Technikatörténeti szemle 10. (1978)

A MÉRÉS ÉS A MÉRTÉKEK AZ EMBER MŰVELŐDÉSÉBEN című konferencián Budapesten, 1976. április 27–30-án elhangzott előadások II. - Maula, E.: A szögmérés kezdetei

would have been useful in Eudoxus's observations, but apart from such remarks as those of Plutarch, Eutocius, Hipparchus and Vitruvius, we know little about his instruments and techniques of observation. Yet, and this is the hallmark of the professional, of the „man of science if there ever was one", given one and the same instrument and one and the same method of computation, the expert is bound to investigate the whole compass of their applicability and draw the most immediate inferences from their use. We may rest assured, therefore, that a mathematician of Eudoxus's competence investigated what else could be achieved by means of the same instrument that served so excellently in obtaining a practical solution to the problem of the two mean proportionals. Contrariwise, we can safely assume that an astronomer of Eudoxus's calibre also investigated other aspects than the observational of his astronomical instruments. For the very praxis of instruments and tools may teach the hand to continue the work of the intellect, presupposing that the instruments and tools have been constructed on sound, prolific theories. Now we must emphasize that our reconstruction, too, is based on theoretical considerations of Eudoxus's work. These in turn are based on a series of studies in Plato's Timaeus, referred to in (1—8). But the further we have proceeded, the more we have also gained feed-back that reinforces the previous, at times tentative results. Take for instance the philosophical and philological study of Plato's agalma (E. Maula, „Plato's Agalma of the Eternal Gods", Yearbook of the Philosophical Society of Finland, vol. xxxi. 1969). Starting from Platonic premisses it pointed out the remarkable role of a rotating model ascribed to the World-Soul in the Timaeus. It is a model that fully corresponds to physical reality at given times only. On the other hand, the reconstruction of Eudoxus's methods of computation in astronomy (5), being a study in the history of the exact sciences and starting from Eudoxan premisses, led to exactly the same concept of a model. And in the structure of the arachne we have a concrete manifestation of this concept, just as the usages of this instrument reflect not only Eudoxus's method of exhaustion and the Pythagorean approximative method, but finally also Plato's view on language (as described in E. Maula, „0n the Semantics of Time in Plato's Timaeus", A. Acad. Aboensis, Ser. B, Tom. 169. 1, 1970). That these results, obtained from fairly divergent premisses, tend to converge towards a new synthesis of the ancient scientific world-view, cannot be mere coincidence. For just as it was the case with our reconstruction of Eudoxus's cosmological system, there are too many exact parameter values deduced from the relatively few known values by one and the seme method and constituting a sound logical system, to be explained away be mere chance. Nay, the arachne reconstructed here stands at the watershed between theory and praxis, between proof and heuristics, between the axiomatic method and the methods of invention, between geometrical and numerical analysis, between rational and irrational numbers, and between the static and dynamic world-views. But owing to the depth of Eudoxus's insight, these seemingly opposite traditions unite. The approximative and the exact, the practical and the theoretical, turn out to be two aspects of the same synthesis, which is the bearing force behind Eudoxus's lasting contribution to the development of mathematical analysis. The arachne is a ,,living statue" just as Plato's agalma, a paradigm of radiant ingenium commemorating the