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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.
To divide an Oblique Circle, in the Plane of the Projection, into its proper Degrees.
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.
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.
First describe the
lure A EP 2; then cross it with the Horizon of
on a Line of
H to E,
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
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.
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
Set off each way
from the Cen-
6, on the pa- H
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.
To divide the Eclipiic according to the twelve Signs of the Zodiack. See the following Scheme.
and having drawn the Ecliptic Tarva:
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.