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Euclid’s fifth postulate runs: “If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the straight lines, if produced indefinitely, will meet on that side on which are the angles less than two right angles.” Saccheri took up the quadrilateral of Omar Khayyam (1048–1131), who started with two parallel lines AB and DC, formed the sides by drawing lines AD and BC perpendicular to AB, and then considered three hypotheses for the internal angles at C and D: to be right, obtuse, or acute (see figure ).

Pages: 266

Publisher: Birkhäuser; Softcover reprint of the original 1st ed. 1985 edition (October 4, 2013)

ISBN: 146849161X

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