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.

II. A Sphericall Triangle being projected, to find the quantity of any Side thereof.

A Ruler laid upon the Pole of the Circle which is to be measured, and to the extreme ends of the Side of the Triangle; note where the Ruler, so laid, cuts the Me∣ridian at both ends of the Side: that distance, taken in your Compasses and measured upon the Line of Chords, will give you the quantity of the Side of the Triangle.

Example I.

LET it be required to find the Side E Z of the Triangle Z E P.—Lay a Ruler to ☉ (the Pole of the Circle Z E N) and the angular Point E, it will cut the Meridian in M; and a Ruler laid to Z will cut the Meridian in Z. So the distance M Z, taken in the Compasses and measured upon the Line of Chords, will be found to contain 78 degr. And such is the quantity of the Side Z E.

Example II.

LET it be required to find the Side ☉ B of the Sphericall Triangle A ☉ B.—Lay a Ruler upon X, the Pole of the Circle P B S, and the Point B, it will cut the Meridian Cir∣cle in ae.—Also lay a Ruler from X to ☉, it will cut the Meri∣dian in the Point ♌. The distance between ae and ♌, being taken and measured on the Line of Chords, will contain 20 d. And such is the quantity of the Side ☉ B.

I could instance in divers other Examples concerning the Mea∣suring of the Sides and Angles of Triangles upon the Projection; but I here omit them, because in the resolving of the following Propositions they will come in practice, and the Manner of the performance is there plainly expressed: onely I deemed it conve∣nient here to give some taste thereof, as a Preparative to that which followeth.—But before I come to shew the Manner of resolving of particular Questions in Astronomie, Geogra∣phy, &c. I will declare the Variety of Sphericall Problems that will naturally arise out of every Sphericall Triangle, being pro∣jected.