¹ Opere, Edizione Nazionale, reprint Florence, 1934, x, 228–230Google Scholar (cited below as Opere simply).

² I thank Dr. Whitrow for reminding me to add these three words.

³ Ibid., x, 22–23.

⁴ Cf. Ibid., x, 46–47.

⁵ Galileo Galilei on Motion and on Mechanics, trans. Drabkin, I. E. and Drake, Stillman (Madison, 1960), 49Google Scholar, note; cited hereafter as On Motions or On Mechanics simply.

⁶ On Mechanics, 137.Google Scholar

⁷ On Motion, 63.Google Scholar

⁸ Ibid., 65.

⁹ Opere, x, 97–100.Google Scholar

¹⁰ This was first pointed out to me by my former student, Mr. Willard C. Humphreys, to whose Galilean researches I am much indebted throughout this lecture.

¹¹ Opere, x, 114–116.Google Scholar

¹² Opere, x, 170.Google Scholar

¹³ Ibid., x, 244–245.

¹⁴ Ibid., x, 248–249.

¹⁵ Ibid., xi, 85. Daniello Antonini in a letter to Galileo of 9 April 1611 discusses the latter's proposition: ‘Mobile secundum proportionem distantiae, a termino a quo movetur velocitatem acquirens, in instanti movetur.’

¹⁶ Opere, viii, 215Google Scholar; Dialogues concerning Two New Sciences, trans. Crew, Henry and de Salvio, Alfonso (Evanston and Chicago, 1946), 174.Google Scholar This passage was drafted by Viviani under Galileo's direction for addition to re-issues of the Discorsi. Cf. the definition of horizontal in Opere, viii, 371.Google Scholar

¹⁷ On Motion, 66.Google Scholar

¹⁸ On Mechanics, 170–171.Google Scholar

¹⁹ Ibid., 177.

²⁰ Dialogue concerning the Two Chief World Systems… trans. Drake, Stillman (Berkeley 1953), 147.Google Scholar

²¹ Opere, x, 115.Google Scholar

²² Ibid., viii, 373.

²³ Dr. Hoskin kindly pointed out in discussion that if the acceleration is quoad tempus the demonstration can be quite respectable. In Galileo's case, however, it seems to be quoad spatia (see below). Did anyone ever follow the process I sketch here?

²⁴ Ibid., viii, 383–384.

²⁵ Ibid., viii, 383.

²⁶ Dialogue concerning the Two Chief World Systems, 25–26.Google Scholar

²⁷ Opere, viii, 384–385.Google Scholar

²⁸ Observe, again, the difference with regard to empirical certainty between the letter to Sarpi of 1604 and the earlier letter to Guidobaldo about the pendulum.