IX. A Great Circle of the Sphere, is that whofe Plane paffeth through the Center thereof, and whofe : Center is the fame 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 diftant 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 defcribed on the Plane of the Projection, and within which the Projection is finifhed, as RPHE.

XII. A Right Circle is that whofe Plane ftands at Right Angles with the Plane of the Projection, and paffeth thro' the Eye, in the Stereog. Projection; and is always a Diameter of the Primitive; fuch are RH, PE, AQ

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

XIV. Parallel Circles are thofe Leffer Circles of the Sphere, whofe Planes are parallel to the Planes of any Great Circles thereof; thus OVS is a small Circle pa rallel to the Great Circle RH.

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 thefe two Great Circles; fuch is the Angle APV, or VCB.

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

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 : VOL. II. В 2

90 De

90 Degrees diftant 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 Bafe AV. 2. The Perpendicular AP. 3. The Complement of the Hypothenufe VP, (viz. the Arch VB.) 4. The Complement of the Angle at the Bafe V 5. The Complement of the Angle at the perpendicular P ; (viz. the Arch CB.): Thefe are fo 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 Treatife.

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

XX. The Extreme Parts Conjunt or Adjacent, are thofe 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 Disjunct, are thofe 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 eafy in Chap. 11. and the Scheme therein.

XXII. Planifphere 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

!

XXIII. The Nearest Distance on the Surface of the Globe or Sphere between any two Places, is the Arch of a Great Circle paffing thro' both.

XXIV. The Poles of the Globe or Sphere, are the two Points of the Surface which make the Extremities of its Axis; each of which is 90 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 paffing thro' the Poles of the World; which may be conceived infinite in Number ; but are generally drawn at 10 Degrees Distance on Artificial Globes fuch are the Primitive EN 25, and the Oblique Circle SAN; for they pass thro', and interfect each other in the Poles N and S. See Fig. 4.

XXVI. The Equinoctial or Equator, is a Great Circle every way equally diftant (viz. 90 Degrees) from either Pole Nor S, and therefore divides the Globe or Sphere into two Halfs or Hemispheres; as the Great Circle ÆC 2

XXVII. The Ecliptic is a Great Circle interfecting the Equinoctial in the two oppofite Points V and, and maketh an Angle therewith (call'd its Obliquity) of 23° 29' equal to the Meridional Arch ; and

is the Circle V 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 alfo are contained all the twelve Signs or Conftellations, thro' which the Sun paffeth once a Year in the Ecliptic..

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

cer,

cer, the Crab, . 5. Leo, the Lion, . 6. Virgo, the Virgin, R. 7. Libra, the Ballance, . 8. Scorpio, the Scorpion, m. 9. Sagittarius, the Archer, 7. 10. Capricornus, the Goat, vs. 11. Aquarius, the Waterer,. 12. Pifces, the Fishes, . To each of thefe is allotted the Portion of 30 Degrees in the Ecliptic. The Six firft 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 fpeaking, 'tis a Great Circle every way diftant from your Eye 90 Degrees ; fuppofe therefore your Eye at Z, your Horizon would be HCO; this is called the Rational, the other the Senfible Horizon.

XXXI. The Colures are two Meridians dividing the Equinoctial and Ecliptic into four Equal Parts. One of which paffeth thro' the Points Aries V and Libra, and is called the Equinoctial Colure, as NCS; the other, called the Solftitial Colure, paffeth thro' the Points Cancer and Capricorn VS, as NS v.

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

XXXIII. The Solftitial Points, or Solftices, are the firft Scruples of Cancer, and Capricorn VS; becaufe in and near them (Solis Statio) the Sun feemeth not to move for fome Days together.

. XXXIV. The Zenith and Nadir are two Points Diametrically oppofite to each other. The Zenith is the Point which is Vertical to us in the Heavens, or juft over our Heads as Z; and the Nadir is oppofite

thereto,

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 interfecting each other in the Zenith and Nadir; as ZD X; and that which paffeth thro' the Eaft and Weft Points of the Horizon, as ZC X, is called the Prime Vertical, or Azimuth of East and West.

XXXVI. Circles of Pofition, are Great Circles of the Sphere which all meet and interfect one another in the Points of Interfection of the Meridian with the Horizon; fuch is HBO.

XXXVII. The Tropics are two fmall Circles parallel to the Equinoctial, and diftant (on each Side) therefrom 23° 29′; they are the Limits of the Sun's greateft Declination from the Equinoctial. The Northern Tropic paffeth by the beginning of Cancer, and therefore called the Tropic of Cancer, and is the Parallel of the Longest Day; as R. For the fame Reason the other is called the Tropic of Capricorn; and is the Parallel of the Shorteft Day (in Northern Climes) as I v.

XXXVIII. The Arctic and Antartic Circles are other fmall Circles, and Parallel to the Equinoctial; and distant from it 66° 31′; or from either Pole 23° 29'. That towards the North Pole is EFG; the other towards the South TWV. Thefe are commonly called the Polar Circles alfo..

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

XL. Parallels of Latitude (on the Terreftrial Globe,) or of Declination (on the Celestial,) are fmall Circles parallel to the Equinoctial, and fuppofed to pass thro'