240 A. Ranüm : Lobachefskian Polygons Trigonometricallj Equivalent to the Triangle.

The Non-Intersecting Birectangular Quadrilateral, Eight Angles Adjacent.

22 . See the quadrilateral ABC^C^ of figure 2.

The common perpendicular of с and c' and the perpendiculars from A and J5 to a' and b\ respectively, meet in an actual point.

The perpendicular bisector of с is concurrent with the interior bisectors of a and ß and also with the exterior bisectors of a and ß.

The common perpendicular of a and the exterior bisector of a and the common perpendicular of V and the exterior bisector of ß are concurrent with the perpendicular from the middle point of с to c.

The Intersecting Birectangular Quadrilateral, Eight Angles Adjacent.

23 . See the quadrilateral ABG^C^ of figure 3.

The perpendicular from A to a! and the perpendicular from В to }/ have a common perpendicular passing through 0.

The perpendicular bisector of с is concurrent with the interior bisector of a and the exterior bisector of ß, and also with the exterior bisector of a and the interior bisector of /3.

The common perpendicular ^of the interior bisectors of a and ß and the common perpendicular of their exterior bisectors, both pass through the middle point of c.

The following three points are coUinear: (1) the actual point of intersection of с and the perpendicular bisector of c, (2) the point of intersection of a' and the exterior (interior) bisector of a, and (3) the point of intersection of V and the exterior (interior) bisector of ß.

The Non-Intersecting Birectangular Quadrilateral, Eight Angles Opposite.

24 . See the quadrilateral AB^A G^ of figure 2.

The line joining (&, V) and (c, c') is perpendicular to the line joining A and A'. If (6, V) and {c, c) are ultrainfinite points, this means that the common perpendicular of Ъ and V and the common perpendicular of с and с are concurrent with the line joining A and Ä,

The Intersecting Birectangular Quadrilateral, Eight Angles Opposite.

25 . See the quadrilateral AB^A'C^ of figure 3.

The line joining 0 and (b, V) is perpendicular to the line joining A and A\ If Çby V) is an infinite point, this means that the dicular from 0 to the line joining A and Ä is parallel to Ъ and Ъ\