CHAP. I. Of the Circles of the Sphere in general.

THE material Sphere, is an Instrument, where­by all the Phenomena of the Primum Mobile, are most easily known.

It is composed of Ten Circles chiefly, which are, the Equinoctial, the Zodiack, the two Colures, the Horizon, the Me­ridian, [Page 2] the two Tropicks, and the two Polars.

Those Circles, are three manner of ways distinguished among themselves. First, Some of them are called Circuli Maximi, the Greatest Circles; others are called Circuli Minores, the lesser Cir­cles. The Greatest are, the Equinoctial, the Zodiak, the two Colures, the Ho­rizon, and the Meridian; because there cannot be greater Circles in the Sphere, than they are.

The lesser Circles are, the two Tro­picks, and the two Polars. They are so called, because there are found in the Sphere greater ones.

Secondly, The Circles of the Mate­rial Sphere, while the Primum Mobile is turning about, are either Parallel one to another, Right, or Oblique, that is, to ly crosly. The Parallel Circles, are the two Polars, the two Tropicks, and the Equinoctial, which ly middle be­tween them, together with their Equi­noctial, who live under the Poles. The Oblique Circles are, the Zodiack, and [Page 3] the Oblique Horizon. For this cutteth the Equinoctial, at Oblique Angles; the other by reason of its Situation doth the same to the rest of the Circles. The Circles called Right Circles, are the two Colures, the Meridian, and the Right Horizon, because they cut the Equi­noctial at Right Angles.

Thirdly, The Circles of the Sphere, are either Moveable, or Immoveable. The Moveable Circles, are these which are turned about with the Sphere, be­ing eight in number, to wit, the Equi­noctial, the Zodiack, the Equinoctial Colure, the Solstice Colure, the Tro­pick of Cancer, the Tropick of Capricorn, the Polar Artick, and the Polar Antar­tick. The Circles Immoveable, are the Meridian, and the Horizon; so called, because while the Sphere is carried about, they stand stedfast, and unmove­able.

CHAP. II. Of the Equinoctial.

THe Equinoctial, is one of the greatest Circles, of the Sphere Moveable, and equally distant from the Poles of the World. It is called one of the greatest, that it may be distinguish­ed from the lesser, as well from those, which are fixed in the Sphere, as from others, which we must imagine to be in it. It is called Movable, that it may be distinguished, from the Horizon of those, who live under the Poles, which coinciding with the Equinoctial, must differ from it in this, that the one is Movable, the other Immovable. Last­ly, by reason of the third difference (equally distant from the Poles of the Sphere) it is distinguished from the Oblique, and Right Circles of the Sphere.

It is called by divers Names. For [Page 5] sometimes it is called the Equator, sometimes the Equinoctial, and some­times the Middle, and greatest of the Parallels.

The Uses and Offices of the Equino­ctial are these. 1. It measureth the first Motion. For this Circle, of all the Cir­cles of the Sphere, under any Position whatsoever, moveth equally; and there­fore, it ought to be also the Measure of Time, it being most fit for deter­mining the quantity of the Artificial, and Natural Days. For this cause, it is, that the Degrees of the Equinoctial, are called by some, Tempora, Times. 2. It pointeth forth to us in the Eclip­tick, the two Equinoctial Points; those Points, in which the Equinoctial, and Ecliptick cut one another, in the be­ginning of Aries and Libra. For when the Sun cometh to these Points, the Day and the Night are of equal length over all the Earth, which falleth out on the 10 or 11 of March, and on the 13 or 14 of September. 3. That which is Anomolous, and Irregular in the Ob­lique [Page 6] Motion of the Zodiack, is re­duced to a sure Rule, by the help of the Equinoctial. 4. It divideth the Sphere into two equal parts; the one called the North part, in which is the Pole, named Polus Septentrionalis, Bo­reus, or Articus: the other called the South part, in which is the Pole, nam­ed Polus Australis, Meridionalis, or An­tarticus. 5. By this means, it divideth the Zodiack into six Signs, called Nor­thern Signs, and into other six called Southern Signs. 6. From the Equino­ctial are numbred the Declinations of all, and whatsoever Points in Heaven, as well South as North. The Declina­tion of any Point, or Star, is an Arch of a Circle of Declination, measured between the Equinoctial, and the said Point, or Center of the said Star. Cir­cles of Declinations, are of the Greatest Circles in the Sphere Movable, passing thorow the Poles of the World, and any point given. 7. Upon the Equino­ctial, we reckon the Right Ascension of any, or whatsoever Point in Heaven. [Page 7] Right Ascension, is nothing else, but an Arch of the Equinoctial, measured between the first Point of Aries, and that Circle of Declination, which passes thorow the point given. 8. Upon the same Equinoctial, we measure the Ob­lique Ascension, and Descension of any point in Heaven whatsoever. Oblique Ascension, is an Arch of the Equino­ctial, measured between the first Point of Aries, and that Point of the Equi­noctial, which riseth in the same Mo­ment of Time, with the Point given. Oblique Descension, is an Arch of the Equinoctial measured between the Point foresaid, and that Point of the Equino­ctial, which sets in the same Moment of Time, with the Point given. 9. Upon the Equinoctial, we count and reckon the Ascensional Difference, which is no­thing else, but an Arch of the Equino­ctial, by which Right Ascension differs from Oblique. 10. Upon the Equino­ctial, we measure the Rising and Setting Amplitude. This Rising and Setting Amplitude, is nothing else, but an Arch [Page 8] of the Horizon, measured between the Rising, or Setting of the Equinoctial, and the Rising or Setting of any Star, or Point given. 11. Upon the Equi­noctial, we number the Longitudes of Places, and upon the same, we reckon the Latitudes of Places. The Longitude of a place, is an Arch of the Equinoctial, measured between the first Meridian, and the Meridian of the Place. The Latitude of a Place, is an Arch of the Meridian measured between the Equi­noctial, and Zenith of the Place. 12. The Equinoctial is most useful for making of Sun-Dials: for there must be as many Hours upon the Plain, as there are 15 Degrees in the Equinoctial, four and twenty times numbred.

CHAP. III. Of the Zodiack.

THe Zodiack, is one of the Great­est Circles of the Sphere, Mov­able, [Page 9] under which the Planets perpetu­ally haunt.

The first and second Difference are added, as in the Definition of the Equi­noctial. The third, which is in these words (under which the Planets per­petually haunt) do distinguish the Zo­diack from all other Circles. For it may come to pass, that, this or that Planet, by his proper motion, may be under the Meridian, may be under some Horary Circle, may touch lightly the Horizon, but that is not always, nor do they always abide in the same Situation: but their stay is perpetual under the Zodiack. And because the Planets wander in the Heavens, viâ obliquâ, therefore this Circle is made oblique, and seing in this obliquity, they make digression, from this side, to that side, and from that to this, therefore Astro­nomers have granted to this Circle Lati­tude, whereby also it may be differenced from all other Circles, none of which ever claimed Latitude.

The Zodiack is divided, first in rela­tion [Page 10] to its Latitude, into North Lati­tude, and South Latitude. North La­titude, is that half part of the Zodiack, which from the Ecliptick (the middle Line of it) declines toward the North. South Latitude is opposite to this. Each one of them contains Eight Degrees, whereof the Equinoctial contains 360.

The Ecliptick, or middle Line of the Zodiack, is one of the Greatest Circles of the Sphere, Moveable, under which, the Sun from West to East moves per­petually. This Line, as likewise the Zodiack, is divided according to Lon­gitude into twelve Parts, which are cal­led in Greek [...]. Every one of these twelve, are subdivided in­to 30 parts, so that the whole Zodiack contains 360 Degrees. These twelve Divisions are called Aries, Taurus, Ge­mini, Cancer, Leo, Virgo, Libra, Scor­pius, Sagittarius, Cap [...]s, Aquarius, Pisces. But seing there are four Cardi­nal Points, two of the Equinoctial, and two Solstice Points, it hath pleased Astronome [...], to make the beginning of [Page 11] their reckoning, from the Vernal Equi­noctial Point; because the Sun being there, he not only begins the Spring, but openeth the Earth, and giveth life to all Vegetables, and things which grow; which cannot be done, either in any of the Solstices, or when he is in the Autumnal Equinoctial Point. Next, the distinction of the Signs is manifold. For some of them are called Northern Signs, and others are called Southern. The Northern, decline from the Equinoctial towards the North, which are Aries, Taurus, Gemini, Can­cer, Leo, Virgo. The Southern decline from the Equinoctial towards the South, which are Libra, Scorpius, Sagittarius, Capricornus, Aquarius, Pisces.

Secondly, Some of them are called, Signs Ascending, others are called Signs Descending. The first sort, are these, wherein the Sun, and the rest of the Planets do ascend from the South to­wards our Zenith, which are Capricornus, Aquarius, Pisces, Aries, Taurus, Gemini. The Descending are these, wherein the [Page 12] Sun, and the rest of the Planets, do move from our Zenith towards the South, which are Cancer, Leo, Virgo, Libra, Scorpius, Sagittarius.

Thirdly, The Signs of the Zodiack, are either Vernal, Estival, Autumnal, or Hybernal. The Vernal, are Aries, Taurus, Gemini. The Estival, are Cancer, Leo, Virgo. Autumnal, are Libra, Scorpius, Sagittarius. And the Hiber­nal, are Capricornus, Aquarius, Pisces.

Fourthly, The Signs are either Car­dinal, Middle, or Fixed, or Common, or Two-bodied. The Cardinal Signs, are Aries, Cancer, Libra, Capricornus: so called, because their beginnings are the very Cardinal Points. The Middle or Fixed Signs, are Taurus, Leo, Scor­pius, Aquarius. They are called Mid­dle or Fixed, because they keep the Middle place between the Cardinal and Common Signs. They are Fixed, be­cause when the Sun is in them, we have a perfect temperament of the Air, agree­ing to the given Quadrant of the Hea­vens. As when the Sun is in Taurus, [Page 13] we have a perfect Spring; in Leo, a perfect Summer; in Scorpius, a perfect Harvest; and in Aquarius, we have a perfect Winter. They are called Common, or Two▪ bodied, as Gemini, Virgo, Sagittarius, and Pisces; because each one of them, hath two Bodies in­deed. For Gemini are two Twins. Virgo hath an Ear of Corn in her Hand. Sagittarius is made up of a Man, and a Horse. And lastly, The Fishes are double. They are called Common, be­cause Astrologers find, that they parti­cipate of the Nature, both of the Fixed Signs, and the Cardinal which follow.

Fifthly, The Signs are divided into four Triplicities, which are called by Astrologers Trigons. The first is called the Fiery Trigon, which contains Aries, Leo, and Sagittarius. The second is the Earthy, which contains, Taurus, Virgo, and Capricorn. The third is the Aerial, which contains, Gemini, Libra, and Aquarius. The fourth is the Watery, which contains, Cancer, Scorpius, and Pisces.

[Page 14]If it happen, that Saturn, and Iupi­ter be in Conjunction this year in Leo, their next Conjunction will happen 20 years after, or truly 19 years, 315 days, and 19 hours, after in Sagittarius. From Sagittarius to Aries, from Aries to Leo, and so in round till 198 years and 236 days passing, they make a Transit into a new Trigon; so that the Revolution of one Trigon, consumes almost 200 year.

The uses of the Zodiack and Eclip­tick are these. 1. As the Equinoctial, is the Measure of the Pri [...] Mobile, so is the Zodiack and Ecliptick, the Square and Rule of the second Mov­ables. For as the Sun is always, in or under the Ecliptick; so are the rest of the Planets always, in or under the Zo­diack. Therefore as in the Celestial Globe, the Zodiack hath the chief place, so in the Terrestrial Globe the Equi­noctial. 2. Upon the Ecliptick we reckon the Longitude of Stars, and from the same Ecliptick, we count their La­titude. The Longitude of a Star, is an [Page 15] Arch of the Ecliptick, measured between [...]e true Equinoctial Point, or begin­ [...]ing of Aries, and the Circle of Lati­ [...]de passing thorow the Center of that [...]tar. Circles of Latitude, are great Movable Circles, passing thorow the Poles of the Ecliptick, and the Center [...]f the Star given. They are of that [...]umber of Circles, which cannot be [...]aced Artificially in the Sphere. Ne­ [...]ertheless, of that same Number, is the [...]olurus Solstitiorum fixed in the Sphere. The Latitude of a Star, is an Arch of a Circle of Latitude, measured between [...]he Ecliptick, and the Center of the [...]tar. 3. According to the Degrees, and [...]arts of the Zodiack and Ecliptick, the whole Heavens, and the whole Universe [...] divided into twelve Signs; nay eve­ [...]y Point contain'd in the Sphere of the Fixed Stars, is said to be in this or that Sign; tho, to be in a Sign, is said many ways. For first, To be in a Sign, is nothing else, but to be under any [...]welfth part of the Zodiack. In this [...]ense, the Sun is said to [...]e in a Sign, [Page 16] because he is always under the Eclip­tick. Then the Stars are said to be in a Sign, which are indeed out of the Ecliptick, nevertheless are under the Zodiack. In this sense, the Planets, which wander from the Ecliptick, are said to be in the Sign of Aries, and Tau­rus, &c. Thirdly, Any thing is said to be in a Sign, which is included, in any of the twelve parts, which arise from the division of the whole Heavens, passing thorow the beginnings of the Dodekatemoria, or the Poles of the E­cliptick; they being six great Circles, which mutually cut one another, in the same Poles. In this sense, any Star, as well fixed, as wandring, or new ap­pearing, as a Comet, are said to be in the Sign of Aries, Taurus, &c. 4. The obliquity of the Ecliptick, is the cause of the inequality of days: for seing it moves unequally, and not evenly, the Sun, which is the true Parent of Time, must of necessity make the days unequal. 5. The Year, the Month, and the four Seasons of the Year, are determined by [Page 17] the Ecliptick. 6. When the Sun and Moon, are both of them in the Eclip­tick, of necessity there must be Eclipses; and for this cause, it is called the E­cliptick. 7. How much is the obliqui­ty of the Ecliptick, so much is the di­stance, between the Poles of the World, and the Poles of the Ecliptick: so much also is the distance, between the Equi­noctial, and either of the Tropicks.

CHAP. IV. Of the Colures.

THe Colures are nothing else, but Circles of Declination, defined above, in the second Chapter of the E­quinoctial. They are called Colures from two Greek words, Kolos, or Kolo­bos, Mancus, maimed or defective, and Oura, Cauda, a Tail, because in an ob­lique Sphere, they have some part un­seen, as if they were maimed, or want­ting. But all the rest of the Circles of [Page 18] the Sphere, while it is going about, may be seen: but the Colures, have al­ways some of their parts towards either of the two Poles, lying hid, and un­seen. There are only two of them, which use to be placed in the Sphere, one whereof is called the Solstice Co­lure, the other the Equinoctial Colure. The Equinoctial Colure, is one of the greatest Circles of the Sphere, Movable, passing thorow the Poles of the Sphere, and the Equinoctial Points, the first of Aries, and the first of Libra, which are called Cardinal. By the word mov­able, the Colures are differenced; First, From the Meridian; Secondly, From the Right Horizon; And thirdly, From the Horary Circles, with all which, by one turning about of the Sphere, they are twice united. But in this they dif­fer, that those do not move, but these follow the motion of the Primum Mo­bile. The Solstice Colure, is one of the greatest Circles of the Sphere, mov­able, drawn thorow the Poles of the Sphere, and the two Solstice Points, by [Page 19] which difference, they are distinguish­ed from other Colures.

The uses of all the Colures in com­mon are these. First, We reckon up­on them, the Declinations of all the Points of the Heavens whatsoever. 2. They terminate and bound the Right Ascensions. 3. They are like unto a Right Horizon, and a Meridian in any Sphere, whether Right, Oblique, or Parallel.

The Uses of the Colures, which are set down in the Sphere, are these in common, 1. Without them, the Paral­lel Circles in the Material Sphere can­not stand, 2. By their mutual cutting one another, they shew the Poles of the Sphere. 3. They divide the Ecliptick into four Quadrants.

The peculiar Uses of the Equinoctial Colure are these. 1. It demonstrats to us the Equinoctial Points, by its mutual Section, with the Ecliptick; in which Points when the Sun is existing, there is an Universal Equinox over the whole Earth. 2. It is divides the Ecliptick [Page 20] into two halfs, the one called the North part, the other the South part. 3. It distinguishes the Signs, in which when the Sun is existing, the Days are longer than the Nights, from those Signs, in which when the Sun is existing, the Nights are longer than the Days.

The proper Uses of the Solstice Co­lure are, 1. It demonstrats to us the two Solstice Points, in which when the Sun is existing, he is either nearest to our Zenith, or furthest removed from it. 2. Upon this Colure, we reckon the Suns greatest Declination, or the greatest Obliquity of the Ecliptick, which is found to be this day twenty three De­grees, and thirty Minuts. 3. It divides the Zodiack into two halfs; the one called Ascending, the other Descending. 4. It distinguisheth the Signs, in which when the Sun is existing, the Days be­come longer, and the Nights become shorter, from those Signs, in which when the Sun is existing, the Nights become longer, and the Days become shorter. 5. In this Circle, are the two [Page 21] Poles of the Ecliptick, as many Degrees, distant from the Poles of the World, as the greatest obliquity of the Ecliptick contains. 6. Upon this Colure, the Latitudes of the Zones are determined. For between the Tropicks, is contained the breadth of the Torrid Zone, be­tween the Tropicks, and the nearest Polar Circles, are contained the two Temperate Zones, and the other two remaining Arches of this Circle, con­tain the breadth of the two Frigid, or Cold Zones.

CHAP. V. Of the Horizon.

THe Horizon, is one of the greatest Circles of the Sphere, Immov­able, and equally distant from the Ver­tical Point. It is called Immovable, that it may be differenced from the rest of the Movable Circles; but especially, First, From their Equinoctial, who live under [Page 22] the Poles. Secondly, From their Eclip­tick, whose Zenith is placed in the Po­lar Circles: for their Ecliptick every day is twice united with their Horizon, but without delay. Thirdly, From their Circles of Declination, or their Colures, who live under the Line: for there, the forementioned Circles, and the Horizon, are twice, by every Re­volution of the Sphere, united: but the Circles of Declination follow the Motion of the Primum Mobile, but the Horizon stands Immovable. The Ho­rizon is said indeed to be Immovable, but not Unchangable, for there are as many Horizons, as there are Vertical Points; and while we change our Ver­tical Point, of necessity we change our Horizon also.

Two ways is the Horizon divided. First, In relation to the Equinoctial, which is called a Right Horizon, an Oblique Horizon, and a Parallel Hori­zon. The Right Horizon, is so called, because it cuts the Equinoctial at Right Angles. It is called Oblique, because [Page 23] it cuts the Equinoctial at Oblique An­gles. And it is called a Parallel Hori­zon, when it lies Parallel to the Plain of the Equinoctial, or rather when it is united, with the Equinoctial. And according to this Relation, it hath to the Equinoctial, the Sphere it self, hath obtained the same Division.

Secondly, The Horizon is either Ra­tional, or Sensible. The Rational Ho­rizon, is defi [...]ed above, and is under­stood to divide the whole World, or Sphere of the World into two equal parts, the first whereof is called the uppermost Hemisphere, the second the nethermost Hemisphere. It is called Rational, because tho we cannot see the whole World, or the exact half of it, yet Reason tell us, by the Rising and Setting of the Sun, Moon, and Stars, that the inferior part of the World, is equal to the superior part. The Sen­sible Horizon, is nothing else, but so much of the Earth, as a man, by turn­ing his eye once, doth behold round about him.

[Page 24]The Uses of the Horizon are these. First, it divides that part of the Hea­vens, which is seen, from the other which is not seen, the Superior part from the Inferior part. 2. Thorow the Poles of the Horizon the Meridian ought to pass: therefore the Description of the Meridians depend from the Horizon. 3. By the Situation of the Horizon, we know whether it be a Right Sphere▪ Ob­lique Sphere, or a Parallel Sphere. 4. In the Horizon, the Rising or Set­ting of the Stars are observed 5. The Horizon sheweth, what Degree of the Ecliptick, what part also of the Equi­noctial, or what Degree, with any gi­ven point of the Heaven riseth or set­teth. 6. It boundeth and terminats the Ascensional Difference. 7. Upon the Horizon is numbred, the Rising or Setting Amplitude, of any point in the Heaven. 8. It demonstrats, and shew­eth the Cause and Reason of the equa­lity of Days and Nights in a Right Sphere, and of the unequality of the same in an Oblique Sphere. For the [Page 25] Horizon in a Right Sphere cutteth all the Circles of the Natural Day equally, but unequally in an Oblique Sphere. 9. From the Horizon we number the Morning-Twilight: for when the Sun [...]s distant, in some Vertical Circle 18 or 19 Degreees from the Horizon, so that [...]rom that Moment, he approach nearer [...]nd nearer unto it, then begins the Mor­ning-Twilight. But the Evening-Twi­light ends, when the Sun after his Set­ [...]ing comes to that 18 or 19 Degree [...]oresaid; for then doth the Light turn [...]nto Darkness. 10. From the Horizon, we number the Elevation of the Pole, [...]nd Equinoctial. 11. From the Hori­ [...]on are numbred various and divers [...]inds of Hours, as the Italick, and Iewish Nocturnal Hours from the West part of the Horizon: but the Babylonish Hours, [...]nd the Iewish unequal Diurnal Hours, [...]rom the East part.

CHAP. VI. Of the Meridian.

THe Meridian is one of the greatest Circles in the Sphere, passing thorow the Poles of the World, and the Poles of the Horizon. By the words, thorow the Poles of the Horizon, it is distinguished from the Horary Cir­cles, of which none but it self, passes thorow the Poles of the Horizon. It has acquired divers and sundry Names, by reason of its manifold uses, by Astro­logers, which are not fit to repeat now. What was said above concerning the Colures, and Circles of Declination, to wit, that they are in number equal to the Vertical Points, the same may be said of the Meridian, for as many of them may be imagined, as there are Vertical Points, which are infinite, pro­viding a man travel from East to West: for if a man go from North to South, [Page 27] or from South to North, he travels round about the World, without variation of his Meridian. The Brasen Meridian in the Celestial, or Terrestrial Globe, sup­plyes the office of them all, which are innumerable. But in Geographical Ta­bles, and Mapps, Geographers use to extend one Meridian, thorow two, and two opposite Degrees of the Equinoctial, for finding out, the more easily the La­titudes of Places. Of all these Meridians there is a common beginning se [...]led in the Fortunate, or Canary Islands, be­cause the Antient Geographers deemed those Islands to be the Westmost part of the World, and therefore they fixed their first March-stone there, whence they begin to reckon. But the later Geographers, have removed this March­stone 10 Degrees more Westerly, and have made the common beginning of the Meridian to pass thorow one of the Islands called Osores, whence they be­gin to reckon from West to East, imi­ta [...]ing the order of the 12 Signs.

The uses of the Meridian are these, [Page 28] 1. It distinguisheth the Eastern part, of the World, from the Western part, the Anterior part, from the Posterior part. 2. It lets us know the South part of the World, and the North part. For when the Sun is in the Meridian, [...]en is Mid-day, and when the Sun is in the Northern part, of the Meridian, then is Mid-night. 3. It divides the Nocturnal and Diurnal Time into two halfs: that is, when the Sun is come to the Meridian in our Hemisphere, as much of the day is past, as what is to come: and when the Sun is come to the Northern part of the Meridian, as much of the Night is past, as what is to come. 4. The Meridian supplies in every Oblique Sphere the place of the Right Horizon: therefore, as the Stars do ascend above the Right Horizon, so they pass over the Meridian, and those [...]ransitions are called the Right Ascen­sions of the Middle Heaven. 5. From the Meridian, Astronomers begin their Time. 6. In the Meridian, we find out the Zenith; therefore when the [Page 29] Stars come to it, they are either high­est above the Horizon, and are said by Astrologers to culminate, or they are in the lowest, and opposite part of it, which is the Nadir. 7. In the Meri­dian, we find out the distances between the Tropicks, and the whole Obliquity of the Ecliptick. 8. Upon the Meri­dian, we number the Latitude of Places upon the Earth, and likewise the Ele­vation of the Pole, and Equinoctial. The Elevation of the Pole, is defined, an Arch of the Meridian, measured be­tween the Horizon, and the apparent Pole of the World, which may be found out, after the following manner. Ob­serve the greatest and least Altitude of any of the Stars, which do not set. Subtract the least Altitude from the greatest, and divide the difference. This difference being subtracted from the greatest Elevation, or added to the least, gives the true height of the Pole. December 17. 1669, I observed with a large Quadrant, half 9 a Clock at night, the foremost Guard-star, when it was [Page 30] in the Meridian, and lowest, to have 41 Degrees, 22 Minuts of Altitude. And on Ianuary 7. 1670, at 7 a Clock in the Morning, I found it, when it was in the Meridian, and heighest, to have 70 Degrees, 27 Minuts. I subtract 41 Degrees, 22 Minuts, from 70 Degrees, 27 Minuts, and the difference is 29 De­grees, 5 Minuts. Divide this, and you have 14 Degrees, 32 Minuts, and 30 Seconds. This being added to 41 De­grees, 22 Minuts, gives you 55 De­grees, 54 Minuts, 30 Seconds. Or subtract 14 Degrees, 32 Minuts, and 30 Seconds, from 70 Degrees, 27 Minuts, and there remains 55 Degrees, 54 Mi­nuts, and 30 Seconds, for our height of the Pole at Edinburgh. 9. The Me­ridians do terminate, and bound the Longitudes of Places, as well in the Terrestrial Globe, as in the Mapps, and Cards projected in Plano. 10. The Meridians do terminate, and bound the Breadths and Latitudes of the Zones, and also of the Climats. 11. We find out in the Meridian, the Antipodes, the Anteci, and Perieci.

CHAP. VII. Of the Tropicks.

THe Tropicks are lesser Movable Circles of the Sphere, described from the Solsticial Points, by the mo­ [...]ion of the Primum Mobile. They are called Lesser, because there are in the Sphere Greater Circles, than they are. They are called Movable, that they may be distinguished chiefly, from the Paral­ [...]els of their Horizon (called Almican­ [...]ars), who live under the Poles; and [...]rom the antient Polars of those, who [...]ive under the Polars, with whom the Tropicks are equal to those Circles, which comprehend the Stars, which ne­ver come above the Horizon, nor ever go under it.

They are two in number, to wit, the Tropick of Cancer, and the Tropick of Capricorn. The Tropick of Cancer, is a lesser movable Circle, described from [Page 32] the Summer-Solstitial-Point of the Eclip­tick, by the motion of the Primum Mo­bile. The Tropick of Capricorn, is lesser movable Circle, described fro [...] the Winter-Solstitial-Point of the Eclip­tick, by the motion of the Primum Mo­bile.

The uses of the Tropicks are these 1. They demonstrate to us, in the E­cliptick, the two Tropical or Solstic Points, to wit, the beginning of Can­cer, and the beginning of Capricorn 2. They terminate and bound, the Sun greatest Declination, and consequently the greatest Obliquity of the Ecliptick 3. When the Sun comes to either of th [...] two Tropicks, he is either nearest t [...] our Vertical-Point, or furthest removed from it. 4. In an Oblique Sphere, they ly Parallel to the longest, and shortes [...] Day. 5. Between the Tropicks, i [...] comprehended the Torrid Zone, as well in the Heavens, as in the Earth: and by the same Tropicks, the Torrid Zone is divided from the Temperate Zones.

CHAP. VIII. Of the Polars.

THe Polars are lesser Circles of the Sphere, movable, described from the Poles of the Ecliptick, by the mo­tion of the Primum Mobile. For this cause, they are called the Polar Circles. They are two in number, the Polar Artick, and the Polar Antartick. The Polar Artick is a lesser Circle of the Sphere, movable, described from the North Pole of the Ecliptick, by the Mo­tion of the Primum Mobile. The Po­lar Antartick, is a lesser Circle of the Sphere, movable, described from the South Pole of the Ecliptick, by the motion of the Primum Mobile.

They let us see first, the Poles of the Zodiack, and they measure their distance from the Poles of the World. 2. They bound the Temperat Zones, and sepa­rats them from the Cold Zones, which [Page 34] are bounded and inclosed by their cir­cumferences. It is to be observed, that the antient Astronomers, Proclus, Cleo­medes, and the rest, had not the same description of the Polars, which we have. For the Antients, did not de­scribe them, as passing thorow the Poles of the Ecliptick, but thorow the com­mon Sections of the Meridian, and Ho­rizon, equidistant to the Equinoctial▪ and therefore, so much was their di­stance from the Poles of the World, a [...] the height of the Pole was above the Horizon. And by this means, where there is no Elevation of the Pole, as in a Right Sphere, there are no Polars. But from thence, they are more, and more gradually augmented, and enlarg­ed, according to the increment of the Poles Elevation.

The uses of the Polars, according to the Antients, are these, 1. They com­prehend the Arch of the Elevation of the Pole. 2. Of all the Parallels of the Equinoctial, which are always seen a­bove the Horizon, they are the greatest [Page 35] and of all the Parallels of the Equino­ctial, which ly hid under the Horizon, they are the greatest also. But contra­ [...]iwise, of all the Parallels of the Equi­noctial, which arise and set in twenty four Hours, they are the least. There­fore (3.) the foresaid Polars, compre­hend within their Compass, and Circle, [...]he whole Stars and Points of Heaven, which are always in sight, and do not [...]et. Hence, there ariseth a threefold [...]istinction of the Stars. 1. There are [...]ome, which have a perpetual Day, and [...]ever set, or fall under the Horizon, to [...]it, those which are comprehended within the Circle of the Polar Artick. 2. There are others, which have a per­petual Night, which never rise, or come [...]p above the Horizon, to wit all those, which are included within the Circle of [...]he Polar Antartick. There are (3.) o­thers which both rise and set in four [...]nd twenty Hours, to wit those, which [...]ither on this side, or that side of the Equinoctial, tend towards and come nearest to the foresaid Polars.

CHAP. IX. Concerning other Circles of the Sphere, both greater and lesser, which cannot be conveniently drawn upon it.

BEside the Circles of the Sphere hi­therto explained, there are yet in­numerable more, both of the greatest and lesser sort, which Astronomers have excogitated for attaining a more perfec [...] knowledge of the Heavenly Motions▪ 1. There are of the greatest sort Verti­cals, which pass thorow every point o [...] the Horizon, cutting one another there which by the Arabians are called Azi­muths. 2. There are the Horary Cir­cles, which divide the Heavens, into four and twenty parts, which are o [...] three sorts. For either they have the beginning in the Meridian, and pa [...] thorow the Poles of the World, or the have their beginning in the East, o [...] West-part of the Horizon, by whic [...] [Page 37] means they touch lightly, the two Cir­cles lying parallel to the Equinoctial, of which one is the greatest of all, which are always seen above the Horizon, the other the greatest of all, which are not seen above the Horizon: or lastly, they have their beginning in the Horizon, but neither go thorow the Poles, of the World, nor go near to the foresaid Pa­rallels, but divide all the Segments of the Parallels, which are above or be­low the Horizon, into twelve equal parts. 3. There are Circles of Decli­nation, which pass thorow the Poles of the World, and every point of the Equi­noctial. There are 4. Circles of Lati­tude, which pass thorow the Poles of the Ecliptick, and every one of his Degrees.

The lesser Circles are infinite also; for there is no great Circle, which hath not his own Parallels. As first the Ho­rizon, which hath Circles of Altitude, called by the Arabians Almicanthars. The Equinoctial, hath its own Parallels, to wit, described by the Primum Mo­bile, [Page 38] from all, and whatsoever Points are in the Heavens. So hath the Zo­diack his Parallels, described about the Poles of the Ecliptick, which Parallels every Star, or point of the Heavens, ac­cording to the proper motion of the eight Sphere, do describe, and many more are there invented by Astrono­mers for Astronomical uses.

CHAP. X. Of the Zones.

TO the Doctrine of the Sphere, is commonly annexed the Geogra­phical Tractat of the Zones. The Zones therefore are nothing else, but as much bounds, of the Heaven, or of the Earth, as is comprehended between both the Tropicks, or between either of the two Tropicks, and the next Polar, or be­tween either of the two Polars, and the neighbouring Pole. Therefore the [Page 39] Zones, are either Celestial, or Terre­strial. The Celestial Zones, are bound­ed by themselves, and their own Circles in the Heavens. The Terrestrial Zones, ly directly under the same places of the Heavens. They are five in number, one Torrid, two Temperate, and two Frigid. The Torrid Zone, is that space of the Heavens, or the Earth, compre­hended between the two Tropicks. This is divided into two parts, of which one is called the Northern, the other the Southern part. It is called Torrid, because here, the Rays of the Sun are more perpendicular, and so hotter, that the Inhabitants are in a manner scorch­ed, and burnt up with Heat. The Temperate Zones, are that space of the Heavens, or of the Earth, comprehend­ed between either of the two Tropicks, and the neighbouring Polars: and that which is included, between the Tropick of Cancer, and the Polar Artick, is cal­led the Temperate Northern Zone, wherein are contained, all Europe al­most, and a great part of Asia, and also [Page 40] a part of America. But that which is included between the Tropick of Capri­corn, and the Antartick Polar, is called the Southern Temperate Zone. This contains more Sea, and less Land. They are called Temperate, because the Rays of the Sun, being more oblique, there is not such a reflection of Heat, but of­fer a most commodious Dwelling to the Inhabitants. The Frigid Zones, are that space of the Heavens, and of the Earth, comprehended between either of the Polars, and the neighbouring Pole of the World. And that bounds, which is included between the Polar Artick, and the North Pole, is called the Northern Frigid Zone: and that bounds which is included, between the Polar Antartick, and the South Pole, is called, the Southern Frigid Zone. They are called Frigid, because the Rays of the Sun are most Oblique, and are absent almost half a Year; so that all things become rigid and stiff, with Frost, Yce, and Snow. In this Zone, lyes Island and Greenland, but in the [Page 41] Southern cold Zone, the parts are un­known to us.

The Inhabitants of the five Zones, have obtained divers names. For those, who inhabite the Torrid Zone, are called Amphiscii, as having a shadow on both sides. I say on both sides, in respect of the Vertical Point. For the Sun with them, is sometimes on this side, and sometimes on that side of their Ver­tical Point: sometimes the shadow of their Dials is projected from South to North, and sometimes from North to South, when he is in the Meridian. The Inhabitants of the Temperate Zones, are called Heteroscii, as having but one shadow. For at 12 a Clock in the Day, the shadow is either casten to­wards the North, as with us, or to­wards the South, as with those, who dwell in the Southern Temperate Zone. But those, who live in the Frigid Zones, are called Periscii, as having a shadow, which goes round about them; because they have the Sun for several Months of the Year, above their Horizon, and [Page 42] the Heavens there, like a Milstone, is whirled about, so that the Sun and Stars describe Parallels to the Horizon, and therefore in four and twenty Hours, he runs about without rising and set­ting, and projects his shadow into an Orb, or Circle.

There are likewise, the Antipodes, Anteci, and Perieci. Antipodes, are those, who have the same Meridian, but dwell in points of it, diametraliter opposite, and are under opposite Parallels, (to wit in an oblique Sphere,) of which the one is Southern, the other Northern. These following Phenomena, are proper to them. 1. Though they have the same Rational Horizon, yet beholding the opposite Faces, all things fall out to them contrariwise. For when we have Day and Mid-day, our Antipodes have Night and Mid-night. When we have Summer, they have Winter. When the Sun rises to us, he sets to them. We have North Latitude, they have South Latitude.

The Anteci are those, who dwell un­der [Page 43] opposite Parallels, equally distant from the Equator, towards both the Poles, under the same Meridian, but not in Points diametraliter opposed, but in a Semi circle of the Meridian inter­cepted between the Poles. They have these Phenomena proper to them. First, They agree in the same Longitude, and Latitude; for how much is the South Pole elevated to those, so much is the North Pole elevated to these. 2. In the same Moment of Time, both of them have the Sun in their Meridian. But in this they differ; while the Sun is coming to the Tropick of Cancer, those have Summer and longer Days, but these have Winter, and shorter Days. Again, when the Sun is returning, those have Harvest, the Days Decreasing, but these have the Spring, the Days Increasing. Hence it is, that the Sun doth not rise, and set to both, at the same time.

The Perieci are those, who dwell un­der the same Parallel and Meridian, but in Points of the same Parallel diametra­liter [Page 44] opposite; so that both of them be­hold the same Pole, with equal height above the Horizon. First, They dwell in the same Zone. Secondly, They have the same Elevation of the same Pole. They have the same Winter, the same Summer, the same longest Day, and the same increment, and decrement of the Natural Days. But here they differ; those having the Sun rising, these have it setting; those having the Sun in the Meridian, these have it at our Mid-night: and contrariwise, when to those the Sun is setting, to these he is rising, when to those it is Mid-night, to these it is the Meridian.

CHAP. XI. Of the Rising and Setting of the Stars ac­cording to the Poets.

HItherto we have treated of the Hypotheses, to wit, the Circles of the Sphere, which so much conduce [Page 45] for explaining the Phenomena of the Primum Mobile. It now remaineth, that we speak and treat of the thing it self, to wit, the Phenomena themselves. And in the entry, we ought to have spoken of the rising and setting of the Stars, called Ortus & occasus stellarum Astronomicus; but the knowledge of those things, cannot be taught here com­pendiously, nor without the Science of Spherical Trigonometry; therefore pas­sing this, we come to explain the rising and setting of the Stars, called Ortus & occasus Poeticus, which is the second Phenomenon of the Primum Mobile.

This rising and setting of the Stars according to the Poets, is nothing else, but the rising of a Star above the Ho­rizon, and the setting of a Star under it, in relation to the various Position of it, with the Sun. It is called Poetical, not because it doth not belong to Astrono­mers; for it is a part of their Science to determine those Risings and Settings, but because the Poets in describing cer­tain [Page 46] Seasons of the Year, use this me­thod, as will be seen afterward.

Of this Poetical Rising and Setting, there are three forms. First, That which is called the Rising and Setting of a Star Cosmice. Secondly, That which is cal­led the Rising and Setting of a Star, A­cronyce. Thirdly, That which is called the Rising and Setting of a Star Heliace. Each one of those hath a double signifi­cation; one general, the other special. The Rising of a Star Cosmice generally taken, is the Rising of a Star above the Horizon, falling out from the Rising of the Sun to his Setting. The Setting of a Star Cosmice, generally taken, is the Setting of a Star, falling out from his Rising to his Setting. The Rising of a Star Acronyce, generally taken, is the Rising of a Star above the Horizon, fal­ling out the whole time, the Sun is un­der the Horizon. The Setting of a Star Acronyce generally taken, is the Setting of a Star under the Horizon, falling out all the time the Sun is under the Hori­zon. The Rising of a Star Heliace gene­rally [Page 47] taken, is the appearing of a Star after the Sun is Risen. The Setting of a Star Heliace generally taken, is the disappearing of a Star, after the Sun is set. But their special signification de­notes, and determines, a certain, and definite time. Therefore, the Rising of a Star Cosmice, is the ascending of a Star above the Horizon, in the same mo­ment, wherein the Sun Rises. The Set­ting of a Star Cosmice, is when a Star goes down, while the Sun is Rising. The Rising of a Star Acronyce, is when a Star comes above the Horizon, the Sun go­ing down under the Horizon that same moment. The Setting of a Star Acrony­ce, is when a Star Sets with the Sun, that same moment. The Rising of a Star Heliace, is when a Star, which could not be seen, by reason of its nearness to the Sun, is now seen in the night time. The Setting of a Star Heliace, is when a Star, by reason of the Suns great distance from it, might have been seen in the night time, but the Sun coming nearer to it, it disappears out of our sight.

[Page 48]We have an Example of the Rising of a Star Cosmice, in the first Book of the Georgicks.

Virgil doth express here the Spring time, when the Millet-seed is to be sown [...] which is in the beginning of April: An [...] seing the Sun at that time, is about th [...] [Page 49] end of Aries, it must be understood of the Rising of Taurus, which at that time riseth with the Sun Cosmice. At this time the Romans used to sowe their Beans, their Claver-grass, and their Mil­let, which every year must be renewed; whereas the Claver-grass is to be sown but once in ten years.

We have likewise an Example of the Set­ting of a Star Cosmice, from that same place in Virgil.

Before you sowe your Ground (says [Page 50] he) let the Pleiades, or Seven-stars be set, which about October 18, go down in the West, in the same Moment of Time, while the Sun is Rising in the East, which is called Occasus Cosmicus.

We have an Example of the Rising of a Star Acronyce, from Ovid, in his first Book de Ponto.

Ovid is here speaking of the Harvest time, when the Sun is in Scorpio, there­fore when the Sun is Setting, Taurus or the Bull, and the Pleiades are Rising Acronyce.

[Page 51]We have also an Example of the Set­ting of a Star Acronyce, from the same Ovid, in his second Book of his Fasts.

This time, is the second day of Fe­ [...]uary, at which time the Constellation [...]lled the Harp, sets Acronyce, with the [...]u.

We have likewise an Example of the Rising of a Star Heliace, from the first Book of the Georgicks.

'Tis eviden [...] that Virgil speaks here of the Rising of this Constellation He­liace, called Aridnes Crown, when the Sun is in the beginning of Scorpio. For seing this Constellation rises at Rome, where Virgil lived, with the 27 Degree of Virgo, it is needful to conceive this Crown to be seen in the Morning, the Sun being yet under the Horizon.

Note, That there is a Figure called Hypallage in the word Decedat: for the Crown doth not recede from the Sun, but the Sun from it.

And lastly, We have an Example of the Setting of a Star Heliace, from the same place of Virgil.

[Page 53]The Poet is here speaking of the Suns ingress into Taurus, which fell out in Virgils time on the 1 [...] of April. But seing the Dog-star sets at Rome with the 22 Degree of Taurus, therefore, the Sun setting in the Evening, the Dog­star setteth Heliace, or disappears out of our sight, by reason of the Suns Rays, which now are nearer him.

Observe, That what Stars do arise Cosmice, which is also called Ortus Ma­tutinus, they set Acronyce, which is cal­led Occasus Vespertinus: and what Stars do arise Acronyce, which is called Ortus Vespertinus, they set Cosmice, which is called Occasus Matutinus, according to the following Rhyme.

Aliter.

Note secondly, That the word Cos­micus, comes from Kosmos, the World. That the word Chronicus, comes from the Greek word Chronos, Time. But Acronycus comes from Acra & Nux, which is the first part of the Night, or the Evening▪Twilight. That Heliacus comes from Helios, the Sun. Lastly, That Chronice, and Acronyce have the same signification.

CHAP. XII. Concerning the Natural, and Artificial Days.

NOw follows another Phenomenon of the Primum Mobile, to wit, the Doctrine of Days Natural and Artifi­cial. [Page 55] Days are twofold, Astronomical, and Civil. Astronomical Days, are such as are measured, by the Revolu­tions of the Equinoctial, and deter­mined by a certain quantity. Days Civil, are such as every Nation, accor­ding to their own Custom make use of. The Astronomical Day, is either Na­tural, or Artificial. The Natural Astro­nomical Day, is a space of time, where­in the Sun, by the Motion of the Pri­mum Mobile, being carried about, from whatsoever immovable point of the Hea­vens, returns to that same point again. These Astronomical Days have their be­ginning in the Meridian, as was insinuate before. The Artificial Astronomical Day, is a Space of Time, wherein the Center of the Sun remains above the Horizon. And the Artificial Night, is as much Time, as the Center of the Sun remains under the Horizon.

The Doctrine of the Artificial Days and Nights, is contained in the follow­ing Theorems. 1. The Artificial Days and Nights, with the Amphiscii, Hete­roscii, [Page 56] and partly with the Periscii, are parts of the Natural Day: but with the Periscii, in those parts of the Earth, wherein the Sun, by the going about of the Primum Mobile, perfects some Circumgyrations, either above the Ho­rizon, without setting, or under the Horizon, without rising, one Artificial Day, or one Artificial Night, doth ex­cresce into many Natural Days; so that indeed under the Poles, the Artificial Day contains half a Year, and the Ar­tificial Night as much; and so to speak properly, the whole Year consists but of one Day, men looking to the Analo­gy of the Natural Day. 2. Under a Right Sphere, the Artificial Day, is equal to the Night: for the Horizon, in this Position of the Sphere, cuts the Circuli Dierum, the Day-Circles, into two equal parts. The Day-Circles, are called those Parallels of the Equator which the Sun doth dayly describe, by the Motion of the Primum Mobile. 3. In an Oblique Sphere, there are only twice a Year, two Equinoxes, when the Sun [Page 57] is in the beginning of Aries and Libra. The Reason of this appears, from the mutual Section of the Horizon, with the Circuli Dierum, or Day-Circles, which is indeed unequal, except when the Sun is in the Equinoctial. 4. In an Oblique Sphere, which hath the vicissi­tude of the Artificial, and Natural Day, by one Revolution of the Equator, the Sun being in the. Tropick of Cancer (we are now speaking of this upper­most part of the Sphere) we have the longest Day in all the Year, and the shortest Night: but the Sun being in the Winter Solstice, the Day is shortest, and the Night longest. 5. In the same Position of the Sphere, thorow the whole half of the Ecliptick descending, the Sun maketh the following Days shorter, than the Days going before, but the Nights longer. But in the half of the Ecliptick ascending, the Sun maketh the Days following longer, than the Days going before, but the Nights shorter. 6. When the Sun is existing, in places of the Ecliptick, equally di­stant, [Page 58] from the same Solstitial Point, Days are equal to Days, and Nights to Nights. 7. When the Sun is existing in places of the Ecliptick equally di­stant, from the same Equinoctial Point, the Day of one Place, is equal to the Night of another. 8. In an Oblique Position of the Sphere, the greater the Elevation of the Pole is, the greater are the increments of the longest Day, and shortest Night, until coming under the Polars, the longest Day contains twen­ty and four Hours. 9. In an Oblique Sphere, of such as dwell between the Polar, and next Pole, the longest Day excresceth into many Natural Days, as also the longest Night. But there are certain intermediat Horary Circles, a part of which is above the Horizon, and a part under, in which, when the Sun is existing, the Artificial Days, as also the Nights, are▪ parts of the Natu­ral Day. 10. In a Parallel Sphere, such as they have, who live under the Poles, the whole Year, is divided into one Artificial Day, and one Artificial Night.

[Page 59]The length of every Artificial Day, is known by the Diurnal, and Nocturnal Arch. First, find the Oblique Ascension or Point of the Equinoctial, which ris­eth with the Sun, and Oblique Descen­sion, or Point of the Equinoctial, which setteth with the Sun. Subtract the les­ser from the greater, and half the diffe­rence, is the Ascensional difference, which added to six Hours in the Sum­mer half Year, but subtracted therefrom in the Winter half Year, gives half the Diurnal Arch, whose double is the whole Diurnal Arch, and the Complement of the Diurnal Arch to 24 Hours, is the Nocturnal Arch. For Example, The tenth day of April 1687, the Oblique Ascension of the Sun (being in the first Degree of Taurus) is 10 deg. 21. m. the Oblique Descension is 45 deg. 27 m. whose difference is 35 deg. 6. m. whose half is 17 deg. 33 m. the Ascen­sional difference, which being added to 90 deg. or 6 Hours, is 107 deg. 33 m. which make 7 hours, 10 m. fere, for the time of the Suns setting, which is [Page 60] always half the Diurnal Arch. There­fore the Diurnal Arch is 14 hours, 20 m. Which taken from 24 hours, there remains 9 hours, 40 m. for the No­cturnal Arch required. Note, That the Ascensional difference added to the Oblique Ascension in the Summer half Year, but subtracted from it, in the Winter half Year, gives the right A­scension of the Sun, or any of the Stars.

What is said of the Day in respect of the Sun, may be most commodiously applyed to the Stars. For the Day of a Star, is rightly called the space of Time, wherein it is above the Hori­zon: and the Night of a Star, the space of Time, wherein it is below the Hori­zon. Concerning the days of the fixed Stars, let the following Theorems be observed. 1. In a Right Sphere, the Stars have a perpetual Equinox. 2. But in an Oblique Sphere, the fixed Stars, whose North Declination, is greater than the Complement of the Altitude of the Pole, are said to have an Eternal Day: but those Stars, whose South De­clination, [Page 61] exceeds the Complement of the Altitude of the Pole, are said to have an Eternal Night. The interme­diate Stars, have the course of rising and setting. 3. In a Parallel Sphere, the fixed Stars are said to have Eternal Days, and Eternal Nights.

Days Civil, are called the space of Time, of one Revolution of the Equi­noctial, which according to every Na­tion, or Countrey, is divers ways be­gun, and made use of. For as there are various and divers Nations in the World, so each one hath a different way of be­ginning their Hours. For the Iews, by Divine Institution, began their Day, from the setting of the Sun, which cu­stom the Italians do observe. The Ba­bylonians began their Day from Sun ri­sing, whose practice, the Norinbergers, the People called the Umbri, and the Egyptians do imitate. The Arabians as the Astronomers, begin their Day from the Meridian. The Romans from Mid­night. The Germans, the Frenches, and Spainards begin their Day from the [Page 62] Meridian, and Mid-night. For their Clocks, and Watches are so contrived, that they return from one a Clock in the Night-time, to twelve a Clock in the Day-time, and from one a Clock in the Day-time, to twelve a Clock at Night-time. Their Days are divided, as the Astronomical Days, into one Ar­tificial Day, and likewise into Forenoon, and Afternoon.

And because Hours are parts of the Days, therefore we must speak a little of them. The Hour is the twentieth and fourth part of the Natural Day, or the space of Time, wherein the twen­tieth and fourth part of the Equino­ctial, or 15 Degrees thereof, riseth a­bove the Horizon. But this Definition is not sufficient, because it doth not agree to all Hours: for every twelfth part of every Day, and every Night whatsoever, was called by the Iews, and the Antients an Hour. But 15 De­grees of the Equinoctial, do not al­ways ascend above the Horizon, every one of these Hours; but sometimes [Page 63] more, and sometimes fewer, as will ap­pear afterward. Therefore, an Hour may rather be defined thus, a certain part of the Artificial Day, and Night, made use of by divers Nations, after a divers manner, that it may be known generally, what the Hour is. For in effect, that definition agrees only to to those Hours, which are called Hor [...] Aequales, equal Hours. The Hours then, which are called unequal, ought to be defined thus. The twelfth part of every Artificial Day and Night: therefore according to the divers Sea­sons of the Year, the Hours are some­times shorter, and sometimes longer: in Summer longer, and in Winter shor­ter, as are th [...] Iewish Hours: for they divide both the Day, and the Night in­to twelve parts, both in Summer and in Winter, calling the rising of the Sun, the beginning of the first Hour, and consequently nine their third Hour; twelve their sixth Hour, three a Clock in the Afternoon their ninth Hour, and the setting of the Sun, the end of their [Page 64] twelfth Hour, by which means, their Hours must be far longer in Summer, than in Winter.

The equal Hours are of three sorts: for some take their beginning from the setting of the Sun, as the Italian Hours. Others take their beginning from the rising of the Sun, as are the Babylonish Hours, and the Hours of the City of Norimberg, who from the rising of the Sun begin the number of the Hours of the Day; the Circles of which Hours do lightly touch the greatest Parallels, of all, which do appear above the Ho­rizon, and of all which do not appear. Lastly, Others do take their beginning from the Meridian, which Astronomers make use of, and these Nations, which either take their beginning of Hours from the superior part of the same Cir­cle, or from the inferior part.

CHAP. XIII. Concerning Years.

AS Hours make up Days, so Days make up Years, therefore we must speak somewhat of Years. The Year then is twofold, Astronomical, and Po­litical. The Astronomical Year, is the space of Time, wherein the Sun returns, either to the same Point of the Ecliptick, or to the same fixed Star. And this is twofold, the Tropical Year, called An­nus Vertens, or the Syderial Year. An­nus Vertens, is a space of Time, where­in the Sun leaving some Point of the Ecliptick, returns again to the same Point. The quantity of this Year is changeable; for sometimes it is more, and sometimes it is less. Between these two extreams, the middle Year contains 365 days, hours 5, m. 49, sec. 15. thirds 46. But the true or apparent Year is sometimes 365 days▪ hours 5, [Page 66] min. 56. sec. 53, thirds 1. Sometime it is 365 days, hours 5, min. 42, sec. 28, thirds 27. The Syderial Year, is a space of Time, wherein the Sun un­der the Starry Sky, returns to the same fixed Star. The quantity of this Year is 365 days, hours 6, min. 6, sec. 39. It is always equal to it self, and there­fore the measure of the Year called An­nus Vertens. The beginning of this Annus Vertens, is taken from the Vernal Equinox, but the beginning of the Sy­derial Year, from the first Star of Aries.

The Political Year, is an Annual space of Time, which is either accom­modated to the course of the Sun, or the Moon, or to both, according to the common reckoning of several Countries and Nations. This Political Year is manifold; for it is either Iulian, which contains 365 days, hours 6, which six Hours, if they were reckoned every Year, would make confusion: there­fore the Masters of Astronomy have ap­pointed, they should be omitted, till the fourth Year, and then four times six, [Page 67] make 24, which make up a full and compleat Day, which being inter caled, that is, interlaced, or put between, as in Leap Year there is a Day put be­tween the 28 of February, and the first of March, the Year is called Annus In­tercalaris, or Bissextile Year. It is to be adverted, that the cause of correcting the Iulian Calendar, by Pope Gregory the 13, in the year 1582, was the un­just quantity of it. For by this, it came to pass, that after some Ages, the four Cardinal Points did anticipate and pre­vent their Seats; and so at length the four Seasons of the Year, might be in­terchanged. From this it is evident this Day, that according to these times, the Equinoctial, and the Ingress of the Sun into the 12 Signs have anticipated almost 13 Degrees. That is, the en­tering of the Sun, into Aries, Taurus, &c. falleth out sooner by 13 Degrees, than to the Romans: which comes to pass, because more, than what is just, is given to the space of the Year. For there were given to the Year, by the corre­ction [Page 68] of Iulius Cesar, 365 days, and six hours: for which hours, every fourth year, one day is added, and so the com­mon Iulian year contains 365 days, but the Bissextile 366. But seing the Solar year, in which the Sun runs thorow the whole Ecliptick, is less than this space, by almost eleven Minuts of Time every Year; it comes to pass, that in 50 year, and a half, one hour remains, and in the space of 130 years, a whole day remains.

I said the Political Year, was mani­fold, either Iulian, of which hitherto, or Egyptian, or Iudaical. The Egyp­tian year contains always 365 days. This Year was esteemed most useful by the antient Astronomers, for the Art of reckoning the Celestial Motions. The Iudaical Year is accommodated and fitted to the Motion of the Moon, and contains, for the greatest part, twelve, and sometimes thirteen Lunations. This Year did the Astronomers use, before the reformation of the Calendar, insti­tuted by Iulius Cesar, by the help of [Page 69] one Sosigenes, a famous and learned Ma­thematician. The beginning of these Years is divers also. For the antient Romans, began their Year from March: the later Romans from the midst of Win­ter, called Bruma. The Iews, by Di­vine Institution, began their Year from the New Moon, which was next after to the Vernal Equinox. That we this day begin our Year from the first of Ianuary, it is for this, because we fol­lowing the custom of the late Romans, beginning their Year from the midst of Winter, which was nearest to the first of Ianuary, by little and little the Win­ter Solstice did prevent, and anticipat its Seat, and Place. The Egyptian year, hath not a sure beginning, by reason that six hours are omitted. Hence is it, that every fourth Year it anticipats one Day: and therefore within 365 Years, four times numbered, or 1460 Iulian Years, the beginning of the Egyptian Year, wanders over all the Days of the Iulian Year.

CHAP. XIV. Concerning the divers Phenomena, which are to be seen in the various Positi­ons of the Sphere.

THe last part of this little Tractat, shall be in examining the Pheno­mena, which are proper to the various Situations, and Positions of the Sphere. The Sphere may have seven different Positions, 1. When both the Poles of the World do rest in the Horizon, which is called a Right Sphere. The second Po­sition is Oblique, when our Vertical Point, is terminated between the Equi­noctial, and either of the Tropicks. The third Position is, when our Zenith is un­der either of the Tropicks. The fourth is, when our Zenith is between either of the Tropicks, and the neighbouring Polar. The fifth is, when our Zenith is in the very Polar itself. The sixth is, when our Zenith is between either of [Page 71] the Polars, and the neighbouring Pole of the World. And lastly, when the Poles of the World, do fall in with the Poles of the Horizon, which is called a Parallel Sphere.

CHAP. XV. Concerning the Phenomena of the first Position.

1. EVery Star in the Heavens riseth and setteth, neither is there one of them, without this property: and therefore in this Position, there is nei­ther Polar Artick, nor Antartick, ac­cording to the Antients. 2. There is here a perpetual Equinox. 3. The Sun every Year passing twice over their Heads, is to them twice Vertical, to wit, when he is in the Equinoctial Points. 4. As much, as the Sun declines from their Vertical Point, towards the North, as much also doth he decline from their [Page 72] Vertical Point, towards the South. 5. They have four Solstices, two when the Sun is highest in their Vertical Point, and two, when he is lowest, in Cancer, and Capricorn. 6. They have two Sum­mers and two Winters, but only Ana­logically: for even in Winter, their Bodies are scorched with heat. 7. There are here in this Position, five different Shadows, the Meridional, or South Shadow, the North Shadow, a Shadow from the East, a Shadow from the West, and a perpendicular Shadow, which falls out only, when the Sun is in the Equinoctial Points. 8. The end or ex­tremity of their Gnomons, upon their Horizontal Dialls, which are our Polar Dialls, describe the whole Year, the Fi­gure called Hyperbole, except when the Sun, is in the beginning of Aries and Libra, where he describes a straight and right Line.

CHAP. XVI. Of the Phenomena of the second Position▪

1. SOme Northern Stars tarrying al­ways above our Horizon, have Eternal Days; and contrariwise, there are some about the South Pole, which never come above the Horizon, but have Eternal Nights. 2. The Artick, and Antartick Circles, according to the Antients, are not as yet equal to our Polars. 3. The Artificial Day is not equal to its own Night, two Days only ex­cepted, when the Sun is in the Equino­ctial Points, at which time, there is thorow the whole World an Equinox. 4. The longest Day there, doth not ex­ceed thirteen Hours and a half. 5. The Sun is to them, twice Vertical every Year, to wit, when he comes to those Degrees of the Ecliptick, whose Decli­nation, is equal to the Latitude of the Place; for he describes then, a Parallel [Page 74] thorow the Zenith. 6. The Sun in the Meridian, goeth further towards the South, than towards the North. Note, That we are now speaking, and in the following Discourse, of those seven Po­sitions, which are in the Northern Sphere. 7. There are here, four Sol­stices, two high, and two low. The two highest fall out, when the Sun is in that Parallel, which passeth thorow the Zenith. The two lowest are, when the Sun is in the Tropicks. Yet that which falls out in the Tropick of Capricorn, is lower, than that which falls out in the Tropick of Cancer. 8. They have two Summers, and two Winters, but une­qual, as appears from the various Situa­tion of the Parallels. 9. The longest Day is not, when the Sun is in the highest Solstices, but in the Tropick of Cancer. 10. There are five different Shadows, as we observed in the first Position. 11. The end or extremity of the Gnomon, by its Shadow, when the Sun is out of the Equinoctial, de­scribes (as in the first Position) the [Page 75] Figure called Hyperbole, but the oppo­site sides are not equal as there, but un­equal. 12. In any part of this Position, where the Elevation of the Pole, is less, than the Declination of the Sun, the Shadow of a Style perpendicularly e­rected upon a Plain, may have a natu­ral, visible, Retrocession. In the mat­ter of Ahaz his Dial, the Retrograda­tion of the Shadow was miraculous, be­cause it was done without, and not within the Tropicks, neither is it possi­ble in nature, it can happen, but where the Elevation of the Pole, is less than the Suns Declination, which is only within the Tropicks. But the foresaid Dial was placed far without, to wit, under the Latitude of 35 Degrees.

CHAP. XVII. Of the Phenomena of the third Position.

1. ALL the Stars, which are com­prehended within the North Polar, remain always above the Hori­zon, neither do they ever set, unless it be, by a general setting Heliace: and contrariwise, all the Stars, which are comprehended within the South Polar, have a perpetual Night▪ therefore the Polars, according to the Antients, are now equal to our Polars. 2. The longest Artificial Day is, when the Sun passeth over our Zenith; the shortest, when the Sun is farthest in the Meridian removed from it. 3. Once a Year on­ly is the Sun Vertical, to wit, when he is in the beginning of Cancer. 4. The Sun in the Meridian, never descendeth from the Zenith towards the North, but returning from the Tropick of Can­cer, he is alway in the South. 5. There [Page 77] are here, but two Solstices, one high, another low. The highest, when the Sun is in the Tropick of Cancer; the lowest when the Sun is in the Tropick of Capricorn. 6. The Day is longest, when the Sun is in the Tropick of Cancer, it is shortest when the Sun is in the Tropick of Capricorn. 7. There is one Summer, when the Sun is in the Zenith, and one Winter, when he is in the Winter Solstice. 8. They have four different Shadows, one Perpendicular, one Oriental, one Occidental, and one Meridional. Here begin the Heteroscii, for the Meridional Shadows begin there to decay, that is, the Shadows project­ed towards the South. 9. The extre­mity or end of their Gnomon, upon their Dials, describe also the Figure cal­led Hyperbole, the sides opposite being unequal.

CHAP. XVIII. Of the Phenomena of the fourth Position.

AS the Artick and Antartick of the Antients, are greater than our Po­lars, so there are more Stars in this Po­sition of the Sphere, seen perpetually, and more perpetually lurking under the Horizon, than in the last Position. 2. The unequality of Days and Nights, are also augmented. The Artificial Day is at the longest, when the Sun comes nearest to our Zenith, and at the short­est, when he is furthest removed from it: and as the shortest Artificial Day cannot be less, than 13 Hours and a half, so the longest Day cannot be 24 Hours. This least Artificial Day, is truly the longest Day, our Vertical Point coming nearest to the Tropick. It is called the least Artificial Day, because it is the shortest of all the longest Days, which can arise from the variation of [Page 79] the Vertical Point, between the Tropick and the Polar: and therefore, itis not cal­led Minima the least, in respect of the rest of the days of the same Elevation of the Pole, but in respect of the rest of the longest Days, which may be found be­tween the Tropick and Polar. The longest Day in this fourth Position of the Sphere, the Zenith coming nearest to our Tropick, cannot be less, than 13 Hours and a half, as the longest Day cannot contain 24 Hours. For this comes to pass, when the Zenith is in the Polar: therefore we must read, as the shortest Artificial longest Day, cannot be less, than 13 Hours and a half, &c. 3. The Sun can never come to their Ze­nith, neither can he ever touch lightly ( stringere) their Horizon, when he is in the Meridian. 4. There are two Solstices, one when the Sun is in Cancer, and highest, another lowest, when he is in the Tropick of Capricorn. 5. There is one Summer, and one Winter. 6. There are only three different Shadows, one Oriental, the second Occidental, and [Page 80] the third Northern. 7. The extremity or end of their Gnomons, fixed upon the Ground perpendicularly, describe as yet Hyperboles.

CHAP. XIX. Of the Phenomena of the fifth Position.

ALL the Stars, whose distance from the Equinoctial, is greater than the Obliquity of the Ecliptick, either do not set under the Horizon, if they be Northern Stars, and do not rise above the Horizon, if they be Southern Stars: Therefore the Artick, and Antartick of the Antients are equal to the Tropicks. 2. The longest Day contains 24 Hours, and then there is no Night: and con­trariwise, the longest Night consists of twenty and four Hours, and the Artifi­cial shortest Day is nothing. 3. The Sun every year toucheth lightly the border of the Horizon twice, without rising and setting, namely when he is in [Page 81] the Tropicks. 4. The Sun at twelve a Clock in the Day, is alway South, nevertheless, when he is in the Tropick of Cancer, the half of his Body may be seen in the North, at 12 a Clock at Night. 5. There are here two Sol­stices, one high in Cancer, the other low in Capricorn. But according to the simi­litude of Solstices, which are in other Zones, we may say there are three Sol­stices there, one high in Cancer, when the Sun is high in the Meridian, to wit, 47 Degrees above the Horizon, which is the distance of the Tropicks; there are two lower, of which one is in the same Tropick of Cancer towards the North, when he toucheth lightly the border of the Horizon, the other in the Tropick of Capricorn, where he also light­ly toucheth the border of the Horizon. 6. There is one Summer, and one Win­ter. 7. There are four different Sha­dows; one Eastern, one Western, one Northern, and one Southern; tho this happens but once a Year, the Sun shine­ing with the half only of his Rays, which [Page 82] makes the light more obscure and dark, than when he shines with his full Rays. Here begin the Heteroscii. 8. The ex­tremity or ends of the Gnomons, de­scribe the Figure called Parabola, upon the Horizontal Dials, but an Hyperbole, so soon, as the Sun is gone from the Equinoctial, whereas on all other Plains, he describes always straight and right Lines.

CHAP. XX. Of the Phenomena of the sixth Position.

THere are very few Stars, which can rise or set, to wit, those on­ly, whose Declination is less than the distance of the Tropicks; because the Artick, and Antartick Circles, compre­hending within them, the Stars which do set, and do not set, are greater than the Tropicks. 2. They have an Equi­noctial, as other parts of the Earth. But when the Sun is in that Parallel [Page 83] whose Declination from the Equino­ctial, is equal to the distance of the Poles of the World from the Zenith, the Day is twenty and four Hours, and the Ar­tificial Day excresceth, and shoots out, into many Natural Days. 3. The Sun being in the same Parallel, he lightly toucheth, the border of the Horizon, and coming to it, she shines only with an half Orb. 4. They have but only one Solstice, in the Tropick of Cancer; for the other in the Tropick of Capricorn cannot be seen. But Analogically, and [...]n similitude there are six Solstices. Two high, when the Sun is in the Tropick of Cancer: for there, as well to the [...]outh, as to the North, the hight of [...]he Sun in the Meridian is highest, al­ [...]eit the Northern be greater than the [...]outhern: and four lowest, when the [...]he Sun toucheth lightly the Horizon. [...]. They have one Summer, and one [...]inter, but their Summer may be so [...]alled only Analogically: for these [...]laces of the Earth, are perpetually stiff [...]ith Snow and Yce. 6. They have [Page 84] four different Shadows, one from the East, one from the West, one from the South, and one from the North. Here are the Periscii. 7. The Gnomons, and stiles of their Dials, describes with their Points, Elliptical Figures.

CHAP. XXI. Of the Phenomena of the seventh and last Position.

1. THere are here no Stars, which either rise or set, but all of them are whirled about, equally distant from the Horizon. The Artick and Antartick Circles, are one and the same with the Horizon, and Equinoctial, which are now united. Understand this of the fixed Stars only; for the Pla­nets absolving their course, rise and set, in their appointed times. 2. The Ar­tificial Day is extended to half a Year; so is the Artificial Night, and therefore the quantity of the Natural Day, and [Page 85] the whole Year is one and the same. 3. When the Sun is in the Equinoctial, he shines only with half his Orb, and toucheth lightly the Horizon, and there he riseth and setteth only at those times. 4. No point of the Heavens, can be cal­led, either West, East, South or North, seing the Pole of the World doth not incline to any part of the Horizon, by which Inclination the four Points of the Universe, have their distinction. 5. They have only one Solstice, to wit, in Can­cer, but Analogically two other may be added, to wit, when the Sun is in the beginning of Aries, and Libra. 6. There is one Summer and one Winter: but their Summer is rather to be called a slender slaking of the Cold. They have one Winter, because the Sun is under their Horizon a whole half Year together. 7. The Gnomons of their Dials, describe with the extremity of the Shadow, upon an Horizontal Plain, perfect Circles.