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Is there an accepted rule for naming all of our various distant relatives (Kinship Terms)?

What is the difference between second cousin and first cousin once removed? Is "[ordinal] cousin once removed" generally used in English?

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    Your parent’s first cousin is your own first cousin once removed, and that person’s child is your second cousin. Your grandparent’s first cousin is your own first cousin twice removed, and that person’s child is your second cousin once removed while their grandchild is in turn your third cousin. Easy peasy. Yes, we use them. – tchrist Jan 06 '13 at 17:35

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"Removed" here describes vertical as opposed to lateral relationship on the tree of life.

removed adj
2. (Law) (postpositive) separated by a degree of descent or kinship the child of a person's first cousin is his first cousin once removed

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