48 SCIENCE ABSOLUTE OF SPACE. 



exception of 2, which alone may occur any 

 number of times) occurs only once as factor, 

 we can, by the theory of polygons of the illus 

 trious Gauss (remarkable invention of our, 

 nay of every age) (and only for such values 

 of z] , construct a rectilineal figure =tan 2 ^n = 

 area Qs. For the division of a (the theorem 

 of 42 extending easily to any polygons) mani 

 festly requires the partition of a st. ^, which 

 (as can be shown) can be achieved geomet 

 rically only under the said condition. 



But in all such cases, what precedes con 

 ducts easily to the desired end. And any rec 

 tilineal figure can be converted geometrically 

 into a regular polygon of n sides, if n falls 

 under the Gaussian form. 



It remains, finally (that the thing may be 

 completed in every respect), to demonstrate 

 the impossibility (apart from any supposition), 

 of deciding a priori, whether l\ or some S 

 (and which one) exists. This, however, is re 

 served for a more suitable occasion. 



