SCIENCE ABSOLUTE OP SPACE. 31 



areas bounded by these lines could also be ex 

 pressed. 



We know, that a surface /, III to a plane fig 

 ure/ (at the distance g), is to p in the ratio of 

 the second powers of homologous lines, or as 



It is easy to see, moreover, that the calcula 

 tion of volume, treated in the same manner, 

 requires two integrations (since the differen 

 tial itself here is determined only by integra 

 tion); and before all must be investigated the 

 volume contained between p and /, and the ag 

 gregate of all the straights JLp and joining 

 the boundaries of/ and t. 



We find for the volume of this solid (whether 

 by integration or without it) 



f 2Q - 



The surfaces of bodies may also be deter 

 mined in S, as well as the curvatures, the 

 involutes, and evolutes of any lines, etc. 



As to curvature; this in S either is the curv 

 ature of L, or is determined either by the 

 radius of a circle, or by the distance to a 

 straight from the curve HI to this straight; since 

 from what precedes, it may easily be shown, 

 that in a plane there are no uniform lines other 

 than Lrlines, circles and curves ||| to a straight. 



