SCIENCE ABSOLUTE OP SPACE. 35 



done successively, as long as we are not con 

 ducted to an absurdity. Supposing therefore 

 that, in such an expression, the letter 2, in 

 case S is reality, designates that unique quan 

 tity whose I=e/ but if 2 is actual, the said 

 limit is supposed to be taken in place of the 

 expression : manifestly all the expressions or 

 iginating from the hypothesis of the reality 

 ofS (in this sense) will be true absolutely, 

 although it be completely unknown whether 

 or not I is reality 



So e. g. from the expression obtained in 30 

 easily (and as well by aid of differentiation as 

 apart from it) emerges the known value in J, 



from I ( 31) suitably treated, follows 



1 : sin a = c : a; 

 but from II 



cos 



sin 



H j 

 = 1, and so 



the first equation in III becomes identical, and 

 so is true in l\ although it there determines 

 nothing; but from the second follows 



These are the known fundamental equa 

 tions of plane trigonometry in i\ 



