QA455 dept. 'Copyright, 1925 The Bruce Publishing Company gift og ry, G. Hoeloitt to EDUCATION DEPT. PREFACE The geometry textbooks now on the market are, in the main, stuffy. They contain an overabundance of matter, which neither teacher nor pupil ever reads, and which is put up in a form that will never appeal to the elementary student. In offering to the public another textbook in plane geometry, we are endeavoring to present the subject-matter in the order and in the form in which the pupil is prepared to receive it. When the student begins his study of geometry, he can handle equations, make algebraic reductions, find the square root of numbers, and draw. Why should the first work that he does in geometry make him forget those things, and his later work make him learn them over again? Basing everything on the pupil's experience, and fitting the exercises carefully to conditions as every teacher of high school mathematics must have found them, we have prepared an introduction which is intended to get the student interested in the study of geometry proper. In a simple and very elementary way, we have presented the area of a triangle, of a trapezoid, of a regular polygon, and in our wanton recklessness, we have even initiated the young student into the mysterious theory of limits and the area of the circle. How bold of us, to make the young mind know the principle of the square of the hypothenuse a little better than he knew it when he used this principle in arithmetic and algebra. In textbooks generally, the plan has been to introduce, very early, some work in applying one figure to another. Do authors understand that this looks to the beginner in geometry like finding out something by experiment? How much unripe, indirect method, folding a figure on itself, turning on pivots, vague definition and axiom work, will be required to give a formal demonstration that such a performance is not experimenting? In our introduction, we have endeavored to raise certain questions in the pupil's mind-questions which are not answered readily, and which he is not expected to answer just yet. People, too often, eat when they are not hungry, and drink when they are not thirsty. Did Pythagoras, or any other philosopher of the ancient world, get the principles of equal triangles first, and from M55992 |