SCIENCE ABSOLUTE OP SPACE. 15 



16. If AM is the axis of any L; then L, 

 in I is a straight J_ AM. 



N M F For suppose BN an axis from any 

 point B of L; in i, ZBAM+ZABN 

 =st.Z, and so ZBAM=rt.Z. 



And if C is any point of the 

 straight AB, and CPU AM; then 

 J c(by 13) CP^AM, and so C on L 



B A 



FIG. 12 



But in S, no three points A, B, C on L or 

 on F are in a straight. For some one of the 

 axes AM, BN, CP (e. g. AM) falls between 

 the two others; and then (by 14) ZBAM and 

 ZCAM are each <rt.Z. 



17. L in S also is a Line, and F a sur- 

 face. For (by 11) any plane _*_ to the axis 

 ray AM (through any point of F) cuts F in 

 [the circumference of] a circle, of which the 

 plane (by 14) is J_ to no other axis ray BN. 

 If we revolve F about BN, any point of F (by 

 12) will remain on F, and the section of F 

 with a plane not J_ ray BN will describe a sur- 

 face; and whatever be the points A, B taken 

 on it, F can so be congruent to itself that A 

 falls upon B (by 12) ; therefore F is a uni- 

 form surface. 



