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

On the Sources and Choices Our strategy has accordingly been to approach the interwined problems of Eudoxus's observational and computing techniques, and their heuristic ideas, by exploring his astronomical and geographical theories. Although our reconstructions in these directions have been presented earlier, it may be worthwhile to outline their general character even here. For, as is known, there is the now canonical interpretation of the theory of the homocentric spheres by Schiaparelli, whom most historians of science still follow, and as regards Eudoxus's method for the determination of geographical latitude, the later Hellenistic method is usually taken to account for his few numerical results, even though the resulting inaccuracies in geographical location are simply unbelievable and incompatible with biographical tradition. Now Schiaparelli's interpretation is essentially qualitative in the sense that he makes conjectures about the Eudoxan parameter values in order to ascertain a fair correspondence between the general outline of Eudoxus's system and observable facts. But he does not attempt a deduction from the known Eudoxan parameter values to observations, which might turn out to be even grossly mistaken. On the contrary, Schiaparelli and others in his wake, like Heath and Dreyer, are willing to jettison even Aristotle's presumably wellinformed testimony on the details for the sake of their own interpretation. In this process, Eudoxus's computing techniques must be represented by qualitative geometrical constructions. It is as well to remember that the choice between a "geometrical" and a "physical" interpretation is a moot point (see e.g. Larry Wright, "The Astronomy of Eudoxus: Geometry or Physics?", Stud. Hist. Phil. Sci., 4, 1973, No. 2), but we cannot consider such qualitative interpretations satisfactory. For we know for sure that Eudoxus used at least some exact parameter values, for instance that he gave the planetary periods in days and years. What we offer, therefore, is a quantitative interpretation. Our program for a quantitative interpretation is this: we begin from the relatively few known numerical parameter values and construct one and only one method of computation which yields numerical values for all other Eudoxan parameters described so far only qualitatively. Among these computed values there are some that represent instrumental observations. Yet one cannot know in advance, as Schiaparelli thought, whether these observations were fairly accurate or idealized, or even fictitious. On the contrary, we know that some were utterly fictitious, for instance those pertaining to the third solar motion postulated by Eudoxus. Hence modern observations (combined with modern mathematics and astronomical tables giving e.g. the real loxotes in Eudoxus's day) will not help us in the way Schiaparelli believed. For a genuine reconstruction of Eudoxus's method of computation and observation must be capable of reproducing even his idiosyncracies. But even though this might be achieved, the reconstructed method might do no more than illustrate a possible way of invention—presuming that Eudoxus, too, started from just those parameter values that have been preserved. Pains must be taken to demonstrate that the reconstruction remains within the general framework of ancient mathematics, just as the observational instruments must lie within the scope of ancient technology. Moreover, one must outline a plausible route of actual computations from the observations to the resulting parameter values. Now it is not likely for instance that Heath would have overlooked any relevant