28 SCIENCE ABSOLUTE OF SPACE. 



member of which may be easily reduced to a 

 form symmetric or invariable). [15 



Finally, from 



-^(A+A" 1 ), and ~ -^(B+B" 1 ), we get 

 sin p sin a 



(by III) 



COt a COt fi=% 



(equation for , /5, 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 

 theory shows. 



I. Take AB a line in a plane, and y=f(x] 

 its equation in rectangular co- 

 ordinates, call dz any increment 

 of z, and respectively dx, dy, du 

 the increments of x, of y, and of 

 )A the area u, corresponding to 



FIG. 24. 



BH 



this dz; take BH III CF, and ex- 



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

 ax* 



the limit of - when dx tends towards the 

 dx 



limit zero (which is understood where a limit 

 of this sort is sought) : then will become known 



also the limit of ^., and so tan HBG; and 



