MACMILLAN AND CO.'S EDUCATIONAL WORKS. Mr I. Todhunter's ELEMENTARY MATHEMATICAL WORKS. The Elements of Euclid. For the Use of Colleges and Schools. New Edition. 35. 6d. 18mo. cloth, In this work each distinct assertion in the argument begins a new line; and at the ends of the lines are placed the necessary references to the preceding principles on which the assertions depend. The longer propositions are distributed into subordinate parts, which are distinguished by breaks at the beginning of the lines. Notes, appendix, and a collection of exercises are added. Mensuration for Beginners. With nume rous Examples. New Edition. 18mo. cloth, 2s. 6d. The book is divided into short independent chapters, which are followed by appropriate examples. A knowledge of the elements of Arithmetic is all that is assumed; and in connection with most of the Rules of Mensuration it has been found practicable to give such explanations and illustrations as will supply the place of formal mathematical demonstrations, which would have been unsuitable to the character of the work. Algebra for Beginners. Examples. Key, bs. 6d. Great pains have been taken to render this work intelligible to young students, by the use of simple language and by copious explanations. In determining the subjects to be included and the space to be assigned to each, the Author has been guided by the papers given at the various examinations in elementary Algebra which are now carried on in this country. Provision has been made for the introduction of easy equations and problems at an early stage for those who prefer such a course. Trigonometry for Beginners. With nume With numerous New Edition. 18mo. cloth, 2s. 6d. rous Examples. New Edition. 18mo. cloth, 2s. 6d. The same plan has been adopted as in the Algebra for Beginners;" the subject is discussed in short chapters, and a collection of examples is attached to each chapter. Answers are appended. Mechanics for Beginners. With numerous Examples. New Edition. 18mo. cloth, 45. 6d. The Author has endeavoured to provide a suitable introduction to the study of applied as well as of theoretical mechanics. The work consists of two parts, namely, Statics and Dynamics. It will be found to contain all that is usually comprised in elementary treatises on Mechanics, together with some additions. Algebra. For the Use of Colleges and Schools. Fifth Edition. Crown 8vo. cloth, 75. 6d. The Examples, about sixteen hundred and fifty in number, have been selected with a view to illustrate every part of the subject. The work will be found peculiarly adapted to the wants of students who are without the aid of a teacher. The Answers to the Examples, with hints for the solution of some in which assistance may be needed, are given at the end of the book. An Elementary Treatise on the Theory of Equations. Second Edition, revised. Crown 8vo. cloth, 75. 6d. Examples for exercise have been selected from the College and University Examination Papers, and the results have been given when it appears necessary. In order to exhibit a comprehensive view of the subject, the treatise includes investigations which are not found in all the preceding elementary treatises, and also some investigations which are not to be found in any of them. Plane Trigonometry. For Schools and Colleges. Fourth Edition. Crown 8vo. cloth, 5s. The design of this work has been to render the subject intelligible to beginners, and at the same time to afford the student the opportunity of obtaining all the information which he will require on this branch of Mathematics. Each chapter is followed by a set of Examples. Mr I. Todhunter's ADVANCED MATHEMATICAL WORKS. A Treatise on Spherical Trigonometry. Third Edition. Crown 8vo. 45. 6d. With Ex A Treatise on Conic Sections. amples. Fourth and Cheaper Edition, revised. Crown 8vo. 75. 6d. A Treatise on the Differential Calculus. With Examples. Fifth Edition. Crown 8vo. 10s. 6d. A Treatise on the Integral Calculus. With Examples. Third Edition. Crown 8vo. 10s. 6d. Examples of Analytical Geometry of Three Dimensions. Second Edition, revised. Crown 8vo. 45. A Treatise on Analytical Statics. With Examples. Third Edition. Crown 8vo. 10s. 6d. Researches in the Calculus of Variations. Principally on the Theory of Discontinuous Solutions. 8vo. 6s. Arithmetic in Theory and Practice. By J. BROOK-SMITH, M.A. Crown 8vo. Part I. 35. 6d. Complete, 45. 6d. Arithmetical Examples, progressively ar ranged, with Exercises and Examination Papers. By the Rev. T. DALTON, M.A., Assistant-Master of Eton College. 18mo. 2s. 6d. Algebraical Exercises, progressively ar ranged. By C. A. JONES, M.A., and C. H. CHEYNE, M.A., Mathematical Masters of Westminster School. New Edition. 18mo. 2s. 6d. Elementary Geometry. Angles, Parallels, Triangles, Equivalent Figures, the Circle, and Proportion. By J. M. WILSON, M. A., Mathematical Master of Rugby School. Second Edition. Extra fcap. 8vo. 35. 6d. Solid Geometry and Conic Sections, with Appendices on Transversals and Harmonic Division. For the Use of Schools. By J. M. WILSON, M.A. Extra fcap. 8vo. 35. 6d. Note-Book on Practical, Solid, or Descriptive Geometry, containing Problems with Help for Solution. By J. H. EDGAR, M.A., and G. S. PRITCHARD. Second Edition, enlarged. Globe Svo. 35. An Elementary Treatise on Conic Sections and Algebraic Geometry. With numerous Examples and Hints for Solution; especially designed for the Use of Beginners. By G. H. PUCKLE, M. A. New Edition, revised and enlarged. Crown 8vo. 75. 6d. Geometrical Conic Sections. An Element ary Treatise, in which the Conic Sections are defined as the Plain Sections of a Cone, and treated by the Method of Projection. By J. S. JACKSON, M.A. Crown 8vo. 45. 6d. Geometrical Treatise on Conic Sections. By W. H. DREW, M.A. Fourth Edition. Crown 8vo. 45. 6d. Solutions, 45. 6d. A Book of Mathematical Problems, on Subjects included in the Cambridge Course. By J. WOLSTENHOLME, M.A. Crown 8vo. 8s. 6d. MACMILLAN AND CO., LONDON. LATE FELLOW OF TRINITY COLLEGE, CAMBRIDGE, AND MATHEMATICAL MASTER AT RUGBY. SECOND EDITION, REVISED. London: MACMILLAN AND CO. 9078 PREFACE. BEGINNERS in Geometry are met with two main difficulties, the one of grasping Geometrical ideas, and the other of seeing the force of Geometrical reasoning. These two giant difficulties are usually attacked together, and many boys are so encumbered with the double combat that they do not slay either of their giants. It is the object of this book to make some way in overcoming the difficulties of Geometrical conception, before the mind is called upon to attack Geometrical theorems. It is a safe guide in all teaching to make your pupils familiar with things before you give your theories. Accordingly a few simple methods of construction are given, which, if in some cases rather long, at any rate satisfy the eye of the learner. By the graphical application of these methods to problems, it is thought that the ideas of the determination of points by the intersection of lines, of comparison of triangles, and of the indirect measurement of lines, will be gradually developed. It is not intended that this book should do more than exercise the learner for some few months before he commences Geometry, either in the shape of Euclid or in some more modern form. |