In the summer, when this house is open to the public I will check all this in person and take a good picture to post here. However, in the meantime, http://en.wikipedia.org/wiki/Van_Alen_House has an excellent photograph of the main house and the wing.
The Van Alen House is a simple home, built on the Hudson River by Dutch immigrants in 1737. Its character is not applied; it comes from its material - brick. The brick pattern, Dutch cross bond, ties the brick courses together. The voussoirs are the traditional way to bridge an opening. The saw tooth brick pattern - tumblings - at the edge of the gable allowed the bricks to be turned for a smooth edge.
Its grace comes from its shape and the rhythm created by the doors and windows. I think it is possible that both were a byproduct of how the house was built. Not that the builder and owners didn't see and enjoy what they built, but:
I think the builders here used geometry for construction, not for design parameters.
The circle defines the rectangle. It can be used without dimensions to confirm that the angles laid out are true. So: here is the foundation, laid out within the circle.
It is the inside of the foundation that needs to be true. The stone would have been set with a plumb line on the inner side of the wall. The outer side would have been a buttress wall – sloping down into the ground – wider at the bottom than the top. It would have been covered with fill taken from the foundation hole.
The circle does not seem to fit when the outside dimensions are used. The right wing which was originally a barn does not fit the geometry.
I've done some work on the elevations which also use circles to determine structural dimensions. I will post that next. I am well aware that when I have recorded and studied 20 more, 40 more, houses I may see this in new light.
1934, HABS, Adam Van Alen House, Kinderhook, NY, E. J. Potter, delineator