A Word about HALF COUSINS:
The word "Half" means only one of two parents is the blood parent, so where two siblings share only one parent, they are half-siblings.
The children of these two half-siblings would be half-cousins, because they share only one of the grandparents.
So, half-cousins are called that, because they share only one of the two grandparents commonly. As far as Half-Cousin and Removed is concerned, the same rules apply as to full cousins.
A Word about DOUBLE COUSINS:
Double Cousins are the result when two brothers marry two
sisters (of another family). The children of each married pair are
cousins to each other, not only by way of their father's family, but by way of their mother's family as well. Otherwise, the same rules
apply as to full cousins; so one (whos grandparents were brothers who married sisters) could have a SECOND DOUBLE COUSIN ONCE REMOVED.
A Word about marriage between COUSINS:
Most of us in the USA have at least one case of first cousin marriages
somewhere in our ancestry. In some cases, it was due to the
relatively small populations of newly settled areas - where there was not much other choice for marriage partners.
It must be noted here that first-cousin marriage taboos are pretty much restricted to North America; and, in fact, about half
of the states in the USA allow first-cousin marriage. Also, there are no imprimatured prohibitions of first-cousin marriage by the
Roman Catholic Church.
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