Oa the Relatively Aboliau Corpora. i n 



Changing Y^, vmtou + r, u-r re^pecüvely, we get 



where y,- ^(-2,,), y'^^ ^^2yj. 



Let us repeat the same process successively, until we arrive at tha 

 relation 



where /4, //,; are derived from y,_^. ijl_^ hy changing u, r into 

 u + v, u-v respectivel3\ From these h relations, it can l)e con- 

 cluded that 



iv -Uif^ ^"'Ot)'. (13) 



From the multiplication-formula 



(t— /Orw' 

 we get 



If r</0 be a root of (12), so must also be ^[(l-,o)»] and hX^'ic), and 

 they are evidently unequal. Hence, putting 



in (lo), we get 



^■'{jty^a-oyKiuf. 



Therefore, l»y (7), 



(i-i'yHuy^^ 



If we put 



then a, ;i, y are all algebraic integers in K(.r), such that 



Hence, in the corpus Atr), the principal ideal (•_>) mu^t l^e equal 

 to the cube of some ideal, say 



(^) = [v.v, y. 



