40 SCIENCE ABSOLUTE OF SPACE. 



intersection of the straight BN with the 

 &amp;gt;traight CS (if there is one) having been found, 

 the perpendicular drawn through this inter 

 section, in PCQ, to the straight CS will mani 

 festly be the intersection of plane MAB and 

 plane PCQ. 



37. ( )n the straight AM II BN, is found such 



an A, that AM^BN. If (by m 

 34) we construct outside 

 of the plane NBM, GT II 

 1C BN, and make BG1GT, 

 GC=GB, and CPllGT; 

 and so place the hemi- 

 plane TGD that it makes 

 with hemi-plane TGB an angle equal to that 

 which hemi-plane PCA makes with hemi-plane 

 PCB; and is sought (by 36) the intersection 

 &amp;gt;traight DQ of hemi-plane TGD with hemi- 

 plane NBD; and BA is made -LDQ. 



We shall have indeed, on account of the sim 

 ilitude of tin triangles of L lines produced on 

 tin- F of BN ( 2l\ manifestly DB-DA, and 

 AM^BN. 



Henri- r.-isily appears (L-lines being given by 

 tlu-ir r\t ivmities alone) we may also find a 

 fourth proportional, or a mean proportional, 

 and execute in this way in F, apart from Ax 

 iom XI, all the geometric constructions made 



