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.

PROBL. VI. The Distance that the Ship hath run, and the Difference of Latitude, given, to find the Rhumb and Difference of Longitude.

The Analogie or Proportion.

As the Distance run is to the Radius;

So is the Difference of Latitude to the Co-sine of the Rhumb:

And

So is the Sine of the Rhumb to the Difference of Longitude.

So the distance run being 117 Leagues, and the Difference of Latitude being 2 degr. the Rhumb will be found to be E. N. E. 2 degr. 31 min. Easterly, and the Difference of Lon∣gitude 5 ½ degrees.

Ʋpon the Chart.

SET the Difference of Latitude 2 degr. upon your Chart from A to E, and draw the Line E F parallel to A B. Then out of the Side of your Chart take the Distance run, 117 Leagues; and setting one foot of the Compasses in A, turn the other about till it cross the Line E F, which it will doe in F. Then F E, being measured upon the bottome of your Chart, will contain 5 ½ degr. the Difference of Longitude. And by your Line of Chords or Protracting Quadrant find the Quantity of the Angle E A F, which will be 70 degr. 1 min. the E. N. E. Point 2 degr. 31 min. Easterly.