12 SCIENCE ABSOLUTE OF SPACE. 



what precedes) FS II === both to BN and to CP, 

 and so also BN II ^=CP. 



11. Consider the aggregate of the point 

 A, and all points of which any one B is such, 

 that if BN II AM, also BN^AM; call it F; but 

 the intersection of F with any plane contain- 

 ing the sect AM call L. 



F has a point, and one only, on any straight 

 II AM; and evidently L is divided by ray AM 

 into two congruent parts. 



Call the ray AM the axis of L. Evidently 

 also, in any plane containing the sect AM, there 

 is for the axis ray AM a single L. Call any 

 L of this sort the L of this ray AM (in the 

 plane considered, being understood). Evi- 

 dently by revolving L around AM we describe 

 the F of which ray AM is called the axis, and in 

 turn F may be ascribed to the axis ro,y AM. 



12. If B is anywhere on the L of ray AM, 

 and BN II ^ AM ( 11) ; then the L of ray AM 

 and the L of ray BN coincide. For suppose, 

 in distinction, I/ the L of ray BN. Let C be 

 anywhere in I/, and CP II ^=BN ( 11). Since 

 BN II ^AM, so CP II *=AM ( 10), and so C also 

 will fall on L. And if C is anywhere on L, and 

 CP II ^AM; then CP II ^BN ( 10) ; and C also 

 falls on L' (11). Thus L and L' are the 



