著者

高橋 憲一

出版者

日本科学史学会

雑誌

科学史研究 (ISSN:21887535)

巻号頁・発行日

vol.29, no.173, pp.1-12, 1990 (Released:2021-09-01)

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Contrary to the title of our paper, the Catoptrica is generally regarded as a pseudo-Euclidean work―a late recension of a genuine Euclidean one, probably written by Theon of Alexandria. Almost all historians of science have accepted this interpretation, which was proposed by J. L. Heiberg and later elaborated by A. Lejeune. In this paper the author intends first to examine the validity of this widespread interpretation, focussing mainly on Heiberg's arguments, and secondly to propose an alternative interpretation. Heiberg's arguments can be divided into three groups, which concern respectively : (Gl) theoretical contents of the Catoprica (G2) scanty testimonies in antiquity (G3) stylistic analyses of the Greek text (Gl)is, it seems, the most important reason to have led him to the inauthenticity of the work. His arguments in this regard consist of pointing out, on the one hand, inaccurate proof procedures and lack of mathematical rigor(for Propsitions 7-12, 16-18), and, on the other, fallacious assertions(for Postulates 4 & 5). The present author refutes the former by showing Heiberg's misunderstanding of the propositions, and the latter by proposing a new interpretation of the postulates, a kernel of which is the assumption, indicated by the use of 〇 vKerc and supported by the use of the same word in Euclid's Optica, Prop. 3, that observer' s eye moves around the object of sight, looking at the image in the mirror. With the collapse of reasons in (Gl), Heiberg's argument in (G2) is deemed to lose its force. We havz no right to doubt the truth of both Proclus' ascription of the work to Euclid and Euclid's own allusion to the work in his Optica, Prop.19. Concerning (G3), it is shown that his argument is far from convincing. It never supports a hypothesis that Theon was a pseudo-Euclid who compiled the work, but rather indicates, against his intention, that the work has same characteristic style as the genuine Euclidean Optica, probably inherited from optical research before Euclid. Thus if the Optica has the right to claim Euclidean authenticity, the Catoptrica also has, we must admit, the same right in its extant form as handed down to us.