The Organised Science Series. General Editor : WILLIAM BRIGGS, LL.D., M.A., F.C.S., F.R.A.S., PRACTICAL PLANE AND SOLID GEOMETRY. FOR THE SOUTH KENSINGTON BOARD OF EDUCATION EXAMINATIONS. GENERAL EDITOR-WM. BRIGGS, LL.D., M.A., F.C.S., F.R.A.S., Honorary Associate of Science of the Yorkshire College, Victoria University. FOR THE FIRST STAGE, 28. each Vol. I. First Stage Practical Plane and Solid Geometry. III. First Stage Building Construction. V. First Stage Mathematics (Euclid and Algebra). VI.A. First Stage Mechanics of Solids. Fourth Edition. VI.B. First Stage Mechanics of Fluids. Second Edition. VIII. First Stage Sound, Light, and Heat. Second Edition. IX. First Stage Magnetism and Electricity. Second Edition. VII. First Stage Applied Mechanics. XI. First Stage Organic Chemistry, Theoretical. XXIII. Section One Physiography. X.P. First Stage Inorganic Chemistry (Practical). Second Ed. 1s. XI.P. Practical Organic Chemistry. 1s. 6d. FOR THE SECOND STAGE. 8s. 6d. each Vol. V. Second Stage Mathematics (being the additional Algebra and Euclid, with the Trigonometry required.) Second Edition. VI.A. Second Stage Mechanics (Solids), or Advanced. Part I. DYPart II. STATICS. Third Edition, Revised and NAMICS. Enlarged. VIII.C. Second Stage Heat, or Advanced. Second Edition. IX. Second Stage Magnetism and Electricity, or Advanced. X. Second Stage Inorganic Chemistry (Theoretical), or Advanced. Second Edition. XVII. Second Stage Botany. XXV. Second Stage Hygiene, or Advanced. [In the press. X.P. Second Stage Inorganic Chemistry (Practical), or Advanced. 28. XI.P. Practical Organic Chemistry. 1s. 6d. XX. and XXI.B. Modern Navigation. (For the First and Second Stages.) [In the press LONDON: W. B. CLIVE, 157 DRURY LANE, W.C. FIRST STAGE PRACTICAL PLANE AND SOLID GEOMETRY. WRITTEN TO MEET THE REQUIREMENTS OF THE NEW BY G. F. BURN, A.M.I.Mech. E. HONOURS MEDALLIST IN PRACTICAL PLANE AND SOLID GEOMETRY, HEAD OF THE MECHANICAL ENGINEERING DEPARTMENT AT THE LEEDS TECHNICAL SCHOOL. LONDON: W. B. CLIVE, University Tutorial Press, Ed. (University Correspondence College Press), 157 DRURY LANE, W.C. PREFACE. THIS work has been designed to cover the requirements of the Elementary Stage of the Board of Education in Practical Plane and Solid Geometry. The recent changes in the Syllabus have made imperative the production of a text-book which shall meet the conditions there laid down. A candidate for the examination in the elementary stage must now be prepared in vectors, horizontal projection, trigonometrical ratios, etc.-details formerly considered to be beyond the scope of this stage. These points have in this book been taken up and treated in an elementary manner. While adhering as much as possible to the new Syllabus, the writer has not ignored the good features of the old, nor the examination papers that have been set by the Board of Education in the past few years. At the end of each chapter will be found a few carefully selected. original exercises, followed by a large number of appropriate Examination Questions. With a view of saving valuable time, hints have been given to some of the exercises and questions, where this appeared desirable; and, where appropriate, quantitative answers also have been givenpoints which teachers will certainly not be slow to fully appreciate. No effort has been spared, as will be seen, to render the work experimental and practical in its aims, especially in |