The first Chapter I advise the Learner to ftudy well before II. Plane Trigonometry is next, in which are many use- ful Notes and Definitions, with the Axioms, and alfo the Cafes And here I must advertise the Young Student that would work Trigonometry by the Logarithms, to confult Chapter 1. The Explanation and general Ufe of the Table of Logarithms, and Tables of Sines, Tangents, and Secants, towards the latter End of the Book, in Pape 294. III. Then follows Plane Trigonometry, applied in Pro- blems of Sailing by the Plane Sea-Chart, commonly called And that nothing be wanting, I begin with the common Notes of the Julian Calendar (in this Edition tranfmuted for the Gregorian or New Calendar, or by the late Act of Parliament required) fhewing how to find the Prime, Epact, Dominical-Letter, Eafter-Day, the Moon's-Age, South- ing, and Time of Full-Sea, or High-Water, In 9 Prob. Then proceeding to the Description and Ufe of the Plane- 1. In a Right-angled Triangle, relating to a fingle Curfe, in which are 6 Cafes, commonly called the 6 Cafes 2. In a Right-angled Triangle, relating to feveral Courfes 3. In an Oblique-Triangle, in which are but 4 Cafes, though there may be a Multitude of various Questions; of V. In Chapter 4th is Mercator's Sailing; To the right understanding of which, 'tis neceffary to defcribe Mr. Wright's Projection, commonly known by the Name of Mercator's Chart, and fhew the Ules of it, before I treat of the Problems of Sailing by it; which you will find performed in 12 Problems: In the first 9 the Table of Meridional Parts, or the Meridional Line on Gunter's-Scale is used: And in Cafe that Table or Line be wanting, to fupply their Room I have added Problems of Sailing by the Middle Latitude, which will nearly agree with Mercator's Sailing, a Tbing of good Ufe, In 4 Problems. V. Spheric Trigonometry, or the Dorine of Spheric Triangles Rectangular and Oblique, is next in Order; and And in Spheric Trigonometry properly fo called (the next in Order) you have all the Axioms and Cafes, both in Rectangular and Qbliquangular Triangles, explain'd with neceffary Notes on each Cafe; as to know when a re- quired Angle is Acute or Obtufe, and when a required Side, is more or less than a Quadrant, In 12 Problems, containing VI. The Defcription and Ufe of both Globes, is the next to be confider'd; in which I have plainly and familiarly To which is annexed a fhort Defcription and Ufe of the Hemifpheres, projected on the Plane of the Ecliptic. VII. Geography is the fubject of this Chapter, which is the Application of Spheric Trigonometry in finding the VIII. Great Circle Sailing comes next, which as it's the the Application of both Spheric and Plane Trigonometry, IX. Next you have Spheric Trigonometry, applied in 1. According to the Ptolomaic. Syftem, wherein you In an Oblique Spheric Triangle, you have great Variety 2. According to the Pythagorean, or Copernic System, X. Then follow very eafy Rules to find the Variation of Alfo here you have the way of Projecting the Sphere Or- XI. An Obfervation, either of Sun or Star; what it is, XII. You have next the Ufe of all the foregoing Inftruc- And that fo ufeful and beneficial a Method may be prac Laftly, In the Tabular Part, you have firft a Traverfe Next to that, A Table of Meridional Parts to every 5 And And next adjoining is a Table of 10,000 Logarithms. After which you have a Triangular Cannon Logarithmic, or a Table of Artificial Sines, Tangents and Secants, to every Degree and Minute of the Quadrant, which are corrected with more than ordinary Care, there being no Volume (when this Book was first published in 1686) extant that had Secants befides this: The Defcription and general Uses of thefe Tables are comprehended in 4 Chapters, containing 13 Propofitions, and fet just before the Tables, beginning at Page 294. The Schemes or Figures are contained in 10 CopperPlates, inferted in their proper Places, being orderly Numbered with proper References for the more eafy turning unto, upon Occafion. Thus have you a Summary of what's here treated; what my Labour and Pains have been herein, I leave you to judge who are most like to reap the Fruit and Profit (my Share being a very fmall Part thereof) tho' I dare aver, it's the Compleatest and most Portable Pile of Inftructions (for a Young Learner of Navigation) now extant; it's the very Method I have used for now 50 Years, finding it ever fuccefsful, even to the most indifferent Capacity, among the many Hundreds I have Taught: Therefore if my Reader would be a Proficient herein, let him begin chearfully, proceed gradually, and the End will crown bis Endeavours with anfwerable Succefs. Let not Sloth perfuade to give out at the meeting of any Difficulty, but rather remember that Love, Labour, and Conftancy will overcome the greatest Difficulty; And, That my Learner may fo read as to understand, and fo understand as to be a Proficient, is the Defire of him, who wifheth the Young Student's Welfare, and the Progress of ARTS. JAMES ATKINSON. |