By the same Author. I. PLANE AND SPHERICAL TRIGONOMETRY. PART I., containing Rules, Examples, and Problems. This volume contains the principal Rules in Logarithms, and in Plane and Spherical Trigonometry. The Examples and Problems exceed 400, and the answer or result is given under each. Sixth edition, 4s. cloth. II. PLANE AND SPHERICAL TRIGONOMETRY. PART II., containing the principal Formulæ, Proofs of Rules in Logarithms and Trigonometry, &c. given in PART I.; and a series of upwards of 300 Analytical Examples and Exercises, with Hints and Answers. Sixth edition, 4s. cloth. The two Parts complete in one volume, 7s. 6d. cloth. III. PROBLEMS IN ASTRONOMY, SURVEYING, and NAVIGATION, with their SOLUTIONS. Designed for facilitating Self-instruction in the principles of Navigation and Nautical Astronomy. This volume contains the SOLUTIONS of all the Problems given in Trigonometry, Part I. Second edition, 6s. cloth. IV. HAND-BOOK FOR THE STARS; or Rules for finding the Names and Positions of all the Stars of the First and Second Magnitude. Third edition, 4s. 6d. cloth. V. NAVIGATION AND NAUTICAL ASTRONOMY. PART I., containing Rules and Examples. 78. 6d. cloth. VI. NAVIGATION AND NAUTICAL ASTRONOMY. PART II., containing Investigations and Proofs of the principal Rules and Corrections. 78. 6d. cloth. The two Parts complete in one volume. 14s. cloth. LONDON LONGMANS AND CO., PATERNOSTER ROW. TRIGONOMETRY. PART I. CONTAINING RULES, EXAMPLES, AND PROBLEMS. BY H. W. JEANS, F.R.A.S. LATE MATHEMATICAL MASTER AND EXAMINER AT THE ROYAL NAVAL COLLEGE, PORTSMOUTH; LONGMANS, GREEN, & CO., PATERNOSTER ROW. 1873. 183. PREFACE. THE following pages contain the Practical Rules in Plane and Spherical Trigonometry. The investigations of these Rules, requiring some knowledge of Mathematics, are given in the Second Part of this treatise. The present volume is made to consist entirely of the Rules and their applications, and the demonstrations are placed in Part II., in order that the student may be enabled to proceed with Problems in Surveying, Navigation, and Astronomy, as soon as he is acquainted with vulgar and decimal fractions, and has acquired a sufficient knowledge of algebra to work an easy equation. The Problems at the end of the book have been selected chiefly for Naval Students; most of them can be solved by means of the Rules contained in the book. The Problems marked with the letter (a) have been added for the use of those who have already made some progress in Mathematics : these cannot be solved by a simple application of the Rules; they will present, however, little difficulty to the student who has made himself acquainted with the contents of Part II. The table of log. haversines* contained in Inman's Nau * This table, under the name of logarithmic versed sines, may be found in Mendoza Rios, calculated to five places of decimals; the table in Norie, called log. rising, may be formed from it by the addition of the constant log. 5.30103. The above table of Mendoza Rios was re-calculated by the Author of the present work, and carried to |