令a:b=c:d=x>1
则a=bx.c=dx
a+d=bx+d,b+c=b+dx
(a+d)-(b+c)=(bx+d)-(b+dx)
=bx+d-b-dx
=b(x-1)-d(x-1)
=(x-1)(b-d)>0
所以a+d>b+c