SCIENCE ABSOLUTE OF SPACE. 



11 



ily that the hemi-planes MAP and NBD inter- 

 sect if the sum of the interior angles which 

 they make with MABN is <st.Z. 



10. If both BN and CPU ^AM; also is 



BNII ^CP. 



For either MAB 

 and MAC make an 

 angle, or they are in 

 a plane. 



If the first; let the 

 hemi-plane QDF bi- 

 sect _L sect AB; then 

 DQlAB, and so DQ 

 II AM ( 8) ; likewise if hemi-plane ERS bisects 

 1 sect AC, is ER II AM; whence ( 7) DQ II ER. 

 Hence follows easily (by 9), the hemi- 

 planes QDF and ERS intersect, and have ( 7) 

 their intersection FS II DO, and (on account of 

 BNIIDQ) also FS II BN. Moreover (for any 

 point of FS) FB=FA=FC, and the straight 

 FS falls in the plane TGF, bisecting J_ sect BC. 

 But (by 7) (since FS II BN) also GT II BN. 

 In the same way is proved GT II CP. Mean- 

 while GT bisects 1 sect BC; and so TGBN^ 

 TGCP (1), andBNll^CP. 



If BN, AM and CP are in a plane, let (fall- 

 ing without this plane) FS II AM; then (from 



