Your great grandfather's nephew was your grandfather's first cousin. You are two generations removed from your grandfather and his cousin. Therefore you and your great grandfather's nephew are first cousins, twice removed.
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The child of your nephew is your great nephew (if a son) or your great niece (if a daughter).
Your nephew's daughter is your great niece and you are her great Aunt (or Great Uncle).Correction:Your nephew's daughter is your grand niece. You are her grand aunt or grand uncle.
She would be his Great Aunt
Your child and your great nephew's parents would be first cousins. Their children would then be second cousins. And if they have children, they will be third cousins.
Your grandfather's brother is your great uncle (some would say your grand uncle). You are his great niece (if you are a girl) or his great nephew (if you are a boy).