SCIENCE ABSOLUTE OF SPACE. 51 



q -q q\ _i.v i oV LY i 



So 32- -^ .=co(-f{=L) 



*-4 



= COS(?Y ZT); 



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 



y y -\ 



f_^T , which, for i\, 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 //, /?, rt.^., (for /I), 

 in I, 



and so 



l:sin = Whence 1 : sin 



2V_i 2v / _i 



