is zero requires that either or

should be zero; by reference to (i) of [49.7] and to (i) of [51.1] this supposition is seen to lead to results in such obvious contradiction to experience as to preclude the necessity for further examination. Let us name the types retained (according to the familiar habit) the 'hyperbolic,' the 'elliptic' and the 'parabolic' types of kinematics.

[52.2] First consider the hyperbolic type and put

for

. The equations of articles [49] and [51] then become