OF PLANE TRIGONOMETRY. BY JAMES HANN, K MATHEMATICAL MASTER OF KING'S COLLEGE SCHOOL, LONDON; HONORARY MEMBER OF THE PHILOSOPHICAL SOCIETY OF NEWCASTLE-UPON-TYNE, AUTHOR OF A TREATISE ON THE STEAM ENGINE, AND OF THEORETICAL AND PRACTICAL MECHANICS &c. SECOND EDITION CORRECTED. LONDON: JOHN WEALE, 59, HIGH HOLBORN. I 854. ADVERTISEMENT TO THE SECOND EDITION. MR. HANN'S Rudimentary Treatise on Plane Trigonometry having been carefully revised and corrected, the publisher submits this new edition to the judgment of Mathematical Teachers and Students with an increased amount of confidence. He would also respectfully invite their attention to his cheap collection of Mathematical Tables, forming Vols. 94 and 95 of his Series of Scientific Treatises; they will be found amply sufficient for all the practical purposes of Trigonometry, and will therefore furnish every necessary aid in computations connected with the present subject. The following brief extract, from the Author's Preface to the former edition, is perhaps sufficiently descriptive of the character of the work: "I have given, to illustrate the principles, a great number of examples fully worked out, and which I hope will be of service to those who have not the aid of a teacher. "In compiling the work, the best authors, whether French or English, have been consulted. I may refer to the excellent Works of Bonny castle, Cape, De Morgan, Gaskin, Hall, Hind, Hymers, Snowball, Woodhouse, and Gregory; and to Davies's edition of Hutton's Course. "The problems have been principally taken from the Ladies and Gentleman's Diaries, the Cambridge Problems, and Leybourn's Repository. "The demonstration of Demoivre's Theorem is taken from an able French work on Trigonometry, by Lefebure De Fourcy." J. HANN. TRIGONOMETRY. CHAPTER I. 1. TRIGONOMETRY was originally considered to be the doctrine of triangles, but in its present improved state it has a much more extensive signification, which we shall hereafter shew even in this rudimentary treatise. 2. In estimating angular measures, we suppose the right angle to be the primary one, and to be divided into 90 equal parts, each of which is called a degree; each degree is supposed to be divided into 60 equal parts, each of which is called a minute; each minute is supposed to be divided into 60 equal parts, each of which is called a second, and so on to thirds, fourths, &c. Here one degree is considered as the angular unit. 3. Modern French writers, instead of using the sexagesimal division, use the centesimal; and it is to be regretted that the latter is not universally used, from the great ease with which all calculations are made in that division. We shall, however, shew how to reduce French into English measures, and vice versa. If E and F represent the number of English degrees and French grades in the same angle, 4. The circumference of a circle is known to be about 3.14159 times its diameter, or, in other words, the ratio of the circumference to the diameter is represented by 3.14159; for this number writers generally put the Greek letter π. B |