io SCIENCE ABSOLUTE OF SPACE. 



though BN II CP. But every ray BQ (in CBN) 

 cuts ray CP; and so ray BQ cuts also ray AM. 

 Consequently BN II AN. . 



9. If BN II AM, and MAPlMAB, and the 

 Z, which NBD makes with 

 NBA (on that side of MABN, 

 where MAP is) is <rt.Z; then 

 MAP and NBD intersect. 

 B For let ZBAM=rt.Z, and 

 AClBN (whether or not C 

 falls on B), and CElBN (in 

 FIG. 9. NBD); by hypothesis ZACE 



, and AF (j_CE) will fall in ACE. 

 Let ray AP be the intersection of the hemi- 

 planes ABF, AMP (which have the point A 

 common); since BAM MAP, ZBAP-ZBAM 

 = rt.Z. 



If finally the hemi-plane ABF is placed upon 

 the hemi-plane ABM (A and B remaining), ray 

 AP will fall on ray AM; and since AClBN, 

 and sect AF<sect AC, evidently sect AF will 

 terminate within ray BN, and so BF falls in 

 ABN. But in this position, ray BF cuts ray AP 

 (because BN II AM) ; and so ray AP and ray BF 

 intersect also in the original position; and the 

 point of section is common to the hemi-planes 

 MAP and NBD. Therefore the hemi-planes 

 MAP and NBD intersect. Hence follows eas- 



