“Being tolerably familiar with solids, he may now substitute planes.  The transition may be made very easy.  Let the cube, for instance, be cut into thin divisions, and placed on paper; he will then see as many plane rectangles as he has divisions; so with all the others.  Globes may be treated in the same manner; he will thus see how surfaces really are generated, and be enabled to abstract them with facility in every solid.

     “He has thus acquired the alphabet and reading of geometry.  He now
     proceeds to write it.

“The simplest operation, and therefore the first, is merely to place these planes on a piece of paper, and pass the pencil round them.  When this has been frequently done, the plane may be put at a little distance, and the child required to copy it, and so on.”

A stock of geometrical conceptions having been obtained, in some such manner as this recommended by Mr. Wyse, a further step may be taken, by introducing the practice of testing the correctness of figures drawn by eye:  thus both exciting an ambition to make them exact, and continually illustrating the difficulty of fulfilling that ambition.  There can be little doubt that geometry had its origin (as, indeed, the word implies) in the methods discovered by artizans and others, of making accurate measurements for the foundations of buildings, areas of inclosures, and the like; and that its truths came to be treasured up, merely with a view to their immediate utility.  They would be introduced to the pupil under analogous relationships.  In cutting out pieces for his card-houses, in drawing ornamental diagrams for colouring, and in those various instructive occupations which an inventive teacher will lead him into, he may for a length of time be advantageously left, like the primitive builder, to tentative processes; and so will learn through experience the difficulty of achieving his aims by the unaided senses.  When, having meanwhile undergone a valuable discipline of the perceptions, he has reached a fit age for using a pair of compasses, he will, while duly appreciating these as enabling him to verify his ocular guesses, be still hindered by the imperfections of the approximative method.  In this stage he may be left for a further period:  partly as being yet too young for anything higher; partly because it is desirable that he should be made to feel still more strongly the want of systematic contrivances.  If the acquisition of knowledge is to be made continuously interesting; and if, in the early civilisation of the child, as in the early civilisation of the race, science is valued only as ministering to art; it is manifest that the proper preliminary to geometry, is a long practice in those constructive processes which geometry will facilitate.  Observe that here, too, Nature points the way.  Children show a strong propensity to cut out things in paper, to make, to build—­a propensity which, if encouraged and directed, will not only prepare the way for scientific conceptions, but will develop those powers of manipulation in which most people are so deficient.