Galileo, Two New Sciences, First Day: Aristotle’s wheel, indivisibles, and the bowl and cone (1638; Crew and de Salvio 1914)

Companion source

Source: Internet Archive, Cornell scan cu31924012322701; local OCR excerpt .txt, lines 655–5861 of the archive’s _djvu.txt, retrieved 2026-09-08. The Italian original is stored separately from Wikisource. Metadata: Galileo Galilei, Discorsi (Leiden, 1638), First Day; English by Henry Crew and Alfonso de Salvio (New York: Macmillan, 1914), pp. 1–108. Extraction: archive.org OCR with page headers; clean dialogue. Rights: public domain.

Source digest

The First Day treats the continuum through Aristotle’s wheel, the infinite number of indivisible vacua, and the bowl and cone taken from Luca Valerio: a plane cutting a hemispherical bowl and an inscribed cone leaves equal areas at every height, and as the plane rises both vanish, one into a point and the other into a circumference. Galileo lets Salviati draw the moral that the last cut may be equal and yet incomparable. For this project, this is the early modern form of Democritus’s dilemma and the objection Galileo put to Cavalieri, answered in the letter of 2 October 1634.

Passage anchors

• Archive lines 1147–1174: Aristotle’s wheel and the infinite indivisible vacua.
• Archive lines 1932–1960: the bowl and the cone.
• The Day ends before “SECOND DAY” at archive line 5862.

Coverage and limits

Reading level passage for the wheel and the bowl; metadata for the rest of the Day.