Afo bore you bave the way of Projecting the Sphere Or-
thographically, In 2 Problems, with many Examples.

XI. An Obfervation, either of Sun or Star; what it is,
bow or with what, and when 'tis taken; with Rules to find
the Latitude of the Place of Obfervation, and all the Varieties
therein reduced into one Propofition, containing two General
Cafes, fully explained by many Examples.

XII. You bave next the Ufe of all the foregoing Inftruc-
tions fummarily comprehended in a new Form of keeping a
Sea Reckoning or Journal, wherein the Log-Book and
Journal in Words at Length, and Tabular in Figures, are
kept together in one Book; whereby the whole Proceedings,
and every particular Tranfaction of any Voyage at all times
may be seen and known, which will be no fmall Satisfaction to
thofe concerned in Ships and Goods, nor a little Augmenta-
tion to the MARINER's Credit and Reputation.

t

And that fo ufeful and beneficial a Method may be prac-
tifed by all who defire to keep a compleat and exact Reckoning,
and fo be enabled to render a good Accoun, thereof, I have.
largely deferibed the Form and Manner of it, with plain Rules
and Directions how to Correct the Reckoning by the ob-
ferved Latitude, and how to find what Latitude and Lon-
gitude the Ship is in every Day; with an Example of a
Seven Days Journal; and how each Days failing is managed,
in taking it from the Log-Board cafting it up, and bring-
ing it into one Course and Distan e; with framing the Dead
Reckoning, and transferring into the Journal; fo that
by this the Whole is moore intelligible.

Laftly, In the Tabular Part, you have first a Traverse
Table; which tho' it stands in fo little Room as two Pages,
yet by it the Difference of Latitude and Departure from the
Meridian may be found for any Distance under 10,000, and
for every Quarter Point of the Compass.

Next to that, A Table of Meridional Parts to every 5
Minutes of Latitude, which together with the Table of Pro-
portional Parts annexed, the Meridional Parts for each fingle
Minute are found

And next adjoining is a Table of 10,000 Logarithmns. 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 bad Secants befides this: The Defcription and general Ufes 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 Occofion.

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 small Part thereof) tho' I dare aver, its the Compleatest and most Portable Pile of Inftructions (for a Young Learner of Navigation) now extant; it's the very Method I bave used for now 50 Years, finding it ever fuccefsful, even to the most indifferent Capacity, among the many Hundreds I bave Taught: Therefore if my Reader would be a Proficient berein, let him begin chearfully, proceed gradually, and the End will crown bis Endeavours with anfwerable Succefs.

Let not Sloth perfuade to rive out at the meeting of any Difficulty, but rather remember at 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.

EPITOME of the Art of NAVIGATION.

CHAPTER I.

Practical Geometry explained by Definitions, Problems and Pro

G

portions.

;

Eometry is a Mathematic Science, explaining the Kinds and Properties of continual Quantity, or Magnitude that is, a Line, a Superficies, and a Solid, whose Original is from a Punct.

Section I. Of Lineal Geometry, or the firft Kind of Magnitude.

Definitions. A Punct or Point is that which cannot be divided

into Parts, and is the End of a Mathematic Line, as the Punct A. Plate 1. Fig. 1.

2. A Mathematic Line hath no Breadth or Thickness, only Length; it is made by the Motion of a Punct, and (confidered in itself) is eitheir Regular or Irregular.

3. Regular, is either a Right-line or an Arc.

4. A Right-line is the fhortest Distance between two Puncts, as the Line BC. Plate 1. Fig. 1.

5. An Arc is not the fhorteft Diftance between two Puncts, but bendeth evenly, as the Arc DE.

6 Irregular, as any crooked Line that bendeth unevenly, as FG. Plate 1. Fig. 1.

7. Lines, compared, are either parallel, or inclining; from whence proceed many Problem..

Problem I. To draw a Line parallel to a given Line.

Definition. Parallel Lines are of equal Distance, and if infinitely produced (being in the fame Superficies) will never meet, as the Lines AB and CD. Plate 1. Fig. 2. Example. AB the Line

}

C is a Punct given.

Through which Punct C, and parallel to the Line AB, a

Line is required to be drawn.

1. Take (with a pair of Compaffes) the neareft diftance between the given Punct C, and the Line AB.

2. With that Distance (in the Compaffes) and one Foot of the Compaffes (any where in the Line AB,) draw (on that Side the Punct C lieth) an Arc D.

3. From the Punct C, draw a Line to touch the Arc D, and it's done; for the Line CD, is parallel to the Line AB, as was required.

Problem II. To bifect or divide a given Line into two equal Parts.

I.

Example, AB is a given Line. Plate 1. Fig. 3.
To find the Middle thereof is required?

WITH any Distance, (greater than half the given Line

Arc CD.

AB) and one Foot of the Compaffes on A defcribed the

2. With the fame Distance, and one Foot on B, cross the former Arc in C and D.

3. By C and D draw a Line which will cut AB in E, the middle; and if AE is equal to EB, it's done true; which Point E is the middle of the Line AB, as was required.

Prob. III. To erect a Perpendicular from a Punët in a given Line.

Definitions.

I.

Nelining Lines are not of equal Diftance, and if produced, will meet as the Lines AB and CD.

Plate 1. Fig. 4.

2. The meeting of inclining Lines, (called an Angle) is either Direct or Oblique.

3. Direct-meeting of Lines is when the Angles on each Side are equal, as EGF, and GH and this kind of meeting is called Perpendicular. Plate 1. Fig. 4.

Example AB is a Line given.

The Punct A, one end of it, from whence to erect a Perpendicular is required. Plate 1. Fig. 5..

1. With any Diftance, and one Foot in A, draw an Arc to eut the Line AB in D.

2. With the fame Distance, and one Foot in D, draw an Arc, to cut the former Arc in C.

3. With the fame Distance and one Foot in C, defcribe an Arc DE, to cut the Line AB-in D..

4. By C and D, draw a Line to cut the Arc DE in E.

5. Then by A and E draw a Line and it's done; For the Line AE is perpendicular unto AB as was required.

Problem IV. To let fall a Perpendicular, from a given Punct, to a given Line.

Example. AB is a Line given, C is a given Punct; from whence to let fall a Perpendicular to the Line AB is required? Plate 1. Fig. 6.

1. Draw a Line (at pleasure) from C to AB, as is the Line CD. 2. By Problem 2. bisect the Line CD in E.

3. With the Distance EC, equal to ED, and one Foot in E, erofs the Line AB in A.

4. By A and C draw a Line, and it's done; For AC is a Perpendicular let fall from the Punct C to the Line AB, as was required.

Problem V. To make a Plane Angle.

Definition 1. The meeting of inclining Lines is called an Angle, and the Lines fo meeting are called Sides of that Angle, as AB and AC. Plate 1. Fig. 7.

2. An Angle is either a Right-Angle, or an Oblique Angle. 3. A Right-Angle is where two Lines are perpendicular to each other, as ED and DF. Plate 1. Fig. 7.

Note, A Right-Angle is juft 90 Degrees.

4. An Oblique-Angle, is either a Acute lefs than ge Degrees, as BAC, or Obtufe more than 90 Degrees, as GHI. Figure 7. Note; An Angle is written with three Letters, the middle Letter fignifieth the Angular Punct, as BAC fignifieth the Angle A.

An Angle is measured by an Arc, whofe Center is the Angular Punct, and is drawn from one Side to the other of the Angle, as the measure of the Angle KLM is the Arc NO. Plate 1. Fig. 7. What a Degree is you may fee in Problem 9. Definition 1. Example. 1. At A in the Line, AB, to make a Right-Angle, Plate 1. Fig. 7.

The Rule. Upon A (by Problem 3.) erect the Perpendicular AC, and it's done; For the Angel BAC is a Right-Angle. Example 2. At A in the Line AB to make an Acute-Angle equal to 41 Degrees. Plate 1. Fig. 8.

1. Take (always) a Chord of 60 Degrees from your Scale, and with one Foot on A draw an Arc DE, to cut the Line AB in D. 2. Make the Arc DE, equal to the Chord of 41d. that is, take 414. from the fame Scale of Chords, and lay it on the Arc from D to E.

3. By A and E draw the Line AEC, and it's done; for the Angle BAC is an Acute Angle, containing 41 Degrees.

Example 3. At B in the Line BC, to make an Obtufe-Angle equal to 102 Degrees, Plate 1. Fig. 8.