INTELLECTUAL EDUCATION 239
That the table leg is a prism, or a truncated cone, or an elongated cylinder, will come to his knowledge long after he has observed that the top of the table upon which he places things is rectangular. We do not, therefore, speak of the fact of recognising that a house is a prism or a cube. Indeed, the pure solid gRometric forms never exist in the ordinary objects about us; these present, instead, a combination of forms. So, putting aside the difficulty of taking in at a glance the complex form of a house, the child recognises in it, not an identity of form, but an analogy.
He will, however, see the plane gRometric forms perfectly represented in windows and doors, and in the faces of many solid objects in use at home. Thus the knowledge of the forms given him in the plane gRometric insets will be for him a species of magic hey, opening the external world, and making him feel that he knows its secrets.
I was walking one day upon the Pincian Hill with a boy from the elementary school. He had studied gRometric design and understood the analysis of plane gRometric figures. As we reached the highest terrace from which we could see the Piazza del Popolo with the city stretching away behind it, I stretched out my hand saying, " Look, all the works of man are a great mass of gRometric figures; " and, indeed, rectangles, ovals, triangles, and semicircles, perforated, or ornamented, in a hundred different ways the grey rectangular fagades of the various buildings. Such uniformity in such an expanse of buildings seemed to prove the limitation of human intelligence, while in an adjoining garden plot the shrubs and flowers spoke eloquently of the infinite variety of forms in nature.