The greater number of objects which we look upon every day present more nearly the aspect of our plane geometric insets. In fact, doors, window-frames, framed pictures, the wooden or marble top of a table, are indeed _solid_ objects, but with one of the dimensions greatly reduced, and with the two dimensions determining the form of the plane surface made most evident.
When the plane form prevails, we say that the window is rectangular, the picture frame oval, this table square, etc. _Solids having a determined form prevailing in the plane surface_ are almost the only ones which come to our notice. And such solids are clearly represented by our _plane geometric insets_.
The child will _very often_ recognise in his environment forms which he has learned in this way, but he will rarely recognise the _solid geometric forms_.
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 geometric 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 geometric 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 geometric insets will be for him a species of magic _key_, 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 geometric design and understood the analysis of plane geometric 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 geometric figures;" and, indeed, rectangles, ovals, triangles, and semicircles, perforated, or ornamented, in a hundred different ways the grey rectangular façades 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.