Cavalieri, Geometria indivisibilibus (1635): preface and the opening of Book II with “all the lines”

Companion source

Source: Internet Archive, BNCF scan ita-bnc-mag-00001345-001; local OCR excerpt .txt, lines 136–821 and 6357–6700 of the archive’s _djvu.txt, retrieved 2026-09-08. Metadata: Bonaventura Cavalieri, Geometria indivisibilibus continuorum nova quadam ratione promota (Bologna: Clemente Ferroni, 1635), Praefatio and Liber II, definitions. Extraction: archive.org OCR of a 1635 Latin printing in italic and roman types; heavily damaged, with long s as f and many mis-readings. Anchors are by position, and every quotation needs the scan. Rights: public domain.

Source digest

The preface presents the method; Book II defines “all the lines” of a plane figure, taken with a common regula, and “all the planes” of a solid, and states the fundamental theorem that figures are in the ratio of their aggregates of lines. For this project, this is the printed form of the position defended in the 1634 letter, and the source Guldin attacked.

Passage anchors

• Archive line 6388: “Omnes lineae talis figurae” in the definitions of Book II.
• Archive line 136: “PRAEFATIO”; archive line 822: “LIBER PRIMVS”.

Coverage and limits

Reading level metadata with position anchors only; the OCR is a finding aid, not a transcription.