KEY то ROBINSON'S NEW GEOMETRY AND TRIGONOMETRY, AND CONIC SECTIONS AND ANALYTICAL GEOMETRY. WITH SOME ADDITIONAL ASTRONOMICAL PROBLEMS. DESIGNED FOR TEACHERS AND STUDENTS. NEW YORK: IVISON, BLAKEMAN, TAYLOR, & COMPANY, 138 & 140 GRAND STREET. CHICAGO: 133 & 135 STATE STREET. 1875. ROBINSON'S Series of Mathematics, The most COMPLETE, most PRACTICAL, and most SCIENTIFIC SERIES of II. Robinson's Progressive Primary Arithmetic, - XIV. Robinson's Key to New University Algebra, XV. Robinson's New Geometry and Trigonometry, XVI. Robinson's Surveying and Navigation, XVII. Robinson's Analyt. Geometry and Conic Sections, XX. Robinson's University Astronomy, XXI. Robinson's Mathematical Operations, XXII. Robinson's Key to Geometry and Trigonometry, Conic Entered, according to Act of Congress, in the year 1862, by In the Clerk's Office of the District Court of the United States for the Northern HARVARD 047172 PREFACE. A KEY to a Text-book on the Higher Mathematics, if not a new creation, is by no means a common thing. And it is a question undecided in the minds of many, whether a Key to any mathematical work is an aid, or a hindrance to the teacher. The value of a Key depends upon the use to which it is applied. Class, and school-room duties so fully occupy the time of a majority of teachers, as to make a Key a great convenience, if not a necessity. And teachers of limited acquirements, as well as private students, will often find a Key of great service. A Key should never be used to supersede investigation and labor, but to give direction to study, and make labor more effective. It should lessen the mechanical labor of teaching, by showing how to study, and how to teach, by giving the best forms of analysis, the best arrangement of the work, new and improved methods of operations, and often by developing methods of solu |