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

we are inclined to interpret Proclus's commentary on Eudoxus continuing Plato's work on the section (on Eucl. I, p. 67) as referring to harmonious points created by overlapping line segments. Be that as it may, we now have outlined the theoretical foundation of the arachne, and these are the main points of interest: (i) the solutions to (3) in terms of x:y = q:p can be given an instrumental interpretation tan (a/2) = = q:p, (ii) harmonious points occur both in the practical calculations and in the scales of the instrument, and (iii) an algebraic description of the heuristical aspect displays the disappearance of an auxiliary parameter in the course of the methods of analysis and synthesis. The Ingenious Spider We have built an instrument by means of which we can measure precisely those observational parameter values that Eudoxus needed in his astronomy (Fig. 3). Its construction does not in any way exceed the ancient technician's skills. The instrument consists of four main parts, (i) A stand permitting rotation about two ortogonal axes supports (ii) a meridian circle adjustable and lockable at any position in two dimensions and supporting in turn (iii) a circular plate rotating about the diameter of the meridian circle, with respect to which the plate can be adjusted and locked. On top of the plate (iv) the measuring unit resembling the sliding callipers turns on a gnomon. In addition there is a plumb hanging from a string for purposes of calibration and to demonstrate certain angles. If the measuring unit is removed, the instrument looks like a big copper mirror, and one may well call it an enoptron after a lost work of Eudoxus. In the measuring unit and the plumb-string one may perhaps see a spider and its thread, and hence call the whole instrument an arachne. We presume that if there really was an instrument on Plato's table (see Cornford's Plato's Cosmology p. 74 ff.) it might have been of this type. On the circular plate two scaled axes are grooved; there are thirteen units in all four directions measured from the centre to the perimeter. In the main trunk of the measuring unit and in its two arms there are both unit scales and also others based on harmonious points, as explained in the Abstract. An auxiliary trunk, moving parallel to the main trunk, has no scales but is provided with sights (dioptra). The measuring unit perhaps merits a separate picture (Fig. 4). It is not necessary to engage in entomological debates on the precise number of a spider's feet. Suffice it to say here that while the main trunk (0) and the two arms (M, N) at right angles to it are essential, the auxiliary trunk (P) is only needed in the demonstration of a parallel to the main trunk. As this could be done by means of the string or a separate ruler, too, (P) is perhaps superfluous. In any event the motions of the parts are indicated by small arrows: (M) and (N) move parallel to one another, and can be locked with respect to (0). Finally, it is advisable to attach a runner (R) to both (M) and (0) so that the string may run via them. In fact, the measuring unit may be conceived of as consisting of four gnomons, and its correct place in the history of astronomical instruments is between an ordinary gnomon and a cross-staff or Jacob's staff. By means of the arachne, however, observations and measurements can be executed which exceed the capacities of these kindred instruments. It may be noted also that although the arachne combines