DOCTRINE OF PLAIN and SPHERICAL TRIGONOMETRY: WITH ITS Application and Use in the following Parts of MATHEMATICKS; VIZ. I. NAVIGATION in all its Kinds; as Plain Sailing, Mercator's Sailing, Middle Latitude, and Parallel Sailing. II. ASTRONOMY; wherein all the Problems relating to the Doctrine of the Sphere are solved. III. PROJECTION of the SPHERE in Plano. V. FORTIFICATION. VI. MENSURATION of Heights and Distances, both acceffible and inacceffible. VII. DIALLING, Arithmetical and Inftrumental, on all forts of Planes. By WILLIAM HAWNEY, Author of The Compleat Meafurer. LONDON; Printed for J. DARBY, A. BETTES WORTH, F. FAYRAM, J. PEMBERTON, C. RIVINGTON, J. HOOKE, F. CLAY, J. BATLEY, and E. SYM ON. M.DCC.XXV. 9-9-31 TO THE 24577 READER. T HE Author of the following Work, lately deceas'd, is already fufficiently known by a former Piece of his upon Measuring, which for its Usefulness was recommended to the Publick by the late Reverend Dr. John Harris, F. R. S. and has fo well pleafed to the World, as to render a fecond Edition of it neceffary fome time fince. This Treatife feems to be drawn up for the Use of Learners, whether inclin'd to the Study of the feveral Parts of Mathematicks it treats of, or oblig'd to be employ'd in the Prattice of fome of them; and the Benefit receiv'd by this Method of handling thefe Subjects, I am apt to believe, was a Motive as well as Encouragement to publish the fame. I have no more to do than to affure the Reader that the following Sheets are the genuine Performance of the late ingenious Mr. Hawney; and that the Whole of it was fairly written out by him for the Prefs fome little time before he died. PAC ERRATA. P. 119. AGE 12. lin. 9. dele to. P. 25. 1. 9. r. in the Line of Numbers. P. 41. 1. 14. r. let the. P. 46. l. 10. r. t. A+B. P. 59. 1. 3. r. AEB +EAB. P. 100: 1. 2. put; after acute. P. 111. l. 16. r. to a Tangent. P. 110. 1. 5. infert 2. 1. 8. r. letting. P. 124. l. 14. r. 25°. P. 131. l. 10. r. vertical. P. 279. 1. 56 P. 181. 1. 13. r. 45°. P. 237. 1. 24. r. Angles. P. 297. I. 10. dele I. nearly. P. 280. 1. 27. r. lay from G to F. it. P. 304. 1. 4. r. 2.77158. P. 313. 1. 7. r. between. P. 317, and 319. the running Title muft be, Sailing by Middle Latitude. P. 342. l. 10. r. Aldebaran, P. 367. 1. 3. . find. P. 378. 1.2. 45° 5. P. 395. 1. 7. r. the left. P. 397. L. 11. r. Horizontal P. 446. l. 11. 5. 7° 9'. CONTENTS. HAP. I. Definitions and Affections of Trian- Chap. II. Concerning Sines, Tangents, and Secants; by which the Angles of Right-lined, and Sides and Angles of Spherical Triangles, are meaured.. Chap. III. Of the Dimenfions of right-angled Plain Tri- ΙΟ Chap. VI. Of fuch Affections, Definitions, and Theo- Chap. VIII. The Solution of the fixteen Cafes of right- |
