PARTS I., II., AND III. Part I. Lines and Angles. Rectilineal Figures Part III. Circles (Containing the substance of Euclid Book I., Book III. 1-34, BY H. S. HALL, M.A. AND F. H. STEVENS, M.A. SECOND EDITION REVISED MACMILLAN AND CO., LIMITED 1921 First Edition July 1903. Second Edition, Revised, March 1904. Reprinted 1905 (twice), 1906, 1907 (twice), 1908, 1909, 1910, GLASGOW : PRINTED at the UNIVERSITY PRESS BY ROBERT MACLEHOSE AND CO. LTD. PREFACE. THE present work provides a course of Elementary Geometry based on the recommendations of the Mathematical Association and on the schedule recently proposed and adopted at Cambridge. The principles which governed these proposals have been confirmed by the issue of revised schedules for all the more important Examinations, and they are now so generally accepted by teachers that they need no discussion here. It is enough to note the following points : (i) We agree that a pupil should gain his first geometrical ideas from a short preliminary course of a practical and experimental character. A suitable introduction to the present book would consist of Easy Exercises in Drawing to illustrate the subject matter of the Definitions; Measurements of Lines and Angles; Use of Compasses and Protractor; Problems on Bisection, Perpendiculars, and Parallels; Use of Set Squares; The Construction of Triangles and Quadrilaterals. These problems should be accompanied by informal explanation, and the results verified by measurement. Concurrently, there should be a series of exercises in Drawing and Measurement designed to lead inductively to the more important Theorems of Part I. [Euc. I. 1-34]* While strongly advocating some such introductory lessons, we may point out that our book, as far as it goes, is complete in itself, and from the first is illustrated by numerical and graphical examples of the easiest types. Thus, throughout the whole work, a graphical and experimental course is provided side by side with the usual deductive exercises. (ii) Theorems and Problems are arranged in separate but parallel courses, intended to be studied pari passu. This arrangement is made possible by the use, now generally sanctioned, of Hypothetical Constructions. These, before being employed in the text, are carefully specified, and referred to the Axioms on which they depend. * Such an introductory course is now furnished by our Lessons in Experimental and Practical Geometry. |