16 



SCIENCE ABSOLUTE OP SPACE. 



Hence evidently (by 11 and 12) L is a uni- 

 form line.* 



18. The intersection with F of any plane, 

 drawn through a point A of F obliquely to the 

 axis AM, is, in S, a circle. 



For take A, B, C, three points of this sec- 

 tion, and BN, CP ; axes; AMBN and AMCP 

 make an angle, for otherwise the plane deter- 

 mined by A, B, C (from 16) would contain 

 AM, (contra hyp.). Therefore the planes bi- 

 secting J_ the sects AB, AC intersect ( 10) in 

 some axis ray FS (of F), and FB=FA=FC. 



MakeAHlFS, and re- 

 volve FAH about FS; A 

 will describe a circle of 

 radius HA, passing 

 through B and C, and sit- 

 uated both in F and in 

 the plane ABC; nor have 

 F and the plane ABC any- 

 thing in common but O HA (16). 



It is also evident that in revolving the por- 

 tion FA of the line L (as radius) in F around 

 F, its extremity will describe O HA. 



* It is not necessary to restrict the demonstration to the system 

 S; since it may easily be so set forth, that it holds absolutely for 

 S and for I. 



