PRACTICAL PLANE GEOMETRY GIVING THE SIMPLEST MODES OF CONSTRUCTING FIGURES CONTAINED AND GEOMETRICAL CONSTRUCTION ON THE GROUND BY J. F. HEATHER, M.A. LATE OF THE ROYAL MILITARY ACADEMY, WOOLWICH, ETC. Third Edition. TUFTS COLLEGE LIBRARY. Capio Lumen LONDON CROSBY LOCKWOOD AND SON 7, STATIONERS' HALL COURT, LUDGATE HILL 1890 D. VAN NOSTRAND COMPANY, NEW YORK. PREFACE. THE Elements of Euclid form a complete course of the theoretical principles of Geometry, and the problems contained in them are designed to establish the possibility of performing the several constructions required for the proofs of those principles, before assuming these constructions in the succeeding propositions. For this purpose, then, the simplest modes of proof have been adopted. But for the purposes of Practical Geometry the simplest mode of performing the constructions, consistent with the greatest degree of accuracy, is to be looked for. This necessitates variations from the methods of Euclid : and consequently, even for those problems which are contained in the Elements, as well as for the numerous deductions from them in the following pages, proofs of the methods actually employed herein have been given. The theorems, however, upon which they depend have merely been enunciated, and references given to the propositions of Euclid in which they are to be found. Numerous references throughout the work give the num bers of the theorems, problems, or articles stating the principles upon which the processes depend. The objects of the work have been to give such a course of Practical Plane Geometry as shall enable candidates per fectly to master the constructions given in papers for competitive examinations on the subject. A chapter has also been added on Geometrical Construction on the Ground, which it is hoped will be found useful to the engineering student. NOTE. The student who desires to pursue the subject of Geometry beyond the limits of the present work can avail himself of the Author's further treatise (also published in this series) on Descriptive Geometry, in which will be found included a Theory of Shadows and Perspective, and a description of the principles and practice of Isometrical Projection. The volume serves as an introduction to the application of Descriptive Geometry to various branches of the arts. CONTENTS. PAGE 1 1 Definitions of the terms solid, surface, line, point Definition of a plane or flat surface, and mode of testing it. Definitions and explanations of the terms, rectilineal angle, right- angle, oblique angle, acute angle, obtuse angle, complement and Definitions of the terms, right-angled triangle, oblique-angled triangle, Definitions of the terms, quadrilateral, parallelogram, rectangle, Definitions of the terms, circle, circumference, radius, diameter, chord, semicircle, segment of a circle, arc, semi-circumference Definitions of the terms, angle or a segment, angle IN a segment. |
