Nine geometricall exercises, for young sea-men and others that are studious in mathematicall practices: containing IX particular treatises, whose contents follow in the next pages. All which exercises are geometrically performed, by a line of chords and equal parts, by waies not usually known or practised. Unto which the analogies or proportions are added, whereby they may be applied to the chiliads of logarithms, and canons of artificiall sines and tangents. By William Leybourn, philomath.

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Title
Nine geometricall exercises, for young sea-men and others that are studious in mathematicall practices: containing IX particular treatises, whose contents follow in the next pages. All which exercises are geometrically performed, by a line of chords and equal parts, by waies not usually known or practised. Unto which the analogies or proportions are added, whereby they may be applied to the chiliads of logarithms, and canons of artificiall sines and tangents. By William Leybourn, philomath.
Author
Leybourn, William, 1626-1716.
Publication
London :: printed by James Flesher, for George Sawbridge, living upon Clerken-well-green,
anno Dom. 1669.
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"Nine geometricall exercises, for young sea-men and others that are studious in mathematicall practices: containing IX particular treatises, whose contents follow in the next pages. All which exercises are geometrically performed, by a line of chords and equal parts, by waies not usually known or practised. Unto which the analogies or proportions are added, whereby they may be applied to the chiliads of logarithms, and canons of artificiall sines and tangents. By William Leybourn, philomath." In the digital collection Early English Books Online 2. https://name.umdl.umich.edu/A48344.0001.001. University of Michigan Library Digital Collections. Accessed June 16, 2024.

Pages

The Making of the Plain Sea-Chart.

A Sea-Chart may be made either general, or particular. A General Sea-Chart is that whose Degrees of Latitude pro∣ceed from the Aequinoctial to either Pole, which in the com∣mon Sea-Chart may be done; but it will be egregiously false, as the Degrees of Latitude grow nearer the Pole, as I have al∣ready declared.—A Particular Sea-Chart is such a one as is made properly for one particular Navigation: as if your

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whole Navigation were not to exceed the Latitudes of 48 and 60 degr. of Latitude, and not to differ in Longitude above 8 degrees.

Now to project or make such a Chart; First, draw a right Line A B, representing the Meridian, and cross it at right Angles in the Point A with another right Line A D, representing the Parallel of your least Latitude, namely, of 48 degr.— Secondly, consider what Distance you will have your Parallels of Longitude and Latitude to be, (for in this Chart they are both equal,) whether an Inch, 2, 3, or 4 Inches, (for the lar∣ger the better.) But in this Example I have made them one∣ly half an Inch. I take therefore half an Inch out of an exact Scale, and run it up upon the Meridian Line A B, from A to 49, from 49 to 50, from 50 to 51, &c. till I come to my greatest Latitude, which is here supposed to be 60 degr.—Thirdly, run the same Distance of half an Inch from A towards D, upon the Line A D, eight times, because the Difference of Longitude in your whole Navigation will not exceed 8 degrees.— Fourthly, draw the Line C D, parallel to A B, and B C, par∣allel to A D, and run the same Distances upon the Line B C as are upon the Line A D, and the same upon C D as are upon the Line A B.—Fifthly, from each Degree of Latitude in the Line A B draw to the like Degree of Latitude in the Line C D a right Line, as 49, 49; 50, 50; 51, 51; 52, 52; &c. till you have drawn all your Parallels of Latitude.—Sixthly, for your Meridians, they are to be drawn in like manner as were the Parallels of Latitude, all of them equidistant, and par∣allel to your first Meridian A B, as the Lines 1, 1; 2, 2; 3, 3; &c. And by this means have you the Meridians and Parallels drawn.

The grand Divisions, or whole Degrees, being thus set upon your Chart, we now come to sub-divide them. And for the dividing of the Degrees of the Aequinoctial at the top and bottom of your Chart, let each of them be divided into 5 or 10 parts, and each of those parts sub-divided into 5 or 10

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more less parts, according as Quantity will permit; for eve∣ry one of them is supposed to be divided into 100 or 1000 parts.

For the dividing of the Degrees of Latitude; they may be di∣vided as those of Longitude were, into 100 parts. But some∣times each Degree is subdivided into 60 Minutes, or English Miles, or into 20 Leagues.—Now I have divided the Degrees of Latitude in this Chart each of them into 5 parts, by which means it is capable of the Numeration either by Miles, Leagues, Centesms, or 100 parts.—For if you count by 60 minutes, or miles, then every of those Divisions will be 12 minutes, or miles; if by 20 Leagues, then every Division will contain 4 Leagues; and if by Centesms or 100 parts, then every of them is 20 Centesms. And thus much concerning the Making or Projecting of this Chart. I now come to shew

Some Uses of the Plain Sea-Chart.

THE Problems that are to be resolved by (or upon) the Sea-Chart are chiefly such as concern Longitude, Lati∣tude, Rhumb or Course, and Distance.

Longitude is the Distance of a Place from some known Meri∣dian to that Place, and is alwaies counted upon the Aequinoctial.

Latitude is the Distance of any Place from the Aequinoctial, counted upon that Meridian Circle which passeth over that Place.

Rhumb or Course is the Angle that a Ship in his Sailing makes with the Meridian, and is discovered in the general by the Magneticall Needle, which alwaies respecteth the North; and (though not directly, yet) its Variation being often observed, and the Chart rectified thereby, (as I have before shewed how it may be done by severall means) is the best help that Navigators yet have to steer their Course by.

Distance is the number of Leagues, Miles, or Centesms, that any Ship hath sailed.

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Raising of the Pole is when a Ship sails from a lesser to a greater Latitude.

Depressing of the Pole is sailing from a greater to a lesser Latitude.

These Terms thus explained, I will proceed to Practice, as followeth.

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