Provides a rich collection of some of the most important properties of numerous points, lines, and circles related to triangles and quadrilaterals, as they were known by the mid-1950s. These include the nine-point circle, the Simson line, the orthopolar triangles, the Gergonne and Nagel points, the Miquel point and circle, the Carnot circle, the Lemoine point and circles, the Newton-Gauss line, and many others.