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

certain functions of rulers and compasses, it preserves the character of a real instrument permitting heuristic experiments in a sense that escapes the ruler and compasses in the axiomatized Greek geometry. These more ordinary usages, and the obvious usages as a gnomon or a sun-dial, we shall not discuss. The Angles of the Heaven It is possible to measure the angles between any two visible celestial or mundane objects, or the angle between an object and any of the great celestial circles, by means of the arachne, but we may demonstrate an even more representative measurement in ancient astronomy, the measurement of a star's angular distance from the horizon. Eudoxus, for instance, is reported to have observed Canopus (a Carinae) in Cnidus (Strabo C 119 after Poseidonius). Hipparchus (in Arat. p. 114. 20—8) says that Eudoxus put Canopus exactly on the "always invisible circle" and that this was not correct because Canopus was invisible in Cnidus (lat. 36° 43'). Hipparchus's criticism shows that he had not yet discovered precession, for in fact Canopus was barely visible in Cnidus in Eudoxus's time (its declination was —52.8° according to U. Baehr's tables Tafeln zur Behandlung chron. Prdbleme, 1955). In the period between Eudoxus and Hipparchus, the positions of the stars relative to the celestial sphere had bee changed due to the precession, [4, p. 10.] Eudoxus's special concern with Canopus in probably connected with his attempt at an estimate of the circumference of Earth, for Canopus is an easily recognizable object which Eudoxus must have observed even in Egypt. Be that as it may, the observation technique is shown in the attached figure (Fig. 5). The observation is made by means of the dioptra, and the angular distance from the horizon appears as a, the acute angle at the centre. The corresponding angle at the circumference (a/2) can be demonstrated by the string, and tan (a/2) = q/p read from the scales of the measuring unit. Since the arm at right angles to the main trunk can be moved with respect to the trunk, it is quite likely that in some position the ratio q :p corresponds to the prefixed lines of the two scales. Eudoxan Shadows and Hours It was customary in the Hellenistic period to indicate the geographical latitude of an observation site by speaking about either (i) the ratio of the length of the longest day of the year to the shortest night or (ii) the ratio of the two parts of the tropic divided by the horizon at the summer solstice. When the well-known Hellenistic method for the determination of the geographical latitude is used, these two locutions become synonymous. The presuppositions of this development are discussed in [3], where it is also shown that these two locutions could not be considered synonymous before the equalization of hours, and certain other far-reaching conventions. For Eudoxus they must have meant different things. Now it is known that Eudoxus gave two ratios of the tropic divided by the horizon at the summer solstice, K

M = = 5:3 and K

M = 12:7 (Hipp, in Arat. i, 2. 22, 3. 9.). It is shown in [3] that if exactly