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

one (postulated) period and the angular measurement, the directions of rotations being determinable by the Eudoxan tradition (westward). The points A, B, C, D form a set of harmonious points (A, B; C, D) in the ratio of division p:q = 29:1, and BD = y = 30 (days) = the "full" month is postulated to beT£°

mb

, tan — = q:p = 1:29 representing an "idealized" observation by means of 2 the arachne. Hence AB = a = 840 (days), AD = x = T£* = 870 (days), CB == 28 (days), BE = CB + BD = b = 58 (days) = 2Tj^

b

, and AE = c = 842 (days), while a = = 3° 57' represents the Moon's maximum deviation from the Eudoxan ecliptic, and remains within the limits of Eudoxus's observational error (1°—3°, according to Hipparchus's criticism). a

2

+b

2 = c

2

, of course. The central role of this rightangled triangle in Eudoxus's method of analysis and synthesis is explained in [5], and its possible bearing on the emergence of the theory of stereographic projection is discussed in [7]. [/SMW] The Sun, too, is credited with three motions owing to a slightly too small numerical value given to the Eudoxan loxotes. It can be gathered from the Eudoxan tradition that in the case of the Sun the direction of the third (individual) solar motion is eastwards. Hence the Sun represents the second possibility as regards the sign in (2). Otherwise we follow the same procedure as in the case of the Moon. An "idealized" observation by means of the arachne gives the Sun's maximum (fictitious) deviation from the (Eudoxan) ecliptic, which is reproduced by the same a instrument, as tan — = q:p = 1:91, where 91 (days) is the length of Eudoxus's 2 equalized seasons. Hence we obtain the following situation (lines not to scale). (A, B; C, D) is a set of harmonious points, the ratio of division being 91:1. Here CB = T=°

mb = 360 (days) is postulated in advance. Hence AB = x+y = a = = 33120 (days), x = 32760 (days) = TJg = the Sun's long period implied by its „slow" Eudoxan motion, BD = 368 (days), BE = CB + BD = 728 (days) = _ 2T™^

b

, and c = 33128 (days), while /? = 1° 15.5' represents the Sun's maximum deviation from the Eudoxan ecliptic and, being obtained by the same method as Eudoxus's other angular parameter values, speaks out strongly in favour of our reconstruction of Eudoxus's method of computation. So also does the obtained value T°J™

b = 364 (days), for it is well known that notwithstanding the discovery of the inequality of the astronomical seasons by Euctemon and Meton some sixty years earlier, Eudoxus equalized them. Hence 364 = 4x91 days may well be called Eudoxus's 'seasonal year', this being another example of Simplicius's use of the term year in two senses, just as month stands for both 30 and 29 days. As Eudoxus was interested in ealendaric considerations also, there is no need to suppose that his cosmological timereckoning contradicted the calendar. Nor does it conflict with observation either, for the long solar period is too long to be observed. The resulting cosmological model, however, offers some surprises, as explained in [5, 7]. The practical computations and observations by means of the arachne follow the same pattern in the case of the other planets also. It is obvious, too, that the solutions (4, 5) readily follow from considerations regarding harmonious points, and