The study of line geometry by analytical methods involving the use of tangential coordinates and tangential equations is often found difficult by the junior Honours student. In the writer’s view the reason for this is to be found in the fact that, according to the course followed by a good many textbooks, the student finds himself, so to speak, pitchforked into the middle of the subject without any just appreciation of its bearing, or indeed of the need for such a study at all. Some modern writers on analytical geometry have attempted to remedy this by adopting the view that line geometry should be studied from the outset pari passu with point geometry. Unfortunately, however, experience tends to show that this is a mistake, inasmuch as it creates confusion in minds which have had insufficient practice in, and consequently have obtained an inadequate grasp of, analytical methods, which are never at any time found easy of assimilation by the student of elementary mathematics.