SCIENCE ABSOLUTE OF SPACE. 



of which maybe easily reduced to a 

 form symmetric or invariable]. ii5| 



Finally, from 



), we get 



sin ,1 sin 



(by HI) 



cot a cot 0=1 

 (equation for , ,9, and c. 



32. It still remains to show briefly the 

 mode of resolving problems in S, which being 

 accomplished (through the more obvious exam 

 ples), finally will be candidly said what this 

 tlu-ory shows. 



I. Take AB a line in a plane, and yf(x) 

 its equation in rectangular co 

 ordinates, call dz any increment 

 of 2, and respectively dx, dy, du 

 the increments of x, of y, and of 

 , A the area u, corresponding to 

 this &amp;lt;/--; take BHlllCF, and ex- 



&amp;gt; 



press (from 31) by means of y, and seek 

 dx 



tlu- limit of-/ when dx tends towards the 

 dx 



limit xrro (which is understood where a limit 

 of this sort i&amp;lt; sought) : then will become known 



also the limit of , and so tan HBG; and 



