Cavalieri, Exercitationes geometricae sex (1647), Exercitatio III: reply to Guldin’s objections against indivisibles
Source: Internet Archive, Google scan
bub_gb_OXe4dPXGSDMC; local OCR excerpt.txt, lines 9236–12357 of the archive’s_djvu.txt, retrieved 2026-09-08. Metadata: Bonaventura Cavalieri, Exercitationes geometricae sex (Bologna: Giacomo Monti, 1647), Exercitatio tertia, “In Paulum Guldinum e Societate Iesu dicta Geometriae indivisibilibus obiicientem”. Guldin’s Centrobaryca was not located on archive.org. Extraction: archive.org OCR of a 1647 Latin printing; damaged but the running heads and section openings are legible. Rights: public domain.
Source digest
The third Exercitatio answers Guldin’s objections in the Centrobaryca, chiefly that indivisibles cannot compose a continuum and that comparing infinite aggregates is illegitimate, by restating that the method compares aggregates of lines or planes taken with a common regula and by supplying a second method that avoids the aggregates. For this project, this is the seventeenth-century record of the objection that a cut-refinement law changes the object, and of the reply that only ratios of aggregates are asserted.
Passage anchors
- Archive line 9238: the heading of the Exercitatio against Guldin.
- Archive line 12358: “Exercitatio quarta”, the end of the excerpt.
Coverage and limits
Reading level metadata with position anchors; the OCR is
a finding aid.