Giovanni Saccheri entered the Jesuit Order at Genoa in 1685. Five years later he went to Milan where he studied philosophy and theology at the Jesuit College. While in this College he was encouraged to take up mathematics by Tommaso Ceva.
Saccheri was ordained a priest in 1694 at Como and then taught at various Jesuit Colleges through Italy. He taught philosophy at Turin from 1694 to 1697, philosophy and theology at Pavia from 1697 until his death. He also held the chair of mathematics at Pavia from 1699 until his death.
In Euclides ab Omni Naevo Vindicatus (1733) Saccheri did important early work on non-euclidean geometry, although he did not see it as such, rather an attempt to prove the parallel postulate of Euclid.
He also worked on mathematical logic. His Logica Demonstrativa (1697) treats logic with definitions, postulates and demonstrations in the style of Euclid.
Among his other publications was a work on statics Neo-statica published in 1708 and his first work Quaesita geometrica (1693) written with considerable advice and help from Tommaso Ceva.
In fact through Tommaso Ceva he also made the acquaintance of Giovanni Ceva and Viviani. He corresponded with all three of these mathematicians.