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 Base A C 27 degr. 54 min. and the Perpendicular C B 11 degr. 30 min. being given, to finde the Hypotenuse A B.

The Analogie or Proportion is,

As the Radius is to the Co-sine of B C 78 degr. 30 min.

So is the Co-sine of A C 62 degr. 6 min. to the Co-sine of A B.

First, take the Sum and the Difference of the second and third Terms in the Analogie or Proportion; namely, the Sum and Difference of the Complements of the Perpendicular B C 11 degr. 30 min. and the Base A C 27 degr. 34 min.

	degr.	m.
The Base A C is	27	54.	its Comp.	62	06
The Perpendicular B C is	11	30.	its Comp.	78	30
			Sum	140	36
			Differ.	16	24

HAving found this Sum and Difference, draw a right Line B A C; then take 60 degr. out of your Line of Chords, and setting one foot of the Compasses in A, with the other describe the Semicircle B D C, and upon the Centre A erect the Perpendicular A D. This done, take 16 degr. 24 min. (the Difference) out of your Line of Chords, and set them from B to e; also take the Sum 140 degr. 36 min. (or rather 39 degr. 24 min. the Complement thereof to 180 degr.) and set them from C to g, and from the Points e and g let fall the two Perpendiculars e f and g h: then divide the space be∣tween f and h into two equal parts in M, and set the distance

[illustration] geometrical diagram

M h or M f from A to k, and draw the Line k l parallel to A B, cutting the Semicircle in l: so shall D l be the quantity of the Hypotenuse A B, which if you measure upon your Line of Chords, you will finde to contain 30 degr.