Another close match appeared at FamilyTreeDNA for my maternal uncle.
The common ancestors of these three cousins were Mary Zolder (1870-1948) and Samuel Haas (1867-1945). They were born in Slovakia, married in 1890 in New York City, and died in Bayonne, Hudson County, New Jersey. The three cousins who tested DNA descend from three of Mary and Samuel's eleven children.
The actual relation of this newly-appeared person is first cousin, twice removed. (Blue in the screenshot below.) He and my uncle share ten segments* of identical DNA for a total of 198 cM. The longest segment is 40 cM.
The prior close cousin is a first cousin, once removed. (Orange in the screenshot below.) He shares fifteen segments of DNA with my uncle for a total of 355 cM. The longest segment is 80 cM.
What I found remarkable was that none of the shared DNA overlaps; no segments are identical in all three cousins. The chromosome browser at FamilyTreeDNA does not allow me to compare other people, but the "In Common With" function shows that both cousins match each other, just not where or how much.
* Number of segments over 5 cM. I did not include segments below 5 cM in this calculation. FamilyTreeDNA includes these segments in its calculations.