What is the Sphere ?

• The Sphere is a solid body contained under one surface, in the middle whereof there is a point or prick, which is the center of the Sphere, from whence all right lines drawn to the circumference, are equal the one to the other, whereby it is to be understood that the center of the sphere is evenly placed in his midst, as that it hath like distance from all parts of the circumference. And for as much as the Sphere is an Instrument demonstrating unto us the universal Engine of the world, we must therefore understand the Center to be this Terrestial Globe wherein we have our being, which compared to the Celestial Globe or heavenly Circumference doth here proportion, as the Center to his Circle: which earthly Globe by the Divine mighty workmanship of God, doth admirably hang upon his center, being of equal distance from all parts of the Circumference.

What are the distinctions of the Sphere ?

• The Sphere is distinguished by the ten Circles, whereof 6 are great Circles, and 4 are lesser circles: whereof there are only 8 described upon the body of the Globe, limiting the Zones and motion of the Planets, as the Equinoctial, the Ecliptick, the Equinoctial Colure, the Solsticial Colure, the Tropick of Cancer, the Tropick of Capricorn, the Artick Polar Circle, and the Antartick Polar circle. The Horizon and Meridian are not described upon the body of the Globe, but artificially annered therunto, for the better perfection of his use.

Which are the greater Circles, and which the lesser ?

• The Equator, the Ecliptick, the 2 Colures, the Meridian and the Horizon, are great Circles, because they divide the Sphere into 2 equal parts. The 2 Tropicks, the Polar circles are lesser circles, because they devide the Sphere into two unequal parts.

Which is the Equator, or Equinoctial ?

• The Equinoctical is a great Circle dividing the Sphere into two equal parts, leaving the one half towards the North, and the other half towards the South, and equally distant from the Poles of the world 90 degrees, placed evenly between them, and described upon them, this lines crosseth the horizon in the true points of E. & W. & hath always the one half above the Horizon, unless it be under either of the poles, for there the equator is in the horizon: it crosseth the Meridian at right sphere angles, & it also crosseth the ecliptick line in the 1 min. of Aries & Libra, dividing the ecliptick & horizon, & is also by them divided into two equal parts: this line is also divided into 360 equal parts or deg. which are the degrees of longitude beginning the account in the point of Aries, reckoning towards the East, concluding the number 360 in the place where the first account began, viz. where the equator both intersect the ecliptick in the 1 minute of Aries, under which meridian S.Mihels one of the Isles of the Assores to be placed in the Geographical description of the terrestrial Globe.

What is the use of the Equator ?

• The Use of the Equinoctical, is to know the declination of the Sun, Moon, & Stars, whereby the latitude of place is given for that portion of the Meridian which is contained between the equator & the center of the Sun, Moon, or Stars, is their declination:
• Also by the Equinoctical is known the longitude of places, for a quarter of a great circle being drawn from the pole, to the place whose longitude is desired, & so continued to the Equinoctical, that deg. and min.in which the quarter circle both touch the equator is the longitude of the place, or if you bring any place (that is desided upon the globe, whose longit. you would know under the meridian of the globe, that deg. of the equinoctical that is then likewise directed under the meridian, is the longitude desired:
• when the sun commeth upon the equator, then the days & nights are of one length throughout the whole world, & then the sun riseth upon the true point of E. & setteth upon the true point of the W. & not else at any time:
• this circle being fixed in the firmament is moved with the first mover in every hour 15 deg. by which account in 24 hours his motion is performed.
• And there note, that the deg. of the Equinoctical have a double application, the one to time, & the other to measure: in respect of time 15 deg. make an hour, so that every deg. containeth but 4 min. of time, but when his deg. have relation to measure, then every deg. containeth 60 min. - being 20 leag. - of that every min. standeth for a mile after our English account.
• But this allowance of 20 leag. to every deg. of the equinoctical, in sayling or measuring of distances upon the E. & W. corses is only when you are under the same, because the equinoctical being a parallel, is likewise a great circle, & every deg. of a great circle is truly accounted for 20 leag. or 60 miles.
• But in the rest of the parallels where either of the poles are elevated above the horizon, if there you sayl or measure upon the courses of E.or W. there are not 20 leag.to be allowed to every deg. because such parallels are lesser circles, therefore they have the fewer number of leag. to every deg. so that the farther you depart from the equator, the lesser are the parallels, & the lesser any parallel is, the lesser are his deg. because every circle containeth 360 deg. & as the circles & deg. diminished by their quantity in like sort the distance answerable to such degrees must abate, as their circles do decrease, & further know, that the equator, is the beginning of all terrestrial latitude, & destination of the celestial bodies.

What is the Ecliptick ?

• The Ecliptic line is a great circle, dividing the sphere into 2 equal parts, by crossing the equator, in oblique sort dividing him, & being divided by him into 2 equal parts, bending from the equator towdards the N. & S. 23 deg. & 28 min. being in the 1st min. of Cancer & Capricorn, there determining the tropical limits, this line likewise divideth the zodiack, by longit. into 12 equal parts, & is divided together with the Zodiack into 12 equal portions, called signs, & every of these signs is divided upon the ecliptick, into 30 equal parts or deg. so that this line is divided into 360 deg. upon which line the center of the sun doth continually move:
• this circle is described upon his proper poles, namely the pole of the zodiac, being in all his parts 90 deg. from either of them:The zodiac is a circle contrary to all, for they are mathematical lines, consisting only of length, without breadth or thickness: but the zodiac hath latitude or breadth 12 deg. whose limits are 6 deg. or either side of the ecliptick, wherein the sun, moon,& planets perform their motions & revolutions,the center of the sun only keeping upon the ecliptick, but the other planets have some time N.lat. & sometime S.lat.
• And here you must understand,that the lat. of the planets or stars,is that portion of the eliptical meridian which is contained between the center of the planet or star,& the ecliptick line & their longit.is that portion of the line ecliptic, which is contained between the said meridian & the ecliptical meridian that passeth by the poles of the zodiac,& the first min. of Aries.
• The 12 divisions or signs of the zodiac are these, Aries \/, Taurus Ta, Gemini ii, Cancer Cn, Leo Le, Virgo mx, Libra Li, Scorpio Sc, Sagittari ^, Capricorn Cp, Aquarius Aq, Pisces )-(: & these are their characters that stand by them.
• The 7 Planets that keep within the limit of the Zodiac, are these, Saturn St, Jupiter Jp, Mars Mr, Sol Sn, Venus Vn, Mercury Hg, Luna D. St performs his course through all the deg. of the zodiac once in every 30 years: Jp in 12 years: Mr in 2 years: Sn in 365 days & 6 hours, being one year: Vn & Hg as Sn: & D performeth her course in 29 days & 8 hours 44mins, through all the deg. of the zodiac.
• And note that this natural motion of the planets of the zodiac is from the W. toward the E. the diurnal motion is violent, caused by the first mover, or primum mobile, who in every 24 h. doth perform his circular motion from the E. to the W. carrying with him all other inferior bodies whatsoever.

What is the use of the Zodiac ?

• By the Zodiac & Ecliptic is known the longit.& latit. of any celestial body, either planets or fixed stars, for a quarter of a great circle drawn from the pole of the zodiac to the center of any planet or star,& so continued until it touch he ecliptick, that deg.& min. where the said quarter-circle toucheth the ecliptick, is the longit.of the said body, which is to be accompted from the first min.of \/,for the longit.of \/ is the portion of the Ecliptic line, which is contained between the ecliptical meridian passing by the poles of the zodiac, and the first min. of \/,& the ecliptical meridian which passeth by the poles of the zodiac & the center of any planet or star. When the Planets are upon the north side of the ecliptick, they have north latitude,& being south from the ecliptick, they have south latitude.
• Also the motions of the Planets, the time of any Eclipse & the Suns declination by his place in the ecliptick, are known by this circle, whose use is very ample, & to great purpose for all astromomical considerations.

What are the Colures ?

• The Solstical Colure is a great circle passing by the Poles of the world, and the Poles of the Zodiack, and the Solstical points or first min. of Capricorn and Cancer, cutting the Equinoctical at right Spherick angles, in his 90 and his 270 degrees.
• The Equinoctial Colure is likewise a great Circle passing by the Poles of the world, and the Equinoctial point of Aries and Libra, and crosseth the Equator in his 360 and 180 degrees, and these colures do intersect each other in the poles of the world to the right Spherick angles.

What is the use of these Colures ?

• Their use is to distinguish the four principal seasons of the year, Spring, Summer, Autumme, and Winter, dividing the Equator and Ecliptic into 4 equal parte: also that Arc of the Solstical Colure, which is included between the first minute of cancer,& the Equinoctial, is the Suns greatest declination toward the north, the like ark being between the tropical point of Cp, & the equator, is the Suns greatest south declination, being in these our dayes 23 deg. 28 min.

What is the Tropick of Cancer ?

• The Tropick of Cancer, is one of the lesser Circles dividing the Sphere into two unequal parts, and is described upon the pole Artick, a parallel to the Equator 23 degrees, 28 minutes from him, being the farthest limit of the Ecliptick bending towards the north, to which when the Sun cometh, the days are then longest to all those that inhabit the North parts of the world, & shortest to the Southern inhabitants:
• between this Circle and the Equator are concluded the 6 septentrional signes, Aries, Tarus, Gemini, Cancer, Leo, Virgo, in which signs during the time that the Sun abideth, being from the 11th of March to the 11th of September, he hath North declination, and then is the Spring and Summer to all such as inhabit the north parts of the world: and Autumne and Winter to the Inhabitants of the south parts of the world: this circle doth touch the Ecliptick in the first minute of Cancer, where the Sun beginneth his return toward the south, whereupon it took the name Tropick, which signifieth conversion or return, by which point of the Ecliptick, the diurnal motion describeth this circle.

(Readers after 1754 will add 11 days to these dates)

What is the Tropick of Capricorne?

• The Tropick of Capricorn is one of the lesser Circles dividing the Sphere into two unequal parts, and is described upon the Pole Antartick a parrallel to the Equinoctial 23 degrees, 28 minutes from him, being the farthest bending of the Ecliptick towards the south, to which when the Sun cometh, the dayes are then longest to all those that inhabit in the south parts of the world, and the shortest to the northern Inhabitants: between this Circle and the Equator are included the 6 southern signs, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, Pisces;
• in which signs, during the time that the Sun abideth, being from the 11th of September to the 11th of March, he hath south declination,& then is the Spring & the Summer to all such as inhabit the south parts of the world; & Autumne & Winter to all the Inhabitants in the north parts of the world; this circle toucheth the ecliptick in the first minute of Capricorn, by which point the diurnal motion describeth this parallel.

What is the use of the Tropics?

• By the Tropicks the Suns declination is known, as also the Tropicks by the suns farthest motion towards the north and south, for so much as the Tropicks are distant from the Equator, so much is the Suns greatest declination: and such as is the Suns greatest declining, such is the distance between the Tropicks & the Equator: they are also the limits of the durning Zone, separating the burning and temperate Zones For between the two Tropicks, is contained the burning Zone.

What is the Artic polar Circle?

• The Artic polar Circle is one of the lesser Circles, dividing the Sphere into two unequal parts, and described upon the pole Artick in parallel, to the Tropick of Cancer, having such distance from the pole as the Tropick hath from the Equator, being 23 deg. 28 min. upon which circle the Artick pole of the Zodiack is placed, which being fixed in the firmament, by the virtue of the first mover is carried about with the heavene, by which motion the Circle is described.

What is the Antartic Polar Circle?

• The Antartick polar Circle is opposite to the Artick, and parallel to the Tropick of Capricorn, being in all respect of such distance and description, from and about the Pole Antartick, as the Artick polar Circle is about the pole Artick.

What is the Use of Artick and Antartick polar Circles?

• The Use of these two polar Circles, is to shew the distance of the Poles of the Zodiack, from the Poles of the World, for so much as the Solsticial points are distant from the Equator, so much are the Poles of the Zodiack from the Poles of the World: the Circles so also divide and limit the temperate & frozen Zones,
• for between the Tropick of Cancer & the Artick polar Circle is contained the Northern temperate Zone, & between the Artick polar Circle & the Pole Artick, that is within the Artick polar circle is contained the Northern frozen zone.
• Also between the tropick of Capricorn & the Antartick polar circle, is contained the Southern temperate Zone, and within the said polar Circle, is included the Antarctick frozen Zone: And these are all the Circles that are described upon the body of the Globe.

What is the Meridian ?

• The Meridian is a great Circle passing by the Poles of the World, & by your Zenith, dividing the Horizon into two equal parts, in the points North and South: it also divideth the Sphere with all the parallel Circles therein contained, into two equal parts, crossing them at right Spherick angles.
• And this Meridian is not fixed in the firmament as the rest of the Circles are, for if it were, then so it be moved with the first mover as the rest are, but it is not so: therefore the Meridian is manifested upon the Globe by a Circle or ring of Copper fastened unto the Globe upon the two Poles, so that the Globe moveth round upon the two Poles within the Meridian: this Meridian is graduated in every of his quarters into 90 degrees, by which his use is performed: and note, that one Meridian may have many Horizons, but every Horizon hath but one Meridian; for if you travel South or North, you keep still upon the same Meridian, yet in every sensible difference of distance you shall enter into a change of Horizons, for there be as many Horizons as there be sensible difference of distance; so that the difference be not upon the points North & South: but this Copper Meridian annexed to the Globe is to be applyed to all differences & distances whatsoever, as amply as if the number were infinite.

What is the use of the Meridian ?

• The Use of the Meridian is to know the highest ascending of the Sun, Moon, or Stars from the Horizon, for when they be upon the Meridian, then are they farthest from the Horizon, and then is the most convenient time to take the Altitude of the Sun, or Stars, whereby to find the Poles elevation.
• By the Meridian of your Globe is known the latitude & longitude of any place upon the Globe containeth for if you bring any place under the Meridian, the degrees of the Meridian do shew the latitude of the same, and that degree of whe Equator, which the Meridian doth cross is the
  longitude.

What is the Horizon ?

• The Horizon is a great Circle dividing the Heavens into two equal parts, the one half being above the Horizon is always in sight, the other half is not seen being under the Horizon, and therefore is called the finitor or limit of out sight, for where the heavens and seas seem to joyn together, that is the horizon:
• the horizon is not sired in the firmament, & yet is a fixed circle constant to his proper latitude, but because in the Globe one and the same horizon may perform whatsoever is required to all elevations, the horizon is so artificialy annexed to the Globe, that by the motion of the Meridian, in the same there faulteth nothing in his use: and the horizons in all respects distinguished as the Sea Compass.
• There are two kinds of horizons, a right horizon and an oblique horizon: when the Poles are in the horizon, then it is a right horizon, for then the Equator doth cut the horizon to right angles, making a right sphere and a right horizon: an oblique horizon is where either of the poles are elevated above the same, for then the equators doth cut the horizon to unlike angles, making an oblique sphere and an oblique horizon, and although the horizons be divers and many in number, for every sensible difference of distance hath his proper horizon, yet is the horizon of the Globe so conveniently annexed thereunto, as that by the moving of the Meridian in the horizon,& by the Globes motion in the Meridian, both the Horizon and the Meridian are to be applyed as proper to all places whatsoever and note that the place where you are, is always the center of the plain superficial horizon.

What is the use of the Horizon ?

• The Horizon is the beginning of all altitude, for whatsoever is above the horizon, is said to have altitude more or less, and by the horizon such altitudes are given with help of the Cross Staffe, for placing the Cross Staff at your eye, if by the one end of the transversary you see the horizon, and up the other end (at the same instant) you see the body observed, then doth the transversary shew upon the staffe the altitude desired, by the horizon, the Navigable courses from place to place are likewise known, as also the quantity of the rising and setting of the Sun, Moon,& Stars:
• whereby is known the length of the dayes & nights in all climates & all seasons: by the horizon is known upon what degree of Azumuth the Sun, Moon, or Stars are, when they may be seen in what part of the heaven soever, whereby the variation of the Compass is found, and the Poles Altitude may at all seasons be given.

Are these all the Circles appertaining to the Globe ?

There are other circles which are sired & do properly appertain to every particular Horizon, as Azumuths, Almicanter, the Artick, and Antarctick Circle.

What are Circles of Azumuth ?

• Circles of Azumuth, or vertical circles, are quarters of great circles, concurring together in the Zenith, as the Meridians do in the pole, and are extended from the Zenith, to every degree of the horizon.
• And because they cannot be conveniently described upon the Globe to be applyed to all horizons, therefore upon the meridian of the Globe there is a piece of coper artificially placed, to be removed to any degree of the Meridian at pleasure, which piece of Copper representeth the Zenith and must always be placed so many degrees from the equator as the pole is elevated from the horizon, and unto this zenith there is joyned a quarter of a great circle called a quarta altitudo, the end whereof doth continually touch the horizon,& is so joyned to the zenith, as that it may be moved round about the horizon, and to every part thereof at your pleasure: this quarta altitudo is devided into 90 degrees, being the distinction of all Altitude, and beginning the account from the horizon, which is the beginning of Altitude, and concludeth 90 degrees in the Zenith, being the end and extreme limit of all Altitude.

What are Almicanters ?

Almicanters or Circles of Altitude, or parallel circles to the Horizon and are described upon the Zenith, as the parallels to the equator, are described upon the poles, of which circles there are 90 answerable to the distinctions of the quarta altitudo, which are the degrees contained between the horizon and zenith. These circles cannot be described upon the Globe, to be applyed to every horizon, but they are distinguished by the circular motion of the quarta altitudo, for if I desire to see the Almicanter circle of 10 degrees, by moving the quarta altitudo round about the horizon, the zenith degree of their quarter circle, doth shew the Almicanter desired, in what elevation soever.

What is the use of those two Circles ?

The Quarta altitudo performeth the use of both, by the quarta altitudo and horizon, the courses from place to place are known according to the true horizontal position, as hereafter shall plainly appear: it also sheweth the degree of Azimuth, and observed altitude of any celestial body, in what latitude soever: by the Quarta altitudo and Horizon, you may describe a paraboral Compass upon the Globe, the poles height is at all times thereby to be known, and the variation of the Compass is thereby likewise given, as hreafter in the practice you shall be taught.

What are the Artick and Antarctick Circles ?

Every horizon hath his proper artick or antarctick Circle, those horizons that have the pole arctick elevated above them, have their proper artick circle, and those that have the South pole elevated, have their proper antarctick circle, the quantity of which circle is according to the Poles elevation, for if the pole be much elevated, then is the artick circle great, for the Poles altitude is the semidiameter of their circle, if the Pole be in the Zenith, then half the heavens is the arctick Circle.

What is the use of this Circle ?

If the Sun, Moon or any Stars be within this Circle, they are never carried under the Horizon during the time of their abode therein, whereupon it cometh to pass, that such as travel far towards the north, have the Sun in continual view and those that inhabit under the Pole (if any so do) the Sun is in continual sight for six months together, because the six septentrional signs are within the Artick Circle, the Equator being in the horizon.

There is another small Circle, which is called Circulus Horarius, or the hour circle, to be annexed to the Meridian of the Globe, for the perfection of his use, this circle must be divided into 24 equal parts, or hours, and those again into such parts as you please for the better distinction of time: this circle must be fastened to the Meridian, so that the hours 12 must stand directly upon the edge of the Meridian, & the pole must be the center of this Circle, upon which pole there must be fastened an Index to move portionably as the Sphere (upon any occasion) shall be moved. There is also an half Circle, called the Circle of Position, which uth it serveth to no great purpose for Navigation. I here omit, and thus is the Globe fully finished for the perfection of this use.

What are the Poles of the World ?

• There are two Poles, the North Artick pole, and the South, or Antartick pole, which poles are two immoveable pricks fixed in the firmament, whereupon the Sphere is moved by vertue of the first mover, and are the limits of the Axis of the world, as also the extreme term of band of all declination, being 90 deg. from all parts of the Equator.
• By the raising of the pole from the horizon, is known the paralles of latitude of our being. it also giveth the quantity of the Artick circle, and obliquity of the Sphere.

What is the Axis of the World ?

The Axis of the World is a right line passing by the Center of the Sphere, & limited in the Circumference, about the which the Sphere moveth, and is therefore called the Axis of the Sphere;& as all lines commensurable are limited between 2 points or pricks, so is the Axis of the world, & those 2 limiting pricks are called the Poles of the World.

What are the Poles of the Zodiack ?

• The Zodiack hath likewise two Poles, Artick & Antartick, being 2 pricks fixed in the firmament, uniting the Axis or the Zodiack, & are distant from the poles of the world 23 deg. 28 min. which poles by the motion of the sphere do describe the poles circles, performing their motion about the poles of the world in every 24 hours, by vertue of the first mover, upon these poles the ecliptick, & zodiack is described: also a quarter of a great circle graduated into 90 deg. being fastened to either of these poles & brought to the center of the Star, sheweth by that graduation the latitudes of the same star, & where the quarter circle toucheth the Ecliptick, that is likewise his longitude: also the 7 Planets do perform their natural revolutions upon the poles, where motion is from the West towards the East, contrary to the motion of the first mover.

What is the Axis of the Zodiack ?

The Axis of the Zodiack, is a right line passing by the center of the Sphere, & limited in the circumference, whose limiting points are the poles of the zodiack, and his Axis is moved by the Sphere as are his Poles,

What are the Poles of the Horizon ?

There are two Poles of the Horizon, which are the limits of his perpendicular diameter being equidistant 90 degrees from all parts of the horizon, & are the extreme limits of all altitude, that Pole which is in the upper hemisphere is called the Zenith, and his opposite Pole is called Nadir, they are extended in the firmament, but not fixed in it, for they move never, but remain always stable in their proper horizon, which could not be if it were fixed in the firmament, for then should they be moved with the firmament as the rest are, by the help of these poles is found the Azumuth and Almicanter of any celestial body, for a quarter circle devided into 90 degrees, and fixed to the Zenith as is the quarta altitudo, being moved to any celestial body, doth by those deg. shew the almicanter or altitude of the same body from the horizon,& that part of the horizon which the quarter circle traces, is the Azumuth of the same body, always provided that the Zenith stand answerable to the poles elevation, that is, so many degrees from the equator, as the Pole is from the Horizon.