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

墨涅劳斯定理是古代的一个数学结论，与球面上的弧有关。它在托勒密天文学和占星术以及比例数学理论中发挥了重要作用。虽然这个定理的古代和中世纪伊斯兰历史已经被告知，但这个定理在中世纪西方的历史却没有被告知。此外，这段历史的许多核心中世纪文本仍然只存在于手稿副本中。该研究人员目前正在撰写一篇论文，以提供这段历史。撰写上述历史概述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历史中的地位。为了实现这些目标，研究人员将在巴黎的文本历史研究所（IRHT）查阅有关中世纪文本历史的广泛资源。此外，他将利用IRHT的大量手稿复制品，并参考巴黎、伦敦、剑桥、牛津和梵蒂冈图书馆中包含墨涅劳斯定理文本的许多实际手稿。这个项目的智力价值主要在于，它将通过更好地说明墨涅劳斯定理在中世纪比例理论，特别是复比理论中所起的作用，增加我们对中世纪数学历史的理解，复比理论成为中世纪最后三个世纪最强大的数学工具之一。这篇论文还将研究中世纪天文学中这一基本定理的历史，重点关注使用它的学者，以及在中世纪末期引入更容易的替代方法时，它是如何发展的。该项目的一个潜在的更广泛的影响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文本。这样做将为未来的历史学家提供资源。

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.