T R I G O N O M E T R Y, AT CAMBRIDGE, NEW ENGLAND. SECOND EDITION. CAMBRIDGE, N. E. PRINTED BY HILLIARD AND METCALF, soLD BY w. HILLIARD, CAMBRIDGE, AND BY cUMMINGs, HILLIARD, & co. 1826. DISTRICT oF MAssACHUSETTs, To wIT. BE it remembered, that on the seventh day of March, 1820, in the fortyfourth year of the Independence of the United States of America, Cummings & Hilliard, of the said district, have deposited in this office the title of a book, the right whereof they claim as proprietors, in the words following, viz : * An Elementary Treatise on Plane and Spherical Trigonometry, and on the Application of Algebra to Geometry ; from the Mathematics of Lacroix and Bézout. Translated from the French for the use of the Students of the University at Cambridge, New England.'' In conformity to the act of the Congress of the United States, entitled * An act for the encouragement of learning, by securing the copies of maps, charts, and books, to the authors and proprietors of such copies, during the times therein mentioned ;" and also to an act, entitled, * An act supplementary to an act, entitled, * An act for the encouragement of learning, by securing the copies of maps, charts, and books, to the authors and proprietors of such copies, during the times therein mentioned,' and extending the benefits thereof to the arts of designing, engraving, and etching, historical and other prints.'' JNo. W. DAVIS, Clerk of the District of Massachusetts. OF the following work, the treatise on Plane and Spherical Trigonometry is from Lacroix's course of mathematics. The new division of the circle being adopted in the original, a few alterations have been found necessary to adapt it to the sexagesimal notation in use in this country. Where there has been occasion to add any thing on this account, or to supply any thing by way of illustration, it is given in the form of a note, and the reference is made by an obelisk, the author's being always distinguished by an asterisk. The chapter on the Application of Algebra to Geometry is selected from the Algebra of Bézout. It was the intention of the compiler to have made use of the more improved treatise of Lacroix or that of Biot upon this subject; but as analytical geometry has hitherto made no part of the mathematics taught in the public seminaries of the United States, and as only a small portion of time is allotted to such studies, and this in many instances at an age not sufficiently mature for inquiries of an abstract nature, it was thought best to make the experiment with a treatise distinguished for its simplicity and plainness. The original being prepared for the use of the Marine and Artillery, those parts have been suppressed, which were not adapted to the purpose of gen" eral instruction. Where it was apprehended that the student would meet with any difficulty in the course of an investigation, new steps have been supplied, and references are often made to theorems and processes, applicable to the case in question ; the figures also, particularly those relating to conic sections, have been simplified. Moreover, such alterations have been introduced, as were found necessary to make this treatise conform to the other parts of the course of mathematics compiled for the use of the Students of the University. CONTENTS. Plane trigonometry e © e - • e ©. 1 Trigonometrical formulas . © - e © . 24, 25 Examples of the solution of right-angled triangles © . . 35 Examples of the solution of oblique-angled triangles - 36 Spherical trigonometry . © © e 9 , . 44 - spherical triangle ©. - o> © e © 59 JNote on Napier's rules . e © e - e . 63 Of the geometrical construction of algebraic quantities © 70 |