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

ERKKA MAULA* (in cooperation with E. Kasanen and J. Mattila) THE BEGINNING OF ANGULAR MEASUREMENT. EUDOXUS'S ARACHNE Is there another scientist in the whole history of science whose craftsmanship has been as deep-ploughing yet terse, as lasting yet prolific, as Eudoxus of Cnidus's contribution to the development of mathematical analysis ? Aristotle's influence has been lasting, too, but since the Middle Ages mostly retarding, and Plato's mostly indirect. But as regards analysis, Weierstrass and Dedekind, more than two thousand years later, could set out directly from Eudoxus's results, preserved in Euclid's Elementa. Indeed, Eudoxus "was a man of science if there ever was one", as Sir Thomas Heath put it. Yet there is no extant example of Eudoxus's methods of computation, no example of his actual use of analysis, although we know some of his results. Nor do we know more about his methods of proof than that he perfected the method of exhaustion and used indirect proof. His methods of invention are utterly unknown. Thus it seems immensely worthwhile to attempt a reconstruction of Eudoxus's other great achievements, his theories of mathematical geography and above all his cosmological system, in order to obtain new information about his mathematical insights as well. Eudoxus's astronomy is a most rewarding object of research even in itself because, to quote Heath again, "no more ingenious and attractive hypothesis than that of Eudoxus's system of concentric spheres has ever been put forward to account for the apparent motions of the sun, moon and planets". For us, however, our previous reconstructions of Eudoxus's method of determining the geographical latitude [3] and his astronomical methods [4, 5] have served as starting-points for an even more inclusive reconstruction of Eudoxus's scientific portrait and dynamic worldview, containing the nucleus of a dialectics of nature [7, 8]. As an important mile-stone on this highway, we now submit a reconstruction of Eudoxus's main instrument, the arachne (Spider, mentioned by Vitruvius), in which his mathematical methods, observational techniques, and heuristic insights assume a concrete manifestation. Being mainly an instrument for angular measurement, the arachne stands on top of a comprehensive yet strictly coherent theoretical foundation, which admits also of its other usages as a mathematical instrument for the extraction of square and cubic roots, and as an aid in mathematical invention. *E. Maula, 14700 Hanko, Finland