If you've ever been confused by the concept of cousins "removed", you're not alone. Here's an easy way to understand it.
Count the number of generations back on the family tree, beginning with your grandparents, until you come to a common ancestor. That determines the cousin degree. All of your mom's or dad's brothers and sisters have the same grandparents: that's the first generation. So that makes the offspring of your mom's or dad's brothers and sisters your first cousins. The second generation back are second cousins, and the third generation back third cousins, and so forth. That explains the first part of the cousin description.
To determine the "removed" part, count the differences in generations between that person and you.
For example, if you count up to the common ancestor 5 generations, and down the family tree to your cousin 4 generations, then the difference between 5 and 4 is 1, so you are fifth cousins once removed. Another example: If you count up to the common ancestor 10 times, and down the cousin's family tree to them 12 times, the difference between 10 and 12 is 2, so they are your 10th cousin twice removed.
It was relatively common for close relatives to marry in times when people did not travel far and towns were small. We have encountered a number of closely intertwined family relations, which explains something. I'm not sure what.
Ralph Shepard and Thankslord Perkins are my 9th and my wife's 10th great grandparents. My wife is my 9th cousin once removed. I knew there was something special about her when we met.
My fifth great-grandparents, Aaron Phelps and Rachel Bagg, were first cousins who grew up alongside each other in Westfield, Massachusetts. Aaron Phelps' father Isaac Phelps and Rachel Bagg's mother Hannah Phelps were siblings. Aaron Phelps was seven years older than Rachel. They married on 26 Jun 1729 when she was 27 years old. Almost a spinster by standards of the time.
Their grandson Ronald Aaron Noble Phelps, whose maternal grandfather was Moses Noble, married his second cousin, Clarissa Root. Her maternal grandfather was Jacob Noble, Moses' brother.
Periously close on the apple tree were first cousins and husband and wife Thomas J. Claggett and Columbia Claggett. Their common ancestors are their grandparents Dr. Samuel Claggett II and Amey Jane Ramey.
My great-grandfather Luther Sanford Beasley was married to both his first and his second cousin at the same time: Ruth Matella Claggett.
Luther and his wife Ruth were—what do you call this relationship—"Quarter-first cousins?"
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A few generations before that, long enough not to account for any missing words in my vocabulary, John Robertson married Lady Margaret Chrichton, his second cousin once removed. They were also interrelated seven other ways.