Note on the Treatment of Tangents in recent Textbooks of Elementary Geometry

Extract

Several textbooks of Elementary Geometry have recently been put on the market, and in nearly all that I have examined (and I have gone carefully through many of them) the treatment of tangents is based on what the writers call the Method of Limits. The usual form given to the proof that the tangent at any point of a circle is at right angles to the radius to the point of contact is somewhat as follows.