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 II. The Side A B 30 degr. the Angle at E 38 degr. 15 min. and the Side B E 18 degr. 47 m. being given, to finde the Angle at A.

The Analogie or Proportion is,

As the Sine of the Base A B 30 degr. is to the Sine of the An∣gle at E 38 degr. 15 min.

So is the Sine of the Side B E 18 degr. 47 min. to the Sine of the Angle at A.

YOur Quadrant being drawn, from your Line of Chords take 30 degr. the quantity of the Side A B, and set them from B to E. Also take 38 degr. 15 min. the quantity of the Angle at E, and set them from B to F. Likewise take 18 degr. 47 min. the quantity of the given Side B E, from your Line of Chords, and set them from B to N; and draw the Lines E H, and F G, and N K, all parallel to A B.

This done, take in your Compasses the distance A H, and setting one foot in G, with the other describe the Arch L, draw∣ing the Line A M onely to touch the Arch. Then take the di∣stance A K in your Compasses, and setting one foot of them upon the Line A C, move it along that Line gently, till the other Point, being turned about, will onely touch the Line A M; and where the Compass-point resteth upon the Line A C, which it will doe at the Point I, through I therefore draw

the Line I D parallel to B A. So shall B D, being measured on your Line of Chords, contain 23 degr. 30 min. the quan∣tity of the enquired Angle at A.