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. X. The Longitude and Latitude of the Place from whence you came, with the Rhumb and Distance sailed, be∣ing given, to find the Longitude and Latitude of the Place to which you are come.

The Analogie or Proportion.

As the Radius is to the Distance run;

So is the Sine of the Rhumb from the Meridian to the Diffe∣rence of Longitude:

And

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

So the Latitude of the Place from whence you came being 52 degr. and the Longitude 35 degr. the Rhumb upon which you have sailed N. E. by N. 33 degr. 45 min. and the Distance which you have sailed upon that Rhumb 96 2/10 Leagues; you shall find the Difference of Longitude to be 2 degr. 40 min. and the Difference of Latitude 4 degr. So that the Place to which you are come is in the Latitude of 56 degr. and in the Longitude of 37 degr. 40 min.

Ʋpon the Chart.

THE Place from whence you came being in the Latitude of 52 degr. and in the Longitude of 35 degr. is repre∣sented by H. The Rhumb you have sailed upon being N. E. by N. 33 degr. 45 min. upon the Point H protract an Angle of 33 degr. 45 min. and draw the Line H K for the Rhumb. Then out of the Side of your Chart take 96 2/10 Leagues, which is so much as the Ship sailed, and set that upon the Rhumb-Line from H to K, and through the Point K draw the Line K L

parallel to B C, (or perpendicular to A B,) and it will cut the Line A B in L. So K L, being measured on the bottom of your Chart, will be found to contain 2 degr. 40 min. the Dif∣ference of Longitude; which added to 35 degr. the Longitude you came from, gives 37 degr. 40 min. for the Latitude you are in. Also the Line H L, being measured on the Side of your Chart, will be found to contain 4 degr. And such is the Difference of Latitude, which added to 52 degr. the Latitude from whence you came, gives 56 degr. the Latitude in which you are.