I am grateful to Professor H. Post, Professor A. Franklin and the Editor for their critical comments. A special debt is due to the work of Professor G. E. R. Lloyd and to his remarks concerning this article.

¹ ‘Nunc quia contemni non potuerunt, sola igitur haec octo minuta viam praeiverunt ad totam Astronomiam reformandam, suntque materia magnae parti hujus operis facta.’ Quoted by Koyré. (Koyré, A., The Astronomical Revolution: Copernicus-Kepler-Borelli, (tr. Maddison, R.E.W.), London, 1973, p. 401Google Scholar, note no. 22.) See Hon, G., ‘On Kepler's Awareness of the Problem of Experimental Error’, Annals of Science (1987), 44, pp. 545–591.CrossRefGoogle Scholar

² Plato, , Republic, 2nd edn, rev. (tr. with an introduction Lee, D.), London, 1974, p. 338 (529d).Google Scholar

³ Ibid.

⁴ Ibid., (529b–c), emphasis in translation.

⁵ Ibid., p. 339(530b).

⁶ Ibid., (530b–c).

⁷ Ibid., p. 340 (531).

⁸ Ibid., (531b).

⁹ Ibid., p. 342(531c).

¹⁰ Cornford, P. M., The Republic of Plato, Oxford, 1966, p. 241.Google Scholar

¹¹ Lloyd, G.E.R., Magic, Reason and Experience, Cambridge, 1979, p. 132.Google Scholar

¹² Ibid., p. 133. For detailed studies of this issue see Lloyd, G.E.R., ‘Plato as a Natural Scientist’, Journal of Hellenic Studies (1968), 88, pp. 78–81CrossRefGoogle Scholar; Mourelatos, A.P.D., ‘Plato's “Real Astronomy”: Republic 527D-531D’, in Anton, J.P. (ed.) Science and the Sciences In Plato, with an Introduction by J.P. Anton, New York, 1980, pp. 33–73Google Scholar; Mueller, I., ‘Ascending to Problems: Astronomy and Harmonics in Republic VII’Google Scholar, in Anton, ibid., pp. 103–122; and Vlastos, G., ‘The Role of Observation in Plato's Conception of Astronomy’Google Scholar, in Anton, ibid., pp. 1–31. I am grateful to G.E.R. Lloyd for bringing the last three articles to my attention.

¹³ Neugebauer, O., The Exact Sciences of Antiquity, 2nd edn, New York, 1969, p. 152Google Scholar; see also p. 69.

¹⁴ Neugebauer, O., ‘Notes on Hipparchus’, in Weinberg, S.S. (ed.), The Aegean and the Near East, New York, 1956, p. 296.Google Scholar See also Neugebauer, O., Astronomy and History, Selected Essays, New York, 1983.CrossRefGoogle Scholar Quoted by Palter, R., ‘An Approach to the History of Early Astronomy’, Studies in History and Philosophy of Science (1970), 1, p. 127CrossRefGoogle Scholar note no. 3. However, see op. cit. (49).

¹⁵ Lloyd, , op. cit. (11).Google Scholar

¹⁶ Neugebauer, O., A History of Ancient Mathematical Astronomy, Studies in the History of Mathematics and Physical Sciences, (eds Klein, M.J. and Toomer, G.J.), No. 1, 3 vols, Berlin and New York, p. 659.Google Scholar

¹⁷ Ibid., p. 271.

¹⁸ Heath, T., Aristarchus of Samos, the ancient Copernicus (A history of Greek astronomy to Aristarchus together with Aristarchus' treatise on the sizes and distances of the sun and moon), Oxford, 1913.Google Scholar

¹⁹ Ibid., p. 328.

²⁰ Ibid., pp. 333–334.

²¹ Ibid. Cf. Neugebauer, op. cit. (16), pp. 634–643.

²² Neugebauer, ibid., p. 642.

²³ Ibid. Boyer describes Aristarchus' method as unimpeachable; ‘the result,’ he writes, ‘being vitiated only by the error of observation in measuring the angle MES as 87 degrees.’ (Boyer, C.B., A History of Mathematics, New York, 1968, p. 177.)Google Scholar By disregarding the enormous practical difficulty which the measurement of angle MES involves, Boyer misses a crucial element of this method of Aristarchus, namely, that for all intents and purposes, Aristarchus' measurement is a mathematical exercise. Cf., Lloyd, G.E.R., ‘Observational Error in Later Greek Science’, in Barnes, J. et al. (eds) Science and Speculation, Studies in Hellenistic Theory and Practice, Cambridge, 1982, p. 153.Google Scholar

²⁴ Heath, , op. cit. (18), p. 311.Google Scholar

²⁵ Quoted by Heath, ibid., pp. 311–312.

²⁶ Neugebauer, , op. cit. (16), p. 643.Google Scholar

²⁷ Ibid.

²⁸ Ibid., p. 647. Cf., Lloyd, , op. cit. (23), p. 136.Google Scholar

²⁹ Neugebauer, ibid.

³⁰ Quoted by Palter, , op. cit. (14), p. 121.Google Scholar

³¹ Neugebauer, , op. cit. (16), p. 644.Google Scholar

³² Heath, , op. cit. (18), p. 348.Google Scholar Heath suggests that Archimedes was the first to recognize the phenomenon of parallax with respect to the sun. (Ibid.) Neugebauer, on his part, maintains that we do not know who introduced the concept of parallax into Greek astronomy. (Neugebauer, , op. cit. (16), p. 322.)Google Scholar

³³ Neugebauer, ibid., p. 644.

³⁴ Ibid.

³⁵ Ibid., p. 646. Cf., Lloyd, , op. cit. (23), pp. 153–155.Google Scholar

³⁶ Neugebauer, ibid., pp. 100, 1235, Fig. 92.

³⁷ Toomer, G.J., ‘Hipparchus on the Distances of the Sun and Moon’, Archive for History of Exact Sciences (1974), 14, p. 139.CrossRefGoogle Scholar Pappus notes in his account of Hipparchus' procedure that Hipparchus ‘takes the following observation: an eclipse of the sun, which in the Hellespontine region was an exact eclipse of the whole sun, such that no part of it was visible, but at Alexandria by Egypt approximately four-fifths of the diameter was eclipsed’. (Quoted by Toomer, ibid., pp. 126–127.)

³⁸ Pappus' commentary; quoted by Toomer, ibid., 126–127.

³⁹ Toomer, , op. cit. (37), p. 139. Cf.Google Scholar, Neugebauer, , op. cit. (16), pp. 109–112, 327–329.Google Scholar

⁴⁰ Dreyer, J.L.E., A History of Astronomy from Thales to Kepler, 2nd edn (revised with a Foreword by Stahl, W.H.), New York, 1953, p. 184.Google Scholar Neugebauer remarks that ‘it is not surprising that the early attempts at determining the size and distance of sun and moon in relation to the earth ended with wrong results. The ancient methods are of necessity based on trigonometric arguments in combination with visual estimates of very small angles and one naturally had the tendency to falsify such estimates in the wrong direction.’ (Neugebauer, , op. cit. (16), p. 634.)Google Scholar

⁴¹ Toomer, , op. cit. (37), pp. 139–140.Google Scholar Dreyer, ibid.

⁴² Toomer, ibid.

⁴³ However, Kepler did not carry out his plan and wrote instead an elementary text-book of astronomy, Epitome Astronomiae Copernicanae. (Dreyer, , op. cit. (40), pp. 403.)Google Scholar

⁴⁴ Toomer, , op. cit. (37), pp. 139–140.Google Scholar

⁴⁵ Neugebauer, , op. cit. (16), p. 329.Google Scholar

⁴⁶ Quoted by Toomer, , op. cit. (37), p. 126.Google Scholar

⁴⁷ Dreyer, , op. cit. (40), pp. 184–185.Google Scholar

⁴⁸ Neugebauer, , op. cit. (16), p. 111.Google Scholar

⁴⁹ Ibid. In Neugebauer's view ‘Muslim astronomers … restricted themselves by and large to the most elementary parts of Greek astronomy: refinements in the parameters of the solar motion, and increased accuracy in the determination of the obliquity of the ecliptic and the constant of precession’. (Ibid., p. 145.) However, Neugebauer remarks that ‘the conceptual elegance of Ptolemy's cinematic models and the logical consistency of the derivation of the fundamental parameters from carefully selected observations made it extremely difficult to introduce more than insignificant modifications of the basic theory’. Thus, Neugebauer continues, ‘every attempt at a revision of the foundations of the planetary theory must have appeared, rightly, as a gigantic task, not lightly to be undertaken in view of the consistency of the structure erected in the Almagest’. (Ibid.) For Neugebauer ‘it is not surprising that a cosmological theory of such impressive internal consistency was not conducive to serious scrutiny’. (Ibid., p. 919.)

⁵⁰ Ibid., pp. 54, 369, 529, 543 note no. 13, 1082–1083.

⁵¹ Ibid., pp. 807 note no. 15, 1082–1083.

⁵² Ibid., p. 54.

⁵³ Ibid., pp. 292–298.

⁵⁴ However, see the criticism of Aaboe and Price, particularly the discussion of the different accuracy obtained in solstice and equinox observations. (Aaboe, A. and de Solla Price, D.J., ‘Qualitative Measurement in Antiquity: the derivation of accurate parameters from crude but crucial observations’, in Koyré, A., L'aventure de la Science, Mélanges A. Koyré, Vol. I, Paris, 1964, pp. 6–10. Cf. op. cit. (138).Google Scholar

⁵⁵ Neugebauer, , op. cit. (16), p. 293Google Scholar, my emphasis. Apparently, this discovery led Hipparchus to introduce real ecliptic coordinates because longitudes increase proportionally with time whereas latitudes remain unchanged. (Neugebauer, , op. cit. (13), p. 69.)Google Scholar

⁵⁶ Lloyd, , op. cit. (11), p. 181Google Scholar note no. 295. Lloyd, , op. cit. (23), p. 141.Google ScholarNeugebauer, , op. cit. (16), p. 294.Google Scholar

⁵⁷ Neugebauer, ibid., p. 298.

⁵⁸ Quoted by Ptolemy. See Lloyd, , op. cit. (23), p. 141.Google Scholar

⁵⁹ Hipparchus adduces another proof for variation in the length of the tropical year from calculations based on eclipse data. However, Ptolemy criticizes this proof and considers it circular. (Ibid., pp. 142, 156. Neugebaucr, , op. cit. (16), p. 295. See op. cit. (90).)Google Scholar

⁶⁰ Neugebauer, ibid. Cf., op. cit. (85, 86). Copernicus also did not realize that errors of observation were quite sufficient to account for the difference between the various values of the constant of precession. (Dreyer, , op. cit. (40), p. 329.)Google Scholar

⁶¹ Neugebauer, ibid., p. 294.

⁶² Ibid., pp. 294, note no. 15, 296. See also op. cit. (84).

⁶³ Dreyer, , op. cit. (40), p. 203.Google Scholar

⁶⁴ Ibid.

⁶⁵ E.g., Neugebauer, , op. cit. (16), p. 89.Google Scholar

⁶⁶ Dreyer, , op. cit. (40), pp. 161, 166–167.Google Scholar

⁶⁷ Quoted by Dreyer, ibid., pp. 165–166.

⁶⁸ See Neugebauer, , op. cit. (16), pp. 319–321.Google Scholar

⁶⁹ In his ‘Notes on Hipparchus’, Neugebauer concludes that ‘it is our good luck to be able to see in the Almagest how Ptolemy utilized this material with supreme skill’. (Neugebauer, , op. cit. (14), p. 296.)Google Scholar

⁷⁰ Neugebauer, , op. cit. (16), p. 321.Google Scholar

⁷¹ Ibid., p. 320.

⁷² Neugebauer, , op. cit. (14), p. 296.Google Scholar

⁷³ Quoted by Koyré, , op. cit. (1), p. 398Google Scholar, note no. 4. Neugebauer puts it this way: ‘One may perhaps say that the role of Apollonius, Hipparchus, and Ptolemy has a parallel in the positions of Copernicus, Brahe and Kepler.’ (Neugebauer, , op. cit. (16), p. 309.)Google Scholar

⁷⁴ Lloyd, , op. cit. (23), p. 158.Google Scholar

⁷⁵ Toomer, , op. cit. (37), p. 131.Google Scholar

⁷⁶ Ibid., p. 131, note no. 25.

⁷⁷ Neugebauer, , op. cit. (16), p. 106.Google Scholar

⁷⁸ Toomer, , op. cit. (37), p. 131.Google Scholar Lloyd suggests that Ptolemy settled on a one-value parameter, instead of a bounded one in order to simplify the computations. (Lloyd, , op. cit. (23), p. 155.)Google Scholar Cf., op. cit. (115).

⁷⁹ Lloyd, , op. cit. (23), p. 151Google Scholar, emphasis in the original. However, Lloyd points out that ‘in acoustics, as in astronomy, it was sometimes recognised that different observers will get different results’. (Ibid., p. 132, note no. 8.) Indeed, when Plato discusses harmonics in the Republic, he remarks that ‘some say they can distinguish a note between two others, which gives them a minimum unit of measurement, while others maintain that there's no difference between the notes in question’. (Plato, , op. cit. (2), p. 340 (530).)Google Scholar

⁸⁰ Lloyd, , op. cit. (23), p. 151Google Scholar, emphasis in the original. Cf., Lloyd, , op. cit. (11), p. 197Google Scholar; Neugebauer, , op. cit. (16), pp. 892–896Google Scholar; Palter, , op. cit. (14), pp. 121–122Google Scholar; Smith, A.M., ‘Ptolemy's Search for a Law of Refraction: A Case-study in the Classical Methodology of “Saving the Appearances” and its Limitations’, Archive for History of Exact Sciences (1982), 26 no. 3, pp. 221–240.Google Scholar

⁸¹ Neugebauer, , op. cit. (16), pp. 112, 634, 917–922.Google Scholar

⁸² Ptolemy, , Almagest, (trs. and ann. Toomer, G.J.), London, 1984Google Scholar, Bk. VII, Ch. 2. Toomer, , op. cit. (37), p. 131Google Scholar note no. 25. Cf., Dreyer, , op. cit. (40), p. 203Google Scholar; Neugebauer, , op. cit. (16), pp. 54, 160Google Scholar; Lloyd, , op. cit. (23), pp. 147–149.Google Scholar

⁸³ Pedersen, O., A Survey of the Almagest, Odense, 1974, p. 248.Google Scholar Neugebauer, ibid., pp. 986, 1037.

⁸⁴ Neugebauer, ibid., p. 34.

⁸⁵ Quoted by Palter, , op. cit. (14), pp. 122–123.Google Scholar

⁸⁶ Lloyd, , op. cit. (11), p. 181 note no. 295Google Scholar; Lloyd, , op. cit. (23), pp. 140–142, 145.Google Scholar See op. cit. (58, 59).

⁸⁷ Lloyd, , op. cit. (23), pp. 142, 146–147.Google Scholar

⁸⁸ Quoted by Lloyd, ibid., p. 142.

⁸⁹ Ibid., p. 145. However, as Lloyd stresses, it is not in dispute that the paucity of the actual observations cited in Ptolemy's detailed accounts of the movements of the planets in Books IX to XI is remarkable. For each planet he cites almost the minimum number of observations that are necessary to determine the parameters of what is after all a complex model. (Lloyd, , op. cit. (11), p. 186.)Google Scholar Ptolemy is in general quite confident that his theories work well; indeed, he considers approximate or uncorrected figures adequate for the exposition of his model. (Ibid., p. 187 note no. 325.)

⁹⁰ However, Ptolemy criticized Hipparchus' indirect method of determining the length of the tropical year using the data of lunar eclipses. He argued that these calculations presuppose correct determinations of equinoctial points, and cannot be carried out independently of assumptions about the sun's position. Ptolemy thus exposed the circularity of this method. (Lloyd, , op. cit. (23), pp. 142, 156.Google ScholarNeugebauer, , op. cit. (16), p. 295.)Google Scholar

⁹¹ Lloyd, ibid., p. 145. Cf. Hon, op. cit. (1), pp. 557–559.

⁹² Dreyer, , op. cit. (40), p. 195Google Scholar; Neugebauer, , op. cit. (16), p. 99Google Scholar; Palter, , op. cit. (14), p. 126Google Scholar; Toomer, , op. cit. (37), p. 129.Google Scholar However, Lloyd points out that Ptolemy does not always set out his workings in such a way that one can see precisely what margin of error he allowed himself. (Lloyd, , op. cit. (23), p. 149.)Google Scholar

⁹³ Lloyd, ibid., p. 152.

⁹⁴ Neugebauer, , op. cit. (16), p. 148.Google Scholar

⁹⁵ Neugebauer, , op. cit. (13), pp. 155–156.Google Scholar

⁹⁶ Neugebauer, , op. cit. (16), pp. 148, 917–922, 1088Google Scholar; Lloyd, , op. cit. (11), p. 199.Google Scholar Cf. Hon, , op. cit. (1), pp. 562–563.Google Scholar

⁹⁷ Neugebauer, ibid., pp. 103, 657–658. Ptolemy in fact adduces an array of arguments against this method: (1) the hole of the clepsydra gets stopped up; (2) the quantity of water that flows out in a night or a day is not necessarily an exact multiple of the quantity taken at the rising; (3) it is inexact to take the chord as equal to the arc it subtends. (Lloyd, , op. cit. (23), p. 143.)Google Scholar

⁹⁸ Neugebauer, , op. cit. (16), pp. 893–894.Google Scholar

⁹⁹ Ibid., p. 894.

¹⁰⁰ Op. cit. (80), and (137); but see (139).

¹⁰¹ Neugebauer, , op. cit. (16), p. 894; op. cit. (136).Google Scholar Ptolemy lists in the Optics many illusory phenomena and he attempts to account for them. Far from concluding that sight is deceptive, he stresses the difference between exceptional and normal sight. (Lloyd, , op. cit. (23), p. 161.)Google Scholar

¹⁰² Lloyd, ibid., p. 147.

¹⁰³ Ibid., p. 150.

¹⁰⁴ Lloyd, , op. cit. (11), p. 198.Google Scholar

¹⁰⁵ Ibid.

¹⁰⁶ Ibid., emphasis on the original.

¹⁰⁷ Ibid., p. 192; Lloyd, , op. cit. (23), pp. 147, 157.Google Scholar

¹⁰⁸ Lloyd, , op. cit. (11), p. 198.Google Scholar In his account of Venus, Ptolemy claims that the observational data required the introduction of the equant: the ‘centre for the eccenter which produces the uniform motion’, to use Ptolemy's own definition. (Ibid., p. 192; Neugebauer, op. cit. (16), p. 1102.) In Neugebauer's view, the introduction of the equant was an ‘important step in the history of the theory of planetary motion …, a step which was eliminated by philosophical reasons in Copernicus' theory but again fully recognized in its importance by Kepler’. (Neugebauer, ibid., p. 171; cf., Hon, op. cit. (1), p. 559.)

¹⁰⁹ Lloyd, ibid., p. 198.

¹¹⁰ The existence of a Greek star-catalogue of over 1000 stars which gives longitude, latitude and magnitude determinations for each star, is considered another evidence—regardless of the controversy concerning its origin—of sustained observational work. (Ibid., pp. 183–184, 200; Dreyer, op. cit. (40), pp. 202–203; Neugebauer, op. cit. (13), pp. 68–69; Neugebauer, , op. cit. (16), pp. 53–54, 280–292, 577, 836, 1087Google Scholar; Palter, , op. cit. (14), p. 126.)Google Scholar

¹¹¹ Quoted by Lloyd, , op. cit. (23), p. 133.Google Scholar

¹¹² Ibid., pp. 156–157; Lloyd, , op. cit. (11), p. 182.Google Scholar

¹¹³ Palter, , op. cit. (14), p. 122.Google Scholar

¹¹⁴ Lloyd, , op. cit. (11), p. 200.Google Scholar

¹¹⁵ Lloyd, , op. cit. (23), p. 155.Google Scholar Lloyd thus holds that the deductive articulation of Ptolemy's theories has effectively ruled out in most cases the use of upper and lower limits for the main fundamental parameters. (Ibid., p. 156.) Neugebauer on his part observes that Ptolemy ‘resorted to mere approximations when higher accuracy implied too heavy a burden of numerical computations’. (Neugebauer, , op. cit. (16), p. 145.)Google Scholar

¹¹⁶ The epicycle-eccentric model of Hipparchus and Ptolemy for the sun and moon has been hailed as ‘the outstanding example, from the ancient world, of a theory that combined the mathematical rigour the Greek scientists demanded with a detailed empirical base’. (Lloyd, , op. cit. (11), p. 200.)Google Scholar

¹¹⁷ Dreyer, , op. cit. (40), p. 201.Google Scholar Ptolemy indeed records his awareness of this discrepancy. (Lloyd, , op. cit.(23), p. 139.)Google Scholar

¹¹⁸ Dreyer, ibid., p. 196.

¹¹⁹ Ibid., p. 201. The phenomenon of annular solar eclipse is another case in point. Since Ptolemy assumed that the apparent lunar diameter equals the apparent solar diameter when the moon is at its maximum geocentric distance (previous astronomers had assumed equality for the moon at mean distance), he in effect denied the possibility of annular solar eclipse. However, in all probability such a phenomenon was observed still in his lifetime. But, as Neugebauer remarks, ‘neither then nor during the next 1400 years was the obviously necessary modification … undertaken’. (Neugebauer, , op. cit. (16), pp. 104, 111.)Google Scholar Kepler studied carefully reports of such an eclipse and considered them correct. (Hon, , op. cit. (1), p. 579.)Google Scholar In general, Kepler did not rest until he was able to reconcile all aspects of theory and observations, whereas Ptolemy's theory had been accepted for centuries without any attempt to eliminate its defects. (Neugebauer, , op. cit. (16), p. 98.)Google Scholar ‘I have built up a theory of Mars’, Kepler writes to his teacher, Maestlin, , ‘such that there is no difficulty about agreement between calculation and the accuracy of observational data’.Google Scholar (Quoted by Koyré, , op. cit. (1), p. 397 note no. 4.)Google Scholar

¹²⁰ Dreyer, ibid., p. 196.

¹²¹ Ibid., p. 201.

¹²² On the Planetary Hypotheses see Pedersen, , op. cit. (83), pp. 391Google Scholar ff; Lloyd, , op. cit. (11), p. 199Google Scholar; Neugebauer, , op. cit. (16), pp. 900ff.Google Scholar

¹²³ Quoted by Dreyer, , op. cit. (40), p. 196.Google Scholar

¹²⁴ Lloyd disagrees with this interpretation. In his view, Ptolemy's work ‘is not simply and solely a piece of pure mathematics’. (Lloyd, , op. cit. (11), p. 198Google Scholar, my emphasis.) According to Ptolemy, Lloyd ‘hoped for a true physical account, indeed one that covered not just the kinematics, but also the dynamics, of heavenly movement’.Google Scholar (Lloyd, ibid., p. 199.) However, in Neugebauer's view, the Planetary Hypotheses seems on the face of it to suggest some mechanism which connects the motions of the planets within a larger cosmic system, but in fact nothing of this kind is achieved. ‘No planet is influenced by the motion of any other one and the only unifying principle is their confinement into contiguous but strictly separated compartments…’ (Neugebauer, , op. cit. (16), p. 922.)Google Scholar

¹²⁵ Aaboe, and Price, , op. cit. (54), pp. 3–4.Google Scholar

¹²⁶ Neugebauer, , op. cit. (13), p. 185.Google Scholar Elsewhere Neugebauer writes that ‘it makes no sense to praise or to condemn the ancients for the accuracy or for the errors in their numerical results. What is really admirable in ancient astronomy is its theoretical structure, erected in spite of the enormous difficulties that beset the attempts to obtain reliable empirical data’. (Neugebauer, , op. cit. (16), p. 108.)Google Scholar

¹²⁷ Aaboe and Price go on to say that ‘the simple numbers however produce results that agree remarkably well with the facts, so that we must marvel at the way in which the choice and simple numbers were injected into suitably interlocking chains’. (Aaboe, and Price, , op. cit. (54), p. 20.)Google Scholar

¹²⁸ Ibid.

¹²⁹ Lloyd, , op. cit. (11), p. 200.Google Scholar

¹³⁰ Ibid., p. 221.

¹³¹ Aaboe, and Price, , op. cit. (54), p. 16Google Scholar; Neugebauer, , op. cit. (16), p. 1089.Google Scholar

¹³² Hon, op. cit. (1). Cf., Jardine, N., The Birth of History and Philosophy of Science: Kepler's A Defence of Tycho against Ursus with essays on its provenance and significance, Cambridge, 1984.Google Scholar

¹³³ Lloyd, , op. cit. (23), p. 133.Google Scholar

¹³⁴ Ibid., pp. 133–134.

¹³⁵ Ibid., pp. 134–135.

¹³⁶ Quoted by Lloyd, ibid., p. 135; cf. ibid., note 12.

¹³⁷ Ibid., p. 134. However, as Neugebauer remarks, ‘it should be remembered how difficult the problem still appeared to Brahe and Kepler when it was taken up around 1600’. (Neugebauer, , op. cit. (16), p. 896.)Google Scholar

¹³⁸ Aaboe, and Price, , op. cit. (54), p. 9.Google Scholar

¹³⁹ Lloyd, , op. cit. (23), p. 135.Google Scholar

¹⁴⁰ Ibid., pp. 136ff.

¹⁴¹ Op. cit. (28, 30, 97).

¹⁴² Wittgenstein, L., On Certainty, (eds Anscombe, G. E. M. and von Wright, G. H., trs Paul, D. and Anscombe, G. E. M.), Oxford, 1977, p. 84e (#641).Google Scholar

¹⁴³ Hon. op. cit. (1), p. 591.Google Scholar Cf., Hon, G., ‘On the Concept of Experimental Error’, Ph.D. Thesis, London University, (1985)Google Scholar, Ch. IV: A Classification of Types of Experimental Error; Hon, G., ‘Towards a Typology of Experimental Errors: an Epistemological View’, Studies in History and Philosophy of Science, 20.Google Scholar