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.

X. Of the CIRCLES or PARALLELS of ALTITƲDE.

THE Circles of Altitude are likewise small Circles of the Sphere, and are drawn parallel to the Horizon, as the Circles of Declination were to the Aequinoctial. These Paral∣lels are drawn from the Horizon towards the Zenith Point, and upon occasion, in many Cases, quite up unto it. By these Parallels are measured the Altitude or Height of the Sun, Moon and Stars. In the Scheme there is onely one of them, and that is expressed by the Letters M E L.

Thus have I given you a brief and plain Description of the Circles, both great and small, which we shall have occasion to use in this following Treatise. And here note, that every Circle of the Sphere (both great and small) hath his proper Poles, which Poles (of all the great Circles) are 90 Degrees, or a Quadrant of a Circle, distant from the Circle it self. The Poles of the Circles in this Projection are as followeth.

• Z and N Are the Poles of H A O, the Horizon.
• P and S Are the Poles of AE A ae, the Aequinoctial.
• O and H Are the Poles of Z A N, the Prime Verticall.
• Q and R Are the Poles of the Ecliptick.
• AE and ae Are the Poles of P A S, the Axis of the World.

The Poles of these five Circles are all in the Meridian, and so there needeth no farther Precept for the finding of them; and the Pole of the Meridian is the Centre thereof.

But for the three Azimuth Circles, they fall in several Points of the Horizon; and the three Hour-Circles in certain Points in the Aequinoctial. How to finde which Points shall be shewed af∣terwards in due place.

• A Is the Pole of the Meridian, Z H N O.
• T Is the Pole of the Azimuth Circle, Z F N.
• G Is the Pole of the Azimuth Circle,Z ☉ N.
• ☉ Is the Pole of the Azimuth Circle,Z G N.
• X Is the Pole of the Hour-Circle P B S.
• Y Is the Pole of the Hour-Circle P D S.
• V Is the Pole of the Hour-Circle P C S.

The Poles of the World P and S are also the Poles of the Tro∣picks and of all the Parallels of Declination. And

The Zenith and Nadir, Z and N, are the Poles of all the Par∣allels of Altitude.

Having sufficiently acquainted the Reader with the several Circles, Lines, Points and Poles, belonging to every Circle, I will now proceed to my intended purpose; namely, to project (or lay down in Plano) all these Circles, Lines, Points and Poles, in their true Positions.