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Pražlice.

A

Let the Right Circle

projected be AB, and let it be required

to lay off the Quantity of 20 Degrees

therein EGL, on the Central Point E, describe

the Circle ACBD; Then from the Line of

Chords set off 20

Degrees from C to F, Let fall the Pependicular FG: Then shall the Part EG be the Representation of 20 Degrees, by Theorem 7. as required. Q. 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 please.

PROBLEM III.

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

Pratice

Pradlice.

Let the given Oblique

Circle be IC HD,

and let it be required K

to lay off an Arch ot 20 Degrees there

on GH: On the Center E, describe the primitive

Circle ACBD; From the Line of

Chords set off 20 Degrees from B to F; Draw

the Line FK parallel to BE, 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 case 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.

PraEtice.

Practice.

First describe the

Solftitial CO

lure A EP 2; then cross it with the Horizon of

London HO;
Set off 389 30,

on a Line of
Chords, from

H to E,
and draw the E-

quinoctial Line

R

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Set off 23° 30' from E to C, and draw the Ecliptic CL: At right Angles to the Horizon HO, draw the Azimuth of East and West Z N: At right Angles to the Equator E Q draw the Equinoctial Colure or Axis of the World

A P.

Parallel to the Equinoctial EQ: 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 Ato 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 describe the Hour Circles, Azimuths, Circles of Position, &c. which are all Oblique to the Plane of the Projection.

Practice. On the Equato

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:-ÆR,

B.

Set off each way

from the Cen-
ter T,
the Hour from

6, on the pa- H
rallel Sines, to
4, B ;

E
Then on the
Lines AB,

PO,
as the Conjugate

Ni and Tranf

verse Diameters, describe an Ellipfis P A QB, as taught in Prob. I. Then shall this Ellipsis be the Hour Circle described : In the fame manner are described the Azimuth Z CND, and the Circle of Position HFO E. And thus may any of those 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 Sínes is into 10°, 20°, 30°;

&c. from the Center towards the Primitive, as taught in Prob. 2. Also any of those Ellipses may be divided into their proper Degrees, by Prob. 3.

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PRO

PROBLEM VI.

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

Praslice.
Fit the Sector to the Primitive Circle, P EQR;

and having drawn the Ecliptic Tarva:
Set off from the Center Aries and Libra, rn,
the Sine of 30° to Taurus and Virgo above, o 18
and to Pisces and Scorpio below, *m:
Also the Sine of 60° to Gemini and Leo, Il,
and to Aquarius and Sagittarius, ma :
Lastly, the Sine of 90°, or Radius, will reach to
Cancer and Capricorn, oo Vs :
And thus is the Ecliptic divided as required.
2. E, F.

PROBLEM VII.

To annex the Calendar to the Orthographical Projestion, or Analemma. Sce the following Scheme.

Pralice. 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 set off those Degrees and Minutes at each End, and on each Side the

viz. from E to go and K, and from R to T and we respectively ; and let the Weeks be divided into Days; and thus if your Projection be difficiently large enough, you may have a very exact perpetual Almanack in this Analemma. The Manner and Figure

of which you have here exhibited in small. VOL. II.

E

Equator,

PRO

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