Round 5: Tossup 1

Arthur Schopenhauer criticized this statement’s “famous controversy” for trying to show that what is directly certain is merely indirectly certain. Gödel, Escher, Bach pairs this statement’s history with the print Tower of Babel to caution against ordinary language interpretation of logical systems. Ibn al-Haytham’s use of motion to prove this statement was refuted by Omar Khayyam. A mistaken reductio ad absurdum proof of this statement was published by Girolamo (*) Saccheri in a book (-5[1])titled for its originator “freed of every flaw.” This relatively complex (10[1])statement is not used for the first 28 of its originator’s propositions. After centuries of failed proofs, (10[1])Bolyai and Lobachevsky replaced this statement to define hyperbolic geometry. For 10 points, what fifth postulate (10[1])of (10[1])Euclid concerns whether lines intersect? ■END■

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