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
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
where the places bound of colde and moysture be white of body hauing long heare on the head tall and comely of stature and personage cold of qualitie yet in maners or condicions wilde and cruell through the force of the cold in those places and agréeing with these is the greatnes of the winter and the greatnesse of fierce and cruel beasts and other liuing things there bréeding with a furious people inhabiting called generally the Scythians Last those dwelling vnder the temperate zones be a gentler and ciuiler people beeing some tawnie especially toward the South and others toward the North reasonable white of skin and bodie being meane of stature and temperate in nature and quality and of the same like in condicions and behauiuor c. And thus much for the second part of this Treatise FINIS The Table of all the speciall and seuerall points handled in this Booke OF the Rudiments of the Sphere of Heauen of the Stars of the Orbs of the Stars and of the Earth Folio 1 What a Sphere is 2 What the world is and into how many parts the same is deuided with the motion of the celestiall Orbs. 8 What the Stars are and that as to the motion of their Orbes they are caried about 11 That Heauen is drawne round 13 That there are but eight celestiall Orbs that may be seen 14 A generall figure declaring the number disposition and order of the Celestiall Spheres aboute the Globe of the earth 16 That there are two first motions of the celestiall Orbs. 17 That there are two kindes of Starres the fixed and the Planets 19 Of the celestiall images and of their diuers names being in number 48. 21 The 12. signes of the Zodiacke 22 Of the Southerly 23 Of the Planets 25 That Heauen hath a rounde fourme and is carried circularly 29 That the water and earth are round bodies and by a mutuall embracing doe make one body and one hollowe vpper face 31 An Instrument by which the roundnesse of the earth according to latitude may bee prooued and all those may easily bee shewed which are taught of the dayes Artificiall 33 That the water hath a like swelling and runneth round 36 That the earth emploieth the middle place of the world and is the Center of the whole 42 If the earth be not in the middle of the world then of necessity it must possesse some of the standings described in the figure there demonstrated 46 That the earth abideth fixed and vnmoueable in the middle of the world 49 The phisicke reasons 50 That the earth compared vnto heauen is as a point 52 To finde the compasse of the earth and by it the Dyameter 55 The second Part. What the summe of the second part is 59 That the Sphere of the world is either right or thwart 90 That the Circles of the Sphere be some greater some lesse with the number of the Circles 92 The description names and vtilities of the Equinoctiall 62 That this worthy Circle hath diuers names 71 What are the offices of the Equinoctiall 73 What are the Northerly images in respect of the Equinoctiall 78 The description names and offices of the Zodiacke and Ecclipticke line or way of the Sun 98 What are the names of this Circle 100 What is the cause of the thwartnesse of the Zodiacke 109 Of the Ecclipticke line or way of the Sun 113 What the latitude of a Planet is after two destinctions 115 What is the longitude of a Star where he beginneth 116 What are the vses and vtilities of the Zodiacke and Ecclipticke 124 The description names and offices of the Colures 125 What the offices and vtilities of the Colures are 133 The description names and offices of the meridian Circles and Horizon 135 What are the offices and vtilities of the meridian 144 A Table of the Suns declarations c. 155 The common way of measuring of places with their spaces by the rules of longitude and latitude 167 What is to bee done if places differ in the longitudes 169 Other briefe examples 171 The finding of the distances of places or Citties in a more easier manner 173 The first rule 174 An Example 175 Another Ibid Another Ibid Another 179 Another Ibid Another Ibid Another 177 The second Rule Ibid Another excellent Table c. 178 An example of the vse of this Table 179 The second Rule 180 An Example Ibid Another 183 Another Ibid Another 184 Another Ibid An easier working Ibid An Example 185 Another Ibid Another 186 If of two places c. Ibid. A third rule 190 An example of the third rule Ibid. Another 193 Another 124 Another 196 An easier working and lesse curious 197 An Example 198 Another Ibid Another 199 Another Ibid A demonstration of the third rule 200 The declaration of the first rule 201 The declaration of the second rule Ibid. The declaration of the third rule 202 The definition appellations diuision and offices or vtilities of the Horizon 204 The appellations and diuers names of the Horizon 205 The offices or vtilities of the Horizon 215 Of the verticall Circles 217 The Circles of the Altitude 219 The houre Circles 221 The Circles deuiding the twelue houses of heauen 226 The Circle of position 230 The definitions names and vtilities of the foure lesser Circles 231 Which Circles are called the Tropicks 235 Why they are called Tropicks Ibid. The offices or vtilities of the foure lesser Circles 245 The descriptions names qualities c. 247 What the longitude latitude of the celestial zones are 261 What is the longitude and latitude of the earthly Zones 263 Where the beginning and end of euery Zone according to latitude and which places are in which Zones 264 How the Zones and Clymates doe differ 267 What are the qualities of the Zones Ibid What be the vtilities of the Zones 268 FINIS
of the fore-Dog To this fore-Dog doth Ptholomie attribute onely two stars others do number thrée that in Ptholomies time were in Gemini and in our time are in Cancer Of which the fore star which is in the addition of the same doth possesse the magnitude The scond star which standeth on the legge shining bright is Procion of the first bignesse al are of the nature of Mercutie and a litle of Mars The other Dogge being the greater is named of the Arabians Alhabor which properly is named the greater dog And this vnderstand that the same starre is brightest shining which standeth on the mouth or tung of the Dogge being of the first bignesse and named by authors the dog in the name of the whole image The star named Syrius or the Dog is placed in the middle Center of heauen vnto which when the sun shall come the heate is then doubled and mens bodies affected with faintnesse Also they suppose that star to be called Syrius though the brightnesse of his fiery shining The Latins name him the Caniculer or Dog-star Of which the Caniculer or Dog daies were named in that whiles the sun runneth in that part it is dangerous and this through the quality of the season then being that disposeth the time to health or sicknesses And hercos it is that whiles for a time it ariseth the season is not alwaies contagious Ptholomie nameth that Starre which is on the mouth of the Dog and assigneth him to be of the first bignesse most cleare and bright in shining And to that star which standeth or is placed on the head he giueth a small quantity that is to be a star of the fift bignes Auicen thus writing of the Dog-daies willeth men to beware and learne the time in which the greater Dog ariseth and the season in which the snow lieth stil on the high hilles or mountaines and the frosty or sharpe colde time for then is no apt time of ministring medicine But a medicine may safely bee druncke or otherwise giuen in the spring and haruest time Hippocrates beeing of the same minde affirmeth that in the Dog-daies and before them no purgation may safely be ministred The beginning of the dog-Dog-daies varieth according to the diuersity of Regions Climates and Latitudes In our time the dog-Dogge-dayes begin at the suns entrance into the 10. 11. and 12. degrée of Leo. That which aboue was said that the star Syrius is in the middle Center of heauen is ment that the star is in a celestiall cyrcle as the Solsticiall colure whose Center is the Center of heauen in which that cyrcle is described This vnderstand that the sunne is then ioyned with the star Syrius when they both arise together in the Horizont aboue the earth and setteth Heliace West with the sun though it cannot be séene rise in the morning for the bright beames of the sun but after the suns dayly mouing from it the star beginneth to arise and be seene in the morning before the sun To a man of knowledge this is not strange that the Dog-star ariseth once euery naturall day yet the words of Auicen are thus ment that in what time the Dog-star ascendeth with the sun and this at the Horizontall méeting and ioyning together of them in the morning which pestilent Caniculare time do the phisicians determine to be of 40. daies long But the malice of that season is many times ouercome changed through the strong beames of the Planets hapning in this time as of Iupiter Venus and sometimes of Saturne Ptholomie doth assigne to this constellation named the Dog-star 18. stars of the first 3. 4. and 5. magnitude that in his time were all in Gemini and in our time in Cancer except the 17. star which is in the end of Gemini And that which is brightest shining in the Dogs mouth is named Alhabor hauing the quality of Iupiter and a litle of Mars and al the others applied to Venus Hyginus writing of this image named the Southerly Crown which of many is named Vraniscus as if the same appeared fashioned hollow from heauen The same doth he thus describe that before the fore féete of Sagitarius are a fewe stars fashioned into a roundnesse which forme his Crowne that many haue imagined as cast from him in bondage maner And many meane by this Greeke word Ouraniseos the Palat in that this crowne appeareth fashioned like to the Palate which is a hollownesse aboue the toung To this celestiall Crowne fashioned like a litle Palate doth Ptholomie assigne 13. starres of the fourth fift and sixt magnitude that in his time were all in Sagitarius and in our time are in Sagitarius and Capricornus of the nature of Saturne and Mars This image do some name the monstrous Fish the terible fish the monstrous sea beast and sea Lion or Beare This huge fish named the celestiall Whale is placed vnder Aries and both the fishes lying a litle aboue the starry Riuer in the Region of heauen Ptholomie doth assigne to this celestiall Whale 22. stars of the third fourth and fift bignesse that in his time were all placed in Pisces and Aries and at this day are in Pisces Aries and Taurus and most of them are of the nature of Saturne and Venus and some onely of Saturne This Meridiane fish named the Southern or Southerly fish and greate whose Aliances are the fishes named which are placed in the cyrcle of the Zodiacke This signe or image is placed in the South parte and séemeth as it were with the mouth to drincke of the water comming from the signe Aquarius Ptholomie doth number and giue to this Southerly fish 11. stars being of the first fourth and fift magnitude that in his time were all in Capricornus and Aquarius and in our time are all in Aquarius The brghter starre in his mouth hath the quality of Venus and Mercurie But those stars placed on the body of the same are agréeable and a like to the nature of Saturne These hitherto for the images placed on the North and South side of the Equatoure 5 By the fift is the declination of the parts of the Ecclipticke from the Equatoure as at the bound from which it is knowne and both the declinations of the stars and the latitudes of places learned The declinations of the stars are called the distances of them from the Equatour toward either of the Poles of the worlde The latitudes of places the spaces from the Equatoure vnto the highest of them raised in the Meridiane as by the toppes gathered and learned in the standing right ouer Also by the Equatoure doe we learne the declinations of the Planets aswel Northerly as Southerly moued as more euidently doth appeare in the solyde Sphere or Globe So that by the declination of the stars knowne a man may easily place them in proper instrumentes by which greate vtility ariseth And it is the measure of time in that the length of the naturall day is knowne thereby 6 By
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
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
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
from the furthest point of the ecclipticke vnto the equatour By which it appeareth that so much is the distance of the poles of the Ecclipticke from the poles of the worlde as is the suns greatest declination being 23. degrées and 28. minutes and two fiftes almost Or thus that the pole of the Zodiacke is far distant from the pole of the world as is the greatest declination af the sun from the Equinoctiall cyrcle and by the equidistance also on each side of the arctick cyrcle from the Pole of the world that that part of the Colure comprehended betwéene the first point of Cancer and the articke cyrcle is almost double so much vnto the greatest declination of the sun And if cyrcumspectly you consider the maner of the motions you shall readily perceiue that those cyrcles which euer more be of like largenesse increase and decrease togither with the twoe Tropicke cyrcles according to the increase or decrease of the suns declination As appeareth by the letter n. in the foresaid figure that representeth the Northerly pole of the ecclipticke or Zodiack moued from the letter n. into o. by the motion of the first moouer and returning againe into the point n shall be moued the cyrcle describing n o. being distant from the Northerly pole a. asmuch as is the suns greatest declination h g. as hereafter by demonstration shall plainer appeare And this cyrcle named the arcticke in that it is described by the arcticke of the Zodiacke The like is described from the point r. being the pole antarcticke by the motion from r. vnto s. and returning againe vnto r. so that the antarcticke cyrcle r s. is equall to his opposite and equidistaunt to the Equatoure This probation that the distaunce of the Poles of the worlde and Zodiacke is equall to the suns greatest declination doth require before hand these thrée propositions The first that the quarters of each cyrcle any where taken be in themselues or betwéene one another equall The second that the poles by a quarter that is by 90. degrées be distant from their proper cyrcle The third that the equals deducted from their equalles then doe the equalles rest As for example if you borowe two fourthes in one and the same Colure cyrcle that is the Solsticiall of the same parte where it passeth by the beginning of Capricorne and is the like from the pole of the worlde vnto the Equinoctiall and that other is that which is from the Pole of the Zodiack vnto the Zodiacke or ecclipticke and of this I thus reason that when the equals be deducted or abated from the equals the remainer shall be equall Therefore are the foresaid quarters equal in that they be in the same cyrcle and that from either is the equall or common arke deducted that is the same which is contained betweene the Equinoctiall and the pole of the Zodiacke which arke doeth containe 66. degrées and 31. minutes almost So that the arks resting or remaining of these quarters be equall that is the distance of the poles of the Zodiack and the Equinoctiall is equal to the suns greatest declination For if 66. degrées and 31. minutes bee deducted from either quarter the remainer then shalbe 23 degrées and 31 minutes which is the distance betwéen the foresaid poles and the greatest declination of the sun This other example demonstrateth that the suns greatest declination and the distance of the poles of the zodiack or ecclipticke from the poles of the world is equall and of like largenes and that what soeuer hapneth to the distances of the said Poles For as this increaseth or decreaseth the like doth that decrease or increase Of this it is manifest that the two foresaide articke cyrcles is nowe in our time lesser through the decreasing of the suns greatest declination and that the Tropickes are greater then they were in Ptholomies time The offices or vtilities of the foure lesser Cyrcles 1 THe office of the Solsticiall Tropicke after the Gréekes is to define the longest summer day and the winter Tropicke to determine the shortest winter day and longest night For Proclus to finde the longest day did deuide the summer solstice into 8. equall partes of which so deuided he affirmed thrée parts to be continually hidde vnder the horizon and fiue aboue The truth of which is known if the Sphere bee rectified for the latitude of 41. degrées where by this diuisiō the longest day containeth 15 hours and the night but 9. houres 2 Many and notable offices doe the Tropicke cyrcles offer as well vnto the composition of dialles as vnto the preparing many other Instruments in Astronomie 3 They declare the places of the Ecclipticke in which the suns solstices are caused whereof the longest or shortest daies by them are knowne Or thus they declare in euery standing of the sphere the longest and shortest day with their quantity 4 They include the Suns way in that they bee as the bounds including the Region in heauen in which the sun is continually moued 5 They declare the suns greatest declination as afore hath bene often taught 6 They seperate in heauen the burning Zone from the two temperate Zones But of the Polare cyrcles these be the chiefest and especialest vtilities 1 They iudicate or shewe the Poles of the Zodiacke and howe farre they bee distaunt from the Poles of the world 2 They inclose those stars which euer appeare aboue our Horizone and those in like maner right against being alwaies hid vnto vs. But for that euery seueral Climate hath disagréeing from other Climates these cyrcles their distance therefore cannot bee certaine from the other Parallel cyrcles sauing for one Region certaine as neither their quantities nor their order For in that place where the altitude of the pole is lesser then 66. degrées and a half these cyrcles there are lesser then the Tropicks and in order are betwéene them and the poles and is from the pole continually distant by so many degrées as the pole in that country is raised aboue the Horizon So that in the same place the Pole raised more then 66. degrées and a halfe The Tropicke then is aboue the horizone as the like may be vnderstoode by that place called Wardehouse So that in the same Climate the arcticke cyrcle is greater then the Tropicke of Cancer as witnesseth the learned Stoeflerus Iustingensis 3 They distinguish after the mind of the Gréeks the cold Zones from the temperate Which Ferio denieth affirming that the arctick and antarcticke cyrcles kéeping no vniformitie to all countries and béeing vncertaine and variable boundes can limit any certaine place For the temperate Zones are places certaine the arcticke and antarcticke cyrcles bee changeable limits therefore cannot they be as bounds of the temperate Zones yet dooth hee better allowe and agrée vnto that that the Tropickes bee bounds of the temperate zones So that changeable limits by this argument cannot be appointed as bounds to vnchangeable places 4 They deuide togither with the