generall reason is ether in respect of their names or their definition They are named by the Greekes 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Tropickes by the Latines Versiles conuersius Vertentes tourning and the Solstitiall paralleles Their definition conteineth their quantitie and their circumference Their quaÌ„tity is noted either in respect of the other circles these being compted in the number of the lesse circles or in regard of theÌ„selues whereby they are compted equall in asmuch as they are equally distant from the centre of the world beeing separated the one from the other by the double distance of the ☉ greatest declination Their circumference is that round compasse which the ☉ passing throughe the 2 solstitiall points doth describe They are in number 2. the one Septentrionall the other Meridionall The Septentrionall Tropicke is on this side of the Equator in respect of vs which wee call either the Sommer tropicke for that it passeth through the poinct of the Sommer solstice orâ—ls the tropick of ♋ because it is described through the end of ♊ the beginning of ♋ The Meridionall tropicke is situated on the other side of the Equator and is called either the Winter tropicke as passing through the poinct of the Winter solstice or the tropicke of ♑ because it is drawen through the head of ♑ The offices and commodities of them are in number 4. 1 They shewe the Tropes that is the conuersions or tournings of the ☉ aswel in Sommer happening in our age the 3. and 2. of the Ides of Iune as also in winter the 3. 2. of the Ides of December 2 They shew in euery situation of the sphere both the longest day which is as long as the diurnall Arke of the Tropicke of ♋ conteineth howers and the shortest day which is as long as the space of howers conteined within the diurnall arke of the tropicke of ♑ 3 They poinct out the limits of the course of the ☉ and his greatest declinations which are 23. gr 52. mi. as in the time of Aristarchus Ptolemee or 23. gr 28. mi. as it is now in our time 4 They shew the burnt zone which they separate from the temperate and the midst of the second climate which they call dia-Syenes and Anti-dia-Syenes Of the 2. polare circles Chap. 26. The two poles of the Zodiake carried about by the regulare reuolution of the vniuersall frame describe about the poles of the worlde two circles whereof the generall reason the number and the vse is to be noted The generall reason offereth to our consideration their name their definition and their accidents They are called the Polare circles either because they are described about the poles or by the poles Their definition by the Latines t is made by their quantitie and their circumference and plane Touching their quantity they are in the number of the lesse circles equall in all places Their circumference and plane is described either by lines drawen from the poles of the Zodiake vnto the Axe of the worlde at right angles and hauing by the daily motion a perfect reuolution or els they are described by certen semidiameters drawen from the centre of the earth vnto the poles of the Zodiak and turned about by the diurnall and nocturnall motion The accidentes of the polare circles do determine either their equality for they are paralleles compared either one with another in asmuch as they are equidistant from the centre or compared with the tropicks the Equator or else they determine their distance either from the next tropicke which is 43. gr or from the poles of the worlde which is equall vnto the ☉ greatest declination They are two in number The one Septentrionall the other Meridionall The Septentrionall Polare circle is described by the North pole of the Eclipticke the Meridionall by the South pole thereof The Septentrionall polare circle is called Boreall North of the North winde called Boreas and Arcticke and Septentrionall because of the 2. constellations the one of the greater beare called Arctos the other of the lesse beare called Septentriones which are nigh thereunto The Meridional polare circle is called Australl or Southerne of the South winde called Auster and Antarcticke â—s opposite vnto the Arcticke and Meridionall of the South part of heauen called Meridies Their vse is noted in that they comprehende the cold and frozen zones and the inhabitants of the earth called Perison whose shadowes goe round about them and on either side limite the the distances of the poles The Polare circles otherwise described according to the Grecians Chap. 27. THe polare circles are described either according to the greatest declination of the ☉ or the altitude of the Pole aboue the Horizon The greatest declination of the ☉ by means of the motion of inclination of the eight Sphere is diuerse For it was one in times past and is found to be another now and of such circles the reason is declared in the Chapter before The polare circles described according to the altitude of the pole require the consideration of their definition their varietie their offices and the manner of their description In defining the Arcticke polate circle we say 1. That it is the greatest of those circles which are alwaies in our sight that is of those which we may see at the same instant 2. that it toucheth the Horizon in one point 3. that it is altogether aboue the earth In defining the Antarctick polare circle we say 1. that it is equall and parallele vnto the Arcticke 2. that it toucheth the Horizon in one point 3. that it is altogether hidden vnder the earth The varietie is manifolde according to the didiuersitie of the climates For either they are not at à ll as in a right Sphere it happeneth where excluding altogether the polare circles the Grekes recon 3. paralleles onlie or els they are and those sometimes either lesse equall or greater then the tropickes or els they are equal vnto the Equator and the Horizon For by how much the pole shal be higher by so much shal these circles be greater The offices and vse of the Arcticke circle is in that it sheweth the Starres that neuer arise â—nor sette of the Antarcticke circle the conâ—trary is to be conceiued The meanes of their description is by those Starres that in any Region do touch the Horizon Of the Milkie circle Chap. 28. OF all the circles there is none to be seene beside the Milkie circle which for that the Greekes do recon among the other circles we wil expresse the names the definition the causes thereof and the distinct Starres which make the same The names are diuerse as Galaxia the Milkie orbe or circle the Milkie Zone or milkie waye The Arabians dal it Matarati as it were a broad space or arke that moueth It is defined to be one of the greater circles oblique drawen or stretched toward both the Poles most brightly shining apparent vnto the sense inequall both in
on the one side longer from whence are deriued figures long and broade as pillers or cylinders or els they are of other sortes which are infinite from whence diuers formes and kindes of bodies are drawen The regulare bodies conteined vnder surfaces folded one toward another are onely these 5. the Tetraedrons the Hexaedrons the Octaedrons the Dodecaedrons and the lcosaedrons Irregulare bodies are such as inequall surfaces do limit and describe the which surfaces are either turned rouÌ„d or folded one toward another The surfaces turned round and making irregulare bodies are either the sections of circles or els they are inequall right lined figures The sections of circles are either greater then a semicircle wherof the lenticulare bodies are made or els they are lesse then a semicircle and therby are the Onalles made The inequall right lined figures by whose coÌ„uersion the irregulare bodies are made may be of what sorte soeuer wherby diuers kindes of vessels are framed either wanting or exceeding the regulare forme The Irregulare bodies mà de of inequall surfaces folded one toward another may differ infinitely Of the name and definition of the Sphere Chap. 6. IN as much as we make often mention of the Sphere and thereafter do intitle this present treatise the doctrine of the Sphere it shall not be amisse to declare the name and the definition therof The name is vsed in diuers significations 1. It signifieth sometime any solide regulare bodie limited with one surface onely 2. Sometimes it signifieth an instrument that doth instisie the apparences of heauen and conteineth the celestial circles and is otherwise termed a ring or materiall sphere 3. Sometimes it signifieth the whole worlde wherunto all the coÌ„ditions of the sphere may be applied For it is a solide bodie wherin nature abhorreth that any emptines should be giuâ— It hath a sphericall forme running dayly about his owne Axis without intermission It hath a point placed in the midst therof namely the earth The definition thereof as it signifieth any body is by Io. desacro baseo set downe two waies the one after Encl. 11. Elem. the other out of Theodosius The definition thereof taken out of Euclide conteineth the Geometricall description of the sphere For the sphere is described by the fixed and vnmoued diameter and by the aâ—ke of the semicircle which must be fully brought about The definition of a sphere according to Theodosius determineth first the orbiculate forme euery parte whereof is equally distant from the centre secondly the principall partes as the conuexe surface which is but one and the centre that is the point in the midst equidistant from euery parte of the surface and the Axis about which the sphere is tourned and which is limited by the 2 poles viz. The North pole or pole Arctick and the south pole or pole Antarcticke and thirdly the soliditie For it is a complete body hauing all the dimensions The diuision of the celestiall Sphere Chap. 7. THe celestiall sphere according to Io. de sacro bosco admitteth a double diuision according to substance and according to accident The celestiall sphere considered according to the substance is diuided into seuerall orbes in the which we are to note the number and the cause The number is diuersly set downe For the ancientes contenting themselues with 8. orbes only did distinguish them into the orbes of the 7. Planets viz of ♄ ♃ ♂ ☉ ♀ ☿ and ☽ and the firmament of the fixed starres And the later Astronomers vnto the time of Alphonsus into 9. orbes but the Moderne among whom Purbachius was the first added the tenth The cause is considered either in the diuersitie of their number noted both by the former and later Astronomers or in their order The ancient Astronomers noted their diuers number either by the brightnes of the Starres reconing so many orbes as they perceiued to conteine any starres or by the peculiar motion of each seuerall orbe reconing so many orbes as they found simple motions belonging thereunto The later Astronomers for instruction and the better reconings sake added the ninth and the tenth as circles necessarye for the vnderstanding of the motion of the 8. sphere vnknowne vnto the ancient Astronomers The order is proued 1. by the slower motion of the higher and the swifter motion of the lower orbes 2. by the occultation or hiding of the higher starres by the lower 3. by the diuersitie of apect either great or little or insensible The celestial sphere considered according vnto accident that is according to the situation of the heauen or the course of the starres is distinguished into a right or an oblique sphere The right sphere belongeth vnto those that dwell vnder the Equinoctiall who by reason that the poles of the world about the which the starres are carried by the firste moueable haue none eleuation as also for that the Horizon cutteth all the paralleles vnder which the stars do goe at right angles perceiue no reflexion in the diurnall motion of the starres The sphere is said to be oblique wherein the O and the rest of the starres are caryed from the East into the West by an oblique motion and it is Septentrionall vnto those that haue the North pole eleuated and Meridionall vnto those vnder the Southerne eleuation The partition of the whole worlde and the comparison of the celestiall with the Elementall Sphere Chap. 8. THe whole frame of the worlde is made of some certain and those more principall and notable partes wherof there is first the number and the name and then the difference to be considered The number and name is double For the partes are either ethereall or sublunare The aethereall that is the celestial parte without the which Philosophie admitteth nothing to be although the Diuines do adde the third which they call Angelicall and the Platonickes intellectuall is that wherof we intreated in the 7. Chapter The sublunare is that which conteineth the elementall bodies and those either simple as the fire the aer the water the earth or els mixed which are diuerse and innumerable ingendred of the 4. elementes either perfect or imperfect The difference or dissimilitude of the partes of the worlde is that whereby they are distinguished one from another either in respect of their situation or of their dignitie magnitude motion or their office They are distinguished according to their situation For the celestiall parte hath obteined the higher place the elementall the lower Their distinction according to dignitie is noted in the partes conteined by the celestiall Region which partes are bright and immortall and by the elementall region those partes being of their owne nature obscure and decaying or els it is noted in the partes conteyning wherof the one is altogether with out alteration neither increasing nor diminishing the other is continually subiect vnto generation and corruption and is increased and diminished Their distinction according to their magnitude is considered in that the celestiall parte with the great
compasse thereof doth couer all thinges like a thing without measure and ende but the elementall parte is couered within the compasse of the heauen the diameter thereof conteining the diameter of the earth 23. times Their distinction according to their motion is in that the celestiall parte hath a circulare and a sphericall motion the elementall a right motion more imperfect then the circulare Finally they are distinguished according to their office For of those thinges that are ingendred in the elementall parte the heauen working by a continuall motion is as it were the formall and efficient cause from whence life is deriued and the elementall parte which is subiect vnto passion and alteration is as it were the materiall cause from whence nourishment doth proceede The reason of the sublunare or elementall Region Chap. 9. THe Elementall region which the heauen encompasseth comprehendeth within it the elements wherin we are to consider the definition the number and the situation or order The elements are simple bodies aswell in respect of the mixt bodies which are vnderstoode to be compounded of them as of the simple and least partes as also in respect of the diuision for that they cannot be diuided into bodies of diners kindes if they be giuen pure and without mixture For the vse of liuing creatures and things growing doth make them impure The elements are 4. in number found so to be by sense and by reasons The elements are found to be soure by sense which the Physicians doe sollow First for that more simple bodies cannot be shewed 2 nature hath alotted vnto them certaine places to the end that other things might by thē be bred and nourished 3 nothing els can euidently be shewed wherof other things may be made 4 in liuing cretures there are certain parts agreable vnto the natures of the seuerall elements The Elementes are found to be foure by two reasons the former whereof is drawen from the number of the foure prime qualities and the foure folde possible knitting together of them For heate may be ioyned either with drinesse which two make fire or els with moisture which two do make vp aer and colde may be ioyned with moisture as it commeth to passe in the water or with drinesse as in earth The later reason is taken from the fower folde difference of the right motion For the elements are directly moued either vpwarde or downward Such things as moue vpward as light thinges do are said so to do either simplie as the fire which is the lightest of the rest or respectiuelie as the aer which is lighter then the water or the earth Such things as moue downeward as heanye things do are said so to do either respectiuelie as the water compared vnto the fire and aer or simplie as the earth which is the heauiest of all the rest The situation and order of the Elementes is found either by their motion or els by the communication of their qualities And first by the motion For inasmuch as the fire and the aer do naturally moue vpward the fier shall occupy the highest place the aer an vpper place and for that the water and the earth do naturally moue downward the water shall possesse a lower place and the earth the lowest Againe the order of the Elements is found out by the communication of their qualities for it were vnsit that such things as are merely contrary but such as in some sorte can agree together should be nigh one another The fire therefore shal be ioyned vnto the aer by reason of the heate common vnto them both the aer vnto the water by reason of the common moisture and the earth vnto the water by reason of coldnesse common to them both The two folde differences of the celestiall motions Chap. 10. THe whole frame of the world is caried round about with 2. motions each of them being distinguished from the other in name and in reason The one of them is called the first and vniuersall motion likewise the diurnall or worldlye motion because it bringeth the day vnto the world For in this motion the ☉ and all the celestiall bodies do euery day arise and set they call it also the violent and rapt motion because by the violent swiftnes thereof it carrieth with it the rest of the Spheres The other is called the second and particular motion altogether contrary vnto the former as by which all the particular orbes do resist the vniuersall motion They call it also Sinister motus the motion to the left hand as the former is in like sorte called dexter that is the motion to the right hand The 2. motions are also distinguished according to the reason or the substance in the which they are inherent For they differ the one from the other three waies The first difference is in respect either of the whole For the diurnal motion is common vnto all the celestiall bodies or els of the partes or starres either fixed or wandring which haue a motion peculiar and propre vnto themselues The second difference is either in regarde of the situation of the Axes For the diurnall motion is made vpon the Axe and poles of the world and therfore the Equator diuideth it in the middle but the propre motion is made vpon the Axe and poles of the Zodiake and therefore the Zodiake doth cut it in the middle Or els it is in regarde of the position of the termes inasmuch as the diurnall reuolution is made from the East vnto the west or as Plinte termeth it from the right towarde the lefte hand but the propre reuolution is from the West vnto the East or from the left toward the right hand The third difference is in consideration of the swiftnes For the diurnall motion fulfilleth his course within the space of 24. common howers but the propre motion in diuers distances of time according to the largenes of the orbes namely the orbe of the fixed starres performeth his circle in 36000. yeares of ♄ in 30 of ♃ in 12 of ♂ in 2. yeares of the ☉ in 365. dayes and about 6. houres of ♀ in 384. dayes after Plinie the orbe of ☿ in as many dayes as the ☉ and the orbe of the ☽ in 27. daies 8. howres The circulare forme and circulare motion of the heauen Chap. 11. THe Heauen is circulare in motion and in figure The circulare motion of the Heauen is proued as well by 2. experiments as by 2. argumentes The one experiment is taken from the starres of the 8. orbe which both in their rising setting do alwaies keepe one the same habitude both in regarde of the earth and one to another which thing can agree with none other then a circulare motion about the centre The other experiment is also taken from the starres of the 8. orbe alwaies appearing and retaining in diuers places the same distance from the Poles and onestom another which also agreeth with the circulare motion onelie The first
Equator and true place of the starie It is diuided into the Septentrionall and Meridionall declination The relation that the starres haue vnto the Zodiake is also two folde either according to the Longitude of the Zodrake or els according to the transuerse distance towarde either of the Poles In the Longitude of the Zodiake we are to consider the name and the definition It is called Longitude For that it is recoued longwaies on the circumference of the Eclipticke it is also called the true motion of the Starre It is defined to be the Arke of the Zodiake intercepted betweene the head of ♈ and the section of a great circle passing through the poles of the Zodiake and the true place of the starre In the transuerse distance we are to note the name the definition and the diuision It is called Latitude because it is reconed according to the position that it hath from some one side of the Ecliptick It is defined to be the arke of a great circle drawen through the poles of the Zodiake and the true place of the starre the said Arke being intercepted betweene the Zodiake and the centre of the Starre It is diuided into the Septentrional Latitude when the starres are vnder the northerly signes and into the Meridionall Latitude when they are in the Southerly signes Of the propertion and supputation of the declination of every point of the Eclipticke or the regarde of the partes of the Zodtake vnto the Equator Chap. 20. IN the declination of any point of the Eclipticke 2. thinges are to be obserued the proportion and the supputation In the proportion we may note also 2. things For either they haue none obliquation or els their obliquations are equall Those that haue none obliquation are the head of ♈ and ♎ as being the common intersections of the Equator and the Zodiake Those that haue equall obliquations are such as are equally distant from the Equator and they are either greater obliquations or els the greatest The greater obliquations are those that haue any distance lesse then the greatest from either of the sections and of that sorte there are alwaies foure The greatest obliquations are those that haue the greatest distance from the Equator as the head of ♋ that s the Somer solstice and the head of ♑ that is the winter solstice The supputation is made either by the tables of declinations or of Sines The Tables of declinations are calculated in sundrye places by Astronomers and they consist of the 2. sides the Area and of the two extremities or endes The sides are either at the right hand or at the left that at the left hand to be entred into whe you haue the signe in the toppe of the table and that on the right hand when the signe is in the foote therof The Area is that wherein at the common angle the declination is found The 2. extremities are those that conteine the signes of which extremities the one is called the toppe or vpper parte the other the foot or the nether patte of the table The supputation that is made by the table of Sines is performed by the helpe of the rule of 4. proportion all numbers wherein 3. numbers are giuen and fourth is to be sought out The 3. numbers giuen must conteine the right sine of the whole quadrant or of the semidiameter the right sine of the greatest declination of the ☉ and the right sine of the distance of the point of the Eclipticke giuen from the first section of the Zodiake and the Equator The fourth number produced by multiplitation and diuision is the right sine of the declination sought whose subtended arke declareth the number of degrees Of the 2. circles called the colures distinguishing the Equinoctiall and Solstitiall pointes Chap. 21. FOrasmuch as there are certaine pointes of the Zodiake and the Equator more notable then the rest therfore the Astronomers haue thought good to fit vnto those pointes 2. Circles wherof we may consider the reason of their name their definition their number their figuration or description and their vse They are terméd colures that is imperfect in 3. respectes 1. Because they appeare alwaies incomplete or maymed the which thing notwithstanding semeth to be common with diuers other circles 2. Because they haue some partes that do neuer arise 3. Because they are carried about after an imperfect manner not according to the position of Longitude as the motion of the Heauen is The definition conteineth their magnitude their intersection and their motion As touching their magnitude they are of the number of the greater circles As touching their intersection they cut one another in both the poles of the world at sphericall right angles In their motion they are moued together with the sphere Their number is two wherof the one passeth through the Equinoctiall pointes and the poles of the world and is called either the equinoctial colure or the distinguisher of the Equinoctialls the other passeth through the solstitiall pointes and the poles both of Eclipticke and of the worlde and is called both the solstitiall colure the distinguisher of the Solstices and also the circle of the greatest declinations Their figuration is described by the semidiameter of the worlde whose reuolution being fullye perfourmed through the poles of the worlde and the Equinoctiall pointes maketh the Equinoctiall colure but passing through the poles of the worlde and the solstitial points it maketh the solstitiall colure Their vse is manifolde but principallye in 3. thinges 1. In distinguishing the Equinoctiall and Solstitiall pointes 2. In reconing aswell the quantitie of the greatest declinations of the ☉ by the arke intercepted betweene the Equator and the Eclipticke as the space comprehended between the poles of the worlde and the poles of the Ecliptick which is alwaies equall vnto the arke of the greatest declination 3. For better vnderstanding of the ascensions and descensions of the signes Of the Meridian Chap. 22. THe ☉ carried about by the first motion whē it is at the highest designeth a point of a circle whose definition varietie and office we are to consider The definition taketh holde both of the names thereof and of the matter it selfe It is called the circle Meridian Meridionall and Merinoctiall the circle of the midday and midnight either because it diuideth both the day and the night into 2. equall partes the one ascending the other descending or els because so often as the ☉ according to the first motion is vnder the Meridian it is then either midday or els midnight The matter it selfe is that according whereto it is defined to be one of the greater circles drawen through the poles of the worlde and the verticall point of any place geuen and standing still when the Sphere is moued The varietie of the Meridian by reason of the round figure of the earth is either none at all or manifolde It is none at all either in regarde of reason or of sense It is
breadth and in colour The causes are diuers and those either fabulous or naturall The fabulous causes are in number 4. The first is taken from the scorching of the ☉ as if the ☉ had sometimes made his motion there and by his scorching had caused that place to be white The second is drawen from the milke of Iuno that running plentifully out of her pappes painted this circle of that colour The third is fetched from the seate and habitation of strong and valiant men whom the Poets haue placed in this circle The fourth is deâ—iued out of the way of the Gods as if they passed thereby vnto the pallace of Iupiter The naturall causes alleadged although they be many yet are principally but 3. The first by Theophrastus who said that it is that ioyning together wherby the heauen being diuided into two hemispheres is as it were by a certen claye fastened The second by Aristotle who tooke it to be a Meteore set on fire in such sorte as a Comete The third is Astronomicall which affirmeth that it is a girdle caused by many little starres as it were one touching another in the which concurring in that Place the light of the Sunne is diffused The distinct starres that make it are cheiflie these The Arowe the Eagle the bowe of â™ the Altare the 4. feete of the Centaure the ship Argo the head of the Dogge the right hand of Orion Erichthonius or the Wagoner with the Goate on his shoulder Perseus Cassiopeia and the Swanne Of the 5 principall Regions of the worlde commonly called Zones Chap. 29. THe Vniuersall Globe aswell of the heauens as of the earth answerable thereunto is distinguished into certain orbicular tractes which the spaces comprehended betweene the 4. paralleles do make of which tractes we may consider the names the definition the generall nuÌ„ber and their distance one from another Their names are diuerse For they are called either Zones or swadling bandes or girdles or Mashes or coastes They are defined to be the space either of the heauen or of the earth compreheÌ„ded between two lesse paralleles or els included on euerye side with the polare circles Their generall number is twofolde For either they are celestiall and so the causes of the terrestriall or els they are terrestriall of the same proportion with the celestiall The celestiall are either Meane or Extreme or betweene meane and extreme The Meane is that Zone which is included betweene the 2. tropickes and is cut in two equall partes by the Equator The Extremes or polare Zones are those wherof being but 2 the one is called the Septentrionall Zone within the Arcticke circle the other the Meridionall Zone within the Antarcticke circle The Zones between meane and extreme are also 2. whereof the one is Septentrionall comprehended betweene the tropicke of ♋ and the circle Arcticke and the other Meridionall comprehended betwene the tropicke of ♑ and the circle Antarticke The terrestriall Zones haue the same reason with the celestiall aswell in respect of their nuÌ„ber as in regarde of their names The terrestriall Zones are also 5. in number answering proportionallye vnto thé 5. celestiall Zones conically marked out by the 4. celestiall paralleles The terrestriall Zones haue the same reason with the celestiall in respect of their names also For that terrestriall Zone that is vnder the mean celestiall is called meane those which are vnder the extremes or polares are called extremes septentrionall or Meridionall and those which are vnder the Zones betweene meane and extreme haue their name accordingly and are either Northerlie or Southerlie The distance one from another is in this manner the meane or burnt Zone according to the Latitude reconed in the Meridian conteineth 47. gr or 705. miles the extreme intemperate Zones do each of them according to the said reconing conteine as many degrees and miles as the meane the temperate zones betweene meane and extreme do eache of them conteine according to the former reconing 41. gr or 645. miles The difference of the Zones and the manner how all places Vpon the earth may be brought within their compasse Chap. 30. THe difference also of the zones as well celestiall as terrestriall and the reason how all places vpon earth may be referred vnto them is worthie the noting Their difference is to be considered either in respect of their figure or their accidental nature The figure of the meane is vniforme and for the most parte alike The figures of the extremes are either of theÌ„ equall to other yet such as that they seeme rather to carie the shape of circles then of zones The figures of the zones betweene meane and extreme be either of them alike and equall vnto the other yet about the tropicks their figure is limited with a greater compasse then towarde the polare circles The accidentall nature of the zones is that in regarde wherof they are saide to be meane extreme and betweene meane and extreme The Meane or burnt zone is diuided into 2. partes whereof the one is situated vnder the Equator the other about the Tropickes That parte which is situated vnder the Equator seemeth to be temperate and that for three causes 1. By reason of the sodaine and crosse accesse and recesse of the Sunne 2. By reason of the continuall equality of the night and day in that place 3. By reason of the swift carying about of the ☉ by the first motion That parte which is situated vnder the Tropickes is hardlye to be inhabited and that also for 3. causes 1. For the slowe conuersion of the ☉ 2. For the doubled proiection of the Sunne-beames vpon those places 3. For the great increase of the Sommer daies aboue the nights The extreme zones are both of them frozen by reason of the too much colde that falleth out there by meanes of the oblique proiection and reflexion of the Sunne beames The zones betweene meane and extreme are both of them temperate and are diuided into 3. Regions whereof one is situated about the middle parte thereof which we iudge simplie to be temperate by reason of the moderate heate of the ☉ namely from 34. gr vnto 48. gr distance from the Equator the other 2. regions are about the extremes therof the one being about the tropicks and so subiect vnto the intemperate heate of the burnt zone the other nigh vnto the polares and therfore subiect vnto the intemperate colde of the frozen zone The reason how al places vpon the earth may be referred vnto those zones hath two considerations 1. If the places haue Septentrionall Latitude and that lesse then the greatest declination of the ☉ they belong vnto the burnt zone if equall vnto the trop of ♋ if greater and yet not exceeding ♋ gr 30. mi. they belong vnto the temperate zone If the said septentrionall Latitude be equall vnto the complemeÌ„t of the greatest obliquation they must be placed vnder the arctick circle if greater vnder the frozen zone 2. If the
doth ascende therewith and then it is said to haue an oblique ascension by reason of the more oblique angles that it maketh with the Horizon The culmination is defined either the passing of some poinct of the Zodiake or of the world by the Meridian circle or else the degrees of the Equator which with the portion of the Zodiake geuen passe through the Meridian The setting of a signe or of any poinct of the heauen offereth 2. thinges vnto our consideration the definition and the diuersity thereof The definitiō is either according to the name or according to the matter According to to the name it is called the descension or setting which wee measure by the arke of the Equator descending therewith According to the matter it is defined to bee the arke of the Equator cōprehended between the signe or poinct setting and the head of ♈ The consideration of the diuersity of settinge is either that a greater part of the Equator descendeth with the signe or poinct of the heauen and then it is said to haue a right or along and slowe descension or els that a lesse portion of the Equator setterh therewith and then it is said to haue an oblique or a short and swift descension Of the diuersitie of ascensions descensions and culminations in a right sphere Chap. 34. THe Zodiake in a right sphere is fitted vnto the equall conuersion of the Equator and together with the partes thereof passeth by the East or the West or the midst of heauen both in the quadrants or quarters and in the signes The quadrants in equall spaces of time do ascend and descend or do passe through the midst of heauen beginninge either at the Solstitiall poinctes namely at the heade of ♋ ♑ and compting to the end of ♠♓ or els beginning at the Equinoctiall poincts which are the heads of ♈ ♎ and compting to the ende of ♊ ♠The signes applied vnto the motion of the Equinoctiall are considered either whole or in partes The signes considered wholly haue relation either vnto the Equator or vnto the Zodiake The signes in their relation vnto the Equator do ascend inequally For some of them doe rise rightly and some obliquely Those that haue right ascension are ♊ ♋ ♠♑ with the which there do coascende 32. gr 11. mi. of the Equator Those that haue oblique ascension are ♈ ♎ ♓ ♠wherewith there doe coascende 27. gr 54. mi. of the Equator and ♉ ♠♌ ♒ wherewith there arise 29. gr 54. mi. thereof The signes in their relation vnto the Zodiake or considered seuerally apart haue ascensions either equall or inequall one vnto another They haue equall ascensions that come forth in equall times and they are either opposite in the diameter or equally distant from the Equinoctiall poinctes as are ♓ ♈ ♒ ♉ ♑ ♊ ♠♋ ♠♌ ♎ ♠They haue inequall ascensions that neither are opposite nor equally distant from the aforesaid poinctes The signes considered in their parts haue also relation either vnto the Equator or vnto the Zodiake The partes hauing relation vnto the Equator do as before ascend inequally and that either rightly or obliquely The partes hauing right ascensions are comprehended within the foure signes nexte vnto the 2. solstitialles The partes hauing oblique ascensions are conteined within the signes next vnto the Equinoctiall poincts on each side Those partes of the signes that haue relation vnto the zodiake haue their ascensions partly equall and partly inequall Partes hauing equall ascensions are these the first degree is equall vnto the first degree of the opposite signe and the first degree vnto the last of another signe equidistant from the equinoctial poincts Partes hauing inequall ascensions are those in whom neither opposition falleth out nor equidistancie Of the diuersity of ascensions and descensions in an oblique sphere Chap. 35. IN the oblique situation of the sphere we consider either the proportion of the ascensions or of the descensions of the zodiake The ascensions are compared and applyed either vnto the Equator or one with another or vnto the ascensions of a right sphere Beeing compared vnto the Equator they are either equall or inequall vnto the ascensions thereof In their equality they are numbred either in the Northren semicircle from the head of ♈ vnto the end of ♠or from the head of ♎ vnto the end of ♓ In their inequality they are reconed either in the whole semicircles beginning not in the Equinoctiall poinctes but els where or els the reconing is made in some of their partes In their comparison one with another they are either equall or inequall When they are equall they are reconed in some 2. concordant arkes of the Ecliptick as in ♈ ♓ 14. gr 50. mi. ♉ ♒ 18. gr 51. mi. ♊ ♑ 27 gr 16. mi. ♋ ♠36. gr 58. mi. ♌ ♠40. gr 57. mi. ♠♎ 40. gr 58. mi. in the latitude of 40. gr When they are inequall they are reconed either in parts not equidistant or in the semicircle either ascendent or descendent The semicircle ascendent is from the head of ♑ vnto the end of ♊ and that ascendeth more oblique and swift The descendent semicircle is from the head of ♋ vnto the end of ♠it ascendeth more right and slow When the ascensions are compared vnto the ascensions in a right sphere they are either lesse or more oblique or greater or righter then the said ascensions in a right sphere The lesse or more oblique fall out in the North semicircle the greater or more right happeneth in the South semicircle the distance betweene the ascensions of each sphere is called the difference of ascensions The descensions of the Zodiake are vnto the ascensions thereof either equal or inequall They are equall either in regard of the moities of the Ecliptick comprehended betweene the equinoctiall poinctes or else according to the equidistant or opposite partes of the Zodiake The descensions of the Zodiake are inequall being compared either vnto the right sphere or vnto the same climate The descensions of an oblique sphere are more oblique then the descensions of a right sphere whereunto they are compared when as the ascensions in an oblique sphere are more right then in a right sphere The descensions of an oblique sphere are more right then the descensions of a right sphere when as the ascensions in an oblique sphere are more oblique then in a right sphere The inequall descensions of the zodiak compared vnto the same climate are to bee noted either in the parts of the Zodiake which descending oblique doe rise right such as are the parts of the descending semicircle or els in the parts of the zodiake which descending right do rise oblique and such are the partes of the ascending semicircle Of the naturall day and of the inequality and difference thereof Chap. 36. OVt of the premisses wee may not vnfitly deriue some matter concerninge the dayes whereof there are two sortes the one