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. III. There are two Ports at A and B which are distant 6 ⅖ Leagues, and lie directly North and South of each other; from whence two Ships set sail, both for the Port C: the Ship at B sails away upon a South-W. by South Point; and the Ship at A sails directly West.—I demand how many Leagues either of the Ships had sailed when they met at the Port C, and also how the Port C did bear from that at B.

[illustration] geometrical diagram

DRAW a right Line A B, and upon it set off 32 Cen∣tesms, or 6 ⅖ Leagues. Now because the Ship at B steered a S. W. by S. Course, which is three Points from the South-Westerly, therefore upon the Point B protract an An∣gle of 33 degr. 45 min. and draw the Line B C.—Then, because the Ship at A steered a Westerly Course, which is a Quarter from the North, upon the Point A protract an Angle

of 90 degr. and draw the Line A C, cutting the former Line B C in C.—Now to know how many Leagues each Ship sailed, take in your Compasses the length of the Line B C, and measuring it upon your Scale, you shall find it to contain eight Leagues; and so many did the Ship that came from B sail. Also take the length of the Line A C in your Compasses, and measuring that upon your Scale, it will be found to contain 24 Centesm. or 4 ⅘ Leagues; and so much did the Ship that came from A sail. Now to know how the Port at C did bear from that at B, find the quantity of the Angle at C, which you shall find to be 56 degr. 15 min. that is, five Points from the East Northerly, namely, N. E. by N. and so did the Port C bear from B.

The finding of the Distance that each Ship sailed may be done by the third Case of Right-angled plain Triangles by this Analogie.

As the Distance of the two Ports A and B is to the bearing of the Port C from B;

So is the Sine of the Rhumb that the Ship sailed upon from B to C to the Distance that the Ship sailed from A to C;

And so is the Radius to the number of Leagues that the Ship sailed from B to C.