What are the best proofs of Cavalieri's principle without concepts of calculus?
"Best" may be construed as most cogent from the point of view of students of elementary geometry, or as most elegant, or in any other reasonable sense.
2026-04-08 05:51:38.1775627498
What are the best proofs of Cavalieri's principle without concepts of calculus?
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There is a proof of Cavalieri's principle by Minkowski on pages 204-207 of his book "Geometrie der Zahlen", published in 1896. Minkowski needed it because Fubini's theorem did not exist then. The proof is quite elementary (he covers the body with a net of cubes), but of course he uses concepts from analysis by letting the sidelength of the cubes go to zero.