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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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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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Link to this Item
http://name.umdl.umich.edu/A48344.0001.001
Cite this Item
"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

CASE VII. The Base A B 180, and the Perpendicular C A 135, being gi∣ven, to finde the Hypotenuse C A.

DRaw a right Line A B containing 180 equal parts, and upon the end A erect the Perpendicular A C, and out of your Scale of equal parts take the length thereof 135, which set from A to C, and draw the Line C B, which con∣stitutes

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the Triangle C A B. Lastly, take the length of the Hypotenuse C B in your Compasses, and measuring it upon your Line of equal parts, you shall finde it to contain 225.

The Analogie or Proportion is,

1. Operation.

As the Logarithm of A B is to the Logarithm of C A,

So is the Radius to the Tangent of B.

2. Operation.

As the Sine of B is to the Logarithm of C A,

So is the Radius to the Logarithm of C B.

These are the severall Varieties or Cases that can at any time fall out in the Solution of Right-angled plain Triangles, wherefore we will now proceed to the Solution of Oblique plain Triangles.

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