His progress in geometry may serve as a test and a true measure of the growth of his intelligence, but as soon as he can distinguish between what is useful and what is useless, much skill and discretion are required to lead him towards theoretical studies.  For example, would you have him find a mean proportional between two lines, contrive that he should require to find a square equal to a given rectangle; if two mean proportionals are required, you must first contrive to interest him in the doubling of the cube.  See how we are gradually approaching the moral ideas which distinguish between good and evil.  Hitherto we have known no law but necessity, now we are considering what is useful; we shall soon come to what is fitting and right.

Man’s diverse powers are stirred by the same instinct.  The bodily activity, which seeks an outlet for its energies, is succeeded by the mental activity which seeks for knowledge.  Children are first restless, then curious; and this curiosity, rightly directed, is the means of development for the age with which we are dealing.  Always distinguish between natural and acquired tendencies.  There is a zeal for learning which has no other foundation than a wish to appear learned, and there is another which springs from man’s natural curiosity about all things far or near which may affect himself.  The innate desire for comfort and the impossibility of its complete satisfaction impel him to the endless search for fresh means of contributing to its satisfaction.  This is the first principle of curiosity; a principle natural to the human heart, though its growth is proportional to the development of our feeling and knowledge.  If a man of science were left on a desert island with his books and instruments and knowing that he must spend the rest of his life there, he would scarcely trouble himself about the solar system, the laws of attraction, or the differential calculus.  He might never even open a book again; but he would never rest till he had explored the furthest corner of his island, however large it might be.  Let us therefore omit from our early studies such knowledge as has no natural attraction for us, and confine ourselves to such things as instinct impels us to study.

Our island is this earth; and the most striking object we behold is the sun.  As soon as we pass beyond our immediate surroundings, one or both of these must meet our eye.  Thus the philosophy of most savage races is mainly directed to imaginary divisions of the earth or to the divinity of the sun.

What a sudden change you will say.  Just now we were concerned with what touches ourselves, with our immediate environment, and all at once we are exploring the round world and leaping to the bounds of the universe.  This change is the result of our growing strength and of the natural bent of the mind.  While we were weak and feeble, self-preservation concentrated our attention on ourselves; now that we are strong and powerful, the desire for a wider sphere carries us beyond ourselves as far as our eyes can reach.  But as the intellectual world is still unknown to us, our thoughts are bounded by the visible horizon, and our understanding only develops within the limits of our vision.