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 1, 2024.

Pages

Page 192

Ʋpon the Chart.

THE Rhumb-Line A P being drawn, set off thereupon 36 Leagues (which was the way that the Ship made upon the fifth Rhumb before the Wind changed) from A to T, (which Distance must be taken out of the Meridian-line by opening the Compasses from 50 d. to 51, 48. or better, to as much below 50 d. as above 51 d.) So shall the Point T be the Place that the Ship was in when the Wind altered. So a Paral∣lel drawn through T upon the Chart will cut the Meridian at V in 51 d. and in that Latitude the Ship was. Now to find in what Longitude she was; Take in your Compasses the Line T V, and measure it at the bottom of the Chart, you shall find it will reach from E to 2 d. 21 m. And in that Longitude the Ship then was.

This done, upon the Point T (where the Wind changed, and drove the Ship 2 Points more Eastwardly, namely, upon the E. by N. Point) protract an Angle of 22 d. 30 m. namely, the An∣gle P T X, which is the Rhumb upon which the Ship sailed 50 Leagues after the Wind changed. Therefore take 50 Leagues out of the Meridian-line, and set them from T to X. So shall X be the Place that the Ship was in after she had sailed 50 Leagues upon the E. by N. Point; which, by drawing a Parallel through K, will be found in the Latitude of 51 d. 30 m. and by drawing of a Meridian through K also, it will be found to be in the Lon∣gitude of 6 degr. 16 min.

But if these Courses had been protracted according to the Plain Sea-Chart, the Point T would fall in the Latitude of 51 degr. and the Point X in the Latitude of 51 degr. 30 m. But the Longitude of T would be onely 1 d. 30 m. and the Longitude of X in 3 d. 57 min. Both these Longitudes being added, make but 5 d. 27 m. for the Difference of Longitude between X and the first Meridian; whereas by the other Chart it is 6 d. 16 m. So that the Ship at X is 33 m. Westward of the Place to which she was bound.

These Differences, which I have observed to be between the Plain and Mercator's Chart, may be seen by comparing the Scheme of the two Charts together.

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