The Fountain County records book shows that a Peter Brown was from Hamilton County, Ohio, and purchased land in the county in 1826. This land was in Van Buren Twp. in Fountain County. I am also seeing a Simon Brown who was also from Hamilton County, Ohio, who also purchased land in 1826.
This info is from the 1881 Fountain County history book.
Cyrus Brown, farmer, Attica. Simon Brown, father of this subject, and Nancy Reed, to whom he was married in 1824, were reared in the same neighborhood in Cumberland, then Perry countyy, Penn. The same year they moved to Ohio, and were four weeks on the road. In the autumn of the year 1827 he and his father, Peter Brown, came to Fountain County to inspect the country; they entered land and made a little hay, and during their brief stay were entertained by John Lopp, whom they found living here. They returned and brought their families, arriving November 23, the journey having consumed two weeks. They passed some of the finest prairie in the world to settle in the dense woods, where they might toil through tedious years to clear up a home......Peter Brown settled near Chambersburg, and after a few years moved into Warren County, where he and his wife finally died.....

According to what this says, Peter had a son named Simon. Cemetery records for Fountain County show that some of these Browns were buried in the Brown Cemetery in Shawnee Township.