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. IX. There are three Ships, K, L, and M: the Ship K is distant from the Ship L 8 Leagues; the Ship at L is distant from that at M 6 62/100 Leagues; and the Ship at M is distant from that at K 3 77/100 Leagues; and they lie directly North and South.—I demand how the Ship at M bears to that at L, and how that at L bears to that at K.

DRAW a right Line, and out of your Scale take 8 Leagues, and set them thereon from K to L, for the Di∣stance of the Ships at K and L. Then take 3 77/100 Leagues, the Distance of the Ships K and M, out of your Scale; and setting one foot of the Compasses in K, with the other describe the obscure Arch of a Circle o o. Again, take 6 62/100 Leagues from your Scale, which is the Distance that the Ship L was from the Ship M; and setting one foot of the Compasses in L, with the other describe the obscure Arch of a Circle n n, crossing

the former Arch in the Point M. Then draw the Lines M K and M L; so have you their true Positions.

Now to find their Bearing one from another; forasmuch as the Ships M and K did lie North and South of each other, find the quantity of the Angle at M, which is 112 degr. 30 min. that is, eleven Points from the South Eastward, (or 3 Points from the East Northward,) either of which will be the N.E. by E. Point: and so doth the Ship M bear from that at K. And for the Bearing of that at K from that at L, finde the quantity of the Angle at L, which will be 22 degr. 30 min. or two Points; so two Points from the S. W. by W. Point Southward is S. W. by S. and so doth the Ship L bear to that at K.

[illustration] geometrical diagram

The Bearings of the Ships from each other may be found by the third Case of Oblique-angled plain Triangles, by the Analogie in that Case set down.