Giovanni Girolamo Saccheri
Giovanni Girolamo Saccheri
In Euclides ab omni naevo vindicatus (1733), Girolamo Saccheri was the first mathematician to suggest the possibilities of non-Euclidean geometry. He did not follow through with his speculations, however, and thus it would be more than a century before other mathematicians took Saccheri's ideas further.
Saccheri was born on September 5, 1667, in San Remo, Italy, which was then part of lands controlled by Genoa. In 1685, when he was 18 years old, he entered the Jesuit order of priests, and five years later went to Milan, where he studied philosophy and theology at Brera, the Jesuit college. Tomasso Ceva (1648-1737), brother of the more famous Giovanni Ceva (1647?-1734), happened to be a professor of mathematics at Brera, and encouraged the young Saccheri to take up the discipline.
Ordained at Como in 1694, Saccheri went on to teach at a number of Jesuit-sponsored colleges throughout Italy. At Turin from 1694 to 1697, he taught philosophy before moving on to Pavia, where he taught philosophy and theology from 1697. The latter town, where he held the chair in mathematics from 1699, would remain his home for the rest of his life.
Saccheri's first mathematical publication came in 1693, with Quaesita geometrica. The latter shows the influence of Tomasso Ceva, who continued as a friend and mentor for many years. (In fact the hardy Ceva outlived his student.) Tomasso introduced him to his brother Giovanni, as well as to Vincenzo Viviani (1622-1703), a mathematician who had worked with Galileo and Torricelli. Saccheri corresponded with all three men.
Viviani had published an Italian version of the Elements by Euclid (c. 325-250 b.c.), a work that had stood as Europe's foremost geometry text for 2,000 years. With Logica demonstrativa (1697), which discussed mathematical logic by use of definitions, postulates, and demonstrations, Saccheri himself emulated the style of the great Greek mathematician.
In 1708, Saccheri published Neo-statica, a work on the subject of statics; but his most important writing did not appear until shortly after his death on October 25, 1733, in Milan. This was Euclides ab omni naevo vindicatus, a discussion of Euclid's geometry. In it, Saccheri became the first mathematician to discuss the consequences of defying Euclid's fifth postulate, concerning parallel lines. More significant was his suggestion that a non-Euclidean geometry, independent of the fifth postulate, might be possible.
Saccheri did not use the term "non-Euclidean geometry," nor did he even see his idea as such, and was either unwilling or unable to pursue it further. Nonetheless, his work paved the way for groundbreaking achievements many years later.