SCIENCE ABSOLUTE OF SPACE. 35 



done successively, as long as we are not con- 

 ducted to an absurdity. Supposing therefore 

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

 case S is reality, designates that unique quan- 

 tity whose \~e; but if r 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 aC : a; 

 but from II 



COS 



sin - 



^ 



= 1, and so 



the first equation in III becomes identical, and 

 so is true in I, although it there determines 

 nothing; but from the second follows 



These are the known fundamental equa- 

 tions of plane trigonometry in I. 



