SCIENCE ABSOLUTE OP SPACE. 51 



q _q q s Zl. N IIi Q N Z4.\^i 



e -f e e +e 



~~ ~~ =cos( ?v 



if of course also in the imaginary circle, the 

 sine of a negative arc is the same as the sine 

 of a positive arc otherwise equal to the first, 

 except that it is negative, and the cosine of a 

 positive arc and of a negative (if otherwise 

 they be equal) the same. 



In the said Appendix, 25, is demonstrated 

 absolutely, that is, independently of the said 

 axiom; that, in any rectilineal triangle the 

 sines of the circles are as the circles of radii 

 equal to the sides opposite. 



Moreover is demonstrated for the case of i 

 existing, that the circle of radius y is 



= ~i i^__^ j ' which, for /=!, becomes 

 *(*_*-*). 



Therefore (31 ibidem], for a right-angled 

 rectilineal triangle of which the sides are a 

 and b, the hypothenuse c, and the angles oppo- 

 site to the sides a, b, c are , ,9, rt. Z,(for /=!), 

 in I, 



lisin a=*(^-^):*(^-O; 



and so 



c __0- c e*e~* TT ri 1 



l:sin = - -- : -- Whence 1 : sin 

 2v_i ' 2v_i ' 



