50 SCIENCE ABSOLUTE OP SPACE. 



the case if it were not true, is demonstrated 

 (Tom. I. App., p. 13), that there is given a cer- 

 tain /, for which the I there mentioned is =0 

 (the base of natural logarithms), and for this 

 case are established also (ibidem, p. 14) the 

 formulas of plane trigonometry, and indeed so, 

 that (by the side of p. 19, ibidem) the formulas 

 are still valid for the case of the verity of the 

 said axiom; indeed if the limits of the values 

 are taken, supposing that 2=^=00; truly the 

 Euclidean system is as if the limit of the anti- 

 Euclidean (for /=oo). 



Assume for the case of i existing, the unit 

 = ij and extend the concepts sine and cosine 

 also to imaginary arcs, so that, p designating 

 an arc whether real or imaginary, 



!_ -^ _ is called the 



2 

 cosine of p, and 



_ ~ e _ is called 



the sine of p (as Tom. L, p. 177). 

 Hence for q real 



Q -q 



e e e 



1). 



