8 



SCIENCE ABSOLUTE OF SPACE. 



7. 



N M 



A 



FIG. 5. 



If BN and CP are each II AM, and C 

 not on the straight BN; also BN II CP. 

 For the rays BN and CP do not in- 

 tersect (3); but AM, BN and CP 

 either are or are not in the same 

 plane; and in the first case, AM either 

 is or is not within BNCP. 



If AM, BN, CP are complanar, and 

 AM falls within BNCP; then every ray BQ 

 (in NBC) cuts the ray AM in some point D 

 (since BN II AM) ; moreover, since DM II CP 

 ( 6), the ray DQ will cut the ray CP, and so 

 BN II CP. 



But if BN and CP are on the same side of 

 M AM; then one of them, for example 

 CP, falls between the two other 

 straights BN, AM: but every ray BQ 

 (in NBA) cuts the ray AM, and so 

 also the straight CP. Therefore 

 BN II CP. 



If the planes MAB, MAC make 

 an angle; then CBN and ABN have in com- 

 mon nothing but the ray BN, while the ray 

 AM (in ABN) and the ray BN, and so also 

 NBC and the ray AM have nothing in com- 

 mon. 



But hemi-plane BCD, drawn through any 

 ray BD (in NBA), cuts the ray AM, since ray 



B C A 



FIG. 6. 



