The Archaeology of the Inverse Square Law: (2) The Use and Non-Use of Mathematics

Kepler Johannes , New astronomy, transl. by Donahue William H. (Cambridge, 1992), 372.

Kepler , op. cit. (ref. 1), 89.

Kepler , op. cit. (ref. 1), 376 (title of chap. 33).

Kepler , op. cit. (ref. 1), 380.

For Kepler's philosophical motivations in his optical inquiries see Chen-Morris Raz D. , “Kepler's optics: The mistaken identity of a Baroque spectator”, Zeitsprünge: Forschungen zur frühen Neuzeit, iv (2000), 50–71.

Hooke Robert , The posthumous works, ed. by Waller Richard (London, 1705; facsimile repr., New York, 1969), 114.

Kepler , op. cit. (ref. 1), 380.

Kepler , op. cit. (ref. 1), 394 (title of chap. 36).

Kepler , op. cit. (ref. 1), 397.

Kepler Johannes , Mysterium cosmographicum: The secret of the universe, transl. by Duncan A. M. (New York, 1981), 63.

Kepler , Mysterium cosmographicum (ref. 10), 53–55.

“vnam esse motricem animam in orbium omnium centro, scilice in Sole; quae, vt quodlibet corpus est vicinitus, ita vehementius incitet”, Kepler , Mysterium cosmographicum (ref. 10), 198–9.

Kepler , Mysterium cosmographicum (ref. 10), 201.

Kepler Johannes , Optics: Paralipomena to Witelo and optical part of astronomy, transl. by Donahue William H. (Santa Fe, NM, 2000), 19.

“… instrumentum Creatoris, ad figuranda & vegetanda omnia … matrix animalium facultatum, vinculumque corporei & spiritualis mundi, in leges easdem transfixerit”, Kepler Johannes , Ad Vitellionem paralipomena, quibus astronomiae pars optica traditur (Frankfurt, 1604; facsimile repr., Brussels, 1968), 7 (slightly modified from Donahue's translation in Kepler, Optics (ref. 14), 19–20).

Kepler , Mysterium cosmographicum (ref. 10), 59/167.

Kepler , Mysterium cosmographicum (ref. 10), 60/169.

Kepler , op. cit. (ref. 1), 372.

Kepler , op. cit. (ref. 1), 376.

Kepler , op. cit. (ref. 1), chap. 33; 376–8.

Boulliau Ismaël , Astronomia philolaica (Paris, 1645), 23.

Kepler , op. cit. (ref. 1), 378–80, italics added.

“In hunc imminutionis scopulum allidens ipsius Astronomia fibrata naufragium facit”, Boulliau , op. cit. (ref. 21), Liber I, Caput X; 24.

Boulliau , op. cit. (ref. 21), 23.

Hooke , “Lectures of light”, Posthumous works (ref. 6), 114.

Ibid.

For Hooke's vibration theory of matter see Gal Ofer , Meanest foundations and nobler superstructures: Hooke, Newton and the compounding of the celestiall motions of the planets (Dordrecht, 2002), 86–92, 127–31.

Hooke , op. cit. (ref. 6), 113, italics in original.

Hooke , op. cit. (ref. 6), 113.

Trinity College MS 0.11.a.116c.

Hooke , op. cit. (ref. 6), 114, italics added.

His celestial mechanics could benefit even less from the writings of Boulliau's commentators of his own time, the British astronomers of the 1650s and ‘60s — Ward, Streete and Wing — Who had little interest in Kepler's speculations concerning celestial causes. Wing Vincent , Harmonicon coeleste (London, 1651); Astronomia instaurata (London, 1656); Astronomia britannica: In qua, per novam, concinnioremq; methodum hi quinq; tractatus traduntur (London, 1669); Examen Astronomiae Carolinae (London, 1665), and Wing's ephemerides for thirty years, together with his computatio catholica (London, 1669); Streete Thomas , Astronomia Carolina: A new theorie of the coelestial motions (London, 1661), and Examen examinatum, or, Wing's Examination of Astronomia Carolina examined (London, 1667); Ward Seth , In Ismaelis Bullialdi Astronomiae Fundamenta, inquisitio brevis (Oxford, 1653), Idea trigonometriae demonstratae … et inquisitio in Bullialdi Astronomiae Philolaicae Fundamenta (Oxford, 1654), and Astronomia geometrica, ubi methodus proponitur qua primariorum planetarum astronomia sive elliptica sive circularis possit geometrice absolvi (London, 1656).

Turnbull H. W. (ed.), The correspondence of Isaac Newton, ii (Cambridge, 1960), 438.

Turnbull (ed.), op. cit. (ref. 34), 309.

Concerning Newton's alleged discovery of ISL in 1666, see Gal, Meanest foundations (ref. 27), 168–88.

Birch Thomas , The history of the Royal Society (4 vols, London, 1756–7; facsimile repr., New York, 1968), ii, 91: 23 May 1666.

Birch , op. cit. (ref. 37), ii, 92.

Birch , op. cit. (ref. 37), ii, 91–92.

Hooke Robert , Micrographia (London, 1665; facsimile repr., Brussels, 1966), 227.

Hooke Robert , An attempt to prove the motion of the Earth from observation (London, 1674), 27–28.

On Hooke's use of experiments as a means of conceptualization see Bennett J. A. , “Robert Hooke as mechanic and natural philosopher”, Notes and records of the Royal Society, xxxv (1980), 33–48.

Turnbull (ed.), op. cit. (ref. 34), 297.

Cf. Gal , Meanest foundations (ref. 27), 20.

Turnbull (ed.), op. cit. (ref. 34), 301, italics added.

Ibid., 305.

For a different view see Nauenberg Michael , “Newton's early computational method for dynamics”, Archive for history of exact sciences, xlvi (1994), 331–50, and Gal Ofer , “Hooke, Newton, and the trials of historical examination”, Physics today, August 2004, 19–20.

Turnbull (ed.), op. cit. (ref. 34), 308.

Ibid., 309.

Ibid., 313 (17 January 1680).

Ibid., 306, italics added.

Birch , op. cit. (ref. 37), ii, 91.

Ibid., 92.

Ibid., 89.

Wallis John , “An essay, of Dr. John Wallis, exhibiting his hypothesis about the flux and reflux of the sea”, Philosophical transactions, xvi (1666), 263–88.

Ibid., 264.

Ibid., 265.

Ibid., 265. Galileo first presented his “Discorso sul flusso e il reflusso del mare” in 1616 as a letter to Cardinal Orsini. Galilei Galileo , Opere, ed. by Favaro Antonio (20 vols, Florence, 1890–1909), v, 377–95; English version in Finocchiaro Maurice A. , The Galileo affair (Berkeley, 1989), 119–33. Wallis's reference is to the version of the theory of the tides published in the Fourth Day of Galileo's Dialogue concerning the two chief world systems (transl. by Drake Stillman (Berkeley, 1967), 416–65).

Galileo , “Discorso” (ref. 58), 391.

Ibid., 388, 391.

Wallis , op. cit. (ref. 55), 272.

Galileo , “Discorso” (ref. 58), 388.

Hale Mathew , An essay, touching the gravitation and non-gravitation of fluid bodies, and the reasons thereof (London, 1673), 10.

Ibid., 14.

Ibid., 15.

Birch , op. cit. (ref. 37), ii, 89.

Ibid., 91.

“Cæterum totum cœli Planetarij Spatium vel quiescit (ut vulgo creditur) vel uniformiter movetur in directum et perinde Planetarum commune centrum gravitatis … vel quiescit vel una movetur. Utroque in casu motus gravitatis inter se … eodem modo se habent, et eorum commune centrum gravitatis respectu spatij totius quiescit, atque adeo pro centro immobili Systematis totius Planetarij haberi debet. Inde vero systema Copernicæum probatur a priori. Nam si in quovis Planetarum situ computetur commune centrum gravitatis hoc vel incidet in corpus Solis vel ei semper proximum erit.” ( Newton , The preliminary manuscripts for Isaac Newton's 1687 Principia, 1684–1685, facsimile repr. ed. by Whiteside Derek T. (Cambridge, 1989), 20). Translation edited from Herivel J. W. , The background to Newton's Principia (Oxford, 1965), 301.

Cf. Gal , Meanest foundations (ref. 27), chap. 3.

The locus classicus for this view is Duhem Pierre , Aim and structure of physical theory, transl. by Wiener Philip P. (New York, 1974).

Lohne J. A. , “Hooke versus Newton: An analysis of the documents in the case of free fall and planetary motion”, Centaurus, vii (1960), 6–52, p. 9.

Turnbull (ed.), op. cit. (ref. 34), 305.

Lohne , op. cit. (ref. 71), 27; Pelseneer J. A. , “Une lettre inédite de Newton”, Isis, xii (1929), 237–54, p. 44.