In the book's own words, not ours, with obvious scanning errors fixed. Families often supplied these stories to the publisher, so check key dates.
Born 1805
From History of Coshocton County, Ohio: its past and present, 1740-1881. Containing a comprehensive history of Ohio; a complete history of Coshocton County ... a history of its soldiers in the late war ... (1881)
HAMILTON JOHN, White Eyog township; farmer; was born, in 1805, in the county of Tyrone, Ireland. He married Miss Mary Fair, of the same county. They came to this county, in 1842; settled in Keene, but afterward located in White Eyes,, on the farm where he now resides. They have had seven children, two of whom have deceased. Margaret, born in 1840, is married to Jonas Brown. Thomas, born 1842, is married to Miss Margaret Boyd, daughter ol R. R. Boyd, and lives in White Eyes. Claudius, born in 1848, is married to Angie Jack, of this township, and is now living at Bakersville. Mary Ellen, born July 4, 1853, is single, and lives at home. John, born in 1859, lives at home. Mr Hamilton and his family are members of the White Eyes Methodist Episcopal church..
As printed in History of Coshocton County, Ohio: its past and present, 1740-1881. Containing a comprehensive history of Ohio; a complete history of Coshocton County ... a history of its soldiers in the late war ... (1881). See the original pages. Wording is the original; obvious scanning errors have been corrected, and a few may remain.
Their biographies name John Hamilton: Jonas Brown (b. 1831) John Overholt (b. 1831)
The printed record stops around 1881. We trace your line from there down to you, with every source cited.