(ProQuest: ... denotes formulae omitted.)In work1 of Kepler (1 57 1-1630), an archetype meant some pattern or structure that was ordained by God, or, that was in accordance with divine plan. Kepler's belief that astronomy depended above all on primacy of observations is well-known and has been frequently applauded - notably when he abandoned an especially promising solution on his way to finding path of Mars just because it did not match level of accuracy of best available observations.2 By contrast, Kepler's cosmologica! principles often depended on archetypes, which were proposed in circumstances when observations were not feasible or measurements were impractical.The purpose of this Note is to draw attention to an investigation in Kepler's Epitome Book IV (1620) in which reasoning was entirely founded on archetypes, in a situation in which it has always been natural to suppose that Kepler had relied on observation - natural, because all his predecessors had attempted to derive similar results using observational methods (however inadequate). These attempts had arisen in connection with sizing of Sun-Earth-Moon system. It was only after Kepler's era, simply as a result of technical improvement of instruments, that problem indeed became amenable to observation, and later astronomers were able to determine correct value for solar parallax.3 This value was single measurement that provided foundation for accurate determination of Earth-Sun distance (and eventually for dimensions of universe itself).The reasoning that we present here was set out in a self-contained sub-section in Epitome IV, I, 4 (KGW, vii, p. 276 line 40 - p. 281 line 26). Kepler's own diagram of KGW, vii, p. 278 (repeated p. 280), is reproduced in Figure 1, using solid lines. We can appropriately describe it as 'Eclipse Diagram', since it represents situation in which Moon exactly eclipses Sun, viewed from Earth - so that radii of Sun and Moon appear precisely equal.It may not previously have been appreciated that Eclipse Diagram had two separate functions, as an archetype, as well as being an observational tool. For Kepler, though diagram was indeed drawn in accordance with observations, its archetypal significance was over-riding consideration: he believed that universe was embodiment of divine principles, incorporating observations that agreed with archetype ordained by God. Kepler set out many arguments to explain underlying plan of universe (KGW, vii, p. 276 line 41 - p. 277 line 28). Compellingly, it seemed to him self-evident that positions of Sun and Moon relative to Earth had been arranged by Creator for benefit of humankind, so that the contemplative creature (or alternatively, the measuring creature) would be able to calculate dimensions of universe (KGW, vii, p. 280 lines 1-2). Kepler set out to do just this - and results, with citations of his own words, are collected for ease of reference in Table 1.During this limited investigation Kepler avoided discussion of detailed measurements and concerned himself with considerations of relative size alone (KGW, vii, p. 277 lines 13-17). For instance, question of whether distances of Sun or Moon from Earth were apogeal, or perigeal, or intermediate, was irrelevant; instead, Kepler stated what they ought to be, implying a (subsidiary) archetypal reason (KGW, vii, p. 280 lines 2-4).Throughout, we refer to the distance between bodies rather than the semidiameter of sphere and to the radius (a term that was seldom, if ever, used by Kepler) instead of the semidiameter [of body]. This is simply to avoid inaccuracies that have been found in translations and commentaries when 'semidiameter' is mistyped in haste as 'diameter' .4For convenience of modern readers we shall use symbolic notation (as Kepler did not) to write proportions as fractions, and to express Kepler's intentions more concisely by using indices to replace his extended verbal descriptions involving powers and roots. …
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Feb 25, 2014
Boris Aberšek + 2
