I believe that the inkstand and the books in the portrait were added as a way of showing that Washington was the one that wrote and also signed the laws that were in the nation based on his position.
He was the first president of the United States. He was a soldier and was the one that led the army against the British in the American revolution. After the war he was elected the first president of the nation.
The portrait was created by Stuart who happened to create most of his portraits. This one is used to depict who he is as a powerful figure in the nation.
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