Cavalieri to Galileo, 15 December 1621 and 22 March 1622: “all the lines” (Opere XIII)
Source: Internet Archive
le-opere-di-galileo-galilei-edizione-nazionale-volume-13; local OCR excerpt.txt, lines 4628–4690 and 4958–5263 of the archive’s_djvu.txt, retrieved 2026-09-08. Metadata: Le Opere di Galileo Galilei, Edizione Nazionale, vol. XIII, Carteggio 1620–1628, ed. Antonio Favaro (Florence, 1902). Letters from Bonaventura Cavalieri in Milan to Galileo in Florence, 15 December 1621 and 22 March 1622, with Favaro’s manuscript references. The seventeenth-century letters are public domain; the edition is 1902 and its editor died in 1922. Extraction: archive.org OCR; Italian prose is clean, headers and footnote numerals are interleaved. Rights: public domain.
Source digest
In the first letter Cavalieri defines “all the lines” of a plane figure as the parallels drawn through it and asks Galileo whether all the lines of one figure have a ratio to those of another, since they seem infinite. In the second he develops the comparison of all the lines of two figures and the objection that multiplying a figure multiplies its lines. These are the earliest statements of the method of indivisibles, sent to Galileo for judgement. For this project, they show the cut question posed as a question about ratios of aggregates of sections, before the treatise of 1635.
Passage anchors
- Archive lines 4651–4656: the definition of all the lines and the question of their infinity.
- Archive lines 4978–5001: the ratio of all the lines of two figures.
Coverage and limits
Reading level passage for the cited lines;
full-read of both letters for structure.