From The (Allentown, N.J.) Examiner of Oct. 13, 2005:
U.F. boasts ties to U.S. presidentsAccording to Waldo Lincoln's History of the Lincoln family (Worcester, Mass.: Commonwealth Press, 1923)—and every other available source—President Lincoln's immigrant ancestor was Samuel Lincoln of Hingham, Mass., a weaver and mariner [p. 6]. "Abraham" was first used in the family in January 1688/89, when a son was born to Mordecai and Sarah (Jones) Lincoln and named for his maternal grandfather [p. 21]. It was Mordecai, son of the immigrant, who was proprietor of an iron works, though as Waldo Lincoln notes, "Probably the good old name 'blacksmith' more accurately descibes him" [p. 16].
UPPER FREEHOLD — While it is fairly well-known that one U.S. president had ancestors in the township, a link to a later chief executive is less publicized.
According to [Thomas] Frascella's research, "A William Ansley, [who] was born in Monmouth between 1710-1715 and died in 1773 in Upper Freehold, married Rebecca before 1737 in Upper Freehold. Rebecca was born in Middletown in 1715 and died in the 1750s."
According to Frascella, William and Rebecca were the great-great-great-great-great-grandparents of [Jimmy] Carter, the 39th president of the United States.
In 2001, [John] Fabiano told the Examiner that the name Abraham was common in the Lincoln genealogy, and that the original Abraham Lincoln came from England and established the first iron forge in Massachusetts in the 1600s. Several decades later, Richard Saltar, who was establishing his own iron forge, brought Lincoln's grandsons, Mordecai and Abraham, to the Imlaystown area of Upper Freehold in 1714.
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Nor was his the first iron forge in Massachusetts. An iron works was operating on the Saugus River north of Boston as early as 1646—eleven years prior to Mordecai's birth.
Genealogy.com has the Ancestry of Abraham Lincoln.