Various maxims of the ancients, which we are wont to repeat again and again, had a meaning quite different from that which is apt to attach to them in later times.
The saying that no one who is unacquainted with or a stranger to geometry should enter the philosopher's school, does not mean that a man must become a mathematician to attain the wisdom of the world.
Geometry is here taken in its primary elements, such as are contained in Euclid and laid before every beginner; and then it is the most perfect propædeutic and introduction to philosophy.
When a boy begins to understand that an invisible point must always come before a visible one, and that the shortest way between two points is a straight line, before he can draw it on his paper with a pencil, he experiences a certain pride and pleasure. And he is not wrong; for he has the source of all thought opened to him; idea and reality, potentia et actu, are become clear; the philosopher has no new discovery to bring him; as a mathematician, he has found the basis of all thought for himself.
And if we turn to that significant utterance, Know thyself, we must not explain it in an ascetic sense. It is in nowise the self-knowledge of our modern hypochondrists, humorists, and self-tormentors. It simply means: pay some attention to yourself; take note of yourself; so that you may know how you come to stand towards those like you and towards the world. This involves no psychological torture; every capable man knows and feels what it means. It is a piece of good advice which every one will find of the greatest advantage in practice.