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be the Representation of 20 Degrees, by Theorem 7. as required. 2, E. F.

By the Sector, thus ;

Set the Sector to the Semidiameter EB;

Then lay off 20 Degrees on the Sines of Sines from E to G:

Thus you have the Part required EG,

by the fame Theorem 7. as before. 2. E. F And thus may any right Circle be divided into any Number of Degrees you pleafe.

PROBLEM III.

To divide an Oblique Circle, in the Plane of the Projection, into its proper Degrees.

Practice

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cutting the Oblique Circle in G ;

Then the Part GH

will be made 20° in the Oblique Circle, as required. 2. E. F.

PROBLEM IV.

To project, on the Plane of the Solftitial Colure, (which in this Cafe is the Plane of the Projection,) the great Circles of the Sphere, which stand at right Angles thereto, and are projected into right Lines; (by Theorem 6.) as the Horizon, the Equinoctial, the Ecliptic, the Equinoctial Colure, the Azimuth of Eaft and Weft; also the small right Circles.

Practice.

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Set off 23° 30' from E to C, and draw the Ecliptic C L:

At right Angles to the Horizon HO, draw the Azimuth of Eaft and Weft Z N:

At right Angles to the Equator E 2,

draw the Equinoctial Colure or Axis of the World A P.

Parallel to the Equinoctial E 2

draw the Tropic of Cancer above C R,

and the Tropic of Capricorn below TL;

Set 23° 30' off from P to F, G; and A to B, D : Then draw the Arctic Circle FG,

and the Antarctic Circle BD:

Parallel to the Horizon HO,

draw the Almacantars, or Parallels of Altitude ab, cd.

Thus all the great and small Circles at right Angles to the Plane of the Projection are to be drawn by the Sector, or Scale of Chords.

PRO

PROBLEM V.

To defcribe the Hour Circles, Azimuths, Circles of Pofition, &c. which are all Oblique to the Plane of the Projection.

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verfe Diameters, defcribe an Ellipfis PA QB, as taught in Prob. 1. Then fhall this Ellipfis be the Hour Circle defcribed: In the fame manner are defcribed the Azimuth Z C ND, and the Circle of Pofition HFOE. And thus may any of thofe Circles be drawn through every 10 Degrees, if the Equator ÆR, the Prime Vertical Z N, and the Horizon HO, be graduated as the Line of Sines is into 10°, 20°, 30°, &c. from the Center towards the Primitive, as taught in Prcb. 2. Alfo any of thofe Ellipfes may be divided into their proper Degrees, by Prob. 3.

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PROBLEM VI.

To divide the Ecliptic according to the twelve Signs of the Zodiack. See the following Scheme.

Practice.

Fit the Sector to the Primitive Circle, P EQR; and having drawn the Ecliptic v w :

Set off from the Center Aries and Libra, ✅ ✅, the Sine of 30° to Taurus and Virgo above, R, and to Pifces and Scorpio below, m:

Alfo the Sine of 60° to Gemini and Leo, &,
and to Aquarius and Sagittarius, ~:

Laftly, the Sine of 90°, or Radius, will reach to
Cancer and Capricorn, vs:

And thus is the Ecliptic divided as required.
Q2. E. F.

PROBLEM VII.

To annex the Calendar to the Orthographical Projection, or Analemma. See the following Scheme.

Practice.

Let the Sun's Declination be found, for the beginning of every Month and Week, in its proper Degrees and Minutes; and from a Line of Chords fet off thofe Degrees and Minutes at each End, and on each Side the Equator, viz. from E to and K, and from R to T and refpectively; and let the Weeks be divided into Days; and thus if your Projection be fufficiently large enough, you may have a very exact perpetual Almanack in this Analemma. The Manner and Fi

gure of which you have here exhibited in small.

VOL. II.

E

PRO

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