It might be said, for example, that in planning a Gothic window this drawing is needed. The arc BC is drawn with A as a center and AB as a radius. The small arches are described with A, D, and B as centers and AD as a radius. The center _P_ is found by taking A and B as centers and AE as a radius. How may the points D, E, and F be found? Draw the figure. From the study of the rectilinear figures suggested by such a simple pattern the properties of the equilateral triangle may be inferred.
The Gothic window also offers some interesting possibilities in connection with the study of the square. For example, the illustration given on [page 223] shows a number of traceries involving the construction of a square, the bisecting of angles, and the describing of circles.[72]
The properties of the square, a figure now easily constructed by the pupils, are not numerous. What few there are may be brought out through the study of art forms, if desired. In case these forms are shown to a class, it is important that they should be selected from good designs. We have enough poor art in the world, so that geometry should not contribute any more. This illustration is a type of the best medieval Gothic parquetry.[73]
Even simple designs of a semipuzzling nature have their advantage in this connection. In the following example the inner square contains all of the triangles, the letters showing where they may be fitted.[74]
Still more elaborate designs, based chiefly upon the square and circle, are shown in the window traceries on [page 225], and others will be given in connection with the study of the regular polygons.
