Abstract THE "COROLLARIUM II" TO THE PROPOSITION XXIII OF SACCHERFS EUCLIDES

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 cir-cumscribed by alls sides " ; and also why he rejects Euclid's proof. Moreover, the Corolarium has implications for confirmation of Sac-cheri's method; and also for his concept of straight line, which leads him to his paralogism of ignorantia elenchi in proposition XXXIII. The Euclides ab omni naevo vindicatus was published in 1733, the same year of the death of his author Giovanni Girolamo Saccheri. The Euclides is a book of plane geometry in the same sense that the Euclides Elements are; except that the Euclides fifth postulate or postulate of par