But his result had to be submitted to another test, the Law of the Norms. As soon as he found, by trial, that this law was satisfied, he took the final step. " This led me," he says, " to conceive that perhaps, instead of seeking to confine ourselves to triplets,..
Hamilton at once found that the Law of the Norms holds, - not being aware that Euler had long before decomposed the product of two sums of four squares into this very set of four squares.
My relative definition of poverty is "the state of being unable to reliably purchase a bundle of goods that allow one to participate in the economic norms of one's society."
In the modern theory of complex numbers this is expressed by saying that the Norm of a product is equal to the product of the norms of the factors.