The "Corollarium II" to the Proposition XXIII of Saccheri's "Euclides"
ISSN: 0214-1493
Year of publication: 1992
Issue Title: la memória de Pere Menal i Brufal
Volume: 36
Issue: 2
Pages: 533-540
Type: Article
More publications in: Publicacions matematiques
Abstract
This "Corolarium" of the Euclides (1733) contains an original proof of propositions 1.27 and 1.28 of Euclide's Elements. In the same corollary Saccheri explains why he dispenses "not only with the propositions 1.27 and 1.28, but also with the very propositions 1.16 and 1.17, except when it is clearly dealt with a triangle circumscribed by alls sides"; and also why he rejects Euclide's proof. Moreover the corollarium has implications for confirmation of Saccheri's method; and also for his concept of straight line, which leads him to his paralogism of ignorantia elenchi in proposition XXXIII.