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Giovanni Girolamo Saccheri
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Giovanni Girolamo Saccheri
Giovanni Girolamo Saccheri (Italian pronunciation: [dʒoˈvanni dʒiˈrɔːlamo sakˈkɛːri]; 5 September 1667 – 25 October 1733) was an Italian Jesuit priest, scholastic philosopher, and mathematician. He is considered the forerunner of non-Euclidean geometry.
The son of a lawyer, Saccheri was born in Sanremo, Genoa (now Italy) on September 5, 1667. From his youth he showed extreme precociousness and a spirit of inquiry. He entered the Jesuit novitiate in 1685. He studied philosophy and theology at the Jesuit College of Brera in Milan.
His mathematics teacher at the Brera college was Tommaso Ceva, who introduced him to his brother Giovanni. Ceva convinced Saccheri to devote himself to mathematical research and became the young man's mentor. Saccheri was in close scientific communion with both brothers. 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).
Saccheri was ordained as a priest in March 1694. He taught philosophy at the University of Turin from 1694 to 1697 and philosophy, theology and mathematics at the University of Pavia from 1697 until his death. He published several works including Quaesita geometrica (1693), Logica demonstrativa (1697), and Neo-statica (1708). Saccheri died in Milan on 25 October 1733.
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. According to Thomas Heath “Mill’s account of the true distinction between real and nominal definitions was fully anticipated by Saccheri.”
Saccheri is primarily known today for his last publication, in 1733 shortly before his death. Now considered an early exploration of non-Euclidean geometry, Euclides ab omni naevo vindicatus (Euclid Freed of Every Flaw) languished in obscurity until it was rediscovered by Eugenio Beltrami, in the mid-19th century.
The intent of Saccheri's work was ostensibly to establish the validity of Euclid by means of a reductio ad absurdum proof of any alternative to Euclid's parallel postulate. To do so, he assumed that the parallel postulate was false and attempted to derive a contradiction.
Since Euclid's postulate is equivalent to the statement that the sum of the internal angles of a triangle is 180°, he considered both the hypothesis that the angles add up to more or less than 180°.
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Giovanni Girolamo Saccheri
Giovanni Girolamo Saccheri (Italian pronunciation: [dʒoˈvanni dʒiˈrɔːlamo sakˈkɛːri]; 5 September 1667 – 25 October 1733) was an Italian Jesuit priest, scholastic philosopher, and mathematician. He is considered the forerunner of non-Euclidean geometry.
The son of a lawyer, Saccheri was born in Sanremo, Genoa (now Italy) on September 5, 1667. From his youth he showed extreme precociousness and a spirit of inquiry. He entered the Jesuit novitiate in 1685. He studied philosophy and theology at the Jesuit College of Brera in Milan.
His mathematics teacher at the Brera college was Tommaso Ceva, who introduced him to his brother Giovanni. Ceva convinced Saccheri to devote himself to mathematical research and became the young man's mentor. Saccheri was in close scientific communion with both brothers. 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).
Saccheri was ordained as a priest in March 1694. He taught philosophy at the University of Turin from 1694 to 1697 and philosophy, theology and mathematics at the University of Pavia from 1697 until his death. He published several works including Quaesita geometrica (1693), Logica demonstrativa (1697), and Neo-statica (1708). Saccheri died in Milan on 25 October 1733.
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. According to Thomas Heath “Mill’s account of the true distinction between real and nominal definitions was fully anticipated by Saccheri.”
Saccheri is primarily known today for his last publication, in 1733 shortly before his death. Now considered an early exploration of non-Euclidean geometry, Euclides ab omni naevo vindicatus (Euclid Freed of Every Flaw) languished in obscurity until it was rediscovered by Eugenio Beltrami, in the mid-19th century.
The intent of Saccheri's work was ostensibly to establish the validity of Euclid by means of a reductio ad absurdum proof of any alternative to Euclid's parallel postulate. To do so, he assumed that the parallel postulate was false and attempted to derive a contradiction.
Since Euclid's postulate is equivalent to the statement that the sum of the internal angles of a triangle is 180°, he considered both the hypothesis that the angles add up to more or less than 180°.
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