by Spencer among others, is to substitute for Euclid some book of similar kind but less perfect of that kind; some book which mixes up a little real geometry with Euclid's idea of logical concatenation. This does not go to the root of the matter. The remedy is not to substitute for Euclid some inferior and less thorough textbook, but to precede and supplement the use of textbooks by some gymnastic calculated to restore normal vitality to the paralysed natural faculty. A very great deal has been done of late years, by mathematicians, in the way of suggestions towards the creation of such a preparation. The misfortune is that our mathematicians do not yet know how to explain their ideas intelligibly to non-mathematical mothers and lady nurses.
What is emphatically not wanted is that unscientific mothers and nurses should learn something about geometry and teach it before the school age; what is wanted is that we should deal with those type-forms which are the subjects of geometry on the same principles as we ought to deal, and to a great extent do deal, with the other classes of form: the living forms evolved by nature, and the artificial forms created by man for his use, such as furniture, domestic appliances, and ornaments.
First comes the education of the senses
