SV-IKNCE ABSOLUTE OF SPACE. 



For take DElCA; 

 in the triangles ADE, 

 ADB (by 25} 

 OED : OAD : OAB- 



-in n : 1 : sin v. 

 In revolving BACD 

 about AC, B describes OAB, and D describes 

 OED; and designate here by 5OCD the path 

 of the said CD. Moreover, let there be any 

 polygon BFG. . . inscribed in OAB. 



Passing through all the sides BF, FG, &c., 

 planes J_ to OAB we form also a polygonal fig 

 ure of the same number of sides in sOCD, and 

 we may demonstrate, as in ^ 23, that CD : AB 

 -DH : BF=HK : FG, &c., and so 

 DH+HK &c. : BF+FG &c. : =CD : AB. 

 If each of the sides BF, FG . . . approaches 

 the limit zero, manifestly 



BF+FG+...=^OAB and 

 DH+HK+ ...=^OED. 



Therefore also OED : OAB=CD : AB. But 

 we had OED : OAB=sin u : sin v. Conse 

 quently 



CD : AB = sin u : sin v. 



If AC ,LT&amp;lt;H-&amp;gt; away from BD to infinity, CD : 

 AB, and so also sin u : sin v remains constant; 

 but u=rt. Z (1), and if DM II BN, v=z; 

 wlu-nre CD : AB=1 : sin Z. 



