#HE General Approbation of this Book, since it; of first Impression in 1686, hath obliged me not f only to publish my Grateful Acknowledgment thereof; but also excited my diligent Search o 3 into, and exačt Survey of every Part of its Struślure, to find out the Defetis, to know all its Deftciencies, which I have so far laboured in, That in this Impression, I have now Reşified what was amiss; Altered what was Disorderly; Explained what was Dark or Obscure ; Enlarged where it was Scanty; Added where it was Wanting ; And, These Rećlifications, Alterations, Emendations, and Additions, being in diverse Places, I thought it needless to Enumerate them particularly ; for they are obvious to a diligent Reader, that will but compare the Rules, Precepts, and Examples of this with the former Impressions, in the plain and easy Method th;3 are placed in, but which in general is thus; *. I. 2%u bave ProtoGeometry, explained by Definitions, Problems and Proportions; In this Chapter is taught the making the most useful Geometric Figures, with the measuring all Superficies and Solids; Also the Application thereof in Pratlical Measuring, Board, Glass, Plaistering, Painting, Paving, and Land; Timber and Stone ; Gauging of Casks, and a Ship's Hold: All being illustrated with Rules, Proportions and Examples, easy to the Understanding, and not burthensome to the Memory ; and so fated that they may be performed both by Arithmetic, and by the Line of Numbers on Gunter's-Stale, in 37 Problems, A 3 The
The first Chapter I advise the Learner to study well before he proteeds, it being preparative to the next, as indeed they are all depending on one another, as Links in a Chain. II. Plane Trigonometry is next, in which are many useful Notes and Definitions, with the Axioms, and also the work Trigonometry by the Logarithms, to consult Chap- ter 1. The Explanation and general Use of the Table of Logarithms, and Tables of Sines, Tangents, and Se- cants, towards the latter End of the Book, in Page 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 transmuted for the Gregorian or New Calendar, or by the late All of Parliament required) shewing how to find the Prime, Epačt, Dominical-Letter, Easter-Day, the Moon's-Age, South- ing, and Time of Full-Sea, or High-Water, In 9 Prob. Course, in which are 6 Case", commonly called the 6 Cases 2. In a Right-angled Triangle, oto several Courses 3. In an Oblique-Triangle, in which are but 4 Cases, though there may be a Multitude of various Questions ; of understanding of which, 'tir necessary to describe Mr. Wright's Projećtion, commonly known by the Name of Mercator's Chart, and shew the Uses of it, before I treat of in 12 Problems: In the first 9 the Table of Meridional Parts, or the Meridional Line on Gunter's-Scale is used : And in Case that Table or Line be wanting, to supply ther Room I have added Problems of Sailing by the Middle Latitude, which will nearly agree with Mercator's Sailing, a Thing of good Use, In 4 Problems. V. Spheric Trigonometry, or the Doğrine of Spheric Triangles Rectangular and Oblique, is next in Order; and next in Order) you have all the Axioms and Cases, both in Rectangular and Obliquangular Triangles, explain'd with necessary Notes on each Case; as to know when a re- quired Angle is Acute or Obtuse, and when a required Side, o: loss than a Quadrant, In 12 Problems, containing VI. The Description and Use of both Globes, is the next to be consider'd ; in which I have plainly and familiary if the Application of' Spheric Trigonometry in finding the True Distance of Places in the Variety of their Situation on the Globe of the Earth, In 4 Problems. VIII. Great Circle Sailing comes next, which as it’s the most accurate Way, of Sailing, so it’s the most difficult, and |