There's a scanned copy of a book called The Van Gieson Family in America that you can access free through familysearch.org. That provides a very detailed discussion of all of Reinier Van Giesen's descendants. (The name's spelling was changed in the 1700s). If you Google the title of the book, the fourth link that comes up will take you to an LDS Family History Library page with a link that allows you to see a digital version of the book.
My family is descended from Reinier Van Giesen's third son, Abraham.