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.
@article{urn:eudml:doc:41733,
title = {The "Corolarium II" to the proposition XXIII of Saccheri's Euclides.},
journal = {Publicacions Matem\`atiques},
volume = {36},
year = {1992},
pages = {533-540},
mrnumber = {MR1209822},
zbl = {0785.01007},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41733}
}
Dou, Albert. The "Corolarium II" to the proposition XXIII of Saccheri's Euclides.. Publicacions Matemàtiques, Tome 36 (1992) pp. 533-540. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41733/