From the PREFACE. THE aim of the present little work is to supply the youthful student with the fundamental principles of Practical Geometry. It is designed to meet the wants of the latest Syllabus of the First-Grade Examinations of the Science and Art Department. So far as the Author is aware, there exists no text-book which exactly covers the work of the most recent requirements of that Syllabus. In taking their pupils through the book, teachers are advised to attempt the Test Exercises, only on going over the problems a second time. Too much use of the black board cannot be made, while neatness as well as accuracy cannot be too strongly insisted upon. To those who have mastered the problems there should be little or no difficulty in copying the Figures at the end. The Papers set by the Department in the March Examinations (1877-8-9) will be useful for examination purposes, and will also furnish teachers and pupils with a good idea of what is expected from them by the Department.