Page:An Enquiry Concerning the Principles of Natural Knowledge.djvu/157

 NORMALITY AND CONGRUENCE 143 not a mere deduction from the terms of the defini tion.

Fig. 12

-4 The isosceles triangle of 48-3 must lie either on a level or on a matrix. If it lies on a level, all the straight routes of the figure must lie on rects. But on a matrix a pair of normals cannot be of the same de nomination, i.e. not both rects nor both point-tracks. Thus five cases remain over for consideration. These cases are diagrammatically symbolised by the annexed figures where continuous lines represent rects, and dotted lines represent point-tracks.

Fig. 13-

Evidently case (i) is the only case in which the triangle lies on a level; the triangles in the remaining four cases lie on matrices.