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

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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http://name.umdl.umich.edu/A48344.0001.001

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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 17, 2024.

Pages

Ʋpon the Chart.

Through the two given Latitudes 50 d. and 52 ½, at A and O draw two Parallels, O P and A D, upon which set the Dif∣ference of Longitudes from O to P, and from A to Q, 6 degr. Then draw the Line A P, which shall be the Line of the Rhumb leading from one Place to the other: wherefore, by your Chord or Protracting Quadrant find the quantity of the Angle O A P, which shall be the Inclination of the Rhumb to the Me∣ridian, and will be found to be 56 d. 15 m. that is the N. E. by E. Point; which was the First thing that was required.

Then to find the proper Distance upon the Rhumb; Take the Line A P in your Compasses, and measure it upon the Me∣ridian-line, so that one foot may be above the greater Latitude so much as the other is below the lesser; and you will find the Compass-points to rest in E and S, E being one whole Degree below the lesser Latitude, and S one Degree above the grea∣ter. So that there is intercepted between E and S 4 ½ degr. And that is the proper Distance upon the Rhumb; which was the Second thing required.

But if this Problem had been wrought upon the Plain Chart, the Rhumb from the Meridian would be found to be 67 d. 23 m. that is, within 7 m. of the 6^th Rhumb; which is more then the truth by 11 d. 8 m.