Did President Washington want the new captiol to architectually reflect the ideals of freemasonary?
There are different answers to this question, but if you read a lot of Dan Brown or if you've picked up David Ovason's book "The Secret Architecture of Our Nation's Capital," you would certainly subscribe to the theory that yes, Washington was very much in favor of the capital being designed based on the ideals and principles of freemasonry. There are stories of Washington laying the cornerstone of the capital while wearing a masonic robe, and though Ovason likely gets a little bit carried away with some of his symbols and their links to various things, he certainly presents enough evidence to validate a yes answer to this question.
Of course, like almost any question about history, it is open to interpretation and there are certainly a large number of influences on the design of the capital, including Washington's, so any definitive answer claiming the whole truth is likely a bit suspect.
Washington was definitely a Freemason, as were several other founding fathers. That doesn't mean that they tried to incorporate the square and compass into everything. Also, the symbols of Freemasonry are not exclusive to the craft. The same street layouts can probably be found in any large city, they aren't that complex. Dan Brown writes fiction, and lately it seems many people have difficulty distinguishing fact from fiction.