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 XV. The Base A C 27 degr. 54 min. and the Hypotenuse A B 30 degr. being given, to finde the Angle at the Base A.

The Analogie or Proportion is,

As the Tangent of the Hypotenuse A B 30 degr. is to the Tan∣gent of the Base A C 27 degr. 54 min.

So is the Radius to the Co-sine of the Angle at A.

THE Quadrants being drawn, out of your Line of Chords take 30 degr. the quantity of the Hypotenuse given, and set them upon the Quadrant from C to X. Also take 27 degr. 54 min. the quantity of the given Base, from the Line of Chords, and set them upon the same Quadrant from C to V, and draw the Lines A X and A V, prolonging them to T and S.

This done, take in your Compasses the distance between C and T, and setting one foot in D, with the other describe the Arch Z, and draw the Line C Y onely to touch it. Then take in your Compasses the distance C S, and placing one foot upon the Line C D, move it gently along, till the other, being turned about, do onely touch the Line C Y; and where the Point rest∣eth upon the Line C D make a mark, which will be at*. Then take the distance C*, and set it from A to P, and draw the Line P O parallel to C D. So shall B O, being measured up∣on the Line of Chords, give you 66 degr. 30 min. the Com∣plement of the Angle at A, which was required; or, the distance O C upon the Chord shall give you 23 degr. 30 min. the Angle it self.