告诉，该定理的历史在中世纪的西方没有。此外，许多对这段历史至关重要的中世纪文本仍然只存在于手稿副本中。研究人员目前正在撰写一篇论文来提供这段历史。撰写上面概述的历史的研究计划包括检查包含该定理（或以某种方式与之相关）的拉丁文本，以确定谁读过它以及他们这样做的原因，从而确定它在中世纪天文学和数学史上的位置。为了实现这些目标，研究者将在巴黎的文本研究与历史研究所（IRHT）查阅有关中世纪文本历史的广泛资源。此外，他还将利用IRHT大量的手稿复制品，并在巴黎、伦敦、剑桥、牛津和梵蒂冈的图书馆中查阅许多包含墨涅拉俄斯定理文本的实际手稿。 该项目的智力价值主要是它将增加我们对中世纪数学史的理解，通过更好地解释梅内莱厄斯定理在中世纪比例理论中的作用，特别是复合比理论，它成为中世纪最后三个世纪最强大的数学工具之一。本论文还将研究这一基本定理在中世纪天文学的历史，重点是谁使用它的学者，以及它是如何表现时，更容易的替代品在中世纪末推出。一个潜在的更广泛的影响，该项目将导致研究人员的计划，包括在他的论文版本的许多中世纪的文本。因此，这样做将为未来的历史学家提供资源。