||This "Corolarium" of the Euclides (1733) contains an original proof of propositions 1. 27 and 1 . 28 of Euclid'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 Euclid's proof. Moreover, the Corolarium 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.