parts or degrées of the Equatour in his motion and rising aboue the Horizont doe make an houre and euery degrée foure minutes of an equall houre so that the quarters or fiftéene minutes of each degrée doe produce and cause one minute of an houre Also they obserued the ascentions and descentions of the signes in this cyrcle for that in any region or countrie a man may knowe the length of the artificiall day and night by hauing a sphericall instrument and the sun placed in the East Horizont let the note of the Equinoctiall be moued and after the sun being turned into the West Horizont let the note againe of the Equinoctiall be moued into the East Horizont So that the degrées of the Equinoctiall numbred marked with these notes do cause an artificiall day counting alwaies fiftéene degrées of the Equinoctiall for an equall houre To conclude the length of the artificial day known by subtracting the same from 24. houres the quantity of the night remayning shall appeare howe much it is Last the sun being entred into this cyrcle doth rise in the iust East point and setteth full West but in the highest of summer being come to Cancer he riseth Northeast and setteth Northwest at what time the noone-tide is highest But in the shortest time of winter when the sun is come to Capricorne hée contrariwise riseth Southeast and is in the noonetide lowest 4 It distinguisheth the Equinoctials and crosseth the Zodiacke thwartly wrethed and bended to it in two opposite points which when the sun commeth and is in it he causeth like spaces of the day and night and of the same those entraunces of the sunne are named the Equinoctiall points And there are two Equinoctials caused in euery yeare as the one the sun entring the beginning of Aries or the spring poynt of the crossing of the Zodiacke and Equinoctiall in the beginning of the spring which the Latines name the equinoctiall spring and the Gréekes Isemerian earinén And the celestiall point of the same equinoctial the Gréeks name the point of our equinoctiall spring The other equinoctiall is caused when the sun hath his beginning of Libra in the entrance of haruest called the equinoctiall haruest And the celestiall point in which the sun happeneth they name the pointe of our Equinoctiall haruest These points remaine not fixed in one place of heauen but in the going before doe procéede or moue forwarde vnder the eight Orbe and turne before the places of the fixed stars For the point of the equinoctiall spring that in the first yeare of Olimpias folowed the first star of Aries of the eight Sphere 4. degrées and 52. minutes And in the yeare of the death of Alexander one degrée and 58. minutes The same after the beginning of the yéeres of Iulius Cesar followed 4. degrées and 50 minutes And in the yeare of Christes byrth 5. degrées and 16. minutes In Ptholomies time 6. degrées and 40. minutes it went before the same star and in these yeares it went before that star 27. degrées and 35. minutes So that the yearely times of the Equinoctials are come backe from the auncient time and moue before the marked dayes by a long space For that the Equinoctial spring which about the beginning of the yeares of Olimpias hapned in the first or second of Aprill In the beginning of the yeares of Cesar in the 25. day of March. In the time of Christ our Sauiors byrth in the 23. or 24. day of March. In Ptholomies time in the 22. or 23. day of March But in our time it hapneth in the 11. or 12. day of March and in this yeare 1570. it happeneth in the 11. day of March and in the 11. howre before noone on Saturday The Autumnall or haruest Equinoctiall which hapned in Christ our Sauiours time in the 23. or 24. day of september is brought backe and come in this our time vnto the 13. or 14. day of September and in this yeare 1570. shall happen in the 13. day and in the 10. houre and 21. minutes after noone on Wednesday And through this variation of the fixed stars and Equinoctials is caused that the later practitioners haue found an other quantity of the yeare contrary to the auncients For Hipparchus and Ptholomie haue stablished in their time the quantity of the Tropicke yeare to bee of 365. dayes 5. houres 55. minutes and 12. seconds The Alphonsines of 365. dayes 5. houres 55. minutes and 12. seconds Albategnius 365. daies 5. houres 46. minutes and 56. seconds Cardanus of 365. daies 5. houres 48. minutes 41. seconds and 47. thirds And Thebitius hath stablished the starrie yeare to be of 365. dayes 6 houres 9. minutes and 32. seconds which is the space of time in which the sun returneth vnto the same fixed star But the Tropicke yeare is the suns returne after his measuring of the whole Zodiacke vnto the Equinoctiall or soisticiall point So that by the saide pointes changed either in the increasing or comming sooner as hitherto hath béene obserued is the quantity of the yeare found to be in diuerse and sundry wise of the practisioners By it also is learned and knowne which stars and images celestial are toward the North or South from it And by it is the starrieskie deuided into two equall halfes of which the one halfe is toward the North and the other towarde the South So that the denomination so well of the Planets as fixed stars are there by learned whether they bee Southerly or the Northerly An other authour writeth thus of it that it deuideth heauen into two parts of which the one is named Northerly of the seauen stars in the great Beare the other Southerly in that the sun about the South séemeth alwaies to abide with vs in that quarter And if the same may be knowne which stars are named Northerly and which Southerly and when the Planets are named Northerly and when Southerly So that by this reason all the stars and images from it tending toward the North to be Northerly and from it tending toward the South to be Southerly The Northerly images in respect of the Equinoctiall are these THe Bull named in latine Taurus is adorned with 33. stars although an other writer mentioneth but of 32. Of these 5. are in the face and about the eies and in the places where the hornes are described to be are one star a piece which make seauen in number named Hyades in Gréeke and Succullae in Latine in that they stand like to the letter Y. These in the 10. 11. and 12 degrées of Taurus hauing their latitude Southerly of which 4. are of the third bignesse and one brighter then the rest in the Southerly eie named properly Aldebaran of the first bignes and of the nature of Marse The seauen stars on the back of this signe named Pleiades and in Latine Virgiliae but in English the clustring stars in that they stande so neare togither that they can scarcely be numbred yet these more
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
the earth Albategnius affirmeth the Star of Mercurie to be least of all the starres and supposeth or accounteth him to be as one part of 19000. parts of the earth The highest ascention of Mercuries Sphere is from the earth after Albategnius distant 166. semidiametres but the lowest point in the same Orbe is 56. semidiametres distant from the earth THe Moone being lowest of all the Planets doth compasse about the whole Zodiack in 27. dayes 7. hours 43. minutes and 7. seconds She is lesser then the earth after the iudgement of Ptholomie by thrée hundreth nine times and a vnity more then eight parts For the triple proportion of the diametre of the earth vnto the moone by deuiding aboue the fift parts is euen the like as 27. vnto 5. But lesser she is then the sun by sixe thousand fiue hundreth thirty and nine times Copernicus by his obseruations founde the earth greater then the Moone by forty thrée times lesse then an eight part and of this the sunne also is founde greater then the moone by seauen thousand parts lacking thréescore seconds And the greatest distance of the new and full mòone from the earth after the mind of Ptholomie is 64. semidiametres and 10. scruples but after later obseruations 65. semidiametres and 30. scruples And the lowest to the earth is 55. semidiametres and 8. minutes THe Moone digressing from the Sun euery moneth and taking or receiuing a newe light as it were in that she is changed taketh a new light of the sun doeth after encrease by little and litle conceiuing dayly a bigger forme and light vntill shee come in right line against the sunne at what time she shineth with full light after returning againe vnto the sun she waxeth olde by loosing of her light by little and little and in the contrary maner cōmeth vnto the like formes of light vntil she comming vnder the beames of the sun bée quite out of sight Also for that the moone hath a body partly thin partly thicke solyde and shadowed therefore is she not equally filled round about with the beames of the sun but that the same halfe of her Globe or body which turned againe in heauen that beholdeth the sun is it which shineth and the other halfe turned away from the suns light is that which shineth not but remaineth shadowed That Heauen hath a round fourme and to be carried circularly FIrst heauen is equally distant roūd about from the earth and of this is heauen perfect rounde after the definition of the Sphere Which reason is thus proued that if heauen shoulde haue any other forme then perfect round then of necessity must the stars change their distances frō the earth what place vppon earth they shoulde purchase as somewhere more and somewhere lesse they shoulde bee distant and the standing of them changed should also alter their apparant bignesse in that they should appeare greater being séene néere hande and lesser being séene far off Yet neither of these happeneth but that they cōtinually kéeping a sunder are drawn about by vnchangeable spaces and holding a like bignesse and distance to all places of the earth That the stars about the quarters of the East or West appeare sometimes greater is not caused by reason of the shorter distance but for that their beams in the vapours which often times consist in the ayre betwéene the starres and our eie are then broken which breaking of them causeth the body of the star séene to appeare much greater in the eie then in déed it is That heauen is drawne circularly is thus knowne in that wée alwaies sée all the Stars from the East into the West to be drawne vpward and that the hemisphere in our sight is carried continually in distant cyrcles equidistant neuer changing the standing or distance one from another neither in bignesse as far as the iudgement of the eie can descerne neither any whit lessoned For they being drawue from the neather place as from the earth are caried by little and little And after they be thus come vnto the highest of their iourney as vnto the noon-stéede they decline again by little and little till they be brought down vnto the west quarter and there set and hidden vnder the earth and these places and times both of the risings and settings doe they repeate in certaine order Therefore by these it appeareth that they are drawne and carried by round By the second it is euident that the Starres which be néere the Pole Articke are neuer hidden out of our sight but are continually and vniformally drawn round about the Pole as the Centre in such sort that the stars neare to it make the lesser compasses and the stars further off doe define greater compasses So that the starres fastened to their proper Orbs as aforewritten are cyrcularly caried By which two motions of the stars as well tending vnto the West as otherwise it plainly appeareth that heauen is drawn about and caried round A manifest demonstration appeareth of the former argument by this figure here following That the Water and Earth are round Bodies and by a mutuall embracing doe make one Body and one hollovv vpperface THat the earth is round is thus proued Wheras in euery vpper face the length and breadth is considered The length of the vpper face of the earth is from the West into the East or contrariwise The bredth is from the South into the North or contrariwise That the earth also to bee rounde appeareth after length in that the Sun Moone and Stars doe neither arise nor set at one instant time alike to all persons dwelling in any parte of the earth But doe much sooner appeare and shine to them dwelling vnto the East and within a whiles after they shewe to them dwelling in the West By the second appeareth that one and the like Eclipse of the moone in diuers houres is séen both in the East and West For that which appeareth in the first houre of the night to them in the West is séene to them in the East parte in the second thirde or fourth houre euen as they come nearer vnto the East which would not be caused if the night to both places should happen and bée at one moment nor sooner woulde they appeare to them in the East part Againe there bée certaine stars which in their rising doe appeare sooner to them in the East parts then to them in the West as Plinie writeth of Arbelis being a towne in Asiria where an Eclipse of the Moone was séene in the second houre of the night which in Sicily was séene in the first houre of the night For the Assirians are more Easterly then the Sicilians and therefore doeth the sun set sooner with them then with the Siciliaus And when it was also the second houre of the night in Assiria the Sun first set in Sicilia about the first houre of the night Moreouer the Pole of the world acording to the diuersitie of places is eleuated and
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
and Orchades that be into the North and East which is distant from the furthest bound of Scotland but thrée dayes sayling if prosperous windes bée their helpe At this day men haue found beyond Thylen but somwhat into the East and most large bounds stretched and found beyond the articke or Northerly cyrcle these are whole without breaking of any sea betwéene and containe Suetia Norway Iseland Grunland and Lapeland The kingdome of Suetia appeareth most large and containeth sundry nations and people among which they are of most account the East and West Gutland people inhabiting neare to Norway And vnder the King of Suetia are the Lapeland people as the Finelapons and Dikilapons where are a wild and fierce people dwelling almost vnder the pole articke especially the Lapeland people to whome the sun neuer setteth in the summer for 40. dayes space Aboue these inhabit a people of a cubite long or high hauing small and crooked bodies named of some Pigmalions that liue vnder a very darke and bitter cold ayre or sky And aboue Scania néere to the West boundes of Suetia doeth Norway stretch into the North whose vttermost limit extendeth vnto the 71. degrée almost of the Northerly latitude Aboue this is the country named Iseland by reason of the frozen waters and sea where throughout the yeare it so bitterly fréezeth that through the ycie seas there thicke frozen it permitteth no ships to come vnto thē except in the thrée hottest months of the yeare It aboundeth with brimstone and burneth in many places through the sulphure brimstone veines Plinie writeth that the Occean sea in North is very large which in these our dayes is well knowne This also was learned of certaine skillfull sailers which inhabited and very much had traualed this coast that they knew not the limits or bounds of this sea toward the North but supposed that this sea did compasse the whole earth By this sea dwell many and mighty people as the Danes the Swedens Norwaies Gotelandes Finelands Russians and Pruchenians and vnder the pole artick the Laplands The reason why in these places such force of moysture aboundeth is for that a dayly and continuall cold of these places gathereth and thickneth the ayre and by a continual working resolueth into water For when the ayre is not throughly purged by the suns beames then the weaknes of them and far distance of the sun from these places must of necessity bee continually thicke and darke which afterwardes yéeldeth and giueth plentifull floodes by deawes and raines Albert mag in his booke de natura loci and 8. chapter assigneth a witty and laudable reason why the Northerly be inhabitable The cause he setteth downe in that sundry skillfull Mariners affirme that haue many times sailed into the Northerly partes of the Ocean sea that in those places is a continuall darknesse which when men sawe they returned for feare supposing nay rather doubting that none coulde saile any further in that quarter of the worlde through the darknesse and thicke mist which hindreth the direction of their iourney So that the nature of those places cannot bee sufficiently knowne to vs séeing no man as the learned report hath attempted thither through extremitie of colde their bearing sway And for that excéeding cold is a mortifying quality therefore a man may coniecture that few liuing creatures and beasts can there liue c. Yet the part of the Northerly Occean vnto the Easterly side is sufficiently knowne to many trauailers Although the vttermost boundes of the earth are not wholy knowne yet the nearest aprroaching to them shall here bee applied as the longitude of the earth distaunt betwéene Peru the Realme of America and Cathaya to expresse 315. degrées or if any minde to accompt the longitude from the fortunate Iles they may by a whole cyrcle containe them euen as the whole Orbe about in a maner doth partly giue place to the water and are partly dwellings for men beasts and other liuing creatures although some places of the earth bee more inhabited then others But as touching the latitude if towarde the North in the country of Lapous the south toward the vtmost coast of America shal end seing y ◠vtmost distance of the earth hath very litle béene noted of this shall small errour be caused If two places offered or giuen be placed vnder the Equatour of which the space is sought then the arke of the difference of latitude is the same with the arke of the distance neither doth the verticiall cyrcle differ from the Equatour For the equatour of either place doeth containe the verticiall points as may appeare in this tryangle noted with A. B. C. Of which if 15. germain miles be wrought into parts of the difference of longitude and any scruples after remaine deuide those by 4. For by so many minutes of a degrée doth a Germain mile answere that the distance shall make As Ptholomie writeth of the places vnder the Equatour The high lande or mountaine of the Satyres in the country of Syna whose longitude is of 175 degrées and no minutes nor hath any latitude Myrica an Ile of Ethiope vnder Aegipt whose longitude is of 85. degrées the angle of the difference of longitude betwéene the meridians of these places is straight or right and containeth a whole quarter or 60. degrées The like are these places standing vnder the equatour Colipolis a citty of India beyond the riuer Ganges which hath the longitude 194. degrées and 20. minutes Essina the greate Mart-towne of Aethiope vnder Aegipt whose longitude is of 70. degrées and 3. minutes The angle of the differēce of longitude which the meridians of these compasse is blunte and containeth 94. degrées and 17. minutes Againe the same or the like meridians containe and make a sharpe angle of 43 degrées as of the citty Nubarta of Taprobane which at this day is Sumatra and Colipolis of Inde beyond or aboue Ganges for it is distant from the west 122. degrées and 20. minutes and this containeth 164. degrées and 20. minutes If two places be giuen the one standing vnder the Equatour and the other distant toward any other quarter from it The first that the angle of the difference of longitude is straight to these here placed In that if two places giuen the one shall be vnder the equatoure but the other distant from the same toward some quarter thē must the angle of the difference of longitude bee considered If the same shal be right then shal the distance of either place be the quadrant of the greatest cyrcle As in this tryangle A. B. C. where the letter A. representeth the Pole of the equatour and the places giuen that the one be standing in the point B. vnder the equatour and the arke A. B. be the quadrant and that the other consisteth in the letter C. the angle then of the difference of longitude being C. A. B. is right By Regio a montano de trangulis appeareth
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
image named Aquarius hath 24. stars and 3. without forme 12 The images named Pisces haue 34. stars The Summe of all the Starres except Berenices bush are 364. Of the Southerly _1 THe image named Coetus hath 22. stars 2 The image named Orion hath 38. stars 3 The image named the riuer or Eridanus or Potamos hath 34. stars 4 The image named the Hare hath 12. stars 5 The image named the Dog hath 18. stars of which that in the mouth is named Alhabor 12. without forme 6 The image named the little Dog or Caniculare star hath 2. stars of which the brightest is that named Proion or the Dog-starre 7 The image named the Ship hath 45. stars of which a bright star going before in temone 8 The image named the Water Serpent hath 25. stars and 2. without forme 9 The image named the Bucket or great Cup hath 7. starres 10 The Rauen or Crow hath 7. stars 11 The image named Centaurus being one halfe like a man and the other halfe like a horse hath 37. stars 12 The Beast which the Centaure doth holde being a Wolfe hath 19. stars 13 The image named the Aulter hath 7. stars 14 The Southetly Crowne hath 13. stars 15 The Southerly fish hath 11. stars and 6. without forme The Summe of all the starres are 316. THe milkie way which Ptholomie nameth Galaxian of the white and milkie colour is a heape of most small stars and dimme to sight of which is a certaine confused gathering together and abundance as it were encreased that no seuerall light is decerned and the same in the maner of a girdle compasseth and encloseth heauen about The same also is vnequal and differeth in the standing latitude haunt of stars and in the colour very much It is somewhere decerned clefte but the parte going before is neither whole nor maketh a whole swathe or inclosure about but lacketh about the swan and Aulter And the part folowing whole being in no place broken off with a space and stretched thwartly in heauen and from the partes of the Zodiacke Northerly it passeth by Gemini and Sowtherly by Sagitarius and Capricornus Of the Planets THe Planets named otherwise the erring and wandering starres not for that they erre by a wandering and vncertaine motion but in that they are caried aboute by a diuers and vnlike motion For sometimes they goe foreward and sometimes retrograde sometimes are hidden and cleane out of sight after they appear and shew themselues Againe they goe before and follow the Sun They are caried swift and their motions againe so stayed that they are moued in a maner nothing at all but séeme as they were stayed for a time From the sunnes way one while caried into the South and another while caried into the North and then vnto the same way drawne backe againe so that their iourneies being passed and finished they steadyly repeate their old courses by the like order Of these are seauen and each caried in their proper Orbs and compasse about the Zodiacke in vnlike spaces of time SAturne highest of the Planets and most slow in course being cold and dry pale to a leady colour and perfourmeth his course in 30. yéeres being ninty times with an eight part greater then the earth And the highest ascention or pointe of Saturnus Orbe which at this day is in the 29. degrée of Sagitarius is from the earth 20072. semidiametres with a fourth part almost and 15. minutes But the lowest point of Saturns Orbe is distant from the earth 14378. with a third part and 20. minutes IVpiter being next vnto Saturne temperate and so cleare or bright that he giueth in a maner a shadow especially when he is Perigeus or lowest discended to the earthward and he compasseth about the Zodiacke in twelue yeares But Iupiter giueth this proper shadowe when neither the lights bée aboue the earth nor Venus néere to him Hée is greater then the earth by ninty fiue times and a half part almost And the highest ascention of Iupiters Orbe which possesseth the seauenth degrée of Libra is from the earth 14369. with a fourth parte almost and 15. minutes but the lowest point of Iupiters Orbe is from the earth distant 8853. semidiametres with a ninth part and 45. minutes MArs béeing hot and dry and shining with a fiery colour doeth goe about the Zodiacke in the space of two yéeres He is named the fiery Planet of his shining with a fiery colour or of the effect which foloweth by him in that he burneth and dryeth vp He is one time greater then the earth and a little more then a third parte The highest ascention of Marses Orbe that obtaineth the 28. degrée of Leo is now distant after Albategnius from the earth 8022. semidiametres but the lowest poynt from the earth is 1176. semidiametres THe Sunne obtaineth the middle place betwéene the Planets wholy and throughly bright being the fountaine and Author of light which by his motion expresseth and deuideth the spaces of the Zodiacke and by his going about haue the signes their names He is greater then the earth after Ptholomie a hundreth thréescore and sixe times with thrée eight parts But after Capernicus the sun excéedeth the earth a hundreth thréescore two times with eight parts lesse The highest ascention or poynte of the suns Sphere which nâ—w possesseth the seuenth degrée of Cancer is from the earth distant 1179. semidiametres but the lowest poynt of the sunnes Orbe is from the earth distant 1065. semidiametres VEnus next to the Sun being cold and moist white in colour clearer and brighter shining then Iupiter and is caried about like the Sun in a yeares space and both goeth before and foloweth the sun nor is further distant in the spring of the morning from him then 46. degrées and 47. minutes but in the euening she is seene digrssed from him vnto 47. degrées and 35 minutes When she goeth in the morning before the sun thée is named the day star but when she followeth the sun in the euening shée is then named the euening star Lesser shee is then the earth but her true quantity is yet vnknowne for that some affirme her quantity to be the 28. part and others the 37. part of the earth The highest ascention of Venus Sphere that obtaineth the 18. degrée 20. minutes of Taurus is from the earth after Albategnius 1070. semidiametres but the lowest poynt is 166. semidiametres distaÌ„t from the earth MErcurie beeing lower then Venus is variable and apte to bée changed bright but not white in colour and is caried about the sunne like to Venus as one whiles mouing before and an other whiles following the sunne Nor is hee further distant in the morning from him then 29. degrées and 37. minutes and at the euening westwarde 27. degrées and 37. minutes He perfourmeth his whole course in the space of a yéere as the sun doth Also he is iudged to be the seauenth part of 2â— or 22000. parte of
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
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
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
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
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
that C. B. the ark of the distance of places which reacheth out right is a quarter of the greatest cyrcle Wherefore if the degrées bee multiplied by 15. and the minutes deuided by 4. the distance then shal be knowne As for example Nubarta of Taprobone hath the longitude 121. degrées and 20. minutes but no latitude the city Pyse of the Tuscanes in Italie hath the longitude 31. degrées and 20. minutes almost the latitude of 42. degrées and 11. minutes then the angle of the difference of longitude is right for the difference is of 90. degrées or a whole quadrant These then multiplied by 15. do procreate or bring forth the distance to be of 13 50. Germaine miles Essina a Mart-towne or principal â—itty of Aethiope vnder the gouernment of Aegipt hath the longitude of 70. degrées and 3. minutes but it hath no latitude The Ile of Tyrus hath the longitude of 67. degrées and no minutes the latitude of 33. degrées and 20. minutes The difference of longitude betweene the one and the other is of 3. degrées and 3. minutes The complement of the difference of longitude is of 86. degrées and 57. minutes of the latitude of the place not standing vnder the equatour the complement is 56. degrées and 40. minutes The royall citty Colipolis of Inde aboue the riuer Ganges hath the longitude of 164. degrées and 20. minutes but no latitude knowne The longitude of Tyrus is of 67. degrées and no minutes the latitude hath 33 degrées 20. minutes The difference of longitude greater then the quadrant is of 97. degrées and 20. minutes The quadrant being abated there remaineth 7. degrées and 20. minutes The complement of the latitude of Tyrus is of 56. degrées and 40. minutes If of two places giuen either standeth without the Equatoure toward some one of the opposite quarters and the other vnder the equatoure then is the reason of the standing considered and the angle of the difference of longitude For the one differeth either by like spaces from each bound and is nearer to the Pole the other to the Equatoure The same appeareth by the compared latitudes which like toppes of either place containe the same Parallel the vnlike being distant and the Parallell by a space seperated toward each place doe argue peculiar and proper tops But the angle of the difference of longitude either it is right blunt or sharpe This of the placing and diuersitie of the angles doeth much varie or alter the reason methode of the searching of these If two places giuen haue equall arks of the latitudes and from the middle or halfe of the equatoure bee alike distant and how much so euer the angle of the difference of longitude be as here vnder the difference of longitude is in the first of the example taught yet are the arkes of the latitudes agréeing and equally founde so that in this example appeareth no difference but in the only longitudes of the places offered As for example The longitude of Danske is of 39. degrées and twoe scruples or minutes the latitude of the same hath 54 degrées and 48. minutes The longitude of Lubecke is of 28. degrées and 20. scruples the latitude hath 54. degrées and 48. scruples The difference of longitude consisteth of 10. degrées and 42. minutes The halfe difference is of 5. degrées and 21. scruples The distance on earth betwéene Danske and Lubecke is of 92 Germaine miles and a halfe The great citie Alexandria vnder the Turke after Ptolomie hath the longitude of 122. degrées the latitude of the same is of 41. degrées That famous Toletum or Toledo of Spaine hath a longitude to the same of 10. degrées the latitude of the same is of 41. degrees The difference of longitude betwéene the one and the other is of 102. degrées The halfe difference hath 51. degrées The complement of the equall latitudes of either is of 49. degrées The whole distance betwéen both appeareth to containe 1077. Germaine miles and a halfe If of two places giuen the one bee further distant from the equatour then the other and the greatnesse of the complements of either latitude differing as that the arkes of the latitudes be vnequall so that the diuersity of the angle included with the arks of the complements shal varie the methode or reason of the search for that the one giueth and formeth a right angle another a sharpe another a blunt angle yet to these the angle of the difference of longitude is right The example of two places differing alike both in the longitude and latitude here appeareth The citty Tacola which at this day is called Malchaia or Magna a place of much resort of Marchants This from the West hath the longitude of 160. degrées and 30. minutes of latitude from the equatour it is 4. degrées and 15. scruples distant The other city and place in the countrey of Pontus named Trapezus being a head city of Cappadocia and was the auncient seat of the Emperours This hath the longitude of 70. degrées and 30. minutes and the latitude of the same is of 43. degrées and 5. scruples The difference of longitude betwéene the one and the other is of 90. degrées The arke of distance betwéene both places is of 87. degrées and 6. minutes to which 1306. a halfe Germaine miles answere If the vnequall arkes of the latitudes and angle of the difference of longitude be lesser then the right it canseth a diuers reason of the search by which the arke of the complement of the greater latitude doth varie thrée waies as it is greater or lesser and as with the arke by the second in quisition surely knowne and beeing ioyned forme either more or lesse a quarter of the cyrcle Or thus that the angle which the vnequall complements of the vnequall latitudes include be sharpe that is and if the arks of the latitudes of either place be vnequall and the difference of longitude bee lesser then the quadrant As in this example more plainer appeareth of twoe places beeing of sundry longitudes That worthie citty Trapezus of Cappadocia whose longitude is of 70. degrées and 30. minutes the latitude 43. degrées and 5. minutes The longitude of that well knowne city of Rome hath 39. degrées and 8. scruples the latitude 41. degrées and 8. minutes The difference of longitude betwéene the one and the other is of 33. degrées and 22. minutes Another example not vnlike the former and not much varying from the former as the longitude of Ierusalem which is of 66. degrées and no minutes the latitude of 31. degrées and 40. scruples The longitude of Viteberge being of 30. degrées and 30. minutes the latitude 51. degrées and 50. scruples The difference betwéene the one and the other of longitude is of 35. degrées and 50. scruples If in places vnequally distant from the equatoure the angle of the difference of longitude shalbe blunt by which the difference of longitude shall appeare greater than the quadrant Or thus that
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