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.
. The Menelaus Theorem was one of the fundamental proofs in Ptolemaic astronomy and it was also influential in the mathematics of ratios (perhaps the most innovative and used field of mathematics in the Middle Ages). Henry examined the way that this theorem was proved in different ways and how the different versions of the proof utilized ratios. In the Middle Ages, there were competing ideas of what ratios are, and Henry's dissertation answers how some of these ideas were spread. The theorem is also interesting because it continued to be used even when medieval scholars knew of easier alternatives. During the Middle Ages, European scholars translated four works containing the proof and then several works were written that treated the theorem. Most of these have never been published and exist only in manuscripts. To get a complete idea of the medieval history of this influential theorem, Henry was given a doctoral dissertation improvement grant from the NSF to visit libraries in Europe that hold these manuscripts. He visited libraries in Paris, London, Oxford, Cambridge, and Rome on an initial trip in 2010. Living frugally, Henry was able to make a second research trip in 2012 to Munich, Vienna, and Erfurt. Henry is producing critical edition of many mathematical and astronomical works that up to this time have only been available to those who are able to travel to the manuscripts and read the heavily abbreviated handwriting of medieval scholars. He expects to finish the dissertation early in 2013.
