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.

QUEST. VIII. Two Ships set sail from the Port at K; the one sails 3 77/100 Leagues upon the S. W. Point towards M, the other sails 8 Leagues upon the West Point towards L.—I demand how many Leagues the Ships at M and L are asunder, and also how the Ship at M bears from the Port K, and the other Ship at L.

DRAW a right Line K L, and by help of your Scale set off upon it 8 Leagues, the Distance that the Ship sailed from K to L upon the West-Point. Then because the other Ship sailed 3 77/100 Leagues from K towards M upon the S. W. Point, which is 45 degr. or 4. Points from the West, therefore upon the Point K protract an Angle of 45 degr. and draw the Line K M, setting off upon it from K to M 3 77/100 Leagues, the Distance that the Ship sailed from K to M, and draw the Line M L.

[illustration] geometrical diagram

Now to know, First, how far distant the Ships at M and L are from each other, take in your Compasses the length of the Line M L, which applie to your Scale, and you shall find it to contain 6 62/100 Leagues.—And, Secondly, to find how the Ship at M bears from the Port K and the other Ship at L, you must find the quantity of the Angle at M, which you will find to be 112 degr. 30 min. that is, eleven Points. Now because the Course from K to M was S. W. therefore the Ship at M bears from the Port K N. E. And seeing that the Angle at M is 112 degr. 30 min. or eleven Points; therefore eleven Points counted from the N. E. Point is the Bearing of the Ship at M from that at L, which is W. N. W.

The Distance of the Ships M and L may be found by tho fifth Case of Oblique-angled plain Triangles; and the Bear∣ings by the second Case.