The "Corolarium II" to the proposition XXIII of Saccheri's Euclides.

Dou, Albert. "The "Corolarium II" to the proposition XXIII of Saccheri's Euclides.." Publicacions Matemàtiques 36.2A (1992): 533-540. <http://eudml.org/doc/41733>.

@article{Dou1992,
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.},
author = {Dou, Albert},
journal = {Publicacions Matemàtiques},
keywords = {parallels; Euclid's elements},
language = {eng},
number = {2A},
pages = {533-540},
title = {The "Corolarium II" to the proposition XXIII of Saccheri's Euclides.},
url = {http://eudml.org/doc/41733},
volume = {36},
year = {1992},
}

TY - JOUR
AU - Dou, Albert
TI - The "Corolarium II" to the proposition XXIII of Saccheri's Euclides.
JO - Publicacions Matemàtiques
PY - 1992
VL - 36
IS - 2A
SP - 533
EP - 540
AB - 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.
LA - eng
KW - parallels; Euclid's elements
UR - http://eudml.org/doc/41733
ER -