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

Autores: Alberto Dou Mas de Xaxàs
Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 36, Nº 2, 1, 1992 (Ejemplar dedicado a: la memória de Pere Menal i Brufal), págs. 533-540
Idioma: inglés
DOI: 10.5565/publmat_362a92_16
Títulos paralelos:
- El "Corolario II" a la proposición XXIII del "Euclides" de Saccheri
Enlaces
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Resumen
- 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.