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 XII. The Base A C 27 degr. 54 min. and the Perpendicular B C 11 d. 30 min. being given, to finde the Angle at the Base A.

The Analogie or Proportion is,

As the Sine of the Base A C 27 degr. 54 min. is to the Ra∣dius,

So is the Tangent of the Perpendicular B C 11 degr. 30 min. to the Tangent of the Angle at the Base A.

DRaw the two Quadrants A B C and C A D, as before. Then take out of your Line of Chords 27 degr. 54 m. the quantity of the given Base A C, and set them upon the Quadrant from B to E, and draw the Line E F parallel to C D. Also take 11 degr. 30 min. the quantity of the Per∣pendicular B C, and set them upon the Quadrant from C to N, and draw the Line A N, cutting the Line C H in G.

This done, take in your Compasses the distance A F, and setting one foot in D, with the other describe the Arch M, and close by the out-side of it draw the Line C L. Then

take in your Com∣passes the distance C G, and setting one foot of them upon the Line C D, move it along till the other foot, be∣ing turned about, will onely touch the Line C L; and when it so toucheth, mark where the other foot resteth upon the Line C D, which it will do at K. Last∣ly, draw the Line A K, cutting the Quadrant C B in the Point O. So shall C O, being measu∣red on the Line of Chords, contain 23 degr. 30 min. the quantity of the en∣quired Angle at A.

[illustration] geometrical diagram