SOURCES: "Claypool" and "Claypools in America", by Evelyn Claypool Bracken.
Evelyn was a Professor at the University of Indiana, Pennsylvania. She wrote 6 revised volumes of the Claypool Books. It is best to use either volume 5 or 6 when tracing your Osborn/e relatives.
Ann Purrington was never this Jeremiah Osborne's wife, he was born 1729. However, Ann was documented as marrying a different Jeremiah Osborne with the middle name as Jacob.
You can check to see if your local library can do an inner-library-loan to get you a copy of her book.
Volume 3 can be found on line at google.com/googlebooks but it is better to try to get the other volumes instead! 5 or 6.