But the introduction to plane geometry is not so easily disposed of. The pupil at that time is entering a field that is entirely unfamiliar. He is only fourteen or fifteen years of age, and his thoughts are distinctly not on geometry. Of logic he knows little and cares less. He is not interested in a subject of which he knows nothing, not even the meaning of its name. He asks, naturally and properly, what it all signifies, what possible use there is for studying geometry, and why he should have to prove what seems to him evident without proof. To pass him successfully through this stage has taxed the ingenuity of every real teacher from the time of Euclid to the present; and just as Euclid remarked to King Ptolemy, his patron, that there is no royal road to geometry, so we may affirm that there is no royal road to the teaching of geometry. Nevertheless the experience of teachers counts for a great deal, and this experience has shown that, aside from the matter of technic in handling the class, certain suggestions are of value, and a few of these will now be set forth. First, as to why geometry is studied, it is manifestly impossible successfully to explain to a boy of fourteen or fifteen the larger reasons for studying anything whatever. When we confess ourselves honestly we find that these reasons, whether in mathematics, the natural sciences, handwork, letters, the vocations, or the fine arts, are none too clear in our own minds, in spite of any pretentious language that we may use. It is therefore most satisfactory to anticipate the question at once, and to set the pupils, for a few days, at using the compasses and ruler in the drawing of geometric designs and of the most common figures that they will use. This serves several purposes: it excites their interest, it guards against the slovenly figures that so often lead them to erroneous conclusions, it has a genuine value for the future artisan, and it shows that geometry is something besides mere theory. Whether the textbook provides for it or not, the teacher will find a few days of such work well spent, it being a simple matter to supplement the book in this respect. There was a time when some form of mechanical drawing was generally taught in the schools, but this has given place to more genuine art work, leaving it to the teacher of geometry to impart such knowledge of drawing as is a necessary preliminary to the regular study of the subject.