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 I. The Angle at E 38 degr. 15 min. the Angle at A 23 degr. 30 m. and the Side A B 30 degr. being given, to finde the Base B E.

The Analogie or Proportion is,

As the Sine of the Angle at E 38 degr. 15 min. is to the Side A B 30 degr.

So is the Sine of the Angle at A 23 degr. 30 min. to the Sine of the Side B E.

FIrst, draw the Quadrant A B C: then out of your Line of Chords take 38 degr. 15 min. the quantity of the Angle at E, and set it upon the Quadrant from B to F. Also take 30 degr. the quantity of the given Side A B, out of your Line of Chords, and set them upon the Quadrant from B to E, and draw the Lines F G and E H both of them parallel to A B.

[illustration] geometrical diagram

This done, take in your Compasses the distance A H, and

setting one foot of that extent in G, with the other describe the Arch L, and draw the Line A M so that it may onely touch the Arch L. Then setting one foot of the Compasses in I, with the other take the nearest distance to the Line A M: this di∣stance set from A to K, and draw the Line N K parallel to A B. So shall the distance B N, measured upon the Line of Chords, contain 18 degr. 47 min. the quantity of the enqui∣red Side B E.