"It is surprising that the first glimpses of non-Euclidean geometry were had in the eighteenth century. Geronimo Saccheri... a Jesuit father of Milan, in 1733 wrote Euclides ab omni naevo vindicatus (Euclid vindicated from every flaw). Starting with two equal lines AC and BD, drawn perpendicular to a line AB and on the same side of it, and joining C and D, he proves that the angles at C and D are equal. These angles must be either right, or obtuse, or acute. The hypothesis of an obtuse angle is demolished by showing that it leads to results in conflict with Euclid I, 17: Any two angles of a triangle are together less than two right angles. The hypothesis of the acute angle leads to a long procession of theorems, of which the one declaring that two lines which meet in a point at infinity can be perpendicular at that point to the same straight line, is considered contrary to the nature of the straight line; hence the hypothesis of the acute angle is destroyed. Though not altogether satisfied with his proof, he declared Euclid "vindicated.""