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. VIII. The Difference of Longitude and Difference of Latitude being given, to find the Rhumb and the Distance run.

The Analogie or Proportion.

As the Difference of Latitude is to the Radius;

So is the Difference of Longitude to the Tangent of the Rhumb:

And

As the Sine of the Rhumb is to the Difference of Longitude;

So is the Radius to the Distance run.

So the Difference of Longitude being 5 ½ degr. and the Difference of Latitude 2 degr. the Rhumb will be found to be E. N. E. 2 degr. 31 min. Easterly, and the Distance upon the Rhumb 117 Leagues.

Ʋpon the Chart.

COUNT the Difference of Latitude from A to E, and draw the Line E F parallel to A D. Also count the Dif∣ference of Longitude from A to G, and upon the Point G raise the Perpendicular G F, cutting the Line E F in the Point F. Then take in your Compasses the length of the Line A F, and measuring it upon the Side of the Chart, you shall find it to contain 117 Leagues, the Distance that the Ship hath run. And if by your Line of Chords, or Quadrant, you find the Quantity of the Angle E A F, it will be the Rhumb, which you may find to be E. N. E. 2 degr. 31 min. Easterly, or 70 degr. 1 min.