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The Saccheri Quadrilateral

The Saccheri Quadrilateral

Saccheri was a Jesuit priest who lived from 1667 to 1733. Before he passed away he published a book entitled Euclides ab omni nævo vidicatus. (Euclid Freed of Every Flaw). Saccheri suggested that for a line and a point, there are three possibilities. The first is that there is exactly one line through the point parallel to the given line. The second, there is no line through the point parallel to the given line. The third is more than one line through the point parallel to the given line. Saccheri investigated the summit angles of a quadrilateral; his result depended on the postulate chosen. He tried to find a contradiction to prove that Euclids fifth postulate was true. He assumed the negation of the parallel Postulate and tried to arrive at a contradiction. He studied a family of quadrilateral that have come to be called Saccheri quadrilateral.

Saccheri tried to find a contradiction; he started with postulates other than Euclids. He didn’t find one, so he still claimed that Euclids was freed from all defects. Although Saccheri’s work did have on flaw.

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