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 VIII. The Base A C 27 degr. 54 min. and the Hypotenuse A B 30 degr. being given, to finde the Perpendicular B C.

The Analogie or Proportion is,

As the Co-sine of the Base A C 62 degr. 6 min. is to the Radius, So is the Co-sine of the Hypotenuse 60 degr. to the Co-sine of the Perpendicular B C.

HAving drawn your Quadrant A B C, take out of your Line of Chords 62 degr. 6 min. the Co-sine of the Base A C, and set them from B to S. Also take from the Chords 60 degr. the Co-sine of the Hypotenuse, and set them from B to m: and draw the Lines S T and m n both parallel to B A. Then taking the distance A T in your Compasses, set one foot in C, and with the other describe the Arch V, and draw the Line A W so that it may onely touch the Arch V. Then taking A n in your Compasses, move one foot thereof gently along the Line C A, till the other, being tur∣ned about, doth onely touch the Line A W; and where the Point resteth upon the Line C A, which you will finde to be at c, there make a mark, and draw the Line c a paral∣lel to B A. Lastly, take the distance from B to a; and mea∣sure it upon your Line of Chords, where you shall finde it to contain 78 degr. 30 min. the Complement of the Perpendi∣cular; or, C A measured upon the Chord will give you 11 d. 30 min. the Perpendicular it self.

These Five last are all the Cases in a Right-angled Spheri∣call Triangle that are resolvable by Sines alone. Those which follow are to be resolved by Sines and Tangents joyntly, and so will require another manner of Operation then the former.