Epitome of the Art of Navigation; Or, a Short, Easy, and Methodical Way to Become a Compleat Navigator

HARVARD COLLEGE
July 18, 1958

LIBRARY

Deposited by Astronomical Laboratory

NAVIGATION..

HE General Approbation of this Book, fince its firft Impreffion in 1686, hath obliged me not only to publifh my Grateful Acknowledgment thereof; but also excited my diligent Search into, and exact Survey of every Part of its Structure, to find out the Defects, to know all its Deficiencies, which I have fo far laboured in, That in this Impreffion,

I have now Rectified what was amifs; Altered what was Disorderly; Explained what was Dark or Obscure; Enlarged where it was Scanty; Added where it was Wanting; And,

Thele Retifications, Alterations, Emendations, and Additions, being in diverfe 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 Impreffions, in the plain and easy Method they are placed in, but which in general is thus;

I. You have Pract Geometry, explained by Definitions, Problems and Proportions; In this Chapter is taught the making the most useful Geometric Figures, with the meafuring all Superficies and Solids; Alfo the Application thereof in Practical Meafuring, Board, Glafs, Plaistering, Painting, Paving, and Land; Timber and Stone; Gauging of Cafks, and a Ship's Hold: All being illuftrated with Rules, Proportions and Examples, eafy to the Understanding, and not burthenfome to the Memory and fo ftated that they may be performed both by Arithmetic, and by the Line of Numbers on Gunter's-Scale, in in 37

Problems

The first Chapter I advise the Learner to ftudy well before
he proceeds, 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
ufeful Notes and Definitions, with the Axioms, and also the
Cafes depending on each Axiom, orderly fet down in 8 Prob-
blems, containing 13 Cafes.

And bere I must advertise the Young Student that would
work Trigonometry by the Logarithms, to confult Chap-
ter I. The Explanation and general Ufe 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

Plane Sailing.

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 Defcription and Ufe of the Plane-
Chart, in 5 Problems, before I come to the Cafes of Plane
Sailing, which I divide into three Parts.

1. In a Right-angled Triangle, relating to a Single

Courfe, in which are 6 Cafe, commonly called the 6 Cafes

of Plane Sailing.

2. In a Right-angled Triangle, to several Courses

called a Traverse.

3. In an Oblique-Triangle, in which are but 4 Cafes,
though there may be a Multitude of various Questions; of
which you have a Tafe in Turning to Windward, and
Sailing in Currents, in 21 Problems.

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 shew the Ufes 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 supply their
Room I have added Problems of Sailing by the Middle
Latitude, which will nearly agree with Mercator's Sailing,
a Thing of good Ufe, In 4 Problems.

V. Spheric Trigonometry, or the Dorine of Spheric
Triangles Rectangular and Oblique, is next in Order; and
it being fo neceffary you should understand how to make a
Spheric Triangle, and also how to measure any of its Parts,
before the framing and working Proportions therein, I have
fully explained that Matter in the beginning of this Chapter,
being in a Manner a New Invention, which I call Spheric
Geometry; This you have in 21 Problems;

And in Spheric Trigonometry properly fa called (the
next in Order) you have all the Axioms and Cafes, both
in Rectangular and Obliquangular 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
28 Cafes.

VI. The Description and Ufe of both Globes, is the
next to be confider'd; in which I have plainly and familiarly
explain'd and shewed the Ufe of the most neceffary Things be-
longing or relating to each of them, In 24 useful Problems.

To which is annexed a fhort Defcription and Ufe of the
Hemifpheres, projected on the Plane of the Ecliptic.

VII. Geography subject of this Chapter, which
is the Application of Spheric Trigonometry in finding the
True Diftance 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, fo it's the most difficult, and
bardly poffible for a Ship exactly to fail by; yet it's of great
Advantage to keep conveniently near it; for which Purpose
you'll find all that neceffarily belongs or relates to it, both
as to the Projective Part, and that both Stereographic and
Gnomonic; as alfo in the Calculate Part, (which requires

the Application of both Spheric and Plane Trigonometry,
fully made out; With an Intimation of fportning the Work,
by fhewing how to defcribe the Arch of a Great Circle on a
Mercator's Chart; the Whole in 4 Problems,

IX. Next you have Spheric Trigonometry, applied in

fundry Aftronomic Problems useful in Navigation, wherein

the Circles of the Sphere are defcribed, and the necessary

Terms of Art explained to the meanest Capacity, with Respect

to the diurnal Motion; and that either,

1. According to the Ptolomaic Syftem, wherein you

bave in a Right-Angle Spheric Triangle, all the Variety of
Questions and Examples that relate to the Sun, with Re-
Spect to his Longitude, Declination, Right or Oblique Afcen-
fion, or Defcenfion, Rifing, Setting, Amplitude, Altitude and
Azimuth, at the Hour of Six; Altitude and Hour of the
Day, when Eaft or Weft; Hour, Azimuth, and Altitude,
when be is in the Equinoctial, In 24 Problems. Also,

In an Oblique Spheric Triangle, you have great Variety

both with Refpect to the Sun or a Star, in many Questions

and Examples relating to the Sun's Altitude, Azimuth, and

Hour of the Day, in any Place, at any Time of the Year :

And relating to a Star, as to its Longitude, Latitude, Decli-

nation, Right Afcenfion, Rifing, Setting, Amplitude, Alti-

tude, Azimuth, Hour of the Night, its Altitude on the Me-

ridian, and Time of its coming to it, In 12 Problems
Or,

2. According to the Pythagorean, or Copernic System,

which is now generally receiv as most agreeable to the ob-

ferved experienc'd Motion of the enly Bodies; wherein

Spheric Trigonometry is applied in variety of Questions and