48 SCIENCE ABSOLUTE OP 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 Q5. For the division of n (the theorem 

 of 42 extending easily to any polygons) mani- 

 festly requires the partition of a st. Z, 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 , or some S 

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

 served for a more suitable occasion. 



