He used Ceva's ingenious methods in his first published work, 1693, solutions of six geometric problems proposed by the Sicilian mathematician Ruggero Ventimiglia (1670-1698).

[4] The Logica demonstrativa, reissued in Turin in 1701 and in Cologne in 1735, gives Saccheri the right to an eminent place in the history of modern logic.

[7] According to Thomas Heath “Mill’s account of the true distinction between real and nominal definitions was fully anticipated by Saccheri.”[8] Saccheri is primarily known today for his last publication, in 1733 shortly before his death.

He finally concluded that: "the hypothesis of the acute angle is absolutely false; because it is repugnant to the nature of straight lines".

[10] There is some minor argument on whether Saccheri really meant that, as he published his work in the final year of his life, came extremely close to discovering non-Euclidean geometry and was a logician.

One tool that Saccheri developed in his work (now called a Saccheri quadrilateral) has a precedent in the 11th-century Persian polymath Omar Khayyám's Discussion of Difficulties in Euclid (Risâla fî sharh mâ ashkala min musâdarât Kitâb 'Uglîdis).