bodies round but the hollow vpper face is the inwarde compasse about in the hollow Orbe or the bodies hollow A Center is the middle Prick in a Circle from which all right Lines drawne vnto the compasse about the same are equall betwéene the one and the other Also a Centre of the Sphere is a middle Pricke in the Sphere from which all right lines drawn vnto the imbossed vpper face we agrée in length The Exe trée is a right line drawne by the Centre of â—e Sphere and with both his endes pearcing vnto the â—des of the imbossed vpper face about which the Sphere 〈◊〉 turned The Poles are the verie endes of the Exe-trée appeaing on each side about which heauen is turned Also the â—oles of the turning are named the endes and tops and named besides the ending pointes of the Exe-tree drawne by the Centre of the Sphere about which the Shere and Circles of the Sphere are turned The Poles of the Sphere and Circles described in the Sphere are pointes consisting in the vpper face of the Sphere from which all right lynes drawne vnto the compasse of the Circles are equall Although euery greater Circle in the Sphere of the worlde hath his Poles yet is oftner mention made of the Poles of the worlde or Equinoctiall of the Zodiacke and Horyzont The Poles of the world or Equinoctiall are the two extreame poyntes and both endings of the Exe trée of the world about which the Sphere is turned The one of the Poles which eleuated sheweth to vs dwelling into the North and turneth alwaies about in our sight is named the Boreall and North Pole of the litle Beare neare to it which Pole is continualy séene and knowne by the two starres neare to it of which the one is notable and cleare of the thirde bignesse standing at the ende or top of the tayle of the little Beare distant from the very Pole 4. degrées and 9. minutes But the other dimmer of the fourth bignesse not farre distant from the other star afore is come nearer and doeth scarcely differ nowe 50. minutes from the place of the true and very Pole If any will know the Pole of the world or Pole starre let him turne his face towarde the North the sky then being cleare leauing the East on the right side and west on the left side and he shal see in the little Beare seauen stars placed like to the forme of the starres of the great Beare which are brighter Of these stars three doe fashion the tayle and that which is in the top of the tayle is named the Pole star which declineth in our time from the Equatour 85 degrées and 5â— minutes So that beeing no further off by this declination from 90 degrees the distance of it from the very Pole shall remaine and bee 4. degrées and 7. minutes and this starre also in processe of time shall be ioyned with the Pole The other Pole which through the swelling of the earth is continually hid to vs of the North is named the Meridionall or South Pole right against as it were the North Pole Beeing euermore so lowe depressed as the North Pole raysed in any countrey to the North aboue the Horizont The Poles of the Zodiacke are continually so farre distant from the Poles of the world as is the greatest declination of the Sun which in our time is founde and noted by obseruations to be of 23. degrées 28. minutes and 30. seconds But the Borcall or North Pole of the Zodiacke distant from the two dimme starres in the tryangle of the Dragon being stars of the sixt bignesse which a right line by imagination drawne from the third starre in the tayle of the little Beare vnto that constellation named Lyra expresseth the same that it is but a little further distance then two degrées The Poles of the Horizont are the twoe extreame pointes or ends of the right lyne drawne out of the Center of the Earth by the top ouer our head vnto the opposit places of the Dyametre of the Merydyan of which the one directly ouer our heade named the verticall poynte and of the Arabians Zenith the other right against named of them Nadir And the Poles of each of the greater Cyrcles doe differ from their Circles 90. degrées or a quarter of an other greate Circle of the Sphere For by the 23. proposition of Theodosius of the Sphere a right lyne drawne from the Pole of his Circle vnto the circumference is equall to ech of the foure quarter sides descrybed within the same Circle which foure quarter sides doe deuide the Circle into foure quarters Yet are each greater Circles of a Sphere equall betwéene the one and the other But seeing the equall right lynes doe take away the equall compasses of the equall Circles therefore should a lyne drawn from the Pole vnto the circumference of his Circle take away of the greater Circle one quarter of the other Circle drawne by the Pole euen like as the sides of a quarter described within the Circle By which appeareth that the Poles of the greater Circles doe differ or be distant by a quarter from their Circles as is aboue written What the World is and into how many partes the same is deuided with the motion of the celestiall Orbes THe Worlde after Orontius is defined to bee a perfitte and an entire composition of all things a deuine worke but finite and continually to be merueled at adorned with all kindes of formes and shapes of bodies that nature coulde make which in all partes are procreated and appeare and those first created by God so well in Earth as in Heauen by his onely worâ— of nothing to th'end the same might bée a proper mansioâ— place for man in which he might dayly behold and mak knowne Aristotle teacheth two definitions of the world the one that it is an apt frame wrought consisting both of heauen and earth and of the celestiall and inferiour bodies aptly distributed and of other naturall thinges in them contayned The other definition is that the world is a perfit body and most perfit rounde forme contayning the ordinance and distribution of bodies created by God to tend vnto a purpose which by God and through God is preserued The parts or Regions of the worlde are two as the Ethereall and Elementary The Etheriall region is the higher and vpper parte of the world which encloseth the Elementary region being wholy cleare and the light perfitte and contayning the Orbes of all the fixed starres and Planets distinguished by a certaine order frée of all mixture and all strange qualities nor harmed by any alterations In which the celestiall bodies are drawne about by certaine and continuall orders and times of the motions that they may so cause the diuersities of times dayes yeares and moneths and as well in the Elementary nature by his motion and light ingender mixe and temper togither the first qualities and prepare also other effects The Elementary region is the nether part
office of the celestiall cyrcles are these 1 That they deuide heauen into certaine spaces or regions 2 The courses of the Planetes the firmament and first mouer by the helpe of these cyrcles are obserued and brought vnto a rule 3 They shew the points of rising and setting the nearnesse and differences both of dayes and nights 4 The times and varieties of all the celestiall appearances may bee obserued and knowne of the cyrcles by a certaine reason The sixe greater cyrcles are numbred by names standing and vse distinguished As the Equinoctiall Zodiacke Colure of the Equinoctials Colure of the Solstices Meridiane Horizont But there are many others as the Cyrcles defined or descrybed by the Poles of the Zodiacke and Centers of the stars which are named the cyrcles of the latitudes The Cyrcles drawne by the verticial poynts of diuers places which may bee named the cyrcles of the distance or space betwéene places For that the toppes doe knit or ioyne together by the nighest space of the differences of places and doe shew the distance of them The cyrcles by the Centers of the stars and Poles of the worlde drawne are named the cyrcles of the declinations of the stars The sixe cyrcles of the positions through which by the thirty parts of the Equatoure and the poynts touched of the Horizont and meridian drawne ouer the Equatoure doth Regiomontane part and deuide the whole heauen into twelue equall spaces which hee nameth the houses of heauen The sixe greater cyrcles through which by the Poles of the Zodiacke and the thirty partes of the same bended and wrythed doeth Iulius Firmicus deuide the Zodiacke into twelue equall parts but the Equatoure into as many vnequall arks But that former distribution and disposing of the Cyrcles by Regiomontane both deuised and demonstrated of him doth bring and cause a reason of the framing of the figures of heauen which they name Rationall in that the same inuented and taught by principles and demonstrations is declared by certaine reasons The other inuented and exercised of others doth bring and cause another reason of the forming and erecting of the figures of heauen which of the same they name the equall maner in that it parteth or deuideth the Zodiacke into equall arks Many other cyrcles there are which for breuity be here ouerpassed for that they belong not vnto this determined treatise of the principles The lesser cyrcles although there are in a maner infinite of them yet are there foure only recited and especially knowne which also are named Parallelles As the Tropicke of Cancer Tropicke of Capricorne The Articke or Northerly Circle The Antarticke Of the foure greater cyrcles afore written they both are moueable and are continually drawne about with the first mouer and neuer changed But the two neather cyrcles as the Meridiane and horizont doe remaine and abide fixed and immoueable in the going about of heauen and the standing alwaies changed on the earth towarde what quarter soeuer they are varied as they may be and are in a maner infinite in number The Astronomers deuide both the greater and lesser cyrcles into 360. degrées which they so named through the suns passage or iourney in the Zodiacke measuring and defining by his dayly course such like partes and spaces And of these partes or degrées of the greater cyrcles it is found and known that each degrée contayneth in the vpper face of the earth either 62500. paces or 500. furlongs or 15. Germayne miles But each parte of the lesser cyrcles doe comprehend a lesser space by somuch as by howe much more from the magnitude of the Parallell which is the middle and greatest by reason of the distance they lacke or differ And each of the thrée hundreth thréescore degrées are also parted or deuided into thrée score minutes and each minute into thrée score seconds and each second into thrée score thirds and so forth from thirds vnto fourthes and so vnto tenths they distribute them The description names and vtilities of the Equinoctiall THe Equinoctial which the Gréeks name 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 is a greater cyrcle placed in the myddle place of the Sphere betwéene either Pole of the worlde and deuiding both by equall spaces moueable and crossing the Zodiacke in two poyntes which when the sun doth come vnto hee then causeth a like day and night throughout the earth whereof this cyrcle first purchased that name in that the day is equall to the night which happeneth twice in the yeare as in the beginning and entraunce of the sun both into Aries and Libra And a straight lyne drawne out by imagination doeth describe this cyrcle reaching out of the Center of the earth by the Center of the suns body on a plaine or flat of the Equinoctiall being vnto the first moouer or vnto any of the fixed stars to the Equatoure fastned to the eight Sphere as that either of them which with the thirde being somewhat lower and darcker doe fashion the gyrdle of Orione and that by a dayly and continuall turning drawne about of the first moouer vntill the same bee returned vnto the place from whence it began And likewise the sun or any other constellation placed or being in it doth in euery region describe the halfe of the Parallell aboue the Horizont and the other halfe vnder the Horizont which Ptholomie nameth the cyrcle of the Equatoure of the day and Alphraganus the cyrcle of the Equinoctiall and swathe or gyrdle of the first moouer in that it compasseth about the first moouer as Strabo writeth that it parteth the Northerly halfe Sphere from the Southerly For this greater cyrcle of the first moouer is the first measurer both of time and motion In that it causeth the proportionall cyrcumferences by the spaces of times and whiles it is once drawne about a naturall day is performed And whiles the compasse also of the whole haue moued one foure and twenteth part an equall or Equinoctiall houre hath passed by which it doth euidently appeare that this cyrcle belongeth vnto the first mouer This Worthy Circle hath diuers names 1 IT is named the Equinoctiall in that it causeth a like night to the artificiall day 2 It is by the same reason na med the Equatoure for that it maketh equall the night to the day 3 It is named the gyrdle of the first mouer not vnproperly for that as a gyrdle doeth gyrde or deuide our body into two equall halues euen so this cyrcle deuideth the sphere or first mouer by the middle 4 It is named the line of the equality of the day or the line of the equation of the Orbe of the day or the iust deuision of the day and night 5 Of Plinie it is named the Center of the earth and that not incongruently séeing all the Parallell cyrcles described from the Center of the sun by the motion of the first mouer haue their Centers from the Center of the earth and that the Equatour onely which when the sun shall be in the
Cancer Scorpio and Pisces which are distant by the space of foure signes and are in quality colde and moyst waterie flegmaticke and feminine All which signes are agréeing to the foure Elements in their qualities Of the Ecclipticke line or way of the Sunne HEre it is diligently to be considered and noted that it behoueth not onely to know and vnderstand the places of the Planets in the Zodiacke according to the longitude of the same but also to learne and finde their places according to latitude wheather they be in that part of the zodiack which bendeth or declineth into the North or in that parte which leaneth into the South which the better to vnderstand and know the ancient astronomers imagined a certaine line going rounde about the zodiacke and deuiding the same after length by the middle in such sorte that it parteth and leaueth eight degrées toward the North as many toward the South So that this line is a greater cyrcle deuiding the latitude of the zodiacke into twoe equall halfes and hath sundrie names as the suns way the suns â—yrâ—uite the suns iourney the suns place the suns cyrcle the Ecclipticke line and the Ecclipticke place This line named the suns way in that the sun kéepeth alwaies the middle vnder this line not digressing to the one side nor other but describeth the same in his yearely motion But the other Planets doe wander one whiles vnder it and an other whiles on either â—oe which if a Planet tendeth in that part of the latitude which is vnto the North wandring there hee is then named to haue a latitude Northerly as to vs dwelling Northward but if on the other side they haue a latitude Southerly then are they named discending and running lowe And by the like reason the same line is named the suns iourney Also of Cleomedes called the suns cyrcle in that vnder the same the sun continually runneth And he alone being drawne by the middle of the zodiacke neuer wandreth into the North nor South parte from that line as we haue afore written but continually iourneyeth about by the middle of it So that of the same it is called the suns cyrcle It is named the suns place in that vnder this cyrcle the sun continually abideth To conclude it is named by the vsuall name the Ecclipticke line For that no Ecclipse or abating of the suns or moones light hapneth but when the sun and moone are linally vnder that line or néere come vnto the moone as in the same degrée right against For in the same degrée at the chaunge is the moone come right betwéene our sight and the suns body thereby abating his light But the Ecclipse of the moone hapneth at the full when as the sun is right against the moone that the shadowe of the earth falleth betwéen both whereby the moons light is darkned So that the moones Ecclipse is none other then the falling of the earths shadowe betwéene the sun and moone The measure of the large space of either side occupied by the Planets limited and included by twoe lynes and the third drawne or described by the middle is named the Ecclipticke line and suns place The Eccliptick line is a greater cyrcle consisting in the middle of the Zodiacke and deuiding it into twoe equall compasses defined to be eight degrées in breadth on either side which the sunne maketh by a yearely motion going thwartly in one continuall way is deuided by the foure principall points as the two Equinoctials and the Solstices into foure quarters For as the whole Zodiacke euen so the Eccliptick to the Equatour resting as it were in two onely points but in the rest of the cyrcle it bendeth â—â—om either point toward the opposite Poles of the worlde declined by the one halfe cyrcle into the North and by the other halfe into the South The pointes that touch are the Equinoctiall as wee haue aboue written but the other two furthest distaunt from the Equatoure which are as markes or boundes for the suns departure that when he commeth to the one hée is carried no further but stayeth there and from thence drawne vnto the contrary bound through which turning backe of the sunne they are named the Tropickes of the Gréeks and of the Latines the solsticiall points Not for that the sun beeing carried vnto them stayeth and remaineth any space but neuer resteth nor leaueth of his courses séeing within certaine daies the Meridiane or Noone shadowes are varied the day night spaces either lengthened and increased or decreased and shortned notably as the like is yearely séene Of these that which in the Northerly halfe cyrcle is furthest distant from the Equatoure named the pointe of the summer solstice the other standing or being right against that the point of the winter solstice These points change their places two maner of waies as well according to length of the zodiacke by créeping further in the fore going as in going to and comming short vnto the Equatoure First that the Equinoctiall pointes doe ouer go the places of the fixed stars against the order and course of the signes and therefore doe the daies of the solstices begin and goe before For the summer solstice about the beginning of Olimpias the first day of Iuly which began the yeare with the Gréeks at the morning rising of that constellation Syrius being notably knowne to many but in the yeare of Christes birth it hapned in the 24. day of Iune And in the yeare 1570. it hapneth in the 12. day of Iune about 11. of the clocke before Noone The winter solstice in the first beginning of Olympias hapned the first day of Ianuary or there about In the year of Christs byrth it hapned the 15. day of Decmber in which day at the houre of 12. in the night they affirme our sauiour to bee borne The same winter solstice hapneth in the same yeare 1570. on the 12. day of December aboute 2. of the clocke at after Noone In the second then happen vnto the Equatoure by the Ecclipticke as it were winding and remoued againe in the same departing For the obseruations of many times doe witnesse that the arcke of the Colure of the Solstices reached to these points and Equatoure which they name the suns greatest thwartnesse or declinatioÌ„ is deminished by litle litle For before Ptholomies time by forty yéeres Aristarchus Samius founde the same to bee of 23. degrées 52. minutes and 20. seconds And Ptholomie noted that he found it to be iust asmuch Mahometes Aratensir which was after Ptholomie 749. yeares found this declination to be of 23. degrées and 35. minutes Arzahell the Spaniard that was 190. yeares after Albategnius found it to bée of 23. degrées and 34. minutes Prophatius Iudius which was 230. yeares after Arzahell founde this declination to bée of 23. degrées and â—2 minutes Dominicus Maria being in the yeare of Christ 1491. found this declination to be of 23. degrées and 29. minutes Vueruerus being
the tops or highest places ouer the head are ioyned togither in the Center of the earth and the féete are those Parallels of the Ecclipticke ending the swathe which may worthily be called a solide zodiacke Further a signe in the fifte maner is a portion of the sphericall vpper face inclosed betwéene two halfe cyrcles ended at the Poles of the ecclipticke To conclude a signe in the sixt maner is mente a solyde deuider of the Sphere contained in the saide halfe Cyrcles and Sphericall vpper face which is a signe vnderstood in the fift maner These diuers diuisions serueth as they write vnto that end whereby all things might be inclosed within the signes For if signes be described in the first maner then on such wise those stars onely and those points are said to be in the signes whatsoeuer shall be in that cyrcumference of the ecclipticke And in the first signification also is ment to be vnder the ecclipticke which agréeth onely to the sun as at this day the sun is beeing the 23. day of August in the 9. degrée and 9. minutes of Virgo at Noone which is ment to be vnder that part of the eccliptick that is named the 9. degrée of Virgo If in the second maner planets shall be in signes which doe not excéed sixe degrées of latitude or thus in the second signification to be vnder the zodiacke is monte that here a signe is expressed inclosed within a square pinnacle portion This signification agréeth to the other planets except the sun which decline from the ecclipticke as Mars in this yeare 1599. is in the 15. degrée of Virgo which is vnder that parte of the zodiacke that is saide to be the 15. of Virgo Also he hath a latitude Northerly of two degrées and 28. minutes If in the thirde maner the sun or any starre shall bee in signes placed in the plain of the eccliptick or in the third signification to be in a signe signifieth to be referred vnto any signe of the zodiacke For the whole heauen is deuided into twelue Regions in cyrcles passing by the beginnings of the signes and Poles of the Zodiacke of which Regions each is named a signe And this signification agréeth to the stars standing without the zodiacke as the Northerly Crowne which in our time is in Scorpio and referred vnto the signe of the zodiacke that is called Scorpio in that it is betwéene those twoe halfe cyrcles which passe by the beginning and end of Scorpio If in the fourth maner the planets and stars also not further distant then sixe degrées from the ecclipticke Or in the fourth signification is ment or referred vnto any of the twelue Regiōs of heauen into which heauen by those sixe Cyrcles which passe by the beginninges of the signes and Poles of the zodiacke as is afore written is deuided This signification agréeth to those which are in the ayre as be the Comets As if I wrote that a Comet were in Leo here I meane the sixe cyrcles passing by the Poles of the zodiacke and beginnings of the signes deuiding both heauen and the whole neather Region of the worlde into twelue equall partes So that a Comet is saide to bee in Leo séeing it is in that twelfe parte which the twoe halfe cyrcles describe running or stretching by the beginning and end of Leo. If in the fift maner all the stars and points ment in the vpper face of the sphere be included in signes If in the sixt maner then whatsoeuer is in the world whether the same be in the Ethereall or Elementarie region is accounted to be included within a signe Here conceiue where the cyrcumferences of the cyrcles are ment And first imagine the circumference of the Zodiacke and all the other cyrcles as I haue afore written to be in the hollow vpper face of the first mouer and runneth as it were in the first after the second condicion of motions and demonstrateth alike distaunce and continuing of the cyrcles without impediment Although the Horizont the Meridiane the Uerticiall and other cyrcles in respect of the habitation or dwelling place remaine immoueable in that vpper face of the first moouer yet doeth it nothing hinder although heauen or the first mouer be drawne about that such cyrcles be imagined to bee immoueable For there is nothing more agréeable then to imagine cyrcles fixed and those abiding in any vpper face of the earth So that it is necessary that the Zodiacke the Equatoure and the other cyrcles be described moueable in the hollow face of the first mouer as the bound and inclosure of the whole worlde The Horizont and Meridiane and the others placed immoueable in that hollowe and fixed vpper face in which the whole earth is placed by this meanes the fixed cyrcles shoulde stay in the fixed vpper face and the mouable cyrcles shuld be drawne about with the moueable As in a materiall instrument and solide sphere a man may sée in which the zodiacke the Equatoure and other moueable cyrcles are drawne about vpon the Exe-trée betwéene the two Cyrcles remaining steady of which the one representeth the Horizont the other the Meridian Whether the same may be described in the hollowe or in the imbossing of the first moouer of the saide cyrcumference it is little or nothing regarded yet consider this that all men may behold and sée within the heauen or first mouer the hollowe vpper face of his inclosure to describe and imagine the cyrcles in the same The Cyrcles placed without the materiall instrument must of necessity force a man to describe the cyrcumferences of the Cyrcles in that outwarde face of the Instrument To conclude the Zodiacke is ment and described according to his diffinition being a greater Cyrcle whose cyrcumference in the hollowe of the first moouer described into signes degrées and minutes as was afore writen is deuided And séeing that Cyrcle described by the suns yearely motion is imagined straight drawne and defined or determined from the Center of the suns course by the Center of the sun which with the sun is drawne by a perfect reuolution toward the East For this line in that motion cutting the hollowe vpper face of the first mouer doeth describe the cyrcumference of the Zdiacke So that if the plaine vpper face of the suns course bée extended vntill it cutteth the foresaide hollowe vpper face which common section or cutting shall be the selfe same cyrcumference of the Zodiacke vnto which the place of the force and vertue of any star is applied Therefore by the same meanes that vertue of the moone or any of the planets drawne in the same hollowe of the vpper heauen shall be like the same described cording to the diuers eleuation of the Pole whereof the Colures are called vnperfect cyrcles There are two maner of Colures as the Colure of the solstices and Colure of the equinoctials These two greater cyrcles are drawne by the Poles of the world of which the one goeth by the Poles
of the Zodiacke and the other by the sections of the Zodiacke and Equatoure That which passeth by the Poles of the equatour and Zodiack doth deuide in two parts each halfe cyrcle as well of the equatour as the Zodiacke Therefore the one condicion of the Colures goeth by the solsticiall pointes of the Zodiacke which are the beginnings of Cancer and Capricorn and the furthest pointes from the equatour whereof it is named the solsticiall Colure The other is named the equinoctiall Colure séeing it entreth by the saide equinoctiall sections which are the beginnings of Aries and Libra that is the equinoctiall points So that these Colures deuide aswell the equinoctiall as the Zodiacke into foure quarters in that they goe by the foure principall poyntes of them The Colures generally are called al the greater cyrcles drawne by the Poles of the world which take their name thereof insomuch as they neuer are descerned or séene whole in the turning about of the worlde as the other cyrcles but vnperfect and lacking For both the arks right against one another about the Poles in the thwart sphere are not séene both at once For they are either continually in sight to vs and neuer drawne away or hid like vnto those which be neare to the eleuated Pole Or else they neuer appeare in sight to vs but are continually hid from vs as those which be the opposites But the reaching of the Colures fastneth in the two circles extended and passing by the foure principall pointes of the ecclipticke as the equinoctials and solsticials which touching one another in the Poles of the world do in their cyrcumferences make right angles and part the Zodiack and equatoure into foure equall quarters The Colure of the equinoctials resting in the equinoctiall points The other containing the solstiticiall pointes is called the Colure of the solstices The Colure of the equinoctials is a greater cyrcle moueable and euery where alike drawne by the Poles of the worlde or equatour and the equinoctial points as the beginnings of Aries and Libra making with the equatour right sphericall angles with the Zodiack thwart angles For oftentimes the greatest cyrcles by a mutual touching togither doe make right angles in the sphere as they cut in two parts or into equall halfe cyrcles and by the Poles one another and contrariwaise when they cutte one another by the Poles then doe they forme and make right angles with their cyrcumferences and part one the other into equall parts as writeth Theodosius in his first Booke de Sphera and in propositi 18. 19. 20. and 21. Or thus the Colure of the equinoctials which is named the equinoctiall Colure is a greater Cyrcle passing by the poles of the world and the first pointes of Aries Libra where the two Equinoctiall points are said to be in that the sunne causeth a like day and night in euery place or for that these pointes are in the Equator wherof it is called the Colure distinguishing the equinoctials so that the two Colures crosse one another on the Poles of the world at right spericall Angles It is called the Colure of the equinoctials for that it passeth by the equinoctiall pointes as by the beginnings of Aries Libra which they call the Equinoctial pointes for that when the sunne hapneth into either of them the day and night is of equall length throughout the Earth which commeth to passe twise in the yeare as in the Spring and Haruest whereof the one is called the Equinoctiall spring and at this day is about the eleuenth of March which is the day before Gregory the other the Haruest Spring and hapneth in our time the 14. of September that is thrée daies afore Lambert whereof ariseth this auncient verse Lampert Gregori nox est aequata diei The Colure of the Solstices is a greater circle moueable and euery where alike drawn by the solsticiall points or the beginnings of Cancer Capricornus and the Poles of the Zodiacke and Equatoure making right sphericall angles with both for of both is the Poles comprehended And according to Theodosius propo lib. 2. de Spera that by any twoe cyrcles crossing one the other when a thirde deuideth the parts of both equally and in two partes the same is the greater cyrcle and passeth by the poles of both But that which passeth by the Poles of the other Cyrcle doth part it in two parts and at right angles Here may be demanded why the other twoe are called the solsticiall pointes séeing the Sunne stayeth no where Which is thus answered that the sun digressing from either equinoctiall poynt by his proper motion doeth dayly depart from the equinoctiall cyrcle till hée come vnto the solstitiall point where he is furthest distant from the equatoure But immediately after hee beginneth to returne and come againe vnto the equatour till he come vnto the other equinoctiall pointe So that the pointe of the suns furthest distance which is the beginning of Cancer or Capricornus and of the same called the solstice in that the sun stayeth there that is ceaseth from his further going or departure and beginneth againe to come to the Equatoure For the sun after his comming vnto that point departeth and commeth againe to the equatour so that the end the departure and beginning of his comming is the solstice Therefore not for that the sun stayeth there are they called the solstices although about those pointes of the going and comming of the sun it is so small that for foure sire or more daies after he séemeth in iudgement as it were to stay in one declination and therefore for that cause may be named the solstitials These of sundrie as of Campanus are also called Tropicke points through the suns returning And these may be called Uerticiall or Cardinal cyrcles séeing they goe by those tops of the world and expresse or shewe the foure quarters of the Zodiacke Moreouer séeing certaine parts of these cyrcles being neare the pole are hid and the other right against them nothing at all discerned at any time therefore is it that they are called in Greeke Kolouroi which is in English maimed and vnperfect as Proclus Diadochus Mocrobius and Capella write But this agréeth not in the right Horizont séeing there is no part of heauen which doeth alwaies remaine there hid But in the description of the astrolobie howe large soeuer the same bee yet onely these cyrcles appeare continually vnperfect Yet further the Colure of the solstices or the cyrcle distinguishing the solstices which also is called the solstitiall cyrcle is a greater cyrcle drawne and passing by the poles of the world and Zodiacke and the greatest declinations of the same and by the beginnings of Cancer and Capricornus It is called the Colure of the solstices in that it passeth by the solsticiall pointes as by the beginnings of Cancer and Capricornus which are named the solsticiall pointes for that in them the solstice is caused that is the suns comming vnto
the plaine of the same The descriptions names and offices of the Meridiane Circles and Horizont THe foure greater cyrcles which we haue already described that with the motion of the sphere are drawn about and euery where are alike which the other twoe Cyrcles are contrary as the meridiane and Horizont that are not turned in the drawing about of the Sphere but remaine as immoueable and fixed neither are they alike in all places but are continually changed standing or placed on the earth In that all places haue their proper meridians and Horizonts For both by a mutuall touching and ioyning together doe make right angles and they continually deuide the whole heauen into foure equall parts and make the foure angles and quarters of heauen vnto which by a continuall turning aboute of heauen both the one and the other stars as it were by an orderly succession drawne worke and send forth their vertues more effectuous and excercise their qualities in the Elements then in any other places especially the sun being drawne vnto those bonds for hée both beginneth and endeth the dayes and nightes and distinguisheth them equally as it were in the middle parcels of time The sun also come vnto the meridian doeth then more heat dry vp and consume vapors The Meridiane of any place is a greater cyrcle which goeth or reacheth by the poles of the worlde and height of any place and for that it passeth by the poles of the equatour Parallels and the Horizont through the same doth it make right angles with them And of this it deuideth all the arks of the Parallels as well in sight as not in sight into two equall halfes This circle hath sundry names for Varro nameth it the Meridian or midday cyrcle of the noonestéed in that when the sun is in the meridiaÌ„ or any other star aboue the earth then hath it performed halfe the day arke and is then at the bounde of the Noone time But the other halfe of the night is caused at the instant point of midnight the halfe then reaching from East and West So that of the same this cyrcle of all writers in this science named the meridiane but of Ptholomie the cyrcle of midday and middle heauen by the same reason The astrologians call this cyrcle the royall Cuspe the regall quarter the beginning of the tenth house and the middle of heauen in that this place is principall and of worthier dignity then the other quarters of which shall further be written in his proper place Further it behoueth by the addition 31. Primi Theodosij that the Equatâ—ure and Horizont in the contrary maner to passe by the poles of the meridian of the same that those poles is none otherwise placed than in the common sections of the equatour and Horizont By which sections by those poles of the Horizont is a certaine thirde cyrcle greater drawne which Iohannes a Regio monte nameth the verticial circle so that by the foresaid Corolary or addition ensueth that of these thrée cyrcles of each Exe-trée and Pole are they in that common section of the other two cyrcles Like as of the Equinoctiall and two colures by right may be concluded So that a triple deuision is caused by the thrée cyrcles which appeareth on this wise that as the meridian tendeth by our top and height from the South into the North euen so by the same top it behoueth the other cyrcle to be drawne and passe from the east into the west that both cutting one the other at right angle shoulde expresse the foure foresaide quarters of the world As the Horizont distinguisheth the vpper halfe sphere from the neather and the meridiane from the East to the West euen so it falleth out that the thirde cyrcle as that verticiall shoulde seperate the Northerly from the Southerly halfe sphere To these while any standeth vpright toward the Welt on such maner that y â— middle of his body is in the common Center of thrée cyrcles then doth the Horizont deuide his vpper halfe from the neather and the Meridiane the fore part from the hinder and the verticall cyrcle the right part from the left The thrée common sections of these cyrcles are their Exe-trées as is afore written doe indicate or shewe the foure principall points of heauen which are the fixe poles of the cyrcles placed in the sections of the cyrcumferences as the highest or lowest point which are the poles of the Horizont the point also most Easterly and Westerly which are the Poles of the Meridiane to conclude the pointe most Northerly and Southerly which are the Poles of the verticiall cyrcle Those people that séeme to haue their féete against ours in respect of the roundnesse of the earth that they dwell as it were vnder vs haue alike horizont agréeable to ours alike meridian and alike verticial circle But of these two the halfe cyrcles which be extant to vs are hid or as it were vnder them Contrariwise those which be hid to vs are to them extaunt The pointe also highest to vs is lowest to them contrariwise the lowest to vs is highest to them The figure afore placed doth plainer expresse that afore taught where the letters A. B. C. D. represent the Meridiane the letters B. E. D. F. the Horizont the letters F. A. E. C. the vertical cyrcle the letter G. the center of the cyrcles and world the letters A. C. the Exe-trée of the Horizont the letters B. D. the Exe-trée of the verticiall cyrcle the letters E. F. the Exe-trée of the Meridian To conclude the point that to vs is most Easterly is to them most Westerly et è contrario For the pointe most Northerly and Southerly doe not change the surname except you list to change or alter the names like as of the Poles of the worlde For that which is to vs apparant is to them hid and contrariwise to vs hidde to them manifest Here may be demaunded whether that point of heauen most Northerly be not the Northerly Pole of the world and that point most Southerly the Southerly Pole of the world To which is thus answered that if regard be had vnto the Equatoure and right Horizont which passeth by the Poles of the world and hath the equatour for the verticiall or in stéede of the verticiall cyrcle But wee which haue not the Poles of the world in the Horizont in whose cyrcumference these foure principall pointes of the East West North and South are accustomed to be noted are forced to call that Northerly section of the Meridiane and Horizont the most Northerly point and that section right against the most Southerly point For in euery place there are two sections which the meridiane and verticiall cyrcle doe make with the Horizont which are two right sections in the plaine of that Horizont cutting at right angles one an other in the Center that expresse and shew those foure quarters of the worlde from which the principall windes blowe as East West
North and South So that the foresaid right sections doe part the Horizont and cyrcumference of the same into foure quarters The foure principall windes of the common sorte are thus called that which bloweth from the East the Leuant winde and that right against it the Ponent that from the North Transmontanus and that right against it the Merâ—dional These foure of later yeares they haue deuided into 32. windes after the noted lines and pointes drawne in the Saylers carde and other Mappes euery where to be séene Also the Saylers compasse doth expresse so many windes directed by the adamant or lodestone which howe the same doeth direct and shewe the windes needeth not here be shewed séeing the same is sufficieÌ„tly known to euery sayler which by the guide of their compasse direct their course in clowdy weather either by day or night in marking diligently the points of the compasse how they coast To returne vnto the matter of the Meridiane the diuersitie of Meridianes is no otherwise caused then the swelling of the earth as in the first part I haue sufficiently written the cause of which is that one like parte of heauen cannot be the top or height of euery place Therefore one meridiane cannot serue all places but that in all places a proper Meridiane is caused ouer the head The meridiane also is that which when the sun commeth vnto the highest ouer vs foresheweth by his working and heat the midday This meridiane is a greater cyrcle passing by y â— poles of the world and Zenith or a direct pointe ouer the head abiding immoueable at the motion of the sphere This cyrcle is differing to euery Citty and people by reason of the East and West and is a proper meridiane caused ouer the heade For this is manifest that at the chaunging of the verticiall point there is caused an other Meridian through the swelling and roundnesse of the earth Also a man may of one meridian line describe many as writeth Iohannes a regio monte for in that instant of the Noonetide by letting downe right a plum line the shadowe of the line causeth a newe Meridiane line on the platforme Therefore these with the verticiall line in the the Center to the Horizont crossing one an other at right angles doe indicate the foure quarters of the worlde as the meridian line the North and South the verticial line the East and West The Horizont formeth the quarters of the east and west of which the one is called the East rising or easterly quarter or end the other called the West setting and quarter of the West The Meridiane defineth the boundes of the lowest and highest of heauen and the quarters or middle motions of the day and night time of which that consisting the vpper halfe Sphere is named the highest place and middle of heauen the other which containeth the lowest place right against it called the bothom or lowest of heauen The Meridiane is a greater cyrcle immoueable not one and the same euery where but to euery place peculiar and proper drawne by the top of the place and Poles of the worlde vnto which the sun carried by the motion of the first moouer doeth in the day time cause high Noone and in the night time drawne right against it causeth midnight If this cyrcle were moueable like others then at the motion of the sphere woulde it departe from our Zenith and so loose the name of the Meridiane neither woulde it deuide in proper place vnder it the artificial day into two equall parts séeing by that motion the Meridiane should approach néerer to one part of the Horizont then to the other part Nor should it stay the Horizont at right angles of which it is numbred and accompted amongest the outwarde cyrcles of the sphere The like affirmeth Proclus writing that the Meridiane is none of those cyrcles which is noted and decked with starres For the cyrcles of the sphere are distinguished by starres whereby those cyrcles may more easily be knowne in heauen The meridianes are changed by the continuall chaunging of place in the swelling or imbossing of the earth according to longitude For by going continually right forth toward the East and West it doeth purchase newe Meridianes as by going thrée miles forth then is an other pointe of heauen differing from the first ouer a mans heade and gone further by foure minutes of a degrée Proclus affirmeth that 300. furlongs cause no sensible alterations to happen of the Meridian and this is ment of those which are placed vnder diuers Meridianes and Parallelles For those which are placed vnder one Parallell and diuers Meridianes perceiue and sée no alteration at all Hee which goeth strait from the North into the South or they which directly iourney toward either of the Poles of the worlde doe continually trauaile vnder one Meridiane In that all Merdianes doe go from one Pole to another therefore no iourney causeth by this meanes an other meridiane There are as many meridians in number as there bée differences of verticiall points right ouer diuers parts of the earth in going toward the East and West The halfe of the equinoctiall hath 180. degrées whereof the Cosmographers doe assigne and distinguish so many meridians in such sorte that each Meridiane doeth passe by the twoe opposite degrées of that Equinoctiall and Poles of the world The longitude of a place is the arcke of the equinoctiall cyrcle or of any Parallell contained betwéene two Meridianes of which the one lyeth ouer the fortunate Iles and the other streacheth ouer the top of the proper place noted where the same distance of place is gathered from the fortunate Iles at the equinectiall or at the Parallell of the place The fortunate Iles are situated and lying in the sea called Oceanus Libicus beyond Mauritania betwéene the Equatoure and the tropicke of Cancer which in our time is called the Iles of Canarie and lie further into the North from the equatour then Ptholomie noted or acounted them But the latitude they accompted to bee a space of the earth lying betwéene either pole accompted in the Meridiane drawne by the poles of the worlde or a whole tract of the earth knowne and streached beyonde and on this side the equatoure toward either Pole of the worlde They stablished the beginning of the latitude in the equinoctiall as in the middle cyrcle exquisitely betweene either pole and common bound to both the Southerly and Northerly places So that the latitude of a place is the arke of the meridiane betwéene the equinoctiall and Parallell drawne by the top of the place or it is the distance of a place from the equinoctiall This alwaies is accounted in that meridian which hangeth directly ouer the top of the place and to one degrée of the same doe 500. surlongs or 15. Germaine miles answere The arks of the latitudes doe not differ from the eleuations of the pole but in the standing onely For the eleuation of the pole
is the arke of the meridian from the Horizont vnto the Pole raysed on high from the plaine of the Horizont The latitude of a place is the arke of the same meridian placed betweene the equinoctiall and verticiall point To conclude the latitude of a place and eleuation of the pole do not differ in the magnitude or largenes but in standing onely By the former figure appeareth that the Arke of the longitude of places or citties known is forthwith offered at the first sight as the arke E. P. or P. O. or O. N. c. And séeing the equatour being in compasse about 360. degrées doeth wholy ascend in 24. houres aboue the Horizont regularly of this it commeth to passe whiles in ech houre 15. degrées of the equatour doe ascend that through the longitude of cities it is easily knowne the hourely distance of one place vnto an other séeing the sun commeth later to the meridian to them which are nearer to the East then to them in the West whereof if a citty shall be situated in L. and an other in K. the arke L. K. shall be of 30. degrées then shall the sun come sooner vnto the Easterlier meridian K. by two houres then vnto the Westerly But if one citty shall bee in P. and the other in Z. then in latitude onely shall they differ and shall be vnder one meridian which is declared in the last part of the description of the meridian What the offices and vtilities of the Meridiane are 1 THe vtilities and vses of this circle are many of which the first is that it distinguisheth the dayes and nightes into vnequal spaces it determineth the forenoone time or morning and the after noone or euening time of the artificiall day the like of the night into houres which are before night and those which follow vnto morning Many of the astronomers accompt their beginning of the naturall day from this cyrcle It doth besides represent without the equinâ—â—tiall the Horizont of the right sphere and in euery habitude of the sphere it doeth represent the right Horizont and sheweth the points of the midday and midnight 2 This cyrcle in the thwart sphere giueth and suprlyeth the office of the right Horizont for to euery thwart Horizont it leaueth or stayeth at right angles So that the astronomer maketh or accompteth not his day from the rising or setting of the sun through the thwartnesse of the Horizont which causeth the variety notable difference of the inclination of the Zodiacke vnto the horizont of the angles and largenesse of the rising But they begin to accompt from noone or midnight the sun then occupying the Meridian through the Sunne which congruence all the meridianes haue with the right horizont And that a lesser variety of the inclination of the Zodiacke hapneth vnto the meridiane and angles which it maketh with the meridiane Also in this cyrcle is the Zenith or direct point noted from which the distances of the stars and Parallel cyrcles are gathered 4 In the meridianes as in the subiect the distances of the stars from the equatoure the latitudes of places and the eleuations of the Pole are accompted For the studious and skillfull practisioners obserue the latitudes of places and the eleuations of the pole not to differ in the quantity but in the standing onely For the eleuation of the pole is the arke of the meridiane from the horizont raised vnto the pole The latitude of the place is the arke of the same meridian contained betwéen the equatour and verticiall point so that it is manifest that these arks differing in the standing doe agrée in magnitude whose verticiall points one meridiane containeth but not one Parallell by an equall space from the west be vnequall distant from the equatour and are then said to differ in the latitude only Contrariwise to whose tops one and the same Parallell and not one meridian but each place proper those by like spaces from the equatour be distant by vnlike spaces from the fortunate Iles and are said to differ in the longitude onely So that in both they are saide to differ to whome the Parallell only serueth and they to whome the proper meridiane serueth for they haue their spaces vnequall to either bound Therfore the difference of latitude is the arke of the meridiane contained betwéene the Parallelles of the two places distant from the equatour The quantity of the same is thus knowne if from the halfe Equatour toward either pole of the places standing the lesser latitude of the nearer bee abated from the greater latitude more further off if from the halfe equatour the places be deuided vnder that the one half leaneth into the North and the other into the South by the latitudes of both ioyned whether one or both ly vnder one meridian or diuers meridians For it forceth not in the meridian of both that the latitudes bee ioyned togither séeing all meridians are alike in the sphere The difference of the longitude is the arke of the equinoctiall or Parallell inclosed betwéene the meridianes of the twoe places distaunt from the fortunate Iles and in themselues by which the longitude of one place excéedeth the longitude of another The same longitude is the arcke of the equinoctial séeing the places be vnder the equatour For in the only longitude the places the common Parallelles and tops of both bended doe differ in that the Parallelles from the equatour toward the opposite quarters of the equall Parallelles as places to which they be right ouer doe likewise differ The meridians as is afore declared are the greatest cyrcles of the sphere of the worlde bended by the verticiall points of all places but drawn to the equatoure as by the Poles of which they passe vnto right angles and by a mutuall consent make angles in the Poles of the world which the arks of the equatour being placed betwéene those meridians are measured that by so much as a quarter of the cyrcle they bee distant from them euen so the equatoure from his Poles is on either part distant by a quarter of the greatest cyrcle Those arks doe containe the difference of longitude by which one of the meridianes is further distant into the East then the other so that the angles vnto the Poles betwéene the meridianes are rightly named the angles of the difference of longitude and by the arks of the equatour those also come into knowledge for there is a mutuall relation betweene the angles and arkes each one of them towards another which doe measure the angles The latitude of places is the distance of the verticiall points from the equatour gathered in the meridian If then from the whole quarters of the meridians which to the equatoure and Pole of the world toward which the places decline the equall arkes bee stretched to the latitudes then the seates of the places giuen or the verticiall points of them shall be found And the other arks from these points vnto the Pole
vnderstood of yoong students and practisioners in this maner First the side A. B. containeth thrée spaces which multiplied doe bring forthê° The line B. C. comprehendeth 4. distances which multiplied doe produce or bring for 16. which two squares conioyned doe make 25 the square which procéedeth of the 5. multiplied which the line A. C. containeth doe they equate Euen so in the instruction of finding the distances of places according to the third rule the difference of the longitudes is represented by the line B. C. but the difference of the latitudes by the line A. B. Therefore as by the quantities knowne of the lines A. B. and B C. is the quantitie of the line A C. attained Also by the differences of the longitudes and the latitudes of places knowne and those afore taught being multiplied and increased the distance of them is easily knowne which by the line A C. is represented And in the Triangle and quadrate is the side but in the number named the roote These hitherto for the knowledge of finding the distances of places shall suffice The definition appellations diuision and offices or vtilities of the Horizont THe Horizont called the ender and Cyrcle of the halfe Sphere is the edge betwéene the light part that standeth for the same wee sée and the darke halfe that wee cannot sée of the skie The Horizont as Proclus writeth is a greater cyrcle immoueable or fixed not one and the same euery where but to each place proper from the verticiall point and round about equally distant and deuiding the whole sphere of the world into two equall halfe spheres of which the one halfe appeareth in sight to vs and the other halfe hid vnder the earth The description of the Horizont doth Macrobius teach where he writeth that the Horizont is after two condicions the one extendeth on euery side vnto the firmament and serueth peculiarly as it were for the deuision of heauen in deuiding iustly the skie into two halues of which the one appeareth in sight to vs aboue the proper Horizont and the other hid vnder that Horizont from vs. Which Horizont hath his name of the skie and of the same called the celestiall Horizont whose diameter after Macrobius is as large as the diameter of the eight sphere which as he affirmeth is the furthest and highest parte of the skie that men can readily sée and discerne with the eie But the earthly Horizont in that the same serueth for the sightes onely of the earth and water and not stretching vnto the firmament nor that his halfe diameter as Macrobius writeth doeth excéede 180. furlongs which containeth 22. miles and ½ So that the whole diameter after his account is but 45. miles in length Which if any man stand vpon an euen or plaine ground orels on the sea may see round about him 22. miles a halfe euery waies Which rounde compasse of the whole Horizont after Macrobius doth containe 141. miles and 3 7. parts A comparison that as the meridian is an immoueable cyrcle euen so is the Horizone for if the same were moueable it woulde not crosse the meridian at right angles and vnto these should be imagined that if it were moueable in each day the same would mooue with the meridian cyrcle The appellations aud diuers names of the Horizont 1 THis circle is called the Horizon as it were the cyrcle deuiding the halfe spheres or of the greek worde Orizomai which in English signifieth to define determine and set out in that the same defineth the parte of the worlde séene Or of Oros or Orion that is the bound or ender 2 It is named also the gyrdle or the cyrcle of rising 3 Macrobius calleth the Horizone that bounde of heauen that is séene aboue the earth lib. 1. cap. 15. In that it is the end or bound seperating the neather halfe Sphere from the vpper And of him also called the edge of the halfe sphere And Alfragnus called it the cyrcle of the halfe sphere 4 The Horizone also is so defined of his office in that his office is to deuide that part of the worlde in sight from that hidde vnder the earth Whereof it is not vnworthily called the ender séeing it permitteth nor suffereth any to sée but the halfe sphere at one time and therefore is called of some the cyrcle of the half sphere as afore taught This cyrcle is alwaies vnderstood to be described by the verticiall point in that as the verticall point is changed euen so likewise is the Horizone The Horizone is deuided after twoe sortes first into a right and thwart secondly into a sensible and rationall Horizone The Horizone of the right sphere is called right or right cornered aboue which neither of the Poles of the worlde is eleuated which they haue whose Zenith is vnder the Equinoctial or dwell vnder the Equinoctiall Their Horizone is the cyrcle drawne by the Poles of the worlde which deuideth aswell the meridian as the Equatoure at right angle through which rightnesse it obtaineth that name that it is called the right Horizone The sensible Horizone is a space of the earth defined by a compasse rounde about which the sight of the eie attayneth and comprehendeth in a plaine and euen field Or thus the sensible Horizone is that which the eie â—â—â—fectly séeth and describeth according to the â—ounde of â—ight and called of some the artificiall Horizon and that fo the sâ—â—â— cause that which is contained by sight is by a certaine similitude agreeing with the artificiall day And as the artificiall day is so named for that artificers doe especially worke in it euen so the like is the horizone named artificiall in that towers foretresses and castles in time past were built like the horizone The diameter of this horizone after Macrobius which nearer agréeth to a truth then either Proclus or Albertus as afore was taught is of 36. furlongs to which almost foure Germaine miles answere and 22. English miles and so far on a plain and euen ground not hindred by hils or thicke mists may a man fully sée And in the same space the imbossed rounds of the earth being without hils is increased and groweth to 250. féele or 125. cubits so that this horizone is not sodainly changed nor in a short space Therefore of necessity must ensue that those which are distaunt by a lesser space then 360. furlongs to sée alwaies some part of the earth common to both But those which are distant by many spaces doe comprehend diuers compasses by sight of the eie and diuers horizones The rationall horizone is that which afore was described that the same is a greater cyrcle lying by the edge of the earth and reaching round about vnto the skie and deuiding the celestiall Orbs into two equall halfe Spheres as the one halfe in sight and the other hid to vs. Although the plain vpper face of the horizone passeth not by the center of the earth yet by the edge of the same through
but especially at Noone in euery wéeke be well perceiued to discend and go lower and lower vntil he become vnto the Tropicke of Capricorne or the winter cyrcle where he turneth againe as you may plainly learne and vnderstand by the former description of that cyrcle The Tropicke of Capricorne is a lesser cyrcle and one of the naturall cyrcles which is by the like space distaunt from the Equatoure into the South and described of the sun in the beginning of Capricorne as being vttermost toward the South which is the bound of the suns greatest departure from vs and of his longest digression vnto the South that he defineth and maketh This cyrcle also is called the winter Solstice and winter Tropicke in that when the sun coÌ„meth into this cyrcle it is presently winter that is the shortest day of the yeare Also the lessâ—â— portion of this cyrcle is to vs aboue the horizone and the greater beneath or vnder the Horizon Besides the suns iourney endeth at the south and crosseth or deuideth both the burning and temperate Southerly Zone The Brumall or winter tropicke as writeth Proclus that is furthest toward the South of all those which the sunne describeth by his drawing about of the first moouer into which when the sunne falleth he causeth his winterly returne so that the longest night of the yeare and shortest day is at that time procured From which he goeth no further toward the South but returneth vnto the contrary quarter of the world and hereof this Circle is called a Tropicke or circle of returne Now these thrée are principally noted the equatour and the two Tropickes for the course of the sunne That the instructions of the two Tropicks afore spoken of may more perfectly be vnderstoode conceiue this Figure heere demonstrated In which a h b e. is the meridian a d b. the right Horizone d. the Center of the principall a. the Northerly Pole b. the Southerly Pole g d c. the cyrcle of the Zodiacke h d e. the Equatour which here is ment to bée abatingly described when the sun shall bee in the center of the earth or in the true section of the Equatoure and Zodiacke as in the letter d. from which point when the sun returnes toward the Northerly pole a. vnder the cyrcle g d c. he then describeth in each day by the motion of the first mouer each Parallels vntill he be come in the Meridiane vnto the point g from which hee can not further ascend toward our Zenith in the meridian Of which in the same day the sun describeth g f. the parallell to the equatour which is called the Tropicke of Cancer in that the sun beginneth from this place to approach or draw nearer to the Equatoure vnto which when the sun shall come hee then descendeth vnto the neather halfe sphere in the halfe cyrcle d c. Hee being come againe vnto the point c doth from his center by the motion of the principall or first mouer in the Poles of the world describe the Parallell c i. that is the tropicke of Capricorne The Polare cyrcles are two of the lesser cyrcles neare to the Poles of the world being alike equall distant to the equatour which vpon the Poles of the equatour described are drawne by the Poles of the Zodiacke And these are named the Polare Cyrcles in that they bee neare to the Poles of which that neare to the Pole articke is called the arcticke cyrcle of the greater or lesser Beare drawne in it or for that this cyrcle is described about the pole articke the other that is right against is named the antarticke Cyrcle in that it is drawne aboute the Antarticke Pole Or thus the arcticke is a lesser cyrcle which the Northerly pole of the Zodiacke is so far distant from the Pole articke of the world as is the suns greatest declination or as Proclus writeth that the fore foote of the greater Beare by the dayly motion formeth The same cyrcle after the minde of the learned is distant from the equatour 66. degrées and 30. minutes almost To whome this altitude is higher by 23. degrées and almost 29. minutes To those parts of the earth is the pole arcticke extaunt in sight and continually appeareth It also secludeth and parteth the vntemperate Northerly Zone from the next temperate Zone where the Solsticiall Tropicke is made the Northerly cyrcle and in that place vnder this altitude of the pole 66. degrées and 31. minutes there all the stars and images contained from the solsticiall Tropicke vnto the Pole are seene as both the Beares the Dragon Cepheus Cassiopia Perseus Auriga or the Carter whole Bootes except from the knées downeward the crowne Hercules except the head and right arme the Harpe the Swan the great Horse Andromeda except the left Cubit the halfe of the Northerly Fish almost Deltoton a part of the backe of Taurus the necke and Northerly Horne a great parte of Gemini and the head and necke of Leo. And not vnlike to the former doth Proclus describe them where hee writeth that the Northerly cyrcle is the same which of al those that to vs continually be séen or appeare is for trueth the greatest and that also toucheth the Horizone at one onely point being wholy described aboue the earth And the stars that are inclosed within this cyrcle do neither rise nor set but are continually séen all the night drawn about the Pole The South or antarticke cyrcle is thus defined of him that the same is equal and equidistant to the Northerly or articke cyrcle and toucheth the Horizon at one point The whole of this cyrcle is hidden vnder our Horizone so that all the stars placed and drawn in it abide euer out of sight to vs. The like description that the antarticke Parallel is a lesser Cyrcle which the Southerly Pole of the Zodiacke draweth about as it were by the dayly motion doeth describe about the Southerly toppe of the world and is by a like space distaunt from the Equatoure and the antarticke pole of the world as the articke is from his opposite And doth seperate or deuide the vntemperate Southerly Zone from the next temperate Zone Further it is manifest that the distance of the Poles of the ecclipticke from the poles of the world doe agrée with the greatest bowing or declination of the ecclipticke or the sun In that the poles from their cyrcles bee alwaies distant a quarter of the cyrcle and the colure of the solstices is here taken for that which comprehendeth either Pole And when the quarters standing betwéene the poles and the cyrcles of the poles be in themselues or betwéene one the other equall as the arke of the same cyrcle then the middle arke common to both which as exempted goeth betwéene the poles of the world and the ecclipticke and so parteth and leaueth them equall For the one halfe of the other equall arks is from the poles of the ecclipticke vnto the poles of the world and the other is
from the furthest point of the ecclipticke vnto the equatour By which it appeareth that so much is the distance of the poles of the Ecclipticke from the poles of the worlde as is the suns greatest declination being 23. degrées and 28. minutes and two fiftes almost Or thus that the pole of the Zodiacke is far distant from the pole of the world as is the greatest declination af the sun from the Equinoctiall cyrcle and by the equidistance also on each side of the arctick cyrcle from the Pole of the world that that part of the Colure comprehended betwéene the first point of Cancer and the articke cyrcle is almost double so much vnto the greatest declination of the sun And if cyrcumspectly you consider the maner of the motions you shall readily perceiue that those cyrcles which euer more be of like largenesse increase and decrease togither with the twoe Tropicke cyrcles according to the increase or decrease of the suns declination As appeareth by the letter n. in the foresaid figure that representeth the Northerly pole of the ecclipticke or Zodiack moued from the letter n. into o. by the motion of the first moouer and returning againe into the point n shall be moued the cyrcle describing n o. being distant from the Northerly pole a. asmuch as is the suns greatest declination h g. as hereafter by demonstration shall plainer appeare And this cyrcle named the arcticke in that it is described by the arcticke of the Zodiacke The like is described from the point r. being the pole antarcticke by the motion from r. vnto s. and returning againe vnto r. so that the antarcticke cyrcle r s. is equall to his opposite and equidistaunt to the Equatoure This probation that the distaunce of the Poles of the worlde and Zodiacke is equall to the suns greatest declination doth require before hand these thrée propositions The first that the quarters of each cyrcle any where taken be in themselues or betwéene one another equall The second that the poles by a quarter that is by 90. degrées be distant from their proper cyrcle The third that the equals deducted from their equalles then doe the equalles rest As for example if you borowe two fourthes in one and the same Colure cyrcle that is the Solsticiall of the same parte where it passeth by the beginning of Capricorne and is the like from the pole of the worlde vnto the Equinoctiall and that other is that which is from the Pole of the Zodiack vnto the Zodiacke or ecclipticke and of this I thus reason that when the equals be deducted or abated from the equals the remainer shall be equall Therefore are the foresaid quarters equal in that they be in the same cyrcle and that from either is the equall or common arke deducted that is the same which is contained betweene the Equinoctiall and the pole of the Zodiacke which arke doeth containe 66. degrées and 31. minutes almost So that the arks resting or remaining of these quarters be equall that is the distance of the poles of the Zodiack and the Equinoctiall is equal to the suns greatest declination For if 66. degrées and 31. minutes bee deducted from either quarter the remainer then shalbe 23 degrées and 31 minutes which is the distance betwéen the foresaid poles and the greatest declination of the sun This other example demonstrateth that the suns greatest declination and the distance of the poles of the zodiack or ecclipticke from the poles of the world is equall and of like largenes and that what soeuer hapneth to the distances of the said Poles For as this increaseth or decreaseth the like doth that decrease or increase Of this it is manifest that the two foresaide articke cyrcles is nowe in our time lesser through the decreasing of the suns greatest declination and that the Tropickes are greater then they were in Ptholomies time The offices or vtilities of the foure lesser Cyrcles 1 THe office of the Solsticiall Tropicke after the Gréekes is to define the longest summer day and the winter Tropicke to determine the shortest winter day and longest night For Proclus to finde the longest day did deuide the summer solstice into 8. equall partes of which so deuided he affirmed thrée parts to be continually hidde vnder the horizon and fiue aboue The truth of which is known if the Sphere bee rectified for the latitude of 41. degrées where by this diuisiō the longest day containeth 15 hours and the night but 9. houres 2 Many and notable offices doe the Tropicke cyrcles offer as well vnto the composition of dialles as vnto the preparing many other Instruments in Astronomie 3 They declare the places of the Ecclipticke in which the suns solstices are caused whereof the longest or shortest daies by them are knowne Or thus they declare in euery standing of the sphere the longest and shortest day with their quantity 4 They include the Suns way in that they bee as the bounds including the Region in heauen in which the sun is continually moued 5 They declare the suns greatest declination as afore hath bene often taught 6 They seperate in heauen the burning Zone from the two temperate Zones But of the Polare cyrcles these be the chiefest and especialest vtilities 1 They iudicate or shewe the Poles of the Zodiacke and howe farre they bee distaunt from the Poles of the world 2 They inclose those stars which euer appeare aboue our Horizone and those in like maner right against being alwaies hid vnto vs. But for that euery seueral Climate hath disagréeing from other Climates these cyrcles their distance therefore cannot bee certaine from the other Parallel cyrcles sauing for one Region certaine as neither their quantities nor their order For in that place where the altitude of the pole is lesser then 66. degrées and a half these cyrcles there are lesser then the Tropicks and in order are betwéene them and the poles and is from the pole continually distant by so many degrées as the pole in that country is raised aboue the Horizon So that in the same place the Pole raised more then 66. degrées and a halfe The Tropicke then is aboue the horizone as the like may be vnderstoode by that place called Wardehouse So that in the same Climate the arcticke cyrcle is greater then the Tropicke of Cancer as witnesseth the learned Stoeflerus Iustingensis 3 They distinguish after the mind of the Gréeks the cold Zones from the temperate Which Ferio denieth affirming that the arctick and antarcticke cyrcles kéeping no vniformitie to all countries and béeing vncertaine and variable boundes can limit any certaine place For the temperate Zones are places certaine the arcticke and antarcticke cyrcles bee changeable limits therefore cannot they be as bounds of the temperate Zones yet dooth hee better allowe and agrée vnto that that the Tropickes bee bounds of the temperate zones So that changeable limits by this argument cannot be appointed as bounds to vnchangeable places 4 They deuide togither with the
the holow vpper face of the moones Orbe that reacheth vnto the hollow vpper face of the highest heauen being most pure perfitte rounde continually caried about and bright appearing This parte of the world being the Etheriall region is named heauen which alwaies drawne about by a meruelous swiftnesse is deuided into nine Orbes or Spheres Although sundry Astronomers as Alphonsus Iohannes de monte regio Purbachius and others haue added a tenth Sphere through the third contrary motion founde in the eighth Sphere named of Thebit benchore the first inuenter of the same Motus trepidationis or the going and comming of the eight Sphere The first and vppermost Orbe is named the first moouer The second is that which is named the ninth Sphere or Christaline heauen but of Ptholomy named the firmament or Orbe of the fixed starres And the thirde is that which of them named the eight Sphere onely added through that motion of the trembling or as it were a mouing foorth and returne of that eight Sphere which properly is caused in the two small Circles about the heades or beginnings of Aries and Libra through which diuerse motion of the eight Sphere do the Equinoctials and Solstices come and beginne sooner by certaine daies and the suns greatest declination deminished and dayly doeth to that in Ptholomie and Hipparcus time which then was 23. degrées and 52. minutes and 30. seconds And for these haue Alphonsus and sundry others attributed diuers motions to the eight Sphere adding a ninth and tenth Sphere to it That there are but eight celestiall Orbs which may be seene ALthough Ptholomy affirmeth that there are nyne Orbs equally distant yet are there but eight which may perfectly be séene and decerned with the eie both in the standing variety of motions and differing in the periodes or courses Also they are in such order disposed that no Orbe hindereth the motion of another néere to it As the Sphere of the fixed stars and the seauen Orbs of the Planets And most certaine it is that some of the fixed stars are drawn by a swifter motion and others by a slower motion and that the Apogea or ascentions also of the Planets are changed after the order of the signes The Orbs of the Planets thus containe and compasse one an other as first the Sphere of Saturne being nighest the firmament of which being compassed doeth like containe Iupiters sphere and Iupiters doth in the same maner inclose Marses sphere and Marses in like order the sunnes sphere nexte the suns doeth containe Venus sphere which like doth compasse Mercuries sphere and Mercuries doeth containe the Moones sphere being the lowest and smallest sphere And euery of these spheres hath a star a péece named eractical stars or planets which stars haue euery one their proper Orbe seueral his motion seueral and vnlike in time one to another in that they appeare one whiles néere togither and another whiles are séene far distant asunder By which it agréeth that their equall motions to appeare to vs vnequall either through the Poles of the Circles diuers from the Poles of the worlde about which they bée turned as are the Poles of the Zodiacke vnder which the eratical stars are continually drawn and moue rather for that the earth is not the Center of those Orbes by which the Planets are caried and moued about So that when we consider those mouings by the Center of the worlde then is caused that they séeme to vs as they were encreased in a greater bignesse when as we beholde and sée them néere hand and that lesser in bignesse when we sée them placed far off Euen so in the equal circumferences of the Orbes through the diuers distance of sight wée like obserue the vnequall motions by the equall times Yet indéede neyther of these happeneth but that they are drawne aboute by vnchangeable spaces beeing a like distant and kéeping one manner of bignesse For if this were then the sun or any other star being in the middle of heauen should séeme or appeare bigger which it doth not then being in the East or West part And the contrary we sundry times sée when as the sun or any other star appeareth bigger in the quarters of the East and West which is not caused by reason of the shorter distance but for that his beames in the vapors which doe thicke ascend both in the winter time and in raynie weather that hang in the ayre betwéene our sight and the body of the star are then broken which breaking of them doth cause the star to appeare far bigger to the eie then in déede the same is And that a readier and easier knowledge may bee had after the mind of Ptholomie of the first moouer and celestial Orbs with the number of the Circles and Elements inclosed within the first moouer conceiue this figure here following most aptly drawn and set out for thy further instruction This Figure declareth the number disposition and order of the celestiall Spheres about the Globe of the Earth That there are two first motions of the celestiall Orbs. ALthough the celestiall Orbs are seuerally drawne by proper and vnlike motions yet be there two first motions that are manifest both by obseruation and iudgement of the eie The one is of the first mouer which Ptholomy attributeth to the ninth Sphere that is onely drawn about by an equall swiftnesse from the East into the west and from thence againe into the East vppon the Poles of the worlde or Equatour in the space of a naturall day or 24. houres And this first mouer draweth with it al the other Orbs much like a ship which being at full saile doth drawe and cary al her men other liuing things which are in the Shippe So that by this motion of the first moouer the neather Orbes which the first mouer compasseth are drawn once euery naturall day or in the space of a day and night about the earth Also this first mouer doeth not onely describe and measure a naturall day but causeth times and diuersities of dayes and nights with the proper motion of the sun and it dayly bringeth vp stars to be séene and carieth vp to the highest and after hideth them againe vnder our Horizont in the west Besides it is the common measure of al the other motions The other motion is proper to the eight Sphere and to the Orbs of the seauen Planets in the which they are contrarily caried to the first mouer as from the west into the east in mouing vnder the Zodiacke and about the Poles of the same and not in Parallels from the Equatour equally seperated but are drawne much slower yea and vnlike As by a like example when a ship by a most swift course is caried into the west yet may the Mariners and others in the ship walke forwarde in the meane time into the East Euen so is this second motion of all the other Spheres vnder the Zodiack vpon the Poles of the Eclipticke Also by a swifter motion
standings FIrst the earth is placed without the Are trée of the world yet in such sort that it is equally distant from either Pole that is that the Equinoctiall may be in the plaine vpper face as in the letter D. appeareth Secondly that it is standing on the Exe-trée of the world yet without the playne vpper face of the Equinoctiall that is that it be néerer to eyther of the Poles as in the poynt B. or G. Thirdly that it is neyther standing in the Exe-trée of the world nor in the plaine of the Equinoctiall as in the poynts A. C. F. E. The first standing béeing graunted these absurdities shoulde then ensue through the diuers placing in diuers and sundry places of the playne Equatoure 1 In the right Sphere should neuer the Equinoctium or a like day and night be caused in that the Horrizont shoulde neuer cut or part the Equinoctiall into two equall halfes 2 In the thwart Sphere shoulde no Equinoctiall bee and somewhere againe should the Equinoctiall be but not in the middle Parallell betwéene the two Tropickes that is it should not happen the sun being in the Equinoctiall but in an other lesser Parallell Cyrcle being néerer to eyther Tropicke poynt 3 The time from the rising vnto the Noone tide shuld not be equall to the time from the Noone tyde vnto the setting of the sun 4 The magnitudes and spaces betwéen the fixed stars both in the East and West shoulde not be séene equall or a like In the second standing if that the earth should bee placed on the Exe-trée and not in the myddle of the worlde then should these absurdities ensue In euery Climate the playne of the Horrizont shoulde cut heauen into two vnequall halfes except those places hauing the right Sphere yea and the Zodiacke shoulde be deuided into two vnequall Arks so that there should be somewhere more and somewhere lesse then sixe signes of the Zodiacke séene aboue the Horrizont which is contrary to all experience 2 The Equinoctiall shadowes both of the rising and setting of the sun shuld not agrée in such sort that they might fall in right line Neither the shadowe of the rising of the sun in the Solstitial or longest day should make or stretch in right lyne with the shadowe of the suns setting in the Brumall or shortest day et econuerso In the third standing if neyther it should be on the Exe-trée of the worlde standing nor in the plaine of the Equatour then should the same absurdities ensue which are vttered in the two former To conclude wheresoeuer the earth is generally placed without the myddle of the world there is the reason of the dayes equal increasing decreasing in the thwart Sphere confounded and there shall eyther no Equinoctials at all bee caused when the sunne occupieth the myddle way betwéene either Tropicke Nor the Moone alwaies shadow the suns light although she commeth right against the bodie of the sun And the earth not standing in the myddle of the world shall not shed or stretch his shadow to the moon So that all these absurdities and vaine argumentes doe grant that the earth cannot bee in any other place then standing in the middle of the world That the Earth abideth fixed and vnmoueable in the myddle of the world THat neyther the earth in right nor Cyrculare motion is drawn about the Exe tree of the world nor about any other Exe-trée but to rest and stay in the myddle of the worlde both holy scriptures confirme and Phisicke reasons prooue For the Psalme sayth which stablished the earth vpon his foundation that it shall neuer bee moued And Ecclesiastes in the first chapter sayth that the earth standeth for euer and the sun both riseth setteth and goeth about vnto the place where he arose Also that the sun is drawne about the Psalme doth manifestly witnesse where it is saide that for the sun hée hath placed a Tabernacle in them and he as a Bridegroome going forth of his chamber doth reioyce as a Gyant to runne his course which goeth forth from the vttermost bound of heauen and returneth about vnto the ende of it againe Also it is knowne and numbred among myracles that God would haue the sun to continue The Phisicke reasons are these THat of one simple body is onely one simple motion That the earth is a simple bodie therefore therevnto agréeth but one simple motion But of the simple motions I haue before taught that the one is in right maner and the other in Cyrculare forme That the right motion séeketh downwards vnto the myddle whether being caried they settle and rest Therefore is the motion of the earth not cyrculare about By the second appeareth that euerie graue or heauie matter by nature is thrugh his waight caried after a most straite lyne vnto the Center and both fetleth stayeth and resteth at the same where it neither falleth or is caried any further So that all graue matters as the parts of the earth and those which consist of the earth are sent or caried by a most straight leading vnto the earth and at his vpper face shall stay and rest And weare it not that they are staied through the fastnesse of the earth they should so long be caried downwardes vntill they came vnto the Center Also the earth through his fastnesse receyueth and beareth all thinges falling on it Therefore doeth the earth much more beeing within the Center stay and rest fixed and vnmoueable bearing all other heauie things falling on it séeing the earth is heauiest of all others By the third it is euident that if the earth shoulde bee moued or caried it should of necessity be either drawne in right or cyrculare motion If it should be caried in a right maner séeing it is the heauiest of all others it shoulde by his swiftnes moue and goe before all other heauie things and shoulde leaue behinde the liuing creatures and other things fastned to it and shoulde also leaue them hanging behinde in the Ayre If the earth should be drawne about by a cyrculare motion should in a daies turne at the least be caried about the Exe-trée from the West into the East as either alone or with the first Orbe then euery day should many most disordred things and contrary to experience happen For it shoulde bée a most spéedy motion and swiftnesse inseperable which should draw cyrcularly all the whole earthly body rounde about in 24. houres And therefore that the earth is caried with so swifte motion shoulde not onely ouerthrowe buildinges but high hilles and greatly shake and harme all thinges fastned and growing on the earth yea all liuing beasts and other creatures dwelling on the face of the earth shoulde bee likewise shaken and harmed Also the cloudes foules and whatsoeuer liueth and hangeth in the Ayre should bée caried and lefte behinde at the setting in the West For by the swift turning about of the earth should all things be ouer turned and left behind by a
through the difficultie of measuring And this whole compasse is not onely ment of the earth but of the earth and water ioyntly togither both which are saide to make one Sphere Also Eratostenes gathereth the compasse of all the earthly Orbe by the proportion of the perticular or the degree of the celestiall Cyrcle vnto the like space on earth For he affirmeth that to one degrée of the celestiall Equatour answere 700. furlongs or 15. Germayne myles but Ptolomie attributeth to a degrée 500. furlongs Which is thus to be vnderstoode that a Cyrcle be imagined on earth directly vnder the Equinoctiall or Merydian lyne deuiding the earth into twoe halfes and that this Cyrcle be likewise deuided into 360. parts or degrées as the celestiall Cyrcles are And ech of these parts doth like vnto the celestial parts containe 700. furlonges or 15. Germaine myles This nowe being tryed and found what the whole Summe eyther of the furlongs or myles of the whole cyrcumference of the earth which contayneth 360. parts or degrées you shall easily finde and knowe the same by this maner Multiply the whole compasse of the earth that is the 368. degrées by the 700. furlongs or fiftéene Germayne myles and the whole compasse shal either appeare to be 252000. furlongs or 5400. Germayne myles This whole compasse of the earth deuide by 22. and the number comming thereof shall bee the 22. part of the compasse of it that is 11454 12 22. furlongs or 254 â—0 22. Germayne myles And abate this 22. part from the whole Summe of the circumference and the number in furlongs shall remaine and be 240545 10 22. and in GErmayne miles 5154 1â— 22. And if any of these sums be deuided a part by 3. it shal be found in furlongs to be 80181. a halfe and a third part or 3 2. 10 66. And in Germaine myles 1718 4 22. that is the dyameter of the earth aswell in the furlonges as Germayne miles And Archimedes by sundry labours and witty inuentions and by Geometrical practise hath found that the like proportion is of the Circumference of the whole Cyrcle vn to the diameter of the same as is 22. vnto 7. that is the diameter thrice with a seauenth part and a halfe But whensoeuer any man will by the cyrcumference of the Cyrcle gather and finde his diameter worke the numbers thus as this example teacheth First set down 22. at the left hand toward the right hand 7. and the cyrcumference betwéen those two numbers 22. 5400. 7. After multiply the first by the second that is 7. by 5400. the number increased which is 47800. deuide by the thirde that is 22. and you shall finde in the quotient 1718 4 22. Germayne myles Or thus in furlongs the number being set downe alike 22. 252000. 7. then multiplie the first by the second as 7. by 25200. and the increase shall be 1764000. after the increased number deuide by the third as by 22. and the diameter shall be 80181 18 22. If any couet to finde the vpper face of the earth by the dyameter and cyrcumference known worke one into the other and you shal haue that you séeke But if you desire to knowe the thicknesse of the earth then ioyne the superficiall solydenes of the Sphere vnto the sixt part of the diameter and you shall obtaine your desire THE SECOND PART OF THE SPHERICALL Elements of the Celestiall Circles with the vses of the same Circles What is the Summe of this Second Part. WHereas in the first part were only teh rudiments of the Sphere handeled and taught which are also written and contained in diuers Phyâ—â—â—e bookes as of the World and the many parts thereof that is of the Ethereall and Elementarie Region And also of the parts motion and formeâ— of â—he Etheriall Region as Heauen and the forâ—â—â—e 〈◊〉 and quantitie of the Earth Here in this second parte shall fully bee â—etâ—â—â— thâ— and largely handled the manifold vses of the Cyrcle of which the materiall Sphere is framed and made Further this second part is deuided into thrée partes the first teacheth the deuision of the Cyrcles in that the auncient Astronomers for a playner instruction deuided heauen into sundry Cyrcles and of these some in greater and other some in lesser Cyrcles In the second part are the definitions descriptions and vtilities of all the Cyrcles taught In the third and last part are the places of the Zones learnedly described and the vtilities of them So that this second part doeth especially intreate of the Cyrcles séeing the principall poynte of the Sphere is of the celestiall appearances which by reason of the celestiall Cyrcles or of the first moouer are caused as may appeare of the ascentions and descentions of the signes by which the whole knowledge aswell of the naturall as artificiall day is learned Wherefore in that this instruction of the ascentions of the signes consisteth in the Cyrcles which the auncient Astronomers imagined to bée in the first mouer therefore is this second part of the celestiall Cyrcles aptely placed and necessarily before taught That the Sphere of the worlde is either right or thwart THe roundnesse of the earth as is afore taught both altereth the standing of the Poles and the whole Sphere of the worlde in diuers partes of the earth For to them which dwell vnder the Equatour either Pole falleth to the playnesse of the HorizoÌ„t But to others dwelling without the Equatoure the one Pole is raysed and the other depressed hid through which diuersitie of the standinges of them are these differences caused that the risings and settings of the signes are altered the spaces betwéene the dayes and nights varied whose causes ought diligently to be sought Therefore is the right Sphere distinguished from the thwart Sphere of the worlde In this maner as here you may be holde by these figures following That is called the right Sphere in which either Pole resteth and standeth on the plaine of the Horizont and the Equatoure which there doeth exactly possesse the middle place betwéene the Poles and doeth with the Horrizont make a right sphericall angle of which it is so named a right Sphere For they haue such a standing vpon the Sphere of the worlde as that neyther of the Poles is eleuated aboue the Horizont to them which dwell vnder the Equatoure The thwart declined or bending Sphere is that in which either of the Poles of the world eleuated is séene aboue the Horizont and the other iust somuch set and hidde beneath the Horizont and also that the Equatoure frameth and maketh with the Horizont thwart and vnequall angles And that is called a blunte angle which séeth the Pole eleuated and that a sharpe angle declining vnto the contrary They which dwell on this side and beyonde the Equatoure haue such a Sphere But the same forme and condicion of the thwart Sphere is not euery where nor the positure of it the same reason but that the thwartnesse of the Sphere
the sixt is learned that in the same Cyrcle as by the subiect is both the length of the whole earth and perticular places standing in diuers parts of the earth considered and measured For according to the exact doctrine of the sphericall tryangles the longitude or length of places and the difference of longitudes is alwaies the Equinoctiall Arke and not any Parallell By it also the declination of any degrée of the Zodiacke is knowne which being had in any day at noone the sun then shining cleare forth the Northerly latitude or eleuation of the Pole of any Towne may artificially be knowne It is besides the measure of time in that a naturall day is perfourmed by one whole returne of the Equinoctiall with an adition or inerease to that parte of the Ecclipticke which the sun in the meane whiles accomplisheth by his proper motion against the motion of the first mouer 7 By the seuenth it much auaileth and helpeth the doctrine of astrology in that by the guide and leading of the same are the beginnings of the twelue houses of heauen found when astrologiall figures are erected and fashioned to prognosticate or iudge by which can neuer so perfectly be searched and found without the Equatoure and this through the vnlike motion and ascention of the parts or signes of the Zodiacke By it also are all Townes according to their longitude and latitude easily placed and found in the earthly Globe so that by it a man may readily know which Townes are Northerly and which Southerly It hath besides a most great vse in Geography vnto finding the distances of places and vnto placing of Cities in the earthly globe in hauing the true longitude and latitude of them 8 The eight instruction that by it a man may attaine the knowledge of all the celestiall Parallell cyrcles and the earthly Zones lying vnder them As by this example the Parallel streached along by Rodes cannot otherwise be knowne but by his distance from the Equinoctial as by his principall fore noted Parallell which a man may learne and know to bée from the Equatoure toward the North 36. degrées The same knowledge may aptly be had of all the other Parallell cyrcles rightly knowne so that none otherwise can bee prompt and saillfull in Geographicall matters Cleonedes affirmeth prima Meteor that it afterwards behoueth to know how to discribe each turning about of the fixed stars with the first mouer about his Center cyrcle as that all the Parallell cyrcles are knowne Séeing among those cyrcles the Equinoctiall is greatest and those Parallell cyrcles least which are drawne about the Poles of the worlde euen the like are those the greater cyrcles according to proportion from them which are described vnto the Equinoctiall 9 The niuth sheweth that no description of the earth although in platefourme can bee expressed neither by straight nor crooked lines without the knowledge of the Equatoure 10 By the tenth appeareth what commodity of the same hath and serueth in the iudging of genitures is here by silence ouerpassed séeing with breuity it cannot bée vttered The description names and offices of the Zodiacke and Ecclipticke line or way of the Sunne AFter the ancient Astronomers had deuided heauen into twoe equall halfes by the Equinoctiall and diligently obserued and noted the thwart drawing and standing of the Zodiacke and a like forme of a larger Zone the diuers courses motions and wandrings both of the sun moone and other Planets which being drawne about with the first moouer kept no equall spaces in them selues agréeing to the first moouer nor a like distaunt in their motions from the Equatoure but that whiles they were dayly drawn by a contrary motion of the first moouer into the East they in the meane time wandered one whiles into the North and anotherwhiles into the South vnto a certaine elongation and distiance and so returned vnto that cyrcle They abserued also that the Planets kept alwaies one maner of iourney and way and that way cutting or cressing heauen and the Equinoctiall by a thwart manner the same of these they named the Zodiacke This cyrcle of the 12 signes commonly called the Zodiacke which also is a greater cyrcle and thwart lying hauing a latitude moueable vnto the motion of the sphere to which it fasteneth and euery where is a like vnder which the Planettes by a continuall motion are drawne and run This cyrcle also doe the Latines name thwart through the thwart standing of it for the Equatour doth compasse the sphere of the worlde by the iust middle space betwéen either Pole but the Zodiacke is thwartly drawn both to the sphere of the worlde and to the Equatoure so that in some partes it is nearer to the Poles of the same and in some parts further distance from it It is crossed also of the Equatoure into two eqnall halfe cyrcles of which the one is called the Boreall or Northerly halfe cyrcle and the other the Meridionall or Southerly halfe cyrcle therefore by the continuall turning of heauen drawne about vnto any right and thwart Horizont inclined according to the thwart Angles it doeth both chaunge and varie those Angles by the continuall motion and turning about For to certaine Arks it figureth and formeth righter and to certaine others thwarter Angels through that diuers inclination vnto the Horizont which ensueth after the standing of it And the diuersitie of the inclination of it vnto the Horizont doth also cause a varietie in the motion For those doe slower arise which make right Angles with the Horizont and those are sooner drawne vp and appeare which doe cause thwart Angles In the thwart Sphere with that thwartnesse of the Sphere and the Angles which the Horizont and Zodiack performe is the thwartnesse encreased What the names are of this Circle _1 THis Cyrcle is named the Zodiacke of this Gréeke worde zoes that is in English Life in that it is the path or the comming and going of the sun which is called the author of life causer of generations as Aristotle writeth Or of the Gréeke name zódion which in English is the figures of Beastes with the which this cyrcle is imagined to be formed by the concourse of stars 2 This Cyrcle is named thwart or bowing in that it crosseth thwartly the Equinoctiall and first moouer and doth appeare thwart in respect of the Poles of the worlde from which it is not equally distant Or for that it maketh not right but thwart Angles with the Equinoctiall and Colures or Tropickes Or for that it doeth not regularly ascend and discend according to his partes like as the Equinoctiall doth but that certaine parts or signes of the same doe righter and slower and certaine thwarter and swifter arise in either Sphere But the Zodiacke is not named thwart compared vnto the proper Poles séeing from them it is equidistant according to each parte as the Equinoctiall from the Poles of the world Yet compared vnto the Poles of the world in that the
which by a mutuall section doe make an angle the complements of the latitudes be known by the degrées abated from 90. in the degrées of the latitudes Further by the suns meridian had and found you may easily conceiue the eleuation of the pole and habitude of the sphere For the whole quarter is of 90. degrées Séeing the suns meridian altitude in the equinoctiall must be subtracted from 90. degrées the rest shew the eleuation of the Pole As for example the suns meridian altitude of Viteberge in Germanie in the time of the equinoctiall is of 38. degrées and 10. minutes the rest of the degrées of the quarter shall appeare to bee 51. degrées and 50. minutes which eleuation of the pole neer agréeth to London So that by so many degrées is the Pole there eleuated aboue the Horizont And as the quadrant is from the pole vnto the equinoctial euen so is the quadrant from the Zenith vnto the Horizont If therefore in the time of the Equinoctiall the distance of the Horizont vnto the suns altitude be of 38. degrées and 10. minutes which is not the halfe part of the quarter the same yet being subtracted frō the whole quarter doeth shew that the rest shall bee more then halfe part of the quarter that is 51. degrées and 51. minutes For those spaces which are from the pole vnto the Equinoctiall and from the Zenith vnto the Horizont are alike what the distance of the Zenith is from the equinoctiall the same likewise is the Horizont vnto the Pole that is the latitude of the place is equall to the eleuation of the pole To declare that the latitude of a place is equall to the eleuation of the pole these foure propositions are to be conceiued First the quarters of one and the same cyrcle any where taken are equall one to the other Secondly the poles by the quarter that is 90. degrées bee distant from their cyrcle Thirdly the Zenith is the pole of the Horizont Fourthly and last the equals abated from the equals the equals still remaine So that two quarters of the meridian taken as that which is from the equinoctiall vnto the pole and that which is from the Zenith vnto the Horizont which séeing they are quarters of one and the same cyrcle therefore are they likewise equall one to the other that is either containeth 90. degrées when frō these two quarters the common arke is abated which is betwéene the Zenith and Pole of the worlde and the rest of the equals remaine as the arke which is from the equinoctiall vnto the Zenith and called the latitude of the place and the arke which is from the Pole of the world vnto the Horizont also called the eleuation of the Pole as may be vnderstanded of the former Viteberge that is of 51. degrées and 50. minutes Yet that you may easilier finde and knowe the eleuation of the Pole of your City or Towne you must first obtaine and haue the suns meridian altitude which workemanly may be had and obserued by the shadow As when the suns altitude in the time of the equinoctiall is precisely of 45. degrees the shadowe then is like to the Gnomone which is at Venice as Plinie writeth also of Milaine and Lions for the sun to them is in the time of the equinoctial in the middle of the quarter But when the suns altitude excéedeth 45. degrées then is the shadow caused lesser as of Rome where the sunnes meridian altitude in the equinoctiall is of 42. degrées and 10. minutes so that the shadowe is there shorter Also Plinie writeth of Rome that the ninth part of the Gnomon in the equinoctiall doth lack of the noone shadow But when the suns altitude is lesser then 45. degrées the shadow of the Gnomon is caused longer The like is with vs through all winter and the time of the equinoctiall for we sée the shadowes of mens bodies to be longer for that the suns altitude in that time is neuer 45. degrées For how much the shadow is longer then the halfe part of the quarter so much the lesser is the suns altitude then 45. degrées As of Viteberge in the 10. day of September the suns meridian altitude is then of 39. degrees and 21. minutes but when the sun is further distant by the 45 degrée of the quarter or by the halfe of the quarter then ensueth that the shadow is so much longer then the Gnomon or 45 degrées For the Noone shadow in the 10. day of September is the like vnto the Gnomon as the 50. degrées and 39. minutes are vnto 45. degrées Heere you sée how by the meridian shadowe you may finde the suns altitude which obtained you shall easily find the altitude or eleuation of the Pole especially in the time of the equinoctiall For the suns altitude then from the whole quarter that is from 90. degrées must be subtracted and the eleuation of the pole shall remaine and appeare to be as is aboue taught Seeing it is somewhat harde to finde the height of the Pole vnto any day prescribed that the same may more easily and surer be attained and founde you shall vse this table here following by the helpe of which you may without great labour finde and know the eleuation of the pole For to procéede and worke by this manner seeke first the suns meridian altitude at the day offered either by an astrolaby or quadrant but rather by the instrument named the quadrant in whose bordure are 90. degrées drown or written expressed by reason of the Gnomon and shadowe vpwarde After séeke the degrée of the Ecclipticke by the Ephemerides which the sun obtaineth at noone of the day offered next by the table folowing take the declination of the degrée founde by meane of the equinoctiall if the sun then shall bee in Northerly signes abate or subtract from the suns altitude afore found but if in Southerly signes then adde vnto the suns altitude The produce or rest is the eleuation of the equinoctiall which abstracted or abated from the whole quarter that is from 90. degrées leaueth sheweth the eleuation of the pole as in the 10. day of September the suns altitude in the twelfe houre or at noone is of 39. degrées and 21. minutes To finde this eleuation of the pole I enter the table following where I finde and sée the 27. degrée of Virgo to haue the declination of one degrée and 11. minutes which degrée and minutes séeing they are in the Northerly part of the worlde are to be subtracted frō the suns altitude that day and the degrées which remaine are 38. and 10. minutes The altitude of the equinoctial that day which subtracted or abated from the whole quarter that is from 90. degrées the eleuation of the pole which remaineth is 51. degrées and 50. minutes This Table of the Suns declinations containeth the number of the degrees of the Zodiacke increasing in descending on the left hand and increasing by ascending on the right
meridian either hath or may haue the same altitude from the horizon as to the eie is offered in this figure folowing Where a b d c. is the Meridian b e c. the greatest halfe of the Paralels of the horizon f g. the least b. the North and c. the South a. the point of the top o. or q. the place of the starre giuen by which a o k. or a q n the verticall Circle passeth and the like doth the Parallell p l k. The Arke k o. or n q. is affirmed to be the altitude or eleuation of the starre from the horizon that endeth at the parallell p o l r. and p o. is the distance of the starre from the noonestead a p d c. Now when the starre by the motion of the principall is drawne vnto the point q. in which when the same shal be it will be equally distant from the Meridian Circle wherefore through the equal distance of the parallels of which they be named shall the Arke o k. bee equall to the Arke n q. Of this procéedeth and is caused that in the howers equidistant from the noonestead as is the seauenth houre before noone and the fifte houre after noone likewise the eight and the fourth the ninth and the thirde the tenth and second and so of the rest The sunne obtaineth equal eleuations aboue the horizon This much auaileth in the composition or making of dials and giueth great light and breuity to the same practise as may appeare elsewhere but the verticall Circles in the solyde Spheres and Globes by one quarter of the Circle depending of the verticall point vnto the horizon diuided into 90. degrées is declared The houre Circles IN that the whole worke of dialles dependeth vpon the knowledge of the houre cyrcles it is therefore requisite and necessarie to entreate fully of the cyrcles distinguishers of the houres or at the least vtter a brief instruction of this First you shall vnderstande that the Equatoure onely which as afore taught the sunne beeing either in the beginning of Aries or Libra is regularly moued aswel in the right as thwart Horizone and thereof is alwaies the one halfe aboue the horizon the other halfe hid vnder the Horizon Through this his equall motion or regulare motions is it iudged worthy and laudable séeing by it the equall houres as well by day as night are attained and had And this conceaue that there are twelue greater cyrcles vnderstoode which crosse the Equatoure at right angles and passe by both the poles of the first mouer from which the said equatour is distinguished into 24. equall parts which are called the distances or spaces of the houres in that each be distant from other by 15. degrées For they deuide the verticall the Zodiacke and the horizone into 24. partes but vnequally at which Poles the nearer partes to them are narower then those which be and draw nearer to the equatour And that these may clearer and perfecter be vnderstoode imagine your selfe to bée vnder the equatoure that is in the right Sphere in such a standing shall the halfe meridian Cyrcle bee the line of the twelfe houre and the halfe horizontal circle the line of the sixt houre before noon and the other halfe of it the line of the sixt houre at after noone By which imagination firmely conceiued may a man imagine betwéen the halfe horizontall cyrcle and the halfe meridian cyrcle to be other fiue halfe cyrcles firme and immoueable which are not mooued but as the verticall point is moued being distant each from other by an equall distance as by 15. degrées of the equatour The first after the horizon is applied to the seuenth houre so forth of the rest And in like maner betwéen the meridian halfe cyrcle and the occidentall horizone are other fiue cyrcles vnderstoode according to the fourmer deuision and that which followeth the meridian shall be applied to the first houre that which next foloweth to the second houre and so forth of the others Besides imagine the sun to ascend from the horizon and when he shall be come vnto the first halfe cyrcle from the horizon then shall he shed a shadowe furthest westward and being drawne vp vnto the second shal make a shorter shadow and the shadow shal alwaies vntill the sun bee come vnto the halfe noonestéede cyrcle where he sheddeth or sendeth a shadow plum down right to the earth but descending from the Noonstéede vnto the West the Sunne causeth then the like shadowes contrarie Further conceiue that the Exe-trée of the worlde in whose poles as is afore taught all the houre cyrcles méet together in one doeth performe expresse the same which the foresaid cyrcles taught as by the sun dials the like is readily vnderstood and knowne The Circles deuiding the twelue houses of Heauen NOw resteth to entreate of the cyrcles distinguishers of the houses and the cyrcle of the positions but first I will write of the distinguishers of the houses As there are sixe cyrcles that are imagined of the astronomers by which heauen is deuided into twelue parts among which are the Horizone and meridian whereby the whole is deuided into foure equall parts and those twelue parts are of the astronomers called mansions or houses But as touching the constitution and forming of the celestial houses there are sundry old and late opinions but whether opinion is the worthier or to be the rather allowed is not here mente to bee stoode vpon nor aptely belongeth to the matter I entreat of so well as in the proper place is agréeing yet certaine and especially the auncient which were Campanus a singular mathematician and astronmer deuided the houses by the fiue cyrcles of heauen méeting an◠ioyning at the Poles of the world from which they deuided the whole heauen togither with the meridiane into twelue equal houses But for a better and readier instruction they formed and drewe them in this maner After the foure principall quarters or angles of heauen were drawne and that the right ascention of the middle of heauen was had then were the partes of the Zodiacke diligently considered that occupy as well the Easterly as the Westerly Horizone and then were the right ascentions sought of those partes which being done the constitution and making of the two houses in the Easterly part of heauen was the right ascention of the mid heauen deducted from the right ascention of the Horizone and the remayner was distributed into thrée equall parts In the bound of the first part in accompting from the Noonstéed toward the East was there imagined a cyrcle for the beginning of the eleuenth house but in the bound of the second parte from the Noonestéede was the beginning of the twelfe house placed After in the bounde of the third parte from the Noonstéed was the beginning of the first house drawn and the like was wrought and done in searching for the 2. Westerly houses as the ninth and the eight house For they deducted and
the daies in the right Sphere and of the vnequalnesse in the thwart or bowing sphere and where the day spaces are encreased and lengthened there the night spaces be lessened and decreased and being otherwise they shew the contrary In the second the Parallels which the verticial points forme when they expresse the boundes of the latitudes of places then are they standing vnder by which their longitudes or distances from the West are accompted In the third the Parallels which either the Planets or the fixed stars describe referred vnto the Equatour do expresse the boundes of their drawings or motions from the equatour The others or rest which applied vnto the ecclipticke described doe shew the bounds of the latitudes and that for how long time they tarry aboue the earth or otherwise hid within the earth and vnder the Horizone doth either shew In the fourth the greatest and chiefest vtilities of the Parallels are that which on the habitable earth the practisioners seuer by such distances as by how much y e greatest artificiall daies are by a quarter of an houre longer increased and extended For they distinguish the habitable earth and that by obseruation into certain necessary spaces and doe iudicate the regular increasings of the daies and what is common to each dwelling vnder those parallels in asmuch as the quantities the increasings and deminishings of the dayes and nightes the risings and settings of the stars the Noonstéede shadowes and the nature of the Winter and Summer but those which are contrary as that there is a difference diuersity of the dwelling places being vnder diuers Parallelles they indéede bee necessary vnto the distribution and description of the clymate Although the number of these cyrcles bee so infinite as is the infinite variety of the stars and verticall points yet are there foure vsually rehearsed in these Elements or introduction that be especially noted and described by peculiar names and for the same cause as séemeth to mée in that they deuide the whole Globe of heauen and earth into fiue Zones and these applied vnto the plaine or flat of the equatour The tropicke of Cancer or summer tropicke The tropicke of Capricorne or winter tropicke The articke or Northerly Pole The antarticke or Southerly Pole Which Circles are called the Tropickes THe Sun according to the former words through the motion of the first mouer is in 24 houres drawn once about and for that hee is caried in the thwart Cyrcle and in the same by his proper motion chāgeth dayly vnto other places of the Zodiacke it must néeds ensue that he describeth in each day a new parallel And those doeth the sun repeat in the partes of the Zodiack which be equidistant from the solsticiall points in such wise that they be in the whole 182. cyrcles And these do they call the cyrcles of the natural daies of which the vttermost and furthest that include the suns way are named the Tropicks which is in English the sun boūds in that the sunne neuer passeth them neither toward the North nor toward the South but after his touching of each he returneth againe The one of these called the tropicke of Cancer and the other the tropicke of Capricorne Why these are called the Tropickes THey are named the Tropicks of the Gréeke word Tropikoi which is in English the turnings againe in that when the Sun is digressed from the Equatoure and come vnto those hee turneth backe againe Also the Tropicke cyrcles touch the Zodiack at the beginnings of Cancer and Capricorne of which the one is called the Tropicke of Cancer and the other of Capricorne the one being Northerly and the other Southerly And as to our dwelling the one is called the summer Circle and the other the Winter So that when the sun toucheth any of these he turneth againe and is carried toward the other As by this example further appeareth where all that season and time from the twelfth day of December vnto the eleuenth day of Iune a manne may perceiue the Sunne euery day arising higher and higher and when he is at the highest ouer our heades that day doth he by his course describe the summer Tropicke from which againe turning the sunne euery day after draweth lower and lower from our verticall pointe vntill he be come againe vnto the lowest In which twelfe day of December not going any further toward the South but being come vnto the beginning of Capricorne he describeth the winter Tropicke The Tropicke of Cancer is a lesser Circle which the sunne describeth at the entring into the beginning therof and is drawne by the daily motion whose plaine or flat passeth not by the center of the earth and it is one of the naturall Circles which is outermost described of the sun toward the North and drawne by the beginning of Cancer And it hath also his name of the standing in that the same is the bound of the sunnes iourney or course toward the North and the nighest comming vnto vs vnto which being brought he turneth backe and directeth his course into the South of which that place is called Trope It is continually distant from the Equatour by the quantity of the suns greatest declination which at this day is of 23. degrées 28. minutes and two fifts almost and it encloseth also the suns way and doth besides with the other 3. Parallels deuide the Zones of heauen and earth Further this is named the cyrcle of the summer solstice by the same reason in that it is drawne by the pointe of the summer solstice And the Northerly Tropicke in that it is the Northerly part of the world And the summer cyrcle for that the Sun in the summer falleth into this cyrcle Also this cyrcle in all the Northerly tract is on this wise that the greater part or portion is aboue the Horizone and the lesser part as to vs vnder the Horizon so that the sunne runing in that cyrcle causeth the longest day of summer And whiles the sun describeth these cyrcles the dayes bee longer then the nightes For the longest day increaseth from minute to minute from houre to houre and from the latitude of one degrée vnto the latitude of 66. degrées and 30. minutes In which the day artificial is of 24. houres and is thereof called a whole day For in the latitudes following and beyonde hee increaseth into many whole daies A like definition hath Proelus where hee writeth that the summer Tropicke is the furthest cyrcle Northwarde that the sun describeth into which when the sun is come he then maketh his summer turne and causeth also at that time the longest day and shortest night of the yeare from which turning backe he goeth againe toward the contrary coast of the world so that of the same Proclus it is called a Tropicke which is in English a returning cyrcle For it is euident to all men that after the sunne beginneth to turne he may in short time after or at the least within 5. dayes
greate and long space if by such a swiftnesse the earth should be turned about the Exe-trée of the world Or if by the motion of the earth the ayre and all things hanging in the ayre should be drawne with a like swiftnesse then should they appeare to stay or not to be moued at all And further if a stone or any waighty thing cast vpward shuld not light againe downe right on the same place as may be séene in a shippe at sayling So that to all these doeth euident experience deny that by no motion the earth is any thing moued dut continually stayeth and abideth By the fourth it is manifest that in the motion and turning about of the Cyrcle the Center abideth vnmoueable which is the earth placed in the myddle of the world and is as the Center of the worlde Therefore is the Earth knowne to be vnmoueable That the Earth compared vnto Heauen is as a poynt ALthough to the vnskillfull in this Arte the magnitude and largenes of the earth séemeth to be of an excéeding greatnesse that no bond or ende can be decerned with the eie nor any hauing trauailed into farre countries could hytherto finde any bounds of the same yet the greatnesse of the earth compared vnto the mighty largenesse of heauen is accompted but a pricke as the Geomitricall rules declare The earth also is a very small thing in respect of heauen yea so litle in comparison as a pepper corne or seede of Colliander vnto a Cyrcle of a thowsande paces compasse For if the earth compared to the firmament were of any sensible greatnesse a man shoulde not sée the halfe of heauen nor the halfe Cyrcle of the Equinoctiall or Zodiacke And howe much greater the earth shoulde be by so much the lesser should a man sée the halfe of heauen But the contrary is knowne in that on any plaine of the earth or vpper face of the sea a man alwaies séeth the halfe Sphere of heauen the other halfe in the meane time remayning hid and of this the halfe dyameter of the earth is so small vnto the distance of the firmament that it may take away nothing in a maner of the halfe Sphere extant to the eye Besides these if the earth should be imagined to be placed in any of the Orbes of heauen it woulde appeare but small in respect of them for being imagined in the Moones Orb the earth should appeare thrice as great as the moon is decerned from thence and somewhat bigger And from the suns Orbe the earth should be decerned twice so large as Venus doth here appeare to vs. And if in Marses Sphere you would say that the earth is equall to a small star But from the firmament Saturns Sphere or Iupiters if a man could decerne it the earth shoulde appeare so small that a man would be abashed at the sight of it And here an ignorant man might greatly wonder that so small a body yea rather a pricke as it is accounted of the learned should containe in it so many Realmes Prouinces Citties Towns Flouds Mountaines Woods Ualleyes Seas Riuers Lakes and many other greate matters ouer long to be written That the earth also is as a Pricke is declared by sundry reasons following By the first that round about the earth the magnituds and distances of the stars in their times are decerned and séene euery where equall and alike By the second that the Gnomons or dyall shadowes and the Centers of the Sphericall borderes or Cyrcles placed in any part of the earth do somuch auaile and kéep the considerations and guydings about of shadowes so regularly and agréeing to the rule and matter as if those in very déede shoulde bee placed in the myddle poynte of the earth By the third that the Horizont doeth euery where deuide the whole heauen into two equall halues For that in euery moment doe sixe signes of the Zodiacke appeare aboue the Horizont and in the night time being a fayre sky are they to bée séene with the eye and so many at that in stant hid within the Horizont so that by a cōtinuall drawing about of heauen doe sixe signes appeare and as many right against those sixe set vnder the earth If the magnitude of the earth shoulde bée of any light portion vnto heauen then so much of the Center the vpper face drawne aboute shoulde parte or deuide heauen into equall halfe Spheres The other Spheres reatching from any part of the vpper face shoulde deuide the same into vnequall portions Neither halfe the Zodiacke should alwaies appeare but a portion much lesser than halfe the Zodiack should be séen aboue the earth so that the greater parte of the earth through the folydnesse excluded and hidden should not after be séene By the fourth the Equinoctiall shadowes both of the rising and setting of the sun doe make a right line euen as if they should be streached out and lie on the plaine caried by the Center of the earth So that all these should not be caused if the magnitude of the earth in respect of heauen should be of a sensible or of any portion to it To conclude Ptholomie vseth alwaies the body of the earth for the Center of the worlde not deuiding the vpper face from that which is not in sight of the earth Certaine affirme that one degrée of the greatest Cyrcle in heauen contayneth 57051. common Germaine miles Of which one degrée of any earthly Cyrcle in the vpper face of the earth doeth amount to 15. Germayne myles And that one minute of the celestiall degrée expresseth 9509. Germayne miles which if this bée true and certainly knowne then is it not vainely thought and gessed that the earth is as a Pricke in respect of heauen To finde the compasse of the Earth and by it the Dyameter THe whole compasse of the earth according to Ambrosius Theodosius Macrobius and Eratostenes doth contayne 5400. Germaine myles and the dyameter of the same doth contayne 1718 4 22. Germayne miles But the authority of Eratostenes after the minde of Plinie is more to bee regarded then the other thrée Philosophers which prooueth by demonstration and reasons that the compasse of the whole earth is 252000. furlongs Yet Hipparchus finding faulte at Eratostenes doeth affirme the compasse of the earth to be of 277000. furlongs And a furlong is here after the agréement of the Geometricians of a hundreth twenty and fiue paces And this sentence is not here mente that there is any ambiguity or vncertainty in this reason but that the one affirmed lesser and the other more furlongs For after Eratostenes doe 700. furlongs answere to one degrée but after Hipparchus 774. furlongs answere to a degrée So that there is no other diuersity in the matter but onely the number Ptholomie that was after Eratostenes attributed seuen hundred fifty furlongs of the earthly merydiane to one degrée of the celestial meridiane So that by all these appeareth that the magnitude of the earth is as yet vnfounde out
is so much the more increased as by how many degrées either of the Poles are néere to the earth and beeing further distant from the Equatoure is raysed and caried higher which is the cause of many obscure differences which that they may the plainer be expressed and vnderstanded the skillfull practisioners haue deuided Cyrcles in the first mouer by lynes drawn vnto certaine stars or prickes from the Center of the earth and drawn about either by a continuall or dayly motion by which they imagined them to be described That the Circles of the Sphere be some greater some lesser and the number of the Circles HEre it is not to be omitted that one Cyrcle is greater then another by foure meanes First by reason of the magnitude of the celestiall body in which it is imagined to be And of this is the Equinoctiall Cyrcle of the first mouer greater then the Equinoctial Cyrcle of the eight spher in that the first mouer is greatest of all the bodies And although the Equinoctiall of the eight Sphere doth deuide it into two equall halfes yet of the first mouer it is named the greater for that the same includeth all other bodies By the second it is euident that the Equinoctiall Cyrcle is greater by reason of the appearaunce in that the whole is séene aboue the Horizont And by the same reason the Northerly Cyrcle which is named the Arcticke Cyrcle is the greater for that it alwaies appeareth to vs aboue the Horizont By the thirde the Equinoctiall is accompted greater then the other in regarde of the influxiue vertue and for this cause also is the Zodiacke called greater then the others through his greater working into these inferior bodies For that vnder it the sun and all other Planets are drawne And Happarchus writeth that this Cyrcle is the life of all thinges which are in the world c. In that by the ascending of the sun to vs generation is caused and by his falling or going from vs diminishing that is corruption getteth the vpper hand By the fourth is a Cyrcle called greater then the other insomuch as it is one Sphere and thus the equinoctiall is greatest of all the Parallel Cyrcles in the first moouer which is euidently demonstrated by the diameter of the Cyrcle Therefore by the definitions and reasons aboue shewed the equinoctial is the greater Cyrcle described in the vpper face of the first mouer according to each part or the whole of it beeing equally distant from either Pole of the worlde And it is further to bee considered that all the Cyrcles of the Materiall Sphere are imagined to bee in the first mouer which also a materiall Sphere doeth especially represent So that these Cyrcles may also bee imagined in the other Spheres aswell as in the eight Sphere c. And although a man may enter into conference betwéene these Cyrcles and the diameter yet he shall be forced to confesse that they be on such wise vnto the sphere as the Cyrcle is vnto the diameter So that as the diameter deuideth the Cyrcle into two equall partes in that it passeth by the Center of the same euen so doeth euery of the greatest Cyrcles deuide the Sphere into two equal parts because the playne vpper face of it passeth by the Center And by this it may easily bee perceyued that those which are named the lesser Cyrcles of which is a farre greater number than is here set down haue diuers Centers from the Center of the Sphere and yet the playne vpper face of them passeth not by the Center of the same Sphere Of which ensueth that they cannot deuide the sphere into two equall halfes no more then the lyne drawne without the Center into a Cyrcle can deuide the same into two equal halfes And both the greater and lesser of these is mente according to the distance of his Center from the Center of the sphere The inward Cyrcles that be mouable are those which are descrybed in the first moouer and are drawne with it about as is the equinoctiall the Zodiacke the Colures the Tropickes the Polare Cyrcles and others descrybed from the poyntes of the first moouer But the outwarde Cyrcles are they that are as immoueable and not drawn about with the first mouer but abide steady The number of which are these the Meridiane the Horizont the houre Cyrcles the verticiall Cyrcles and Cyrcles of the progressions Further it is to bee noted that many are the Celestiall Cyrcles as is aboue declared whose vse partely vnto Astronomy and partly vnto Astrologie is necessary As the verticiall Cyrcles the Cyrcles of the altitudes the Cyrcles of the celestiall houses The Cyrcles with the which the materiall sphere is descrybed and to bee briefe there are so many celestiall Cyrcles as there may bée poynts ymagined in the first mouer Yet are there but onely ten Cyrcles which are required vnto this sphericall treatise whose names are the Equinoctiall the Zodiacke the two Colures the Meridian the Horizont the twoe Tropickes and the twoe Polare Cyrcles The greater Cyrcles are those which haue the same or a like Center with the earth whose playn vpper face doth passe by the Center of the earth so that they deuide the sphere into two equall parts and especially the equinoctiall which for that it is a greater Cyrcle doth cut the spher into two equall halfes so that his playne vpper face passeth by the Center of the earth according to the definition of the greater Cyrcles And by this consequent when the Sun is in the equinoctiall he falleth into the Center of the earth that is hée is in the vpper face which passeth by the Center of the earth And the sun is neuer in such an vpper face but when he is in y e two equinoctial poynts for other wise he runneth without that vpper face For the greater Cyrcles are a like vnto the Sphere as the diameters vnto the Cyrcle in that as the diameter cutteth the Cyrcle in two equall halfes for that it doeth passe by the Center of the same euen so doth the greater Cyrcle deuide the Sphere into twoe equall halfes in that the playne vpper face of the same doth passe by the Center of the sphere But the lesser Cyrcles are those which haue diuerse Centers from the Center of the sphere so that the playne vpper face of them doeth not passe by the Center of the sphere For how much nearer the Center of the same is to the Center of the sphere and somuch the greater is that Cyrcle as the Tropicke But the further it is from the Center euen so much â—he lesser in sight is the Cyrcle as are the Polare circle And here none may suppose that either these or other like cyrcles to be verily in the first moouer but only to be vnderstoode or imagined For the cause of deuiding heauen into certaine spaces and regions through the helpe of which the courses of the Planets are obserued brought vnto a rule Further the
Equinoctiall poynt is then imagined to be drawne aboute with the motion of the first moouer that hath the same Center with the earth at that time by which the playne of the Equatoure is then noted to passe So that this is the cause why Plinie giueth that name to it séeing a like day and night is caused the sun then running vnder the Equatoure throughout the earth as no man of skill maketh doubt of It is named the cyrcle of the high solstice but this commeth to passe by reason of those which dwell vnder the equinoctiall and haue foure solstices as two on hie two below hauing foure shadowes in the yeare and the sun passing twise a yeare by the Zenith right ouer their heads as when the sunne is in the beginning of Aries and Libra And to them also dwelling vnder the Equinoctial are two summers and two winters and the heat is mightiest and strongest when the sun draweth from them into the North or South yet doeth the sun alwaies burne the earth right vnder it causing a burning Zone and not parteth far from their heades So that their winters are not perfectly and simply named winters as with vs which are cold seasons in déede bnt rather with them is a continuall summer yet for that the causes of heate with them are not vnformally and in a like maner alwaies for that the sun doth not approch equally the Zenith of that parte as the same is known to many whereof the heat to them is not vnifourme and a like in burning But sometimes hotter and sometimes slacker and meaner of heate So that when the sun is in the Zenith as in the beginnings of Aries and Libra and that they are in their high solstices then is the heate most vehement with them yet not without the sun this heate can bee called mighty But when as the sun is gone from their Zenith which happeneth in the beginning of Cancer and Capricorne where their low solstices are the heate is then slacker that is lesser burning So that the weaker heate hapning in the lowe solstices may in a manner bée named colde in respecte of the most burning heate hapning in the high solstices yet it hath the nomination of winter although no cold may bée felt What the offices or vtilities of the Equinoctiall are THe causes whie the skilfull practisioners tooke and vsed the Equinoctiall with the offices which they attributed to it and the mani fold vses that it offereth is herein declared 1 It measureth the motion of the first and vppermost Orbe and sheweth the same to bée drawne about by a continuall and equall swiftnesse For that in euery equall houre doe fiftéene of the thrée hundereth and thrée score degrées of the same arise and so many degrées right against set and are hidden vnder the Horizont and that all the thrée hundreth and thrée score degrées in 24. houres are turned about in the appoynted times and in their periods continually agréeing And as the Equatour from the Poles of the worlde about which the first mouer is drawne and is of either side distant by equall spaces nor the Angle which is comprehended fashioneth with the Horizont doth neuer change euen so by the same order and like motion doeth the first heauen or moouer euidently shew it selfe to be caried about For the Equinoctiall measureth and determineth the motion of the first mouer in declaring his reuolution and yeare which yeare of the first moouer is the time of 24. houres equall But by what meanes the auncient astronomers first found that the Equinoctiall is drawne about in so many houres and it is supposed they came to the knowledge thereof by the office of some starre either in the Equinoctiall or placed neare it they perceiued the same as that the Equinoctial from some note marked of them did returne to it in such a certaine space as afore shewed 2 The diuers motions of the Zodiack which hapneth to it through the twart standing or lying as a cannon or rule doth dyrect and point out the beginnings boundes and time with the which each parts or degrées of the Zodiacke arise or doe set and with which they touch these or those quarters of the worlde For all the arckes of the Equatoure are drawne by a certaine and agréeable motion continually The parts of the Zodiacke drawne thwartly the Equatoure doeth not varie or is distant by like spaces from the Poles of the world nor turned about his but the same Poles of the worlde which doe differ by a long space from his and drawn about by a most vnlike motion and nothing at all agréeing in it selfe For that some parts or degrées are caried vp sooner or quicker and others appeare slower and later So that these vseth a more space of time in the rising slower and those other passe vp by a shorter and quicker space But séeing that in the Zodiack the wandring stars or Planets doe wander continually hither and thither and from one side of it to another and that vnto the middle cyrcle of it or ecclipticke line the places of all the fixed stars are referred and applied therefore cannot the times of the rising or setting of the starres bée knowne and noted except they shoulde be guessed and attained by the next arks of the equinoctiall It also declareth the equinoctialles which are caused in those proper dayes in which the sun hapneth to come into the equinoctiall cyrcle For these are caused the sun being in the first degrées of Aries and Libra in that the Zodiacke and Equinoctiall doe crosse each other in those places whereof Manilius thus writeth That these signes Aries and Libra cause a right Throughout the earth a like day and night 3. It defineth and measureth the spaces both of the naturall and artificiall dayes And although the sun which drawne about with the motion of the first moouer and in the proper motion caried forth in the meane time by force into the contrary when as hee causeth the times of the daies and nightes so wel as the differences of the natural daies mooued and runneth in the Zodiacke yet of his motion the day and night spaces cannot bee gatherrd through the diuersity and vnlikenesse of the ascending or arising of diuers parts or degrées of the Zodiacke But seeing the same motion is of all the partes of the Equatoure therefore are the ascentions of the arcks of the Zodiacke caried vp with the ascending of the nighest parts of the Equatour like arising So that both the dayes and houres by the equall motion of these are not founde and distinguished by the vnlike and vnequall motion of them in that these ascentions can be of these two cyrcles The Greekes by no meanes like of the same in that by a stedfast order they do mark the day and night times therefore they parte and deuide them into equall houres which they named times that from the degrées of the Zodiacke they might distinguish them For euerie fiftéene
in the yeare of Christ 1514. found this declination to be of 23. degrées and 28. minutes and 30. seconds Copernicus being a later writer as in the year of Christ 1525. found this declination to be of 23. degrées 28. minutes and 2. fifts of a minute Of these but by many notes considered that the equalities haue decreased by the regulare motion and yet shal decrease vntill an extreame tearme of diminishing ensueth which hee affirmeth to bée of 23. degrées and 28. minutes the same Copernicus after gathered shal againe increase and that the greatest thwartnesse which may bee caused on the sun or Ecclipticke line is 23. degrées and 52. minutes the least declination to bee of 23. degrées and 28. minutes So that the stablished the difference of the greatest and least to be of 24 minutes But hee defineth the periode motion of the increasing or diminishing to be in 1717. yeares and that so many yeares the motion of the decrease and increase shall be and that the whole restitution also of the thwartnesse to be in 3434. yeares So that as the thwartnesse failing or diminishing euen so the points of the greatest declination which are named the solstices are yearely drawne and moued néerer vnto the Equatoure by 6. minutes 27. seconds 24. thirdes and 9. fourthes but dayly by one second two thirds and so many fourthes caried neare vnto it And the thwartnesse increasing may by the like order and condicion and in the same motion be againe abated As the Equinoctiall points deuide the Ecclipticke lyne into a Northerly and Southerly halfe cyrcle euen so the solstitiall pointes parte the same into a halfe cyrcle ascending and descending as to vs. The ascending beginneth from the beginning of Capricornus and endeth at the last pointe of Gemini and containeth Capricornus Aquarius Pisces Aries Taurus and Gemini And the descending from the beginning of Cancer reacheth vnto the end of Sagitarius and comprehendeth Cancer Leo Virgo Libra Scorpio and Sagitarius So that the sun in that halfe cyrcle ascendeth from the Southerly region vnto vs in that from vs it is digressed into the South and of the same they receiued those names What the latitude of a Planet is after two definitions FIrst that the arke of the great cyrcle is crossed betwéene the Ecclipticke and true place of the Planet and that is named the latitude of the Planet for that according to the same the Planet into latitude that is into the South or North swarueth from the Eccliptick line whereof the Planets are named to haue a latitude one whiles into the North and another whiles into the South But the degrée expressed and shewed by that great cyrcle in the Eccliptick is called the degrée of the longitude of the star or planet which according to longitude from the beginning of Aries vnto that place is the Planet moued The other instructeth and by demonstration sheweth that from this line the other fiue Planettes wander one whiles into the North another whiles into the South beeing not equally caried This wandring from the saide line is named the latitude of the Planets and is the arke of the great cyrcle passing by the Poles of the Zodiacke and true place of the Planet comprehended betwéene the Ecclipticke and Center of the star According to this distance he is named a Planetary star what star soeuer the same be that to latitude from the eclipticke is carried either Northerly or southerly So that it cannot be saide that a planet is without the Zodiacke séeing the auncient obseruers of the stars being moued did attribute to this cyrcle a latitude As may be the Ecclipticke line noted with A. and B. and the letter C. the Pole of the Northerly Ecclipticke by which the Cyrcle noted with C. G. D. and Q. is ment béeing the shewer of the Latitudes and when a star shall be in the point G. he shal then be without or haue no latitude but if in the letter E. he shal then haue a latitude Northerly whose quantity the arke G. E. sheweth If so be a star shall be in the point D. then shall it be Meridional vnto the quantity of the arke G. D. and L. D. K. the letters M. E. N. are the Parallelles drawne about the saide latitudes on either side So that this demonstration euidently sheweth what the latitude of a star is that is when such a latitude is attributed to the Zodiack What the longitude of a Starre is and where he beginneth THe longitude of a star is the arke of the Zodiacke or ecclipticke line from the beginning of Aries reckned euen vnto that point of the eccliptickes which is touched by the great cyrcle drawne by the Poles of the Zodiack and true place and degrée of the longitude of the stars As may be conceiued in the figure aboue where the pointe A. representeth the beginning of Aries the letters A. G. the longitude of the star if the same shall bee in the Ecclipticke the letters C. G. D. the cyrcle ending the longitudes The difference betwéene a declination and latitude is this that a latitude is the distance of a star or Planet from the eccliptick toward either of the Poles which distance is measured in the greate cyrcle drawne by the body of a star and Poles of the Zodiacke But the declination is a distance from the Equinoctial when as the sun is caried by a continual and dayly course in the vpper face of the Ecclipticke and hath no latitude but a declination onely yet the other sixe Planets haue a latitude and declination The declination of Planets is the distance of them or a degrée of the eccliptick from the equinoctiall And this measured by the cyrcle drawne by the body of a starre or degrée of the ecclipticke and by the Poles of the worlde The Planets also are said to ascend and descend by reason of the thwartnesse and bending of the Zodiacke for the sun doeth ascend in the Northerly signes but hee descendeth in the Southerly In the like maner doe all the other Planets as well by the reason of the ascention as also of the place For planets beeing in Northerly signes haue the arke of ascention greater than in the Southerly Besides this part of the world which declineth into the North is supposed and iudged as to vs to be raised higher by reason of the Horizont Further the definition of a signe shall here bee declared that the same is ment sundry wayes one whiles to bee a circumference an other whiles an vpper face and sometime to be a solyde body The Zodiacke as I haue afore declared is one whiles a line all circumference which is named the Ecclipticke line an other whiles a swathe of eight degrées in breadth of either side Sometimes the zodiacke is called the plain vpper face of that Ecclipticke and in an other place the same called a solyde body which of the saide swathe and by the two imagined vpper faces is crossed of which
those pointes departeth not further from the Equinoctiall but commeth againe vnto the Equinoctiall which is caused twice in the yeare as in summer and winter whereof the one is called the summer solstice which in our time hapneth the 12. of Iune or thereabout beeing the nexte day after S. Barnabe the Apostle where the longest day is holden to bée The other the winter solstice which in our time hapneth about the 11. or 12. day of December being a day or two before Lucie where the day is accompted shortest whereof is this auncient verse extant Vitus est Lucia dant tibi solstitia bina Of the former also ensueth that there is certaine fixed and moueable Colures For there is a fixed Colure of the equiâ—octiale which passeth by the poles of the world and section of the equatoure and Ecclipticke of the first mouer The fixed Colure of the solstices doth cut this at right angles in the poles of the world and passeth by the middle of the suns greatest declination Séeing neither the equinoctials nor solstices are caused according to the true meaning of the astronomers as afore may appeare both in these points aswell as in others Therefore a man must conceiue that the Colures be moueable of which the one goeth by the true equinoctiall that is by the section of the suns way and equatour and by the Poles of the worlde and the other of the solstices passeth by the suns greatest declination These hitherto written may more plainer appeare by this demonstration here following In this figure are the cyrcles and parts of the cyrcles noted with their names In which the letter F. expresseth the true and moueable equinoctiall The letter E. is a note of the fixed Equinoctiall The letter D. pointeth out the head of Aries of the eight sphere The letter C. the center of the eight Sphere The letter A. of the ninth and tenth sphere The letters K. N. represent the suns greatest declination truely The letters R. M. the suns middle declination greatest How much the Equinoctials are distant one from another the former large instruction of the equinoctials may easily shew at any time vnto which a man must alwaies resorte The suns greatest declination is the arke of the Colure of the solstices contained betwéene the equatoure and eyther Tropicke this of sundry practisioners is diuersly noted For Ptholomie founde the same in his time to bee of 23. degrées 51. minutes and 20. seconds of which the whole cyrcle is noted to bée 360. degrées but after Alnieon of 23. degrées and 33. minutes But the later practisioners haue founde the same to bee 23. degrées and 30. minutes Purbachius hath found the same to be of 23. and 21. minutes which variation of the suns greatest declination is through the comming and going of the eight Sphere which is named the trembling motion But this is demonstrated and taught more at large in the Theoricks If any desire to obserue the suns greatest declination let him take the altitude of the sunne about the winter solstice in the shortest day at Noone which altitude beeing kept a parte worke the like the sun being about the summer solstice and the suns greatest altitude at Noone found by the rule of the astrolobie looke that in the bordure of the same and take the middle of that arke which is betwéene the suns least and greatest eleuation at Noone which possesseth the myddle and shall bee the Suns greatest declination The knowledge of the suns declinations with the other stars is very profitable in that by the same and the perfection of the eleuation of the pole the true place of the sun if the same be vnknowne may bee knowne the suns greatest declination presupposed after this maner as followeth Marcke and consider diligently the sun being in the Noonestead cyrcle caried vp from the Horizont which founde if the sun run in the Northerly signes abate from the saide eleuation the complement of the eleuation of thâ— Pole If the sun bee caried in the Southerly signes then worke contrary for that which remaineth shall bee the suns particular declination As by a like example vse this The sun beeing imagined to bee eleuated aboue the Horizont 63. degrées 21. minutes and 4. seconds the eleuation of the Pole is 41. degrées and 30. minutes and the compleâ—â—nt of the same altitude of the Pole to bée 48. degrées and 30. minutes with the which subtract the suns altitude at Noone and the remaurer shall be the suns declination which is 14. degrées 51. minutes 4. seconds being the distance of the sun from the beginning of Aries abated for the suns running in the Northerly signes at the time of the obseruation before the summer solstice What the offices or vtilities of the Colures are _1 SHe common offices in generall of the Colures are to shewe the foure principall points of the zodiacke in which through the suns motion the greatest chaunges and alterations of time is caused 2 They serue to demonstrat the solstices and equinoctialles and to deuide the Zodiacke into foure equall partes to which the foure seasons of the yeare doe answere 3. The vse of the one is to expresse and make manifest the pointes of the equinoctials and the other to shewe the points of the solstices 4 They both cut the Zodiacke and equatour into two equall halfe Cyrcles and both deuide either Cyrcle into foure equall quarters 5 But the Colure of the solsticis offereth many other vses for in the same is the sunnes greatest declination or thwartnesse measured and numbred in that the sunnes greatest declination is the Arke of the Colure of the colsticis inclosed betwéene the beginning of Cancer and the Equatour which arcke is either increased or diminished according to the winding in and out of the eclipticke vnto the Equatour as is afore mentioned 6. They serue to distinguish the Equinectiall the Zodiacke and all heauen into foure equall partes the vse of which matter shall appeare in the place of the ascentions of the signes 7 Each Colure besides hath his priuate office or vtilities as the Colure of the solstices which hath foure offices The first demonstrateth the solsticiall pointes The second containeth and measureth the suns greatest declination The third that it stayeth vp the poles of the Zodiack and sheweth their distance from the poles of world The fourth that it deuideth the Zodiack into two halfes as into the ascending and descending Also the same in the thwart Sphere doeth seperate the signes rightly arising from the signes thwartly rising 8 The Colure of the equinoctials hath twoe offices The first that it demonstrateth the Equinoctiall pointes The second that it deuideth the Zodiacke into two halfs as into the Northerly and Southerly halfe 9 To conclude the Colure of the solstices doeth often supply and is vsed in the stead of the Meridiane when as in euery dayly reuolution of the first mouer it doth twice enter into the place of the meridiane or is twice ioyned in
the angle of the difference of longitude be blunt séeing the places are further distant then a whole quarter and thereby causeth a diuers reason and way of serch from the former which semblably the diuers quantity of the complement of the greater latitude doeth thrée manner of waies varie as in the same arke which perfectly knowne by the second is either greater or lesser The example of this appeareth of these two places the noble city Antiochia in Syria which was after caled Seleucia hath the longitude of 106. degrées and no minutes the latitude is of 40. degrées and 40. scruples The other of Toletum whose longitude is of 7. degrées and 4. scruples the latitude hath 37. degrées and 50. minutes The difference of longitude is of 98. degrées and 56. scruples which deducted from the halfe cyrcle or 180. degrées the difference that remaineth vnto the halfe cyrcle is of 81. degrées and 4. minutes The like example not much varying from the former of these two places as the noble city of Portugale named Lysebone whose longitude is of 4. degrées and 18. scruples the latitude hath 39. degrées and 38. scruples The other named Calecute although the latitude differeth hath the longitude of 112. degrées and no minutes the latitude is of 5. degrées and no minutes The difference of longitude containeth 107. degrées and 42. scruples more then the quadrant The same deducted from the halfe cyrcle doth expresse the difference remaining vnto the halfe cyrcle to bee of 72. degrées and 18. minutes The complement of the greater latitude is of 50. degrées and 22. scruples The complement of the lesser latitude is of 85. degrées and no scruples Another example of two places distant from the Equatour of which the one is distant from the middle of the Equatour into the North and the other into the South as this example further instructeth the one beeing the Ile of Thilen which in Ptholomies â—â—me was the vttermost bond of the earth knowne Northward that hath the longitude of 33. degrées the latitude Northerly of 63. degrees The other called the Ile of S. Thomas hath the longitude of 27 degrées and 20. minutes the latitude Southerly of 16. degrées The difference of longitude is of 5â— degrées â—nd 40. minutes The complement of the latitude Northerly is of 26. degrées A third example of the difference of other two places as Basâ—a of Taprobane which Ptholomie affirmeth to bee in longitude 126. degrées and in latitude toward the South 6. degrées and 30. scruples The other named Stocholma in the Realme of Suecia hath the longitude of 42. degrées and 38. scruples and the latitude of 60. degrées 30. scruples The complement of the latitude Boreal is 29. degrées and 30. minutes The common way of measuring of places with their spaces by the rules of longitudes and latitudes HEre before I haue somewhat written of sundry habitable places on the earth whose sundry points differ betwéene the one and the other either in the onely longitude or in the onely latitude or in the longitude and latitude both together Those places which do differ in the onely longitude be distant by equal spaces from the equatoure toward either of the Poles of the worlde the verticiall pointes of those places ended by the same Parallell ioyning next the same space betwéene yet each haue their owne proper meridians being not distant by a like space from the Westerly bounde The distance of these is alwaies gathered and noted in the same Parallel which commonly belongeth to either place standing or hanging right ouer the tops of them Those places which doe differ in the onely latitude are standing â—â—der the same meridiane but they haue diuers Parallels â—â—d each proper and those continually distant vnequally either towarde one pole from the middle of the Equatour if either place declineth vnto one and the same quarter or otherwise from the middle of the equatoure seuered and distant into the contrary quarters by equall or vnequall spaces If that one of the places looke into the South and the other into the North the distance of these is alwaies accompted in the common meridian Those places which do differ both in the longitude and latitude togither or both decline towarde one Pole of the world or seperated and distant from the midst of the equatoure towarde the opposite Poles as the one looking into y â— North and the other into the south or els by equal Parallels distant from the equatour of which two onely are in the Sphere If they bee reduced and applied vnto one great cyrcle per 3. secundi Theodosij or els bee vnder by vnequall Parallels and by an vnequall space The difference of the longitude of those which either bee towarde them or toward the Poles equally distant is alway gathered in the middle Parallell betwéen either of the bonds by arithmeticall proportion as afore taught But in those places which haue equall Parallels and equally dastant vnto the opposite quarters the difference of longitude is imagined noted in eithâ—â— of the equall Parallels Therefore the arke hath the distance of the places standing by the next space drawne ouerthwart by the pointes of those places which with the arks of the differeÌ„ce of either both of the longitude and latitude doth forme and make a sphericall tryangle right cornered alwaies in the vpper face of the Globe If that two meridianes méete and ende at the poles of the worlde and beeing cut by the ouerthwart cyrcumferences of the Parallels doe make with the included arkes of them right cornered tryangles through the foure right lesser angles but the angles beeing not right the arke of the distance of the places doth deuide them into two right cornered tryangles One of those tryangles is vsed in the coÌ„mon accompt for the right cornered because in places not farre distant from the equatoure the angles contained betwéene the mutuall sections of the meridians and Parallelles doe not so much varie from the right angles but in places far distant from the equatour they varie very much Now the rules for the diuers standing of places shall be taught in an easie and common maner If places doe differ in the onely longitude TO the searching and knowing of this like as in the former are the longitudes and latitudes of places giuen required by which they being founde séeing in the latitude there is no diuersity the difference of longitude is onely to be considered by deducting the lesser longitude out of the greater and then howemany miles by proportion of the Parallell vnder which the places stand or lie to the equatoure answere to one degrée of the same The same doth that rule set forth in the fourme of a table here following declare beeing drawne and made vnto this vse by the learned in which the miles that answere to one degrée of each Parallell are there founde and noted vnto one degrée of the distance of the Parallell from the equatour If to the whole
which we sée and obserue the celestiall bodies that rise aboue and set vnder it so that they euidently shew that the same deuideth heauen into two equall halfe spheres as aboue remembred For in euery moment doe sixe signes of the Zodiacke appeare aboue the earth as in the night to the eie may be numbred and noted that sixe signes set vnder the earth and be gone out of sight This is also called rationall séeing the eie cannot descerne vnto the highest heauen nor aptly frame this diuision of heauen into two equall halues yet the mind by examining gathereth and concludeth as by a perseuerance passing before and in the shewing of the starres that rise and set and in considering the tarriances of them in either halfe sphere This besides is called the artificiall horizone in that by the benefite of the astronomicall art it was inuented Or thus not much agréeing to the former the rationall horizone which of some is named natural and according to the mind of Ptholomie Cleomedes and Proclus belongeth vnto the Sphere of the fixed stars and reacheth euen vnto the same Sphere and deuideth heauen into equall halfe Spheres the one halfe appearing aboue the same circle and the other halfe not appearing hid vnder it Such a maner of imagining is not in vaine nor without cause determined and deuised séeing that men in the night and in a cleare season standing on an euen grounde may sée stars arise vnto sight in the East which a litle before appeared not to the sight and those after drawne by the first moouer vnto the West horizone that began to go downe be set and doe not after appeare By which they concluded that there is a cyrcle in heauen deuiding and ending matters in sight from those not séen So that they nothing doubted to call this cyrcle the rationall horizon which togither with the vpper face by the center of the earth stretched round about vnto heauen and by the foure quarters of the world as East West North and South deuided things séene from those not séene And a great helpe it giueth vnto this imagination that the earth is perfect round and imbossed in that of a Globe through his imbossing can be séene but the halfe at a time This also yéeldeth a helpe to reason by the appearances in the celestiall bodies although our sight cannot attaine vnto the starrie sky nor fully descerne heauen although a man earnestly looke vp and behold it yet doe we sée stars whose light extend vnto our eie As by this example may euidently appeare of that royall star named the heart of the Lion which in our time is in the 22. degrée almost of Leo. And the star standing on the left buttocke of Aquarius in the 22. degrée almost of the same signe◠that is diametraly or right against one the other situated Which doe on this wise that as the one appeareth aboue the horizone the other is hidden vnder it et e contra So that as the one riseth the other setteth and on this manner doe they continually Of which reason it is concluded that a certaine cyrcle deuideth heauen into twoe equall halues and do part as afore taught the things séene from those not séene Although the tariance be but small in that this star appeareth a very smal while aboue the earth through the same that this star of Aquarius is Southerly from the ecclipticke line it greatly forceth not The like examples may be applied of the superiour planets when they be situated or appeare opposite in heauen as they also may be euidently seen in the opposition of the sun and moone when they bee séene neare to the East and West horizone and where the moone is neare the suns way The diameter of the rationall horizone although the same cannot be found nor comprehended through his excéeding distaunce by exteriour sence and iudgement yet reason it selfe iudgeth that the same may extend vnto the starry sky whose sight from that not séene it doth describe and the same is of 32655932. Germaine miles and 20. minutes which distance by the outward senses is iudged as infinite The Pole of the rational horizon is the verticall point for it is distant by a quarter of the greatest cyrcle that is 90. degrées from the compasse round about of the horizon yet not to all places serueth one horizon for that as a man changeth place and country euen so ariseth a newe horizon whether so euer he trauaileth And new horizons also appeare and happen if a man either trauaile toward either of the poles of the worlde or in right line toward the East and West and the like vnto diuers quarters as into the North the East or West or contrariwise iourneying by the opposite course the Horizones vary and change And if the places bee either situated partly toward the East or West and partly toward the South or North the horizones there decline and varie them partly toward the East or West and partly toward the south or North which hapneth by reason that the City is not vnder one Parallell And Cities or countries situated vnder one meridiane doe vary their horizons directly either toward the South or North. There be as many horizons as there be meridiās And for so much as that of all places cannot bee one manner of Zenith therefore cannot one Meridiane serue for all places And séeing the Pole of the Horizone is the Zenith of it which is in the Meridiane and that to each place belongeth a proper Zenith and a proper Meridian it followeth that to each place belongeth a proper Horizone Toward the Poles by the chaunging of places are the horizons chaunged and the diuers eleuations of the Pole by a certaine occasion caused also they euidently declare a like alteration to bee caused in the respect of the opposite quarters of the East and West and doe procure and cause diuers beginnings of the daies and nights insomuch that the starres generally appearing and seene doe by order of times and in sundry places arise and set in the West and hide them vnder the Horizon For the same maner of Ecclipse which is seene at Arbela after Plinie in the fifte houre of the night to them of Carthage it appeareth in the second houre so that the sun sooner setteth to them of Arbela by thrée houres then to them of Carthage Therefore the horizon of Arbela is much further distant into the East then the horizon of Carthage The same rationall horizon as it were on the plainesse of the earth drawne and streached vnto the sky doeth the meridian extend to it downward and deuide the same into twoe halfe cyrcles of which the one declineth vnto the East and therof called the East quarter and the other vnto the West and of that named the West quarter And the diuers places of the suns rising and setting doe sundry wise deuide either halfe cyrcle For the Equinoctiall rising and the Equinoctiall setting which are points of the
subtracted the right ascention of y e west part from the right ascention of the mid heauen or noonestead and the remainer or rest as afore taught was distributed into thrée equall parts After that in the ende of the first portion from the noonstead towardes the West the auncients constituted or placed the bound of the ninth house with the circle comming from the poles of y e world and in the bound of the second portion was the beginning of the eight house formed These attained the degrées and partes of the degrées of the Zodiack answering to ech arkes of the Equatoure were sought in the Tables of the right sphere but the houses standing vnder were defined and made like to their opposites And séeing this maner of forming the houses is vnperfect therefore shal here no further be taught of the same In which a e. is the verticall circle crossing a d e c. at right angles f g b. the equatour d g c. the horison d. and c. be the points in which the distinguishers of the houses concurre and méet which also do make equall distinctiōs in the verticall circle and thereby be the houses noted and diuided But the later Astronomers moued by the authority of the incomparable Mathematician Regiomontanus inur̄ted and deuised another order of the houses more agréeing to reason than the former For they deuided the quarters of the equatour comprehended betweene the horison and noonstead into thrée equall spaces and by each section they imagined great circles ioyning in the sections of the Meridian and horison as the former Although all these are plainer and more euidently taught and known in the materiall Sphere yet we thought good to speak somwhat as our possibility serueth in plaine forme Wherefore grant that a f c. is the Meridian a. the Top n. the Northerly pole k. the Southerly pole b. and c. the points of the sections of the horison and Meridian where the distinguishers of the houses concurre and méet which also are imagined by the equall distinctions of the equatour e i l. as to the eie sufficiently appeareth that b i c. is the horison circle d. the easterly point or rising of the equatour from which the first house taketh his beginning The Circle of position AL these Circles being set down the Astronomers notwithstanding do write of another Circle whose vse and office serueth to great purpose for the Art of directing searching other more secret matters in Astronomy and is thereof called the circle of Position which passeth at al times by the former sections of the meridian and Horizone and by the Center of the star or of any other purposed point in heauen like to the soresaid cyrcles whether that star be aboue the earth or vnder the earth That this may clearly appeare marke and consider this figure here expressed where the letter c. representeth the top pointe d. the Northerly Pole e. the opposite pole a g b f. the cyrcle of the position passing by the sections of the horizon and meridian b c d e. the meridian a b. the Horizone g f. the Centers of the stars of which the one is in g. aboue the earth and the other vnder the earth in the point f. And many other cyrcles besides all these which hetherto haue bene described may bee inuented and imagined in the sphere for the necessity of the workings The difinitions names and offices of the foure lesser Circles THe Parallels are lesser cyrcles which from either of the greater circles drawn thwartly on the sphere doe equally difand bee distant from the Equatoure or Zodiacke toward their poles so y ◠they doe not deuide the Sphere into equall halfe Spheres but into vnequall portions For séeing the sphere from the middle streacheth or draweth by litle and litle straighter and narower toward the furthest aud highest toppes euen so must the parallels which are distant from the middle and greatest and that by equall spaces on each side agréeing drawe of necessity narrower and so much the narower as they nearer approach vnto the poles As writeth Theodosius in the sixte proposition of his first Booke of the sphere And the same Author in the 14. proposition of his first Book of the sphere and in the sixt of his second Booke writeth that all the parallels haue the same poles agréeing with the greater cyrcles vnto which the parallels are And certaine of the Paralels are applied vnto the plain of the Equatoure others vnto the plaine of the eccliptick These doe as well the fixed starres as the planets placed without the ecclipticke and drawne about the Exe-trée stretched b◠the poles of the ecclipticke and Center of the worlde discribe yet do all their centers consist in the Exe-trée of the Zodiack and the middle cyrcle of them and the greatest is the ecclipticke These also doe the same stars and the verticiall or toppe points of each places or any other applied vnto the plaine of the equatour drawne as it were by the first mouer about the Exetrée and poles of the world define And the Centers of these be in the Exe-trée of the worlde or equatoure but the middle and greatest of these is the equatour It is manifest by that afore taught that the sun in euery day doth gaine toward the East against the dayly motion one degrée of the Zodiack and of this hapneth that he in each day through the thwartnesse of the Zodiack describeth a certaine newe cyrcle in heauen and in the nexte day another and so forth by order as the like may be compared by a small corde winded close about a Nun or top beginning from the foote vpward euen so the sun beginning to turne againe at the first degrée of Capricorne doth euery day after change a new Parallel vntill hée become backe vnto the first degrée of Cancer and by and by after returned from Cancer he in the like order goeth vnto the Capricorne so that in the next day following the Sun riseth not with the same Parallel aboue the Horizone that hee did in the morning before nor shall not run the nexte morrow in that Parallel that he did in this day And each of these Parallelles euen as the greater cyrcles containe 360. degrées which bée so much lesser then the degrées of the greater cyrcles and occupy or comprehend somuch the lesser space in heauen as answereth to the vpper face of the earth as by how much the more frō the compasse and largenesse of the greatest cyrcle they lacke by reason of the distance And although they yéeld and be lesse in the quantity yet vnto the degrées of the greatest cyrcles be they agréeable and like as writeth Theodosius in the 14. proposition of his second booke of the sphere These lesser cyrcles do offer and teach sundry vtilities First the Parallels of which on this side and beyond the Equatour are 182 that the sun yearly by his dayly motion describeth and doe expresse the causes of the continuall equallity of
Tropicks all heauen into fiue parts or Regions which they call zones The descriptions names qualities and vtilities of the Zones THe foure lesser cyrcles called Parallels that were afore described doe deuide the whole heauen towarde the Poles into fiue spaces which that heauen might bee compassed aboute with these larger swathes the astronomers of the same called them Zones or otherwise of the Latines Gerdils The Cosmographers by the same imagination applied doe also dispose and distribute the whole Globe of the earth into fiue roomes or spaces lying directly vnder and agréeable in proportion to them in heauen Wherefore a zone after the minde of the Gréekes is a portion tract or space of heauen or earth betwéene the two Parallels or lesser cyrcles being nighest equidistant or contained betwéene the roome equidistaunt and Pole of the world and gyrdeth or compasseth as it were the heauen or earth Or thus a zone is a space of earth like to the two Parallels or lesser cyrcles aboue which the astronomers imagine to run on the vpper face of the sphere And as the whole portion included by the two Tropicks called the burning zone doth compasse heauen as a gyrdle euen so imagine the roome of the earth lying right vnder the Tropicks The zones haue sundry names for of the Gréekes they be called zóne and of the Latines by a borowed word Zona as may appeare by Iulius Firmicus Macrobius Virgilius Ouide and other Latines That heauen or earth is imagined to bee gyrded about with these Martianus nameth them swathes Tully and Macrobius nameth them by the like reason gyrdles Ouide nameth them plagues that is roomes or spaces And how many zones they bee may easily appeare in that the astrologians Geographers Phisitions and Poets do deuide as well the heauen as earth into siue roomes or spaces by the foure Parallels or lesser cyrcles of which there bee two maner of zones the celestiall and the earthlie The celestiall are the cause of the earthly in that the earthly lie directly vnder them And of the zones the celestiall bee they which the astronomers by imagination describe and distribute in the hollow of heauen the earthly be they which lie perpendicularly vnder And both also be temperate and vntemperate zones The celestiall zones in that they haue nothing of the elementary qualities therefore doe they not by heat burne and scorch nor by cold make stiffe nor cause a temperate mixture of qualities or temperatnesse yet are they noted and descerned by the names of the qualities as the earthly zones which being the author of the sun and fountaine both of light and heate and running continually in the middle zone of heauen is diuersly felt according to the maner of the distance Or thus there are no qualities formally attributed to the celestiall zones but to them onely vertually which is on this wise to be vnderstoode as that the celestiall zones of themselues be neither cold hot nor temperate but are so called through the suns declination from the equatour as well into the North as into the South quarter of the world In the which declination is the like matter felte as well in the suns right sending downe of beames as in the thwart proiection of thē on the vpper face of the earth which diuersly changeth the heat 〈◊〉 The scorching or vntemperate middle Zone which through the heat and burning beames the sun there causeth when he is ouer the head or in the Noonestéed place is contained betwéene the boundes of the sunnes iourney which the two Tropicks make and includeth 47. degrées of heauen For the two Tropicks are on either side the equatoure so that it vseth the middle roome in the burning zone from which the sun towarde the North and South neuer declineth aboue 23. degrées and 29. minutes By which appeareth that it is there as hot in the middle of winter as it is in Spaine in the middle of summer and therefore not disagréeing to that which the auncient Cosmographers wrote that the countries lying vnder this space or rather vnder the equatour is vnhabited through the burning heate and of them for this cause named the burning or scorching zone But of later yeares it is found contrary in that at Molucca Good-hope Calicute and Samatra rich drugges and other fine spices haue beene there gotten by the Spantards and Portingals and yéerly haunted by them as at this day the same is throughly known to many which also confesse that the places vnder the Equinoctiall and the rich City Calecute being by the sea coast of Inde standing betwéene the equatour and our Tropicke of Cancer and vnto the other Tropicke South vnder the Burning zone that the places is habitable and peopled although very cumbersome with extremity of heat Also that space on earth containeth 685. Germaine miles or 23500. furlongs Ptholomie and Auicen affirme that the places betwéen the equatour and summer Tropicke is habitable and that many Cities bee there although the sunne in those places through his direct beames and especially vnder the equatour doth by the ouer much heat and continual heat burn and mightily scorch The like doe sundry others affirme which write that those places is conuenient for the life of creatures in that vnder the equatour there bee many waters which although resolued and run through the heate yet doe they breath and send vpward colde vapors which the sun continually maintaineth in drawing vp through his vehement heat and sending down mighty showers of raine which vapors in the night through the suns furthest distance vnder the earth and especially at midnight cause a mighty cold and chilling ayre which the sun after his rising vntill he be somewhat ascended aboue the earth cannot sodainly ouercome and put away that cold impression of the ayre So that the people there inhabiting bee monstrous of forme and haue rude wits wondrous wild and terible conditions like to wilde and furious beasts The countries which lie vnder the Southerly Parallels as those which are described by the Equinoctiall line vnto the summer Tropicke where the sun is drawne and runneth ouer the tops of them there through the aboundance of vapors rayne and night colde is the suns heate repressed mitigated and dulled so that the heades of the Ethiopians or Moores be litle hauing but litle and withered braines their bodies short hauing thicke crisped haire on their heades grosse and dull of senses blacke scorched or burned bodies withred or wrinckled faces crooked of stature being in a maner hot by nature and cruell condicions through the mightinesse of heat in those places And the constitution also of the ayre is there such that al liuing and cresent things on that earth are found and known to agrée with them Further it is to be noted and vnderstood that any there trauailing from the Northerly places the further they goe towarde the South somuch the stronger heat or burning they shalbe annoyed with The two temperate zones be next adioining to the burning zone the
one on the Northerly and the other on the Southerly side of it And the beginnings of either bee the hotter the ends colder the middle of them exquisitly temperate in the other parts doth the heat either so much the more excéede or the bitter colde ouercommeth and ruleth as howe much the nearer they approach or come vnto the burning Zone or otherwise vnto either of the extreame Zones which continually cause a bitter and an extreame colde The cause of this diuersity is through the suns beames for the sun continually moouing in the middle iourney of heauen described betwéene the two Tropicks and digressing or going beyond the prefixed bounds of nature doeth not shew his beames vnto diuers parts of the earth in one manner but vnto the places right vnder and in the burning zone the tractes or countries contained vnder them doth he send downe right beames which stretcheth to the vpper face of the earth at right angles And vnto the countries of either temperate zone doeth the sun send downe thwart or slope beames And vnto the places vnder either cold zone doth he streach long beames on the plaine of the earth euen the like as being neare to the Horizone which neither reach vnto the vpper face of the earth nor cause angles but kéep an equall distance vnto it do streach forth infinitely But those beames of the sun doe neither giue light nor heat but turne backeward in that the property of the reflexion which of the beame against a solider resistance prohibiting or letting the penetration is a certaine repercussion and reuerberation that increaseth and doubleth the force of the direct beame and by the reflexed beame to it adioyned or at the least by his vertue applied and communicated Séeing this reflexion is the especiallest cause of the heat and that the angles of the reflexions falling doe continually make or be equal in the angles for that cause do they much vnlike increase the force of the directe beames and their effectes doe notably varie So that in the burning zone the reflexion stretcheth vnto right angles séeing the straight or right beames are caried led into themselues in such sort that as direct and reâ—lexen they méete and bee mixed and in this doubling as it were the vertue and force of the direct beames is on such wise increased that it kindleth burneth and consumeth And in either temperate zone is the reflexion caused at right angles in that the sun beames doe thwartly reach to the vpper face of the earth and are turned and extended backward vnto thwart angles which how much the néerer and liker they bee to the right so much the nearer doe they ioyne either beames togither by which they procéed and come into the nearer parts of the burning zone But so much the blunter as they streach so much the longer do they seperate either beames as howe much the more they are extended vnto the extreame or outmost bounds And for this cause doe they more heat then the fore parts of the temperate zone whose heate is a litle gentler or milder then the heate of the burning zone and the beames a litle further of whose colde notwithstanding differeth somewhat from the extreame or outmost vntemperate zones And those which streach and fall into the middle region of either temperate zone doe cause a meane betwéene the right and very sharp angles and yet not directly matched or ioyned nor doe they by so neare a space communicate their vertue as in the beginning of it neither by so large a distance as in the end but in the middle in a maner So that they cause and increase a temperate heate in the same zone But in the extreame or colde Zones is no reflexion of beames caused for those beames equally distant from the earth are streached forth infinitely and for that cause doe those neither giue light nor moue or procure heat neither doe those zones at any time warme either perfectly cleare or appeare bright but that they continually be foggy misty darke and bitter or extreame cold through the continuall mists which more and more increase especially toward the northerly pole And yet many affirme a reasonable dwelling in those places yea and vnder the Northerly pole but far colder and bitterer dwelling through the far being from the way of the sun and beholding of the comfortabler starres For the Sunne through his ouer far distance cannot by his presence aboue the earth comfort and heate This now is the perfect cause of the diuers and vniuersall coustitutions of the ayre and chiefe qualities in each zones so that of the particular constitutions be other causes But to returne vnto the temperate Zones the latitude of either temperate Zone is of 43. degrées almost of Germaine miles 645. and of furlongs 21500. So that the Boreallor Northerly zone beginning from the Tropick of Cancer endeth at the arcticke cyrcle or at the degrée of latitude 66. and 31. minutes And the Southerly from the Tropicke of Capricorne is extended or reacheth vnto the antarcticke cyrcle or the degrée of the Southerly latitude 66. and 32. minutes The vntemperate cold zones that reach froÌ„ either temperate vnto the poles of the worlde doe mooue continuall cold and frosts So that the beames of the sun although they pearse and enter through yet seeing they extende not backward nor through the reflexion or streaching backeward be strengthned and sharpned therefore can they not so heate that by the thawing they dissolue the earth and yse nor put away or voyde the mist. Now the vntemperate Northerly zone beginning from the 66. degrée and 31. minutes of the Northerly latitude endeth at the Pole arcticke and the vntemperate southerly zone begun from the same bounde of the Southerly latitude extendeth and endeth at the pole antarcticke Those people which dwell vnder the burning zone bee named of the Gréekes Amphiskioi Amphiscij in that the Noone shadowes at diuers times of the yeare goe or be cast to them twoe waies as toward the South or North. And twise also in the year runneth the sun right ouer their heades as is demonstrated in the second Theorme of Euclide so that at Noone it commeth to passe that they haue almost no shadow for the sun being direct or in right line ouer their heades at Noone hee then sendeth downe right Beames which are cast or streached to the plaine of the earth at right angles so that their shadowe falleth and is right vnder the feete and not on any side of them So that the sun in any other time of the yeare beeing without the verticall pointes the shadowes at Noone are one whiles cast into the South and another whiles into the North vnto them euen as the sun digressing from their toppes or Noonstéed is either caried into the North or otherwise declineth into the South This sorte of people which bee vnder either temperate zone are called of the Gréeke Cosmographers Eteroskioi Heteroscij in that they haue a single
and reasonable well furnished of all things néedfull for mans life So that in the same middle Region of the earth vnder the Equatour it appeareth that through the coldnesse of the night it doth there temper sufficiently the burning heat of the day Besides these after the mind of Hiero. Cardane in that Saturne Mercurie and the moon which properly are cold and moyst planets haue a great force in the Regions vnder this zone but especially the moon that worketh her most force there in the night time more then the other twoe and of this cause more temperatnesse in the day time Besides these it is well known that those people haue two summers and two winters in the yeare For in the yeare of our Lord 1530. at the will and charge of Charles the fift Emperor a parte of America westward was discouered where Peru among the rest was found richest both of Gold and other rich things and costly drugges which is situated in longitude of 290. degrées from the West toward the East and is distant 5. degrées from the Equatoure toward the South But what substance of Gold and other rich things hath yearely bene brought from this yle néedeth not here any further rehersall And the like is to be considered and noted of the other two zones contained betwéene the Polare cyrcles and Poles of the worlde Although Albertus Mag. denieth a commodious dwelling for men in those places and confirmeth the same by probable reasons yet experience reclaimeth and denieth those opinions of his and other ancient writers In that it is well knowne that Gothland Norway Russia Lapeland Groueland and diuers other countries towarde the North pole is inhabited and well peopled And Galeottus Naruiensis proueth that men dwell vnder the North pole affirming the same not to bee true that the cause of the cold there is onely the far distaunce of the sun as not of the heate by nearenesse of his comming In that the sun by reason of the signe in which he is either increaseth or diminisheth them with vs. Besides he affirmeth that the colde is not so dispersed rounde about as that it compasseth rounde after the forme of a cyrcle nor that the heate in like sort doeth run round about the whole body of the earth Further Cardane writeth that vnder the poles there is no such coldnes as some suppose in that the Moone Venus and Mars haue the greatest latitudes in respect of the sun and the others besides For the moon hath fiue degrées to the North Venus and Mars excéed vnto eight degrées Northward but Saturne which is the author of cold scarcely performeth thrée degrées Northward Besides these the Moone more auaileth Northward and Southward neare to the poles then the sunne in that she nearer approacheth those parts For the Moone as aboue said hath fiue degrées of latitude as well to the North as South so that when she shall be in the first degrée of Cancer with her greatest latitude Northward that is in the head of the Dragon she shal then be néerer by fiue degrées to the Northerly pole then the sunne And in like maner when she shalbe in the taile of the Dragon at the entrance and beginning of Capricorne she shall bee nearer the pole antarcticke by fiue degrées than the sun Although in the winter the moone should be in the beginning of Capricorn with the Southerly latitude of foure or fiue degrées yet may she worke and cause more in the change of weather and shall cause more in Scotland than the sun in that her power and vertue there is such But in Brasilia and vnder the antarcticke pole for two causes the one in that shee is there of such power and the other for that in her working she is nearer What the longitudes and latitudes of the celestiall Zones are THe longitude of Zones beginneth from the West and is extended by the Noonestéede into the East and from the East againe by the midnight pointe into the West The motions of the sun in the zodiacke and Poles of the zodiacke doe describe the latitude of the zones For the suns motion or the zodiacke do describe the burnt zone séeing the sun on the one parte of the zodiacke goeth toward the North vnto the elongation of 23. degrées 28. minutes and being by his dayly motion in the beginning of Cancer doth describe the Tropick of Cancer which is the bound of the two zones the burnt zone and Northerly temperate Zone And on the other part of the zodiacke doeth the sun goe into the South vnto the same elongation and being in the beginning of Capricorne doth likewise describe the Tropicke of Capricorne which is the bounde of the other twoe zones in that it distinguisheth the burnt from the southerly temporate zone And the space also included in these two cyrcles vsing the middle place is called the burnt zone and thus the burnt zone doth imploy 46. degrées and 57. minutes The Poles of the Zodiacke which are dayly about the Poles of the worlde from which they differ 23. degrées and 28. minutes and are drawn by the motion of the first mouer doe describe two cyrcles in the diuers parts of heauen as the Polare cyrcles which also be the bounds of the zones that distinguish the twoe temperate from the colde zones So that the latitude of either colde zone vnto the poles of the world is of 23. degrées and 28. minutes The other degrées of the semicyrcle are atributed to the temperate zones so that either zone containeth 43. degrées and 3. minutes What is the Longitude and Latitude of the earthly Zones THe longitude of the earthly zones is like to the longitude of the celestiall as from the West by the noon stéed into the East and from thence by the midnight pointe againe into the West And the latitude of them is like to the latitude of the celestial zones for as the maner of the latitude of the celestiall burnt Zone is vnto the whole cyrcumference euen so is the maner of the earthly burnt zone vnto the compasse about of the earthly Globe that is as 47. degrées is vnto 360. and so likewise conceiue of the others And that this may plainer appeare vse the figure following in which a l h e. is the meridian or Colure of the solstices e x l. the Equatoure a x h. the meridian s u p. the earthly Globe s n. the earthly Tropicke of Cancer k o. the Tropicke of Capricorne t u. and q p. the arcticke cyrcles To these answere f r o k b b. and d s m c c. also c ff b a g e e i. the celestiall cyrcles And what the proportion f d. is vnto the whole cōpasse d a k g f the same is as aboue written the proportion r s. vnto the whole cyrcumference of the earthly Globe and on this wise conceiue of the other cyrcles The letters f d. bee the latitude of the celestiall burnt zone and r s. of the earthly d c.
experience gainsayth and denieth muchlesse therefore can it be greater ten times By which is to be concluded that the water is but litle in quantity in respect of the earth although it may séeme very bigge being vp to the edges of the vpper face of the earth And if the waters had béene more bigger then the earth they had drowned or couered the whole earth euen of late yeares That the earth employeth the middle place of the Worlde and is the Center of the whole A Ristarchus Samius which was 261 yeares before the byrth of Christ tooke the earth from the middle of the world and placed it in a peculiar Orbe included within Marses and Venus Sphere and to bee drawne aboute by peculiar motions about the Sunne which hée fayned to stande in the myddle of the worlde as vnmoueable after the manner of the fixed stars The like argument doth that learned Copernicus apply vnto his demonstrations But ouerpassing such reasons least by the newnesse of the arguments they may offend or trouble young students in the Art wee therefore by true knowledge of the wise doe attribute the middle seate of the world to the earth and appoynte it the Center of the whole by which the risings settinges of the stars the Equinoctials the times of the increasing and decreasing of the dayes the shadowes and Ecclipses are declared The earth round about is equally distant from heauen therefore according to the definition of the Center the earth is the Center of the world That the stars haue alwaies one bignes in what place soeuer any shall beholde them therefore are they in an equall distance from the earth The roundnesse of the earthly globe hath a proportion vnto the roundnesse of heauen that is the certaine and proportionall parts in the earthly Globe doe answere to certaine proportionall partes of heauen therefore is the earth the Center of the world In that siftéene Germaine miles on earth doe answere to a degrée of the Meridian and that in euery houre doe fiftéene degrées arise of the Equinoctiall which coulde not be if the earth were not in the middle of the world For the vnequall Arks should otherwise appeare in the equal times and the equall partes of the Meridian shoulde the vnequall spaces on earth answere which experience dayly witnesseth vnto the contrary And hereof it ensueth that the earth stands in the middle of the world In euery Artificiall day doe sixe signes appeare and sixe like set vnder the earth therefore is the earth in the middle of the worlde and is also as a pricke to which the halfe doth regularly moue dayly The like is in the opposition of the Sunne and Moone when either light is in the Horizont which could not be if the earth should approch or come néerer vnto one part then vnto the other If it were néerer to eyther of the Poles then could not the vniuersall Equinoctials bee for that the one Arke alwaies either in the day and night time should be greater then the other The Eccclipses also coulde not bée in the changes and full moones For that there shoulde then bée vneuen spaces from the South vnto the North and from the East vnto the West If the earth were not as the Center of the worlde then of necessity shoulde these ensue that the earth shoulde approch either néerer to the East or West or South part and when any of the starres aswell the fixed as Planets shall come vnto that part they shall appeare nearer to vs then being in any other part of heauen and by that aboue saide they shall also appeare greater which is altogether vntrue and we also sée the contrary in that as aboue writen they alwaies appeare of one greatnesse eyther being in the East or in the West Also one halfe of heauen is alwaies aboue the earth and the other halfe vnder the earth and this is not onely found and knowne in one quarter of the earth but the like in euery place as the Equinoctials do witnes then which there can be no more euident tryal A third reason may bée alleadged if any imagined the earth vpon the Center to be parted into two equal halfes and that the eie is placed in the Center then shall the eie sée no more then the halfe of heauen By which appeareth that the swelling of the earth from the Center vnto his compasse about in making a comparison vnto heauen is as in a maner nothing And it is knowne to the learned in Astronomie that any of the fixed starres is by many times greater then the earth which if any behold them they appeare as poynts in heauen Now how much lesser would the earth appear if a man should behold it from his place Here learne by this demonstration following that the earth standing without the Center in the poynt B. being to the Meridiane as is the poynte A. nearer and when a star shall come vnto that poynte then shall it bée nearer to the earth and in the opposite poynt as is I. shall bee from the same much further than in any other place and shall euen there lesser appeare which by experience is quite contrary Further graunt that C. D. be the thwart Horrizont yet the contrary for the second reason E. B. K. being the Equatour which from the said Horrizont is deuided into two vnequall parts and by this consequent also must the Zodiacke bee deuided into two vnequall partes from the said Horrizont for that those two Cyrcles as hereafter shall bee taught doe crosse one another into equall parts Therefore when the sun by his proper motion carried from the East into the West shall come vnto the crossings of the Equatour and Zodiacke and that the greater part of these Cyrcles shall be vnder the earth it cannot be that the Equinoctium or a like day and night can bee through out the earth no not vnder the right Sphere much lesse can it be vnder the thwart Sphere IF this be vnpossible it shall be also as vnpossible that sixe signes may alwaies bee aboue the earth and the other sixe vnder the earth but rather that more of the signes shall be vnder the earth and more of them aboue euen as the earth is imagined to be deuided from the Horrizont aforesaid into two equall parts like as when it shall bée in the Center of the whole and that from each Center of the greater Cyrcles the earth is deuided into two partes As all these to any beholding the materiall Sphere are forthwith knowne at the first sight so by a third reason is to bee noted that when any imagineth by the lyne E. F. that the earth in the poynt G. standing as in the Center of the whole is deuided by the middle as well beeing in G. as H. for the excéeding distance from the Cyrcumference is vnpossible to sée alwaies the halfe heauen If the Earth be not in the middle of the Worlde then of necessitie shall it possesse some of these