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 IV. The Angle at 23 degr. 30 min. the Angle at B 122 degr. 36 m. and the Side A B 30 degr. given, to finde the Angle at E.

By the foregoing Cases in Rectangled Sphericall Triangles (if you let fall a Perpendicular from the Angle B upon the Side A E, as B C,) you may finde the Angle A B C 69 degr. 22 min. and the Angle C B E 53 degr. 14 min. which being obtained,

The Analogie or Proportion is,

As the Sine of the Angle A B C 69 degr. 22 min. is to the Sine of the Angle C B E 53 degr. 14 min.

So is the Co-sine of A 66 degr. 30 min. to the Co-sine of the Angle at E.

THE Angles being found and the Quadrant drawn, take 53 degr. 14 min. out of your Chord, and set them from B to E. Likewise take 69 degr. 22 min. and set them from B

to G. Also take 66 degr. 30 min. and set them from B to F; and draw the Lines G H, F I, and E K, all parallel to B A.

This done, take in your Compasses the distance between A and K, and setting one foot in H, with the other describe the Arch M, and draw the Line A N onely to touch the Arch. Again, setting one foot of the Compasses in I, with the other take the least distance to the Line A N, which distance set from A to L. Lastly, draw the Line L D parallel to B A, cutting the Quadrant in D. So shall the Arch B D, measu∣red upon your Chords, contain 51 degr. 45 min. the Com∣plement of the enquired Angle at E; or, D C shall give you 38 degr. 15 min. the Angle it self.