Galileo, Two New Sciences, Fourth Day (1638; Crew and de Salvio 1914)
Source: Internet Archive, Cornell scan
cu31924012322701; local OCR excerpt.txt, lines 12924–16676 of the archive’s_djvu.txt, retrieved 2026-09-08. Metadata: Galileo Galilei, Discorsi e dimostrazioni matematiche intorno a due nuove scienze (Leiden: Elzevir, 1638), Fourth Day; English translation by Henry Crew and Alfonso de Salvio, Dialogues Concerning Two New Sciences (New York: Macmillan, 1914), pp. 244–294. The translation is a 1914 work in the public domain; the original text is 1638. Extraction: archive.org OCR; page headers of the form “FOURTH DAY 245” remain in the text and the running dialogue is clean. Wikisource carries the first three Days only. Rights: public domain.
Source digest
Theorem I, Proposition I states that a projectile carried by a uniform horizontal motion compounded with a naturally accelerated vertical motion describes a semi-parabola. Salviati precedes it with two lemmas on the parabola drawn from Apollonius, and the Day continues with the sublimity and altitude of a parabola, the tables of ranges and the discussion of resistance.
For this project, this is the original setting of the parabola-and-chord geometry of C001, and the chord–curve comparison in Newton’s Scholium to Book I, Section I refers back to this construction. The Day’s parabola lemmas are the classical inputs to the lens area treated by Archimedes.
Passage anchors
- Excerpt lines 1–20: Salviati’s opening and the heading “The Motion of Projectiles”.
- Archive lines 12970–12974: “Theorem I, Proposition I” and “describes a path which is a semi-parabola”.
- Excerpt end: “END OF FOURTH DAY”, followed by the Appendix on centres of gravity, which is outside the excerpt.
Coverage and limits
Reading level passage for the opening, the two lemmas
and Theorem I; metadata for the tables and the later
dialogue. Figures require the scan.