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. IX. The Latitude of the Place, and the Declination of the Sun, being given, to find what Altitude the Sun shall have at Six of the Clock.

FOR finding of the Triangles upon the Projection, which will resolve this and the following Propositions, you must suppose another Azimuth Circle to be drawn in the Projecti∣on from Z to N, and through that Point where the Parallel of Declination ♊ ☉ ♌, and the Axis of the World, or Hour-Cir∣cle of Six, P A S, do cross each other. The drawing of which Azimuth Circle I purposely omitted, chiefly because the Scheme in that place is more cumbred with Lines and Letters then any other part thereof: But you may well enough, for the solving of these two Propositions, imagine it to be drawn, the Pole whereof is at *. This Azimuth Circle being suppo∣sed to be drawn, you have upon the Projection two Triangles like-angled, which will perform the Work of resolving this Proposition. In one of which you have given the Base, which is the Complement of the Declination, and the Perpendicular, which is the Complement of the Latitude, to find the Hypo∣tenuse, which is the Complement of the Sun's Altitude requi∣red. This Triangle may be resolved by the first Case afore∣going.—In the other Triangle there will be given the

Hypotenuse, which is the Sun's Declination, and the Angle at the Base, which is the Latitude, to find the Perpendicular, which is the Sun's Altitude at Six a Clock: To find which this is

The Analogie or Proportion.

As the Radius 90 degr. is to the Sine of the Sun's Declinati∣on 20 degr.

So is the Sine of the Latitude 51 degr. 30 min. to the Sine of the Sun's Altitude at Six 15 degr. 30 min.

To resolve the Proposition by the Projection,

Lay a Ruler upon the Point *, and that Point where the Parallel of Declination ♊ ☉ ♌ crosseth the Axis or Hour of Six; the Ruler thus laid will cut the Meridian Circle in the Point g. So O g, being measured upon the Chords, will give you 15 degr. 30 min. And such Altitude will the Sun have at the Hour of Six in the Latitude of 51 degr. 30 min. when he hath 20 degr. of Declination.