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The origin of modern astronomical theories of tides: Chrisogono, de Dominis and their sources

Published online by Cambridge University Press:  05 January 2009

Federico Bonelli  and
Lucio Russo
Federico Bonelli
Affiliation:
Via Cassia 701k, 00189, Roma, Italy.
Lucio Russo
Affiliation:
Dipartimento di Matematica, Università di Roma Tor Vergata, Roma, Italy.
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Extract

From the Renaissance to the seventeenth century the phenomenon of tidal motion constituted one of the principal arguments of scientific debate. Understanding the times for high and low water was of course often essential for navigation, but local variations (which nowadays are attributed to currents, coastal configurations, prevailing winds, seabed shaping and other geographic characteristics) made an inductive approach impractical and precluded the possibility of constructing a universally valid model for predicting these times. Notwithstanding the complexity of the phenomenon and its practical import, however, the early-modern theory of tidal ebb and flow, as clearly emerges from Duhem's analysis, appears to be neither the result of the interpretation of empirical data, nor aimed to their prediction. Rather, the interest in tides was of a theoretical nature and was aroused particularly by their double nature, being at the same time variable and regular, terrestrial and astronomical.

Type
Research Article
Information
The British Journal for the History of Science , Volume 29 , Issue 4 , December 1996 , pp. 385 - 401
Copyright
Copyright © British Society for the History of Science 1996

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References

1 This is not, however, the case for the Mediterranean (where the effect of the tide is negligible practically everywhere), which may account for the little interest shown in this phenomenon by the Romans.

2 Duhem, P., La Théorie physique, Paris, 1914, repr. Paris, 1993, ch. 7.Google Scholar

3 Still very useful on the medieval concepts of tides is Almagià, R., La dottrina della marea nell'Antichità classica e nel Media Evo, Memorie della R. Accademia dei Lincei, Rome, 1905.Google Scholar

4 The work Questio de fluxu et refluxu maris, attributed to Robert Greathead, relies heavily on the theory of tides put forward by Albumasar in his Introductorium maius, as demonstrated in Laird, E. S., ‘Robert Grosseteste, Albumasar, and medieval tidal theory’, Isis (1990), 81, 684–94.CrossRefGoogle Scholar

5 It should be noted that this recognition, although fairly widespread, was not general. In 1666 John Wallis still found it necessary to refute the opinion of Isaac Vossius, who in his work De motu marium et ventorum (The Hague, 1663)Google Scholar had considered purely by chance the synchronization of the lunar cycle and the tides. See ‘An essay of DrWallis, John, exhibiting his hypothesis about the flux and reflux of the sea’, Philosophical Transactions (1666), 16, 263–89, on 286–7.Google Scholar

6 Even Descartes, among others, while recognizing the relationship between the tides and the phases of the moon attributes the tidal action to the moon alone (see Descartes, R., ‘Le monde…ou le traité de la lumière’, in Oevres de Descartes (ed. Adam, C. and Tannery, P.), 12 vols., repr. Paris, 1986, xi, 80–3).Google Scholar

7 Others apart from Albumasar and Robert Greathead behave in this way, for example Albertus Magnus (1193–1280) in De proprietatibus elementorum (ed. del Jammy, A. M.), Lyon, 1651Google Scholar, book I, treatise 2, chs. 4–8; Albertus' exposition is discussed in Almagià, , op. cit. (3), 461 ff.Google Scholar

8 The main extant sources on the Hellenistic theories of tides are the Naturalis historia by Pliny and Geography by Strabo. Such testimonies strongly suggest that in the Hellenistic age an explanation, based on an interaction with the sun and the moon, of the fortnightly cycle of the tides had been obtained. In particular Pliny (who is the preferred source of all medieval authors who are concerned with natural history) states that the sun and the moon cause the tides (Naturalis historia, II, 212)Google Scholar, although he does not give an explicit explanation for the fortnightly cycle, which in all probability he was unable to report. The role of the sun in the phenomenon was presumably clear to Seleucus (who had studied the annual cycle of the tides). For a reconstruction of Hellenistic knowledge on the subject and especially the contribution of Seleucus, see Russo, L., ‘L'astronomo Seleuco, Galileo e la teoria della gravitazione, Quaderni urbinati di cultura classica (1995), 49 (new series), 143–60.CrossRefGoogle Scholar

9 Scotus, J. Duns, Meteorologicorum, II, Quaest. 2, 63–6Google Scholar, in Scotus, John Duns, Opera, Lyon, 1651.Google Scholar

10 In fact, this idea, like many of those quoted above, persisted long after the end of the Middle Ages. Even Kepler asserts that as the moon grows fuller all things containing moistness grow larger. See Kepler, J., De fundamentis astrologiae, Prague, 1602Google Scholar, thesis xv.

11 Obviously this explanation is difficult to reconcile with the observation that the tide is the same at the full and new moons; to resolve this blatant contradiction several elaborate explanations were put forward; it is not necessary to refer to them in full here.

12 See Almagià, , op. cit. (3), 454.Google Scholar

13 The period of teaching in Padua was reported by Almagià, (op. cit. (3), 500)Google Scholar, who took it from Facciolati, , Fasti gymnasii Patavini, Padua, 1757, 117–18Google Scholar. Beyond this, we may glean a little about Chrisogono from his works.

14 Federici Chrisogoni nobilis Jadertini Artium et Medicine doctoris Subtilissimi et Astrologi excellentissimi de modo Collegiandi Prognosticandi et curandi Febris Necnon de humana Felicitate ac denique de Fluxu et Refluxu Marts Lucubrationes nuperrime in Lucem edite MDXXVIII…Editum ab eximio Doctore Federico Chrysogono nobile Jadertino. Et Venetiis impressum a Joan. Anto. de Sabbio et fratribus. Anno a partu Virgineo MDXXVIII. Kal. Aprilis (hereafter Chrisogono). We have used the copy of this very rare work which is preserved in the Biblioteca Angelica in Rome.

15 Almagià, , op. cit. (3)Google Scholar, declines to describe the booklet on the tides in detail for the reason that the particular characteristics of the work would re-establish Chrisogono among modern scholars. Duhem, (op. cit. (2), 368)Google Scholar emphasizes the importance of Chrisogono's writing, but refers very briefly (and not at all accurately) to its content. Other authors seem to hear of Chrisogono only through Duhem.

16 This premise places Chrisogono's work in a very old medico-astrological tradition, going back to Galen at the very least (Galen having associated the critical period of the nasal mucous membrane diseases with the phases of the moon).

17 Chrisogono, , op. cit. (14)Google Scholar, calls all the affirmations in his work ‘conclusiones’ without discriminating between initial assumptions and their logical consequences. Another feature demonstrates his lack of familiarity with the methodology of exact science: he asserts that he is following the habit of mathematicians in using letters to indicate, for maximum clarity, the parts of a figure (‘Quas equidem partes totius figure signabimus cum literis more mathematico: ut facilius demonstrate valeamus ea que intendimus docere’; ‘tertia conclusio’, fol. 24v). He fails to realize that mathematicians had denoted the points of a figure with letters and not generally the zones. Since the time of Vitruvius the concept of a geometrical point had presented great difficulties in attempts to render Greek scientific works into Latin. See Russo, L., ‘The astronomy of Hipparchus and his time: a study based on pre-Ptolemaic sources’, Vistas in Astronomy (1994), 38, 207–48, especially 227–8.CrossRefGoogle Scholar

18 The ‘prima conclusio’ of the work runs ‘Sol et Luna sic maris tumorem ad se contrahunt: quod sub ipsis perpendiculariter est maximus tumor maris: qui quidem tumor fluxus maris dicitur et aquarum crementum et similiter diametraliter in parte opposita (que nadir dicitur) est eadem vel consimilis eleuatio vel tumor maris maximus; ergo duo maximi tumores maris sunt semper et uniformiter: alter scilicet sub luminaribus et alter in parte opposita: que nadir luminarium est vocata que oppositionem significat secundum astronomos’ (Chrisogono, , op. cit. (14), fol. 24v).Google Scholar

19 ‘in orizonte autem medic istorum duorum centrorum oppositorum est semper maxima depressio et decrementum aquarum vel refluxus maris’ (Chrisogono, , op. cit. (14)Google Scholar, ‘secunda conclusio’, fol. 24v).

20 ‘ideo erunt etiam quattuor profunditates maris semper uniformes: quarum due erunt a luna causate et eius nadir: alie vero due a sole scilicet et eius nadir: et omnes predicte figure a dictis centris sunt equaliter terminantes in cuspidem vel quandam piramidem’ (Chrisogono, , op. cit. (14)Google Scholar, ‘tertia conclusio’, fol. 24v).

21 Chrisogono, , op. cit. (14)Google Scholar, ‘septima conclusio’, fols. 25r–25v. Duhem interprets the form here described as an ellipsoid and ignores the previously described peaks. See Duhem, , op. cit. (2), 368.Google Scholar

22 Chrisogono, , op. cit. (14)Google Scholar, ‘sexta conclusio’, fol. 25r.

23 Chrisogono, , op. cit. (14)Google Scholar, ‘decima conclusio’, fol. 26r.

24 ‘Sed causis efficientibus motum equalibus existentibus in posse et oppositum motum intendentibus: mobile non mouebitur: motus enim prouenit a victoria maioris inequalitatis motoris: ergo mare in illa hora non mouebitur…quod bis accidit in singulo mense in prima quadratura scilicet septima die: et in secunda scilicet vigesimaprima die’ (Chrisogono, , op. cit. (14)Google Scholar, ‘undecima conclusio’, fol. 26v).

25 It should be noted that Chrisogono's theory, taken literally, can explain the real motion of the tides with much the same approximation as a theory based on the action of the moon alone. The original introduction of a role for the sun in the theory of the tides presumably produced better results.

26 Chrisogono, , op. cit. (14) ‘decimaquarta conclusio’, fol. 27r.Google Scholar

27 Delfino, F., De fluxu et refluxu aquae maris, Venice, 1559Google Scholar. A second edition of this work was printed in Basel in 1577.

28 Boccaferri, Ludovico, Lectiones… in secundum ac tertium meteorum Aristotelis, Venice, 1570Google Scholar. Chrisogono's theory is given in fols. 14v ff.

29 Cardano, G., De rerum varietate, Basel, 1587.Google Scholar

30 Galluccio, Giovanni Paolo, Theatrum mundi et temporis, Venice, 1588, ch. 12, 70–82.Google Scholar

31 Raimondo, Annibale, Trattato utilissimo e particolarissimo del flusso e del riflusso del mare, Venice, 1589, fols. 3r–7v.Google Scholar

32 Duré, Claude, Discour de la vérité des causes et effects des divers cours, mouvements, flux, reflux et saleure de la mer océane, mer Méditerrannée et autres mers de la terre, Paris, 1600Google Scholar. Duré simply plagiarizes the work by Delfino cited above; see Duhem, , op. cit. (2), 368.Google Scholar

33 Ambrosio, Florido, Dialogismus de natura universa maris ac eius genesi et de causa fluxus et refluxus eiusdem…, Padua, 1613.Google Scholar

34 The work, with an English translation, is to be found in The Principal Works of S. Stevin, 5 vols., Amsterdam, 1961, iii, 323–57.Google Scholar

35 The biography of de Dominis, giving attention to his juridico-religious rather than his scientific work, has been the object of various monographs: Newland, H., The Life and Contemporaneous Church History of Antonio de Dominis, Archbishop of Spalato, Oxford, 1859Google Scholar; Ljubic, S., ‘Prilozi za životopis Markantuna de Dominisa Rabljanina, spljetskoga nadbiskupa’, Starine na sviet izdaje Jugoslavenska Akademij Znanosti I Umjetnosti (1870), 2, 1–270Google Scholar; Ljubic, S., ‘O Markantunu Dominisu Rabljaninu, historičko kritičko iztraživanje’, Rad Jugoslavenska Akademija Znanosti i Umjetnosti (1870), 10, 1–159Google Scholar; Russo, A., Marc'Antonio de Dominis Arcivescovo di Spalato e Apostata, Naples, 1964Google Scholar; Malcolm, N., De Dominis (1560–1624): Venetian, Anglican, Ecumenist and Relapsed Heretic, London, 1984Google Scholar. The works of Ljubic contain richly detailed biographical documentation.

36 The body of the archbishop was taken from the crypt of S. Maria della Minerva, where it was laid waiting for the end of the trial, for public burning, along with his works, in the Campo de' Fiori, Rome.

37 Especially his De republica ecclesiastica. See, for example, Jemolo, A. C., Stato e Chiesa negli scrittori politic: del Seicento e del Settecento, Naples, 1972, 70Google Scholar; Malcolm, , op. cit. (35), 81 ffGoogle Scholar.

38 de Dominis, M. A., De radiis visus et lucis in vitris perspectivis et iride tractatus. Venice, 1611.Google Scholar

39 de Dominis, M. A., Euripus seu de fluxu et refluxu maris sententia, Rome, 1624Google Scholar. We refer to copies of this extremely rare work preserved in the Vatican and Marcian Libraries.

40 Tommaso Baglioni, who printed de Dominis' work, was also the publisher of Sidereus nuncius but had argued with Galileo over, amongst other things, the quality of the print of his work. He subsequently printed a series of scientific works characterized by their distinct anti-Galilean flavour. See Bertolo, F., Tommaso Baglioni, Dizionario dei Tipografi, il '500, Milan, forthcoming.Google Scholar

41 The explanation of the phenomenon of the rainbow is based on experiments with spherical bowls filled with water, which de Dominis claims personally to have conducted. It is probable, however, that the experiments were carried out much earlier, since the same experiments were described both by Theodoric from Vriberg, around the year 1300, and previously by Arabian writers. See, for example, Crombie, A. C., From Augustine to Galileo, 2 vols., Cambridge, 1959, i, ch. 3.Google Scholar

42 This is also the opinion of Ziggelaar, A., ‘Die Erklärung des Regenbogens durch Marcantonio de Dominis, 1611. Zum Optikunterricht am Ende des 16. Jahrhunderts’, Centaurus (1979), 23, 21–50.CrossRefGoogle Scholar

43 The German theologian Otho Casmannus had published the Marinarum quaestionum tractatio philosophica bipartita…, Frankfurt, 1598.Google Scholar

44 De Dominis reiterates, for example, the classical argument of the boats of which the hulls disappear before the sails, as they move away; and of the circular form of the earth's shadow during lunar eclipses.

45 De Dominis, , op. cit. (39), §22, 37–8.Google Scholar

46 De Dominis, , op. cit. (39), §22, 38–40.Google Scholar

47 ‘Itaque dicimus luminaria illa duo Solem & Lunam habere vim magnam, quasi magneticam erga aquas huius mundi inferioris’ (de Dominis, , op. cit. (39), §5, 5Google Scholar). We have already seen that the comparison of magnetic attraction with the action of the sun and the moon on the tides goes back to the thirteenth century and had come into common use. De Dominis, however, in introducing the analogy, described the effect of loadstone on iron not only in terms of attraction but of attraction towards one part and repulsion from the other. (‘Si enim Magnes…trahit ad se ferrum ex una parte, ex alia vero opposita id a se propellit, & amouet, cur aliquid simile esse in caelestibus illis corporibus multo nobilioribus & efficacioribus negabimus?’, ibid., §4, 4). This is exactly what the moon and the sun seem to do, attracting the water in some points and repulsing it at their antipodes. The idea was dropped in the following section, where the high tide in the point opposite to the luminary, instead of being attributed to the repulsion of the sun and moon, was attributed rather to the attraction of the point in the heavens opposite the luminary concerned. It may be asked if the idea had been developed more consistently by other authors.

48 De Dominis, , op. cit. (39), §5, 5.Google Scholar

49 This point is developed in particular in his answer to the fifth query (de Dominis, , op. cit. (39), §§34 and 35, 59–64Google Scholar). De Dominis actually uses here the modified hypothesis (which we shall meet below), which does not substantially alter the deduction of the fortnightly cycle.

50 See especially de Dominis, , op. cit. (39), §3.Google Scholar

51 ‘Putavi ego aliquandiu vim hanc maris tractiuam, & eleuatiuam esse aeque in ipsis Solis, & Lunae corporibus, atque in punctis eis diametraliter oppositis’, de Dominis, , op. cit. (39), §5, 5.Google Scholar

52 ‘Altera difficultas est, quod Nadir Solis, & Lunae, cum ipsi Soli & Lunae diametraliter opponantur, necessario semper motu diurno diuersum & oppositum percurrunt & discribunt parallelum, exceptis solis aequinoctiorum diebus. Si igitur Corpus luminaris sit in tropico Cancri, ipsius Nadir erit in tropico Capricorni: & ita vertex alterius coni describet parallelum extremum borealem, alter vero oppositi coni vertex describet parallelum extremum borealem, alter vero oppositi coni vertex describet parallelum extremum borealem, alter vero oppositi coni vertex describet eodem die alterum extremum parallelum australem, cum differentia notabili graduum 47, quae differentia in cono facit notabile discrimen ipsius crassitici’, de Dominis, , op cit. (39), §5, 6–7.Google Scholar

53 De Dominis, , op. cit. (39), §6, 10.Google Scholar

54 While Chrisogono speaks of pyramids, de Dominis affirms that the oceans form cones; this difference disappears when we consider the figures they both refer to, in which the form of the water is represented by triangles whose vertices are directed both towards the luminaries and away from them. The two authors could therefore have been giving different interpretations to the same figure.

55 Eratosthenes had noted that the phenomenon of tide calls for a modification of the Archimedean theory of the sphericity of the oceans, but Strabo, (Geography, I 3, 17)Google Scholar considered such criticism of Archimedes inconceivable. De Dominis took up both Strabo's position against Eratosthenes (in de Dominis, , op. cit. (39), §§10–25Google Scholar) and, conversely, Eratosthenes' ideas on the tides against which Strabo had argued (ibid., §§1–9).

56 De Dominis, , op. cit. (39), §5, 7.Google Scholar

57 The title refers to one of antiquity's most famous tidal phenomena, that of the Strait of Euripus (between the Isle of Euboea and Boeotia) where the current reverses itself several times a day owing to the tides.

58 De Dominis, , op. cit. (39), §10, 14Google Scholar. Strabo, (Geography, I 3, 11)Google Scholar, taking Archimedes as his authority, criticizes Eratosthenes, who had believed in the difference in level which had been measured on both sides of the Isthmus of Corinth. De Dominis brought Strabo's argument up to the moment of substituting what is now known as the Isthmus of Panama for that of Corinth.

59 Aristotle, , De caelo, II, 287a, 30 – 287b, 14Google Scholar; attributing spherical form only to the water, however. Since the deductions are based on the special property of the water to find its lowest level, the presence of land above it raises no difficulties for those merely taking the opinions put forward in De caelo.

60 The first book of the treatise is in fact dedicated by Archimedes to the demonstration of the spherical nature of the surface of the oceans, based on his hydrostatic postulate. Of course the proof can be interpreted as referring to the entire earth, but in order to do this it is necessary to add to the Archimedean presuppositions the hypothesis that the earth was originally fluid: a hypothesis quoted in various classical sources but not in Archimedes' treatise.

61 Diodorus Siculus states that the earth, while it was still fluid, assumed its form by being compressed by the force of gravity (Biblioteca historica, I, vii, 1–2)Google Scholar; see also Russo, , op. cit. (17), §11.Google Scholar

62 Pliny, , Naturalis historia, II, 2.Google Scholar

63 See, for example, Copernicus, N., De revolutionibus orbium caelestium libri sex, Nuremberg, 1543, book I, ch. 9Google Scholar (see also the edition by Koyré, A. of book I, Paris, 1934)Google Scholar, where the hydrostatic argument is also used to justify the spherical form of the sun, moon and other heavenly bodies. See also Duhem, , op. cit. (2), 344–5.Google Scholar

64 Many sources for the ancient hydrostatic proof of the sphericity of the earth are collected in Duhem, P., Les Origines de la statique, Paris, 1906Google Scholar; see also Duhem, , op. cit. (2), 345 ffGoogle Scholar. It is interesting, however, to compare this with what Whewell wrote in 1837: ‘Newton's attempt to solve the problem of the figure of the earth, supposing it fluid, is the first example of such an investigation, and this rested upon principles which we have already explained, applied with the skill and sagacity which distinguished all that Newton did’ (Whewell, W., History of the Inductive Sciences, 3 vols., London, 1837, ii, 111).Google Scholar

65 Owing to the fact that these notions were reasonably widespread at the time. The law of increase in density with depth had been discussed by, for example, Patrizi and by Casmannus, who, not believing in the earth's sphericity, had not accepted it; see de Dominis, , op. cit. (39), §22, 40.Google Scholar

66 Strabo, , Geography, III 5, 9Google Scholar. Strabo refers to the ‘Erythrean Sea’, which in antiquity comprised both the present Red Sea and Arabian Sea. However, since Strabo reports Seleucus in one place coming from the region of the ‘Erythrean Sea’ (Geography, III 5, 9Google Scholar) and in another as coming from Babylon (Geography, I 1, 8–9Google Scholar), apparently considering them the same place, it appears that in the case of Seleucus Strabo probably means the Arabian Sea when he states ‘Erythrean Sea’.

67 It might seem strange that de Dominis (who quotes passages by Strabo on the tides sometimes explicitly and at other times implicitly) denies the existence of a phenomenon referred to by Strabo. Strabo, however, immediately after mentioning the studies of the tides by Seleucus, relates that Posidonius had tried without success to discover in the Atlantic Ocean the yearly cycle of the daily inequalities that Seleucus had described in the Erythrean Sea (Strabo, , Geography, III 5, 9Google Scholar). De Dominis had probably deduced from this not that the tides in the two seas had different qualitative characteristics but that Seleucus had been mistaken in his affirmations.

68 Important testimony on this point is furnished by one of the greatest experts on the subject: George Darwin. He had read the passage by Strabo on Seleucus' (and Posidonius') studies of the tides in a collection of fragments concerning Posidonius (Blake, J., Posidonii Rhodii reliquiae doctrinae, Leiden, 1810Google Scholar). Darwin noted the correspondence between the description given by Strabo (which he first interpreted correctly) and the actual process of the tides in the Arabian Sea. He observed that the passage by Strabo could not have been understood by Bake by reason of the near ignorance of the tides in such distant regions they had at the time (that is in 1810). See Darwin, G., The Tides and Kindred Phenomena in the Solar System, London, 1898, 76.Google Scholar

69 See Russo, , op. cit. (8)Google Scholar, and Russo, , op. cit. (17), §11.Google Scholar

70 See Ziggelaar, , op. cit. (42).Google Scholar

71 Malcolm, , op. cit. (35), 9Google Scholar, writes ‘no direct source has ever been found for his account’, and records that de Dominis claims personally to have carried out the experiments with the water-filled spheres. However, see note 41 above.

72 See Chrisogono, , op. cit. (14), fol. 24r.Google Scholar

73 Dondi's theory is referred to by Boccaferri, , op. cit. (28)Google Scholar. According to L. Thorndike the original work is to be found in a manuscript, dated to the sixteenth century, preserved in the Ambrosian Library (n334 sup.); see Thorndike, L., ‘Milan manuscript of Giovanni de' Dondi's astronomical clock and of Jacopo de' Dondi's discussion of tides’, Archeion, (1936), 18, 308–17CrossRefGoogle Scholar. The contents of the manuscript referred to by Thorndike, however, seem to be less interesting than the theory referred to by Boccaferri.

74 It is on the basis of this error that we have affirmed that the first effective astronomical explanation of the principal cycles of the tides is that of Chrisogono.

75 It is well known that for Galileo the explanation of the tides constitutes the essential matter of the treatise, to which he had originally given the title Dialogo del flusso e riflusso del mare. The title was changed following the above-mentioned papal censure.

76 Neugebauer, O., A History of Ancient Mathematical Astronomy, Berlin, 1975, 611.CrossRefGoogle Scholar

77 Plutarch, , Platonicae quaestionesGoogle Scholar, VIII, i (= Moralia, 1006C).

78 See especially the passage by Strabo already cited (Geography, III 5, 9).Google Scholar

79 See Diels, H., Doxographi Graeci, Berlin, 1879, 383a, 17–25 and 383b, 26–34.Google Scholar

80 This thesis is sustained in Russo, , op. cit. (8)Google Scholar, where the extant testimonies on Seleucus are examined.

81 The affirmation that the tides are caused by variations in the movements of the earth can be found in the work Quod caelitm stet, terra moveatur, vel de perenni motu terrae, published posrhumously in Caelii Calcagnini Ferrarensis opera aliquot, Basel, 1544.Google Scholar

82 The ideas of Paolo Sarpi on this subject can be found in handwritten notes. Some passages, in which Sarpi gives the same analogy as Galileo between the tide and the movement of water in an oscillating basin, were published by L. Sosio in the essay ‘Galileo e la cosmologia’, in his introduction to Galilei, Galileo, Dialogo sopra i due massimi sistemi del mondo, tolemaico e copernicano, Turin, 1970, p. lxxviiiGoogle Scholar. The notes go back to 1595 and therefore precede Galileo's treatment of the subject.

83 Cesalpino, Andrea, Quaestiones peripateticae, Venice, 1571Google Scholar. ‘Quaestio V’ in book III of this work is entitled ‘Maris fluxum, et refluxum ex motu terrae non lunae fieri’. Sosio, (op. cit. (82), p. lxxv)Google Scholar observes that the title promises more than it delivers. Cesalpino, who was not of a Copernican turn, does not in fact refer to either the rotation or the revolution of the earth but to a strange small movement communicated to the earth by the movement of the heavens. We are dealing therefore with an attempt to explain the tides through movements of the earth by an author who differs from the others quoted in that he has no reason to believe in the movements of the earth and must introduce one ‘ad hoc’. What better confirmation that the association between tides and movements of the earth was suggested to different authors not by having arguments in common, but by having read resources in common?

84 Gassendi, P., De motu impresso a motore traslato, Paris, 1641.Google Scholar

85 Baliani's theory, which he did not publish, came to Wallis' notice by means of a report by Riccioli in his Almagestum novum, Bologna, 1651Google Scholar; see Wallis, , op. cit. (5), 270.Google Scholar

86 This is the main argument in Wallis' paper.

87 See note 35 above.

88 The theory of rainbows by de Dominis is recorded in various works on the history of science; for example, it is several times mentioned by Crombie, , op. cit. (41), i, sections III 3, V 5, VI 4.Google Scholar

89 For example, de Dominis is mentioned neither by Almagià, , op. cit. (3)Google Scholar (who even has a chapter dedicated to modern pre-Newtonian theory of tides) nor by Duhem, , op. cit. (2).Google Scholar

90 Newton, who refers to de Dominis as ‘the famous Antonius de Dominis Archbishop of Spalato’, considers his theory of rainbows the first complete explanation of the phenomenon and suggests that his work was the unacknowledged source of Descartes on the subject. See Newton, I., Opticks, repr. New York, 1952, 169.Google Scholar

91 No cancellation is to be found in the copy in the Vatican Library, however. Since this volume is part of the library stock donated by the Barberini family, it may be the personal copy of the cardinal Francesco Barberini to whom the author had dedicated the work.

92 Some of Newton's scholia concerning classical antiquity were published for the first time in Casini, P., ‘Newton, gli Scolii Classici; presentazione, testo inedito e note’, Giornale critico della filosofia italiana (1981), 60, 7–53Google Scholar. They are the scholia to the propositions iv–ix of book iii of Principia (Royal Society of London, Gregory MSS 247, fols. 6–14). In the introduction to his edition Casini discusses at length Newton's interest in sapientia veterum but without giving consideration to the ancient scientific knowledge in which Newton was interested.