DRaw a right Line, as D B, containing 335 of your Scale of equal parts, which shall be the Base of your Triangle. Then with 60 degr. of your Line of Chords, upon the Point D describe the Arch k l; and because the given Angle at D contains 43 degr. 20 min. take 43 degr. 20 min. from your Line of Chords, and set it from l to k, drawing the Line D k. Again, because the given Side D C contains 100, set 100 of your Line of equal parts from D to C; then drawing a right Line from C to B, you shall by that means find the oblique-angled Triangle C D B. Lastly, being the other two Angles at B and C are to be found, with 60 degr. of your Chord on the Point B describe the Arch e f; also upon the Point C describe the Arch g o h. Then if you take the distance be∣tween e and f in your Compasses, and measure it upon your Line of Chords, you shall finde it to contain 14 degr. 40 min. And that is the quantity of the Angle at B. Then being the Angle at C, which is also required, is obtuse, and contains a∣bove 90 degr. take 90 degr. out of your Line of Chords,
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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- 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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- Leybourn, William, 1626-1716.
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- 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 May 18, 2024.
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Page 25
The Analogie or Proportion is,
As the Log. of the Sum of the two Sides given, C D and C B, is to the difference of those Sides,
So is the Tang. of half the Sum of the two unknown Angles, C and B, to the Tangent of half their difference.