A Neglected Galilean Letter

Drake S. , “An unpublished letter, possibly by Galileo”, Physis, viii (1966), 247–52.

To Andrea Cioli, 19 March, to Geri Bocchineri, 16 April, in Galilean MSS at Florence; to Geri Bocchineri, 5 March and 23 April, in Egerton MSS at London. Watermarked duck over three mounds, encircled. I wish to thank Dr Owen Gingerich for confirming the watermarks of Egerton 48; he agrees that the handwriting of the London Galileo letters closely matches the unsigned letter.

Kepler Johann , Epitome astronomiae Copernicanae, Book III, pt 2; ed. by Frisch C. , Kepleri opera omnia, vi (Frankfurt, 1866), 229: “…vetustissimi faciunt eam 24 praecise graduum, quae est quindecima totius circuli pars….”

The conditions for inscribability of regular polygons were first formulated by Gauss C. F. . From the completion of Lanci's clause in the next paragraph, he appears to have thought that all were inscribable.

Gilbert William , De magnele (London, 1600), 233, where the next quotation is also found.

Not an inscribable polygon, as Galileo probably suspected, since the nonagon is not.

The first clause is pure Aristotle; cf. Metaphysica 994b15–16. The second clause is pure Galileo; he knew the times-squared law of distances in fall from rest to be punctually obeyed, and he also knew how unexpected it had been when he discovered it early in 1604, simultaneously with the pendulum law.

This remark alone would explain Galileo's neglect of ellipticity of orbits, discussed further below.

Galileo's meaning would be better expressed by the phrase: “is that the place to look…?”.

The Platonist position demands that these be drawn from purely geometrical considerations, putting aside mere seen phenomena.

See Drake S. , “Galileo's ‘Platonic’ cosmology and Kepler's Prodromus”, Journal for the history of astronomy, iv (1973), 174–91; idem, Galileo at work (Chicago, 1978), 63–66.

Drake S. and O'Malley C. D. , The controversy on the comets of 1618 (Philadelphia, 1960), 184–5; Galileo , Il Saggiatore, end of Section VI.

Except that Kepler defended it against Galileo, arguing that if Tycho's system was null, so was that of Copernicus; see Drake and O'Malley , op. cit. (ref. 12), 342ff.

Perhaps the most distinctively modern aspect of Galileo's mature physics was his specification of experimental variance of time measurements (± 0.1 pulsebeat, about 0.08 second) in recounting his tests of the times-squared law. His was the first physics built on quantitative probable error, which he also applied ingeniously to astronomy in the first section of the Third Day of his Dialogue.

See Galileo , Dialogue, transl. by Drake S. (Berkeley, 1953), 22, 24, 27, for identification of impetus with speed acquired, and 144–56 for conservation of speed as against “impressed force”.

Ibid., 453, note 15.

See Drake S. , “Analysis of Galileo's experimental data”, Annals of science, xxxix (1982), 389–97.

Cf. Drake , Galileo at work, 297–300, 321–9, for excerpts from these two documents.