SCIENCE ABSOLUTE OP SPACE. 39 



=ECD, and FS II EP; then FS will fall within 

 BFR. For since BN II CP, and so BN II EP, 

 and BN II FS; we shall have ( 14) 



ZFBN+ZBFS < ( st. Z =FBN+BFR) ; 

 therefore, BFS < BFR. Consequently, ray FR 

 cuts ray EP, and so ray CD also cuts ray EG 

 in some point D. Take now DG=DC and 

 DGT=DCP=GBN; we shall have (since CD^ 

 GD) BN^GT^CP. Let K ( 19) be the point 

 of the L-f orm line of BN falling in the ray BG, 

 and KL the axis; we shall have BN^KL, 

 and so BKL=BGT=DCP; but also KL*=CP: 

 therefore manifestly K fall on G, and GT II BN. 

 But if HO bisects J_BG, we shall have con- 

 structed HO II BN. 



36. Having- given the ray CP and the 

 plane MAB, take CBlthe 

 plane MAB, BN (in plane 

 BCPj J-BC, and CQ II BN 

 ( 34) ; the intersection of ray 

 CP (if this ray falls within 

 B BCQ) with ray BN (in the 



FIG. 32. pian CBN), and so with the 



plane MAB is found. And if we are given 

 the two planes PCQ, MAB, and we have CB 

 Ito plane MAB, CR i. plane PCQ; and (in 

 plane BCR) BN1BC, CS_uCR, BN will fall 

 in plane MAB, and CS in plane PCQ; and the 



