BY CLAUDE IRWIN PALMER, A.B. ASSOCIATE PROFESSOR OF MATHEMATICS AND DANIEL POMEROY TAYLOR, A.M. HIGH SCHOOL, OAK PARK, ILL. EDITED BY GEORGE WILLIAM MYERS, PH.D. PROFESSOR OF THE TEACHING OF MATHEMATICS THE UNIVERSITY OF CHICAGO SCOTT, FORESMAN AND COMPANY CHICAGO NEW YORK BY CLAUDE IRWIN PALMER, A.B. ASSOCIATE PROFESSOR OF MATHEMATICS ARMOUR INSTITUTE OF TECHNOLOGY AND DANIEL POMEROY TAYLOR, A.M. HIGH SCHOOL, OAK PARK, ILL. EDITED BY GEORGE WILLIAM MYERS, PH.D. PROFESSOR OF THE TEACHING OF MATHEMATICS THE UNIVERSITY OF CHICAGO SCOTT, FORESMAN AND COMPANY CHICAGO. NEW YORK EDITOR'S PREFACE This text derives its origin and character from the view that geometry is a valuable study for high school pupils in the degree to which they understand and appreciate it at the time they are studying it. Appreciation of the worth of what is being done and insight into the meaning of its tasks go very far toward a real motivation of geometry. The system of thought it embodies is of course the chief claim of geometry to a place in the curriculum, but this system of thought is of no great value to one who neither appreciates nor understands its spirit. Furthermore, this system of thought is a derived product. It arises from the habits formed from doing things geometrically and reasoning about what is done and why it is so done. It must accordingly wait upon many an act of intelligent judging and discriminating. The acts of systematic judging and discerning find a rich genetic background in measurement, in constructive exercises, in comparison of figures, and in geometrical experimentation by the student. This text so organizes the material as to give a concrete, experimental, and somewhat informal approach to the rather highly wrought scheme of demonstrative geometry. This informality pervades the first half of the first chapter, thereby laying a firm conceptual basis for the more systematic geometry. Throughout the text, however, subjects of special difficulty to high school students are approached experimentally. Mental possibilities are nowhere sacrificed to logical refinements. Logical accuracy that is beyond the reach of the learner is held to be only apparent and largely specious. Besides the closer conformity to pedagogical standards of this inductive and informal approach to systematic geometry, |