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SACCHERI, Giovanni Geronimo (1667-1733). Euclides ab Omni Naevo Vindicatus: sive conatus geometricus quo stabiliuntur prima ipsa universae geometriae principia. Milan: Pauli Antoni Montani, 1733.
4o (247 x 195 mm). 6 engraved folding plates. (Red ink number stamp in margin of first text leaf.) Contemporary sheep (crudely rebacked). Provenance: Philip, Earl Stanhope (armorial bookplate); Wooster Woodruff Beman (inscription dated 1897 of front flyleaf, noting that it was sold to:) George Bruce Halsted.
FIRST EDITION OF THE FIRST BOOK ON NON-EUCLIDEAN GEOMETRY. Saccheri attempted to prove Euclid's parallel postulate as a theorem by showing that the supposition that it is not true leads to a contradiction. The path to Saccheri's erroneous "contraction" consists of a series of propositions which are the main elements of non-Euclidean geometry. It was only that Saccheri deluded himself into seeing a contradiction in the final step where none existed. Neither Janos Bolyai nor Lobachevsky seems to have been aware of his work. 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 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. Saccheri's works are very rare, with none appearing in ABPC in at least fifty years.
4o (247 x 195 mm). 6 engraved folding plates. (Red ink number stamp in margin of first text leaf.) Contemporary sheep (crudely rebacked). Provenance: Philip, Earl Stanhope (armorial bookplate); Wooster Woodruff Beman (inscription dated 1897 of front flyleaf, noting that it was sold to:) George Bruce Halsted.
FIRST EDITION OF THE FIRST BOOK ON NON-EUCLIDEAN GEOMETRY. Saccheri attempted to prove Euclid's parallel postulate as a theorem by showing that the supposition that it is not true leads to a contradiction. The path to Saccheri's erroneous "contraction" consists of a series of propositions which are the main elements of non-Euclidean geometry. It was only that Saccheri deluded himself into seeing a contradiction in the final step where none existed. Neither Janos Bolyai nor Lobachevsky seems to have been aware of his work. 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 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. Saccheri's works are very rare, with none appearing in ABPC in at least fifty years.