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. XII. The Latitude of two Places, and the Difference of Longi∣tude between them, being known, to find what Rhumb leadeth from one to the other, and how many Leagues distant they are asunder.

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 of the two Places.

[illustration] geometrical diagram

The Plaine See Chart.

page 172.

So the Latitude of one of the Places being 50 degr. and the other 52 degr. 30 min. and the Difference of Longitude 6 ½ degrees; the Rhumb will be found to be 67 degr. 23 min. and the Distance upon the Rhumb 6 ½ degr. or 120 Leagues.

Ʋpon the Chart.

UPON the Point of the greater Latitude at N 52 deg. 30 min. draw a Line N M, parallel to A D, upon which Line set 6 degr. the Difference of Longitude of the two Places (being taken from the bottom of the Chart) from N to M. Then from the Point M draw the Line to E, the lesser Latitude, 52 degr. which Line, taken in the Compasses and measured upon the Side of the Chart, will be found to contain 6 ½ degr. or 130 Leagues. Also the Angle N E M, being measured by your Chord, or Protracting Quadrant, will be found to contain 67 degr. 23 min. which is the Rhumb leading from one to the other, namely, short of the E. N. E. Point 7 degr. or, N. E. by E. 11 degr. 8 min. Easterly.