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.

PROP. XV. The Hour from Noon, the Latitude of the Place, and the Altitude of the Sun, being given, to find the An∣gle of the Sun's Position.

IN the Oblique-angled Sphericall Triangle Z P E you have given the Side Z P, the Latitude, Z E, the Complement of the Sun's Altitude, and Z P E, the Hour from Noon, to find the Angle Z E P, which is the Angle of the Sun's Position at the time of the Question: So in the Triangle Z P E you have two Sides, with an Angle opposite to one of them, given, to find the Angle opposite to the other Side, which you may find by the 2. Case of Oblique-angled Sphericall Triangles: For which this is

The Analogie or Proportion.

As the Co-sine of the Sun's Altitude 78 degr. is to the Sine of the Hour from Noon 35 degr. 36 min.

So is the Co-sine of the Latitude 38 degr. 30 min. to the Sine of the Angle of the Sun's Position at the time of the Que∣stion 21 degr. 45 min.

By the Projection.

This is the most troublesome Proposition that we have yet

met withall to be resolved by the Projection; and yet it is also thereby easily resolved in this manner.

Take in your Compasses 90 degr. of your Chords; then lay a Ruler upon Y, (the Pole of the Hour-Circle P E S,) and the angular Point E; it being so laid will cut the Meridian Circle in v. Then set 90 degr. of your Line of Chords from v to x upon the Meridian Circle, and the Ruler laid from Y to x will cut the Hour-Circle P E S in the Point y.

Again, lay a Ruler to ☉, (the Pole of the Azimuth Circle Z E N,) and to the angular Point E; it being so laid will cut the Meridian Circle in the Point M. Set 90 degr. from M to z upon the Meridian Circle, and lay a Ruler upon ☉ and z; it will cut the Azimuth Circle (it being continued without the Meridian Circle) in the Point δ.

Lastly, Lay a Ruler to the angular Point E, and this Point δ, it will cut the Meridian Circle in λ; also lay a Ruler from E to y, it will cut the Meridian in λ. The distance θ λ, being taken in the Compasses and measured upon your Line of Chords, will contain 21 degr. 45 min. and that is the quanti∣ty of the enquired Angle Z E P, which is the Angle of the Sun's Position at the time of the Question.