HENRY DALLAS THOMPSON, D.Sc., PH.D. PROFESSOR OF MATHEMATICS IN PRINCETON UNIVERSITY New York THE MACMILLAN COMPANY LONDON: MACMILLAN & CO., LTD. 1896 All rights reserved EdricT 148.76, 02.0 HARVARD COLLEGE LIBRARY GIFT OF GEORGE ARTHUR PLIMPTON COPYRIGHT, 1895, BY H. D. THOMPSON. COPYRIGHT, 1896, BY THE MACMILLAN COMPANY. Norwood Press J. S. Cushing & Co. - Berwick & Smith Norwood Mass. U.S.A. PREFACE As the title of this book implies, the simpler propositions of solid geometry are presented, demanding as a basis the acceptance of our ordinary concepts of space and the geometry in a plane, and the understanding of the meaning. of the common notions which are used in all reasoning. The shortening of the time which can be given to any single branch in a modern curriculum tends to make a demand for a course which shall take as short a time as possible; but when a certain amount of matter is given, as in geometry, this shortening process cannot be carried beyond a certain point without vitiating the conclusiveness of the proof to many minds. On the other hand, if the reasoning be complete, there is a tendency to go beyond the range of the necessary sequence of propositions, and to introduce many propositions which, while interesting, are not necessary to an elementary course. Both of these errors should be guarded against, and to this end the form and arrangement of propositions is here such that those propositions which are not necessary to the development of the subject may be omitted without prejudice to the rest. of the subject. And the endeavour has been to build up a |