The Greek filiation of Hamilton's theory of quaternions.

Often regarded as a mile-stone in the history of algebra, Hamilton's quaternions are rarely remembered in their geometrical character. The unfortunate fate of this theory has obscured its original meaning, and in this communication we will try to restore it by appealing to its creator's own words. In particular, we will argue that quaternions were, in Hamilton's own view, the realization of the Pythagorean conception of mathematics as the science of order rather than of quantity.