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.

CASE XI. The Base A C 27 degr. 54 min. and the Angle at the Base A 23 degr. 30 min. being given, to finde the Perpendicular B C.

The Analogie or Proportion is,

As the Radius is to the Sine of the Base A C 27 degr. 54 min.

So is the Tangent of the Angle at A 23 degr. 30 min. to the Tangent of the Perpendicular B C.

[illustration] geometrical diagram

YOur Qua∣drants be∣ing prepared, out of your Line of Chords take 27 d. 54 m. the quantity of the given Base A C, and set them from A to S, drawing the Line S R paral∣lel to C D. Al∣so take out of your Chords 23 degr. 30 mi∣nutes, the quan∣tity of the gi∣ven Angle at A, and set them from C to r, and draw the Line A r, prolonging it to F.

This done,

take in your Compasses the distance A R, and setting one foot in D, with the other describe the Arch T, and by the side thereof draw the Line C V onely to touch it. Then set one foot of your Compasses in F, and with the other take the nearest distance to the Line C V, which distance will reach from C to X. Lastly, draw the Line A X, which will cut the Quadrant A B C in the Point Z. So shall C Z, being mea∣sured upon the Line of Chords, contain 11 degr. 30 min. which is the quantity of the Perpendicular B C, which was required.