  In this paper it is shown that for the natural density (among the positive
integers) of the orders of the finite quotients of every ordinary triangle
group is zero, using a modification of a component of a 1976 theorem of Bertram
on large cyclic subgroups of finite groups, and the Turan-Kubilius inequality
from asymptotic number theory. This answers a challenging question raised by
Tucker, based on some work for special cases by May and Zimmerman and himself.
