From what I can determine there were two brothers born in Lancashire circa 1615-1625. These were Daniel Ainsworth (certain) and John Ainsworth (certain). Daniel emigrated to Massachusetts in 1647. Daniel’s brother, John Ainsworth, remained in England but sent his son Edward (certain) and Anchor (possible) to work with Daniel. FindAGrave lists a Daniel Ainsworth as born 10/27/1616 and passed 11/13/1680 in Roxbury, Mass, burial at Eliot Burying Ground. Info on death is very probably accurate, info on birth needs confirmation. Date of death 11/13/1680 is consistent with transcript of Massachusetts Town clerk records, Suffolk, Roxbury; unfortunately parents not given. The book “Directory of the Ancestral Heads of New England Families 1620-1670 compiled by Frank R Holmes pub 1923 states that “Daniel, b in Eng., came to Roxbury, Mass., in 1647, later was at Dedham, Mass.” Index of New England Marriages Prior to 1700 lists Daniel Ainsworth ( -1680) married to Alice ( -1685) in 1647 at Roxbury. No subsequent record of children. This information is consistent with “Genealogy of the Ainsworth Families in America” 1894 by Francis J Parker.
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https://archive.org/details/historyoftownofj1749cutt/page/210/mode/2up
The History of the town of Jaffrey, New Hampshire.