Here are a few more fluid restatements of the information you provided:
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"On April 5, 1761, in Fredericksburg, New York, Henry and Abigail Ludington welcomed their daughter, Sybil Ludington, into the world."
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"Sybil Ludington was born to Henry and Abigail Ludington on April 5, 1761, in Fredericksburg, New York."
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"The Ludington family grew on April 5, 1761, with the birth of Sybil Ludington in Fredericksburg, New York, to parents Henry and Abigail."
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"Fredericksburg, New York, saw the birth of Sybil Ludington on April 5, 1761, as she was welcomed by her parents, Henry and Abigail Ludington."
Feel free to choose any of these options or mix and match elements to create a version that fits your style!