SCIENCE ABSOLUTE OP SPACE. 17 



j 19. The perpendicular BT to the axis 

 BN of L (falling in the plane of L) is, in S, 

 tangent to L. For L has in ray 

 BT no point except B (14), 

 but if BQ falls in TBN, then 

 the center of the section of the 

 -Q plane through BQ perpendicular 

 to TBN with the F of ray BN 

 FIG. 14. ( 18) is evidently located on ray 

 BQ; and if sect BQ is a diameter, evidently 

 ray BQ cuts in Q the line L of ray BN. 



20. Any two points of F determine a line 

 L ( 11 and 18); and since (from 16 and 19) 

 L is_L to all its axes, every Z of lines L in F is 

 equal to the ^ of the planes drawn through its 

 sides perpendicular to F. 



21. Two L form lines, ray AP and ray 

 BD, in the same F, making with 

 a third L form AB, a sum of inte- 



rior angles <st.Z, intersect. 



(By line AP in F, is to be 

 understood the line L drawn 

 through A and P, but by ray AP 

 that half of this line beginning at A, in which 

 P falls.} 



For if AM, BN are axes of F, then the hemi- 

 planes AMP, BND intersect ( 9) ; and F cuts 



