The Use of Tangential Coordinates

Extract

There are two reasons why the use of tangential coordinates should be introduced at an earlier stage than is customary into the teaching of analytical geometry and placed on a somewhat different footing. The educational advantages of encouraging the student to follow out a course of reasoning with the help of only a few symbols instead of grinding out hard examples by long meaningless algebra should not require much pressing, although they do not seem to be sufficiently recognised in this country; and on the other hand many theories receive their most appropriate expression in tangentials chiefly owing to the fact that the absolute has a less specialised form in tangential than in point coordinates, being (in two dimensions) the product of two distinct factors in the former and a perfect square in the latter.