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IX. A Great Circle of the Sphere, is that whose Plane paffeth through the Center thereof, and whose Center is the same with that of the Sphere ; it also divideth the Globe or Sphere into two equal Parts ; as Pe Oq, Fig. 3.

X. The Pole of any Great Circle of the Sphere is, that Point in its Surface which is every Way equally distant from the Circumference of the Circle ; or it is that Point which is 90 Degrees above the Plane thereof ; fo P is the Pole of the Right Circle RH. Fig. 3.

XI. A Primitive Circle is that described on the Plane of the Projection, and within which the Projection is finished, as RPHE.

XII. A Right Circle is that whose Plane stands at Right Angles with the Plane of the Projection, and. passeth thro' the Eye, in the Stereog. Projection ; and is always a Diameter of the Primitive ; such are RH, PE, AQ

XIII. An Oblique Circle is that whose Plane inclines to the Plane of the Projection ; or maketh Oblique Angles therewith ; as the Oblique Circle PBE.

XIV. Parallel Circles are those Lesler Circles of the Sphere, whose Planes are parallel to the Planes of any Great Circles thereof; thus OVS is a small Circle

parallel to the Great Circle R H.

XV. A Spherical Angle is that which is contained under or between the Arches of two Great Circles of the Sphere interfecting each other ; and this is the fame, or equal to, the Inclination of the Planes of these two Great Circles ; such is the Angle APV, or VCB.

XVI. A Spherical Triangle is a Figure comprehended under the Arches of three Great Circles of the Sphere ; such is CBV, or V AP.

XVII. The Measure of a Spherical Angle, is the Arch of a Great Circle intercepted between the two Sides thereof, continued out till they be Quadrants, or : YOL. II.

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90 Degrees distant from the Angular Point; thus B H is the Measure of the Angle at P'; and AH of the Angle at C.

XVIII. The Five Circular Parts of a Spherical Tri- . angle APV, are 1. the Base AV. 2. The Perpendicular AP. 3. The Complement of the Hypothenuse VP, (viz. the Arch:V B.) 4. The Complement of the Angle at the Bafe V. 5. The Complement of the Angle at the perpendicular P ; (vizi' the Arch CB.): These are so named from the Lord Neper, à Scotch , Peer, who hath invented a New Method of folving Triangles thereby ; and is the third of the Ten Methods in the following Treatise.

XIX. The Middle Part is one of those five circular Parts, being the Middlemost of the three that are taken for the Solution of a Spherical Triangle ; thus if the three Parts assumed were AV, Complement of V, and Complement of VP; then 'cis plain the Middle Part is the Complement of V.

XX. The Extreme Parts Conjun&t or Adjacent, are those two Parts of the Five which are immediately next to the Middle Part ; thus if the Middle Part be the Complement of the Angle V, the Extremes Conjunct or Adjacent thereto, are AV, and the Complement of PV.

XXI. The Extreme Parts DisjunEt, are those two Parts of the Five which lie remote from the Middle Part, being disjoined therefrom by the Extreme Conjunct ; thus the Complement of V being the Middle Part, the Extremes Disjunct will be the Complement of the Angle P, and the Side AP. See all this made easy in Chap. 11. and the Scheine therein.

XXII. Planisphere is a Projection of the Sphere on a plain Surface ; and is only a general Name for the Orthographic and Stereographic Projections aforegoing.

XXIII. The

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XXII. The Nearest Distance on the Surface of the Globe or Sphere between any two: Plaçes, is the Arch of a Great Circle passing thro’ both.

XXIV. The Poles of the Globe or Sphere, are the two Points of the Surface which make the Extremi.. ties of its Axis ; each of which is go Degrees Distance from the Middle Circumference ; thus P and O are the Poles of the Sphere, Fig. 2.

XXV. The Meridians are Great Circles of the Sphere passing thro' the Poles of the World ; which may be conceived infinite in Number ; but are generally drawn at' 10 Degrees Distance: on Artificial Globes such are the Primitive ÆNQs, and the Oblique Circle SAN; for they pass thro', and intersect each other in the Poles N and S. See Fig. 4

XXVI. The Equinoctial or Equator, is a Great Circle , every way equally distant ( viz. 90 Degrees) from either Pole: Nors, and therefore divides the Globe or Sphere into two Halfs or Hemispheres ; as the Great ) Circle Æ CÆ.

XXVII. The Ecliptic is a Great Circle intersecting the Equinoctial in the two opposite Points V and and maketh an Angle therewith (call'd its Obliquity). of 23° 29! equal to the Meridional Arch Æ S; and is the Circle SP VS.

- XXVIII. The Zodiac is an imaginary broad Circle (like a Zone or Girdle ) in the Heavens extending to 9° 15' on each Side the Ecliptick, (which is in the Middle thereof,) that Space being equal to the Latitude or Deviation of any of the Planets ; in this Circle also are contained all the twelve Signs or Constellations, thro’ which the Sun passeth once a Year in the Ecliptic.

XXIX. The Twelve Signs of the Zodiac, are those twelve constellated Animals, whose Names and Characters follow. 1. Aries, the Ram, r. 2. Taurus, the Bull, 8. 3. Gemini, the Twins, I. 4. Can

cer,

cer, the Crab, 5. 5. Leo, the Lion, 2. 6. Virgo, the Virgin, 11. 7. Libra, the Ballance, . 8. Scorpio, the Scorpion, m. 9. Sagittarius, the Ar. cher, 10. Capricornus, the Goat, vg. 11. Aquarius, the Waterer, at 12. Pisces, the Fishes, *. To each of these is allotted the Portion of 30 Degrees in the Ecliptic. The Six first are called the Southern, the Six latter the Northern Signs ; and when the Sun is in the latter, 'tis Summer ; and when in the former, 'tis Winter.

XXX. The Horizon is the Circle bounding Sight or Vision ; but mathematically speaking, 'tis a Great Circle every way distant from your Eye 90 Degrees ; suppose therefore your Eye at 2, your Horizon would be HCO; this is called the Rational, the other the Sensible Horizon.

XXXI. The Colüres are two Meridians dividing the Equinoctial and Ecliptic into four Equal Parts. One of which passeth thro' the Points Aries in and · Libra –, and is called the Equinoctial Colure, as NCS; the other, called the Solfticial Colure, passeth thro' the Points Cancer go and Capricorn vs, as NO Sv.

XXXII. The Equinoctial Points, or Equinoxes, are the two Points Aries r, and Libra ; in which Points the Ecliptic crosfeth the Equinoctial, at which Time the Days and Nights are equal all over the World.

XXXIII. The Solftitial Points, or Solstices, are the first Scruples of Cancer So, and Capricorn vs ; becaufe) in and near them (Solis Statio) the Sun feemeth not to move for some Days together.

XXXIV. The Zenith and Nadir are two Points Dia-, metrically opposite to each other. The Zenith is the Point which is Vertical to us in the Heavens, or just over our Heads as Z ;' and the Nadir is opposite

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thereto, under our Feet, as X. And these two Points are the Poles of the Horizon HO.

XXXV. Azimuths or Vertical Circles are Great Circles of the Sphere concurring and intersecting each other in the Zenith and Nadir , as ZDX; and that which passeth thro' the East and West Points of the Horizon, as Z C X, is called the Prime Vertical, or Azimuth of East and West.

XXXVI. Circles of Position, are Great Circles of the Sphere which all meet and intersect one another in the Points of Intersection of the Meridian with the Horizon ; such is HBO.

XXXVII. The Tropics are two small Circles parallel to the Equinoctial, and distant (on each Side) therefrom 23° 29' ; they are the Limits of the Sun's greatest Declination from the Equinoctial. The Northern Tropic passeth by the beginning of Cancer , and therefore called the Tropic of Cancer, and is the Parallel of the Longest Day; as R. For the same Reason the other is called the Tropic of Capricorn ; and is the Parallel of the Shortest Day (in Northern Climes ) as I vo.

XXXVIII. The Aretic and AntarEtic Circles are other small Circles, and Parallel to the Equinoctial ; and distant from it 66° 31'; or from either Pole 23° 29'. That towards the North Pole is E FG; the other towards the South TWV. These are commonly called the Polar Circles also.

XXXIX. The Almacanthars, or Parallels of Altitude, are small Circles parallel to the Horizon passing thro' the Degrees of the Meridian between the Zenith and Horizon ; as P L.

XL. Parallels of Latitude (on the Terrestrial Globe,) or of Declination (on the Celestial,) are small Circles parallel to the Equinoctial, and supposed to pass thro'

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