著者

三浦 伸夫

出版者

神戸大学

雑誌

国際文化学研究 : 神戸大学国際文化学部紀要 (ISSN:13405217)

巻号頁・発行日

vol.28, pp.67-103, 2007-07

---

In the first half of the fourteenth-century Oxford many scholars developed the theory of motion in medieval cultural context. The most important figure among them is Richard Swineshead. His opus mains, "Book of Calculations", had a great influence into many scholars in Paris, especially Oresme. They discussed the spaces moved by mobile. For their discussion they used mathematical technique, summation of infinite geometrical series, by adding proportional parts infinitely. In the early sixteenth-century many Iberian students visited Paris to study theology under Scottish John Major, and learned also Aristotelian physics as students of faculty of arts. Some of them developed further the mathematical devices. The most conspicuous figure of this school, Alvaro Thomas, who was born in Lisbon probably during the second half of the fifteenth-century, wrote a voluminous treatise "Book of the Triple Motion" at Paris in 1509. This is a kind of sophism treatise popular in Oxford in the fourteenth-century and perhaps used as a textbook of logical reasoning at the faculty of arts. In this article, first, an overview of the contents of the book is presented and the mathematical techniques used there are discussed. This book elucidates the Mertonian theory of motion discussed in Swineshead's treatise, but went over that text, for he had focus upon pre-infinitesimal calculation. Secondly, novelties introduced by Thomas are discussed, that is the summation of infinite geometrical series of Oxford school. His impressive originality in the theory of series is that even if the exact numerical value was not known, he believed that he could evaluate it by estimations of upper and lower values which had been already known. He also calculated series by dividing it into two series which were easily calculated. However it is reasonable to think that he might use geometry in working his mathematics even if his description was rhetorical. He did not show general rules for solving series. And he usually did not use geometrical figures. His intuitive technique appeared in the later Iberian scholars and had an influence even upon Latin America.