Text: Hamilton: "If we then resolve to retain the assumption of the existence of a fourth proportional ... to three rectangular directions in space, as subject to be reasoned on ... and as determined in direction by its contrast to its own opposite ... we must think of these two opposite directions ... as merely laid down upon a scale, but must abstain from attributing to this SCALE any one direction rather than another in tridimensional space ... and the progression on this scale ... corresponds less to the conception of space itself (though we have seen that considerations of space might have suggested it) than to the conception of time; the variety which it admits is not tri- but uni-dimensional; and it would, in the language of some philosophical systems, be said to appertain rather to the notion of intensive than of extensive magnitude."

See Also: QUATERNION; SCALAR; QUANTUM ARITHMETIC; IMPLOSION; POINT

Source: 164