The "Corollarium II" to the Proposition XXIII of Saccheri's "Euclides"

  1. Dou Mas de Xaxàs, Alberto
Revista:
Publicacions matematiques

ISSN: 0214-1493

Any de publicació: 1992

Títol de l'exemplar: la memória de Pere Menal i Brufal

Volum: 36

Número: 2

Pàgines: 533-540

Tipus: Article

DOI: 10.5565/PUBLMAT_362A92_16 DIALNET GOOGLE SCHOLAR lock_openDDD editor

Altres publicacions en: Publicacions matematiques

Resum

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.

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