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. 441 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. 442 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. 443 Let us remember how great the ancients were; and especially how the Socratic school holds up to us the source and standard of all life and action, and bids us not indulge in empty speculation, but live and do. 444 So long as our scholastic education takes us back to antiquity and furthers the study of the Greek and Latin languages, we may congratulate ourselves that these studies, so necessary for the higher culture, will never disappear. 445 If we set our gaze on antiquity and earnestly study it, in the desire to form ourselves thereon, we get the feeling as if it were only then that we really became men. 446 The pedagogue, in trying to write and speak Latin, has a higher and grander idea of himself than would be permissible in ordinary life. 447 In the presence of antiquity, the mind that is susceptible to poetry and art feels itself placed in the most pleasing ideal state of nature; and even to this day the Homeric hymns have the power of freeing us, at any rate, for moments, from the frightful burden which the tradition of several thousand years has rolled upon us. 448 There is no such thing as patriotic art and patriotic science. Both art and science belong, like all things great and good, to the whole world, and can be furthered only by a free and general interchange of ideas among contemporaries, with continual reference to the heritage of the past as it is known to us. 449 Poetical talent is given to peasant as well as to knight; all that is required is that each shall grasp his position and treat it worthily. 450 An historic sense means a sense so cultured that, in valuing the deserts and merits of its own time, it takes account also of the past. 451