Snyders from New York State

I have a Hendrick Janszen Snyder who was born in the Netherlands about 1605. He Married Geertje Scheerburch in the Netherlands about 1630. They had a daughter Catalyntje who was born in New York
State about 1632. I am interested in connecting the Snyder family members that I have in my file. They are
James Snyder who was born about 1765 in New York and his daughter Gertrude who was born in Mayfield, Fulton County, NY about 1802. Gertrude married Richard Van Slyke about 1820 in Fulton County. I have 6 children for them.

I am missing about 5 generations. Is there anyone who has any information about the children of Hendrick Janszen Snyder or the parents of James Snyder?