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 III. The Base A C 27 degr. 54 min. and the Angle at the Base A 23 d. 30 min. being given, to find the Angle at the Perpendicular B.

The Analogie or Proportion is,

As the Radius is to the Co-sine of A C 62 degr. 6 min.

So is the Sine of the Angle at A 23 degr. 30 min. to the Co∣sine of the Angle at B.

Take the Sum and Difference of the Co-sine of A C 62 d. 6 min. and of the Sine of the Angle at A 23 degr. 30 min.

	degr.	m.
The Sum is	85	36
The Difference is	38	36

BEing thus far prepared, and having drawn your Semicir∣cle B D C, out of your Line of Chords take 85 degr. 36 m. and set them upon your Semicircle from B to 2; also take the Difference 38 degr. 36 min. from your Chord, and set them from B to 3, and let fall the two Perpendiculars, 3 4, and 2 M. Then divide the distance between M and 4 into two

equal parts in the Point 5, and taking the distance M 5 in your Compasses, set it upon the Line A D, from A to 6. Lastly, draw the Line 6 7. parallel to B A; so shall D 7 being mea∣sured upon your Line of Chords contain 69 degr. 22 min. the quantity of the Angle at B required.

These three Cases are all (in Sines alone) that have the Ra∣dius in the first place of the Analogie or Proportion, and so con∣sequently all that can be wrought by this Artifice: wherefore those which follow must be resolved by other means.