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PROBLEM VIII.

To draw a great Circle perpendicular to another gi

ven great Circle.

Practice.

In this Problem are four Cafes. Cafe 1. To draw a Circle at Right Angles to the Primi

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tive Thro' the Pole (or Center) C, draw any Right Circle EF; and it is done as required.

Cafe 2 To draw a Circle perpendicular to a Right Cir

E

H

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cle

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Through the Poles

A, B,

F

draw the Diameter

AB;

and it is the Circle required.

Cafe 3. To draw an Oblique Circle perpendicular

to a Right Circle, as

EF

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defcribe a Circle thro' the three Points H, P. I, and that is the Oblique Circle required.

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Note, If the Point of Interfection, e, be limited, then draw a Circle through e and a, by Prob. 4.

VOL. II.

H 2

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and from its fartheft Pole by

OH = 130°,

130°;

65° ;)

QRST

with the Half-Tangent of

(that is, with the Tangent of

defcribe the Prick'd Circle

divide this Circle into any Number of equal Parts,

in

and laying a Ruler from

to the Points

a, b, c, &c.

P

T, a, b, c,

it will interfect the Oblique Circle in the Points o, p, q,r: then will the Arches op Ta, pq ab, qr = bc, &c. And thus may the whole Oblique Circle IK L M be graduated as required.

CHAP

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CHAP. VI.

Of the Stereographic Projection of the Sphere on the Plane of the General Meridian, of the Horizon of the Ecliptic of the Equinoctial of 4 Small Circle, of an Oblique Circle.

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1. To project the Sphere on the Plane of the General Meridian.

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N the Center E, defcribe the Primitive Circle ABCD, reprefenting the General Brafs Meridian; and crofs it with two Diameters AC, and BD; the firft of which, viz. AC, reprefents the Equator; which, because it is at Right Angles with the Meridian, is projected into a Right Line. The other Diameter, BD, is the Axis of the Sphere, and its Extremities B, D, the Poles thereof, North and South.

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2. If the Primitive Circle be made to represent the Solftitial Colure, then B ED shall reprefent the Equinoctial Colure; and the Right Line Evy is the Projection of the Ecliptic; which is thus divided; Take the Half-Tangent of 30° (or one Sign) and fet it both ways from the Center E, and it will cut the Northern Signs & and ; and the Southern Signs and m Thus the Half-Tangent of 60°, fhews the Signs and ; and and; and thus may each

Sign be alfo divided into its proper Degrees; the Points of Cancer S, and Capricorn w, being 90° diftant from and in the Equinoctial Colure, are projected into the Primitive, 23° 30′ above A, and below C.

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3. The Hour Circles, or Intermediate Meridians, as B 15 D, B 30 D, &c. are all drawn by Problem 8, Cafe 3, and Theorem 7; That is, by fetting the Half-Tangents of 15° 30°, 45°, &c. both ways from the Center on the Equinoctial, which gives the Points of Interfection therewith, and the Secant Complement fet from thofe Points of Interfection (or the Tangent Complement fet from the Center E) upon the Equinoctial, extended when there is occafion, will find the Centers, on which thefe Circles are described, paffing thro' the Interfection and the two Poles B, D,

4. The Parallels of Latitude, (among which the dotted Lines denote the Tropics and Polar Circles, on each fide the Equator,) are all drawn by Pro, blem 7, Cafe 2, and Theorem 8; That is, by cutting off the Half-Tangents of 10°, 20°, 30°, &c. from E the Center, towards either Pole B, and D; and thus you will have the Interfection; the Secant's Complement fet from the Center E on the Diameter BD extended, (or the Tangent's Complement fet from the Interfections ) will find the Centers of those Parallels, on which they are to be described.

5. This Projection may be made for any Latitude, and then the Prime Vertical, aud Azimuth Circles; as alfo the Horzfon of the Place, with the

Çircles

The Projection of the Sphere on the Plane of the general Meridian

30 40 50 60 70 80 B 80 70 60 50 40 30

10 20

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20 10

&

60

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45 30 15

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40
30

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210

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310

410

60

15 30 45 60

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Circles of Pofition; alfo the Circles of Longitude, and Latitude for the Stars; but they would entirely perplex the Scheme, and confound the Eye; and therefore are omitted; they being drawn in the fame Manner as thofe above described.

6. By this Projection all the Parts of the Globe may be laid down, and thus a general Map of the whole World is constructed; but because the projected

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