23 55 14 38 47 17 53 36 7 68 22 29 83 7 19 9 59 16 24 54 49 39 46 38 54 35 16 69 21 30 84 6 16 10 59 5 25 54 23 40 45 58 55 34 25 70 20 31 85 5 14 11 58 54 26 53 56 41 45 17 56 33 33 71 1â— 32 86 4 11 12 58 41 27 53 28 42 44 35 57 32 41 72 18 32 87 3 8 13 58 28 28 52 59 43 43 53 58 31 48 73 17 33 88 2 5 14 58 13 29 52 29 44 43 10 59 30 54 74 16 32 89 1 3 15 57 57 30 51 58 45 42 26 60 30 0 75 15 32 90 0 0 The xviii Chapter of the circuite or compasse of the Earth and Water according to the opinion of the auncient and latter aucthours IT may heere appeare to be necessarie for our purpose to declare what space of the superficie of the earth or water the auncient wryters diâ— suppose to aunsweare to one degree of a greater circle in the heauen for in diuers countries they vsed to count by diuers sorts of measures as the Latines counted by miles the Greeks by furlongs the Spanyards Frenchmen by leagues the Egyptians by signes or marks and the Persians by saguas But they all agree that foure graynes of Barly make a finger breadth four fingers a hand breadth four hands a â—oote fiue foote a Geometricall pase for two simple pases make fiue feete Also 125. Geometricall pases make a furlong eyght furlongs one myle whiche is a thousand pases and three myles one lâ—ague In Germanie they make leagues of more feete and in some places more then in other In Fraunce they count thyrâ—ie leagues to one degree The Spanyards count sixteene leagues and two terces and seuenteene and a halfe for a degree of the great ciâ—cle this difference that one league is bigger then another may come heereof that one Barly corne is bigger then another But to our purpose let vs geue to euery league three thousand pases and to euery pase fyue foote and so shall euery league haue xv thousand foote In the Cardes of the sea that haue their degrees of xvi leagues and two terces we say that of these the roundenesse of the land and the water conteyneth sixe thousande leagues And in the Cardes that haue seuenteene leagues and a halfe for a degree of these we say that it conteyneth sixe thousand and three hundred leagues And who so desyreth to knowe howe muche is the Diameter of the earth and water may knowe it by multiplying the circumference by seuen so that diuiding the summe that riseth thereof by twentie and two the part that ryseth of that calculation shall be the Diameter and the halfe thereofâ— shall be the semidiameter The xix Chapter of the seueâ— Climates THE auncient aucthours did also diuide that part of the superficie of the earth on the North side of the Equinoctiall which they supposed to be most habitable into seuen Climates wherein they did fynde to be dyuers conditions and customes of men and diuersities of beastes and of other naturall thynges the whiche thyngs they perceyued to haue a diuersâ—tie in the countreys as where the day of the one did encrease or differ aboue the day of the other by halfe an houre so that the space of the superficiall of the earth betweene two paralelle lynes wherein the longest day doth increase or differ by halfe an houre is called a Climate The place where they suppose the fyrst climate to begin is distant in Latitude from the Equinoctial by 12. degrees and 45. minutes where the longest day is 12. houres and 45. minutes the place where the last climate doth finishe is in the Latitude of 50. degrees and 30. minutes where the longest day is 16. houres and 15. minutes so that the increase of the longest day in the ende of the seuenth climate dooeth exceede it in the beginning of the fyrst climate by three houres and an halfe and the whole compasse of the earth with all the seuen climates dooeth conteyne in breadth 37. degrees and 45. minutes but their length is supposed to extend to 180. degrees of longitude In that maner a climate the neare it is vnto the Equinoctial the more it conteyneth of the superficiall of the earth because the paralelle circles the nearer they be vnto the Equinoctial the greater is the compasse of the earth which they make in length and the lesser the compasse is the nearer they be vnto the poles as dooth appeare euidently by the Meridians where they doo all concurre and meete in the poles â—heir distaunces waxeth continually lesser and lesser the nearer they be vnto the sayd poles so that the nearer the climate is vnto the pole the lesser it conteyneth of myles in the length In lyke maner shall you vnderstand that greater is the breadth of the first clime then of the second and the second then the third and lykewyse of the other For in how much the more the Equinoctial you come neare to the pole so much the more is the Sphere oblique or crooked and consequently the day encreaseth more by reason whereof in lesse space is found the increaseth of halfe an houre in which the climate maketh difference and doth varye Whiche thyng shall be more manifest to hym that beholdeth the Latitude of them all as may appeare by the Table heere folowyng In whiche you may see the houres whiche the greatest daye conteyneth of euery climate in his beginning middest and ende with also the eleuation of the Pole or distaâ—nce from the Equinoctial and also the degrees of Latitude which euery Climate conteyneth The longest day   The eleuation of the Pole  Differences of the latitude Climates Beginning Midst End beginning Midst End     Ho. M Ho. M Ho. M G M G M G M G M 1 12 45 13 0 13 15 12 45 16 40 20 30 7 45 2 13 15 13 30 13 45 20 30 24 15 27 30 7 0 3 13 45 14 0 14 15 27 30 30 45 33 40 6 10 4 14 15 14 30 14 45 33 40 36 24 39 0 5 20 5 14 45 15 0 15 15 39 0 41 20 43 30 4 30 6 15 15 15 30 15 45 43 30 45 24 47 15 3 45 7 15 45 16 0 16 15 47 15 48 40 50 30 3 15 The fyrst Climate is called Dia Meroes Meroe is a Citie of Aphrike vnder the burnt Zone on this side the Equinoctiall 16. degrees The second is called Dia Siena Siena is a Citie in the conâ—ines of Ethiope where there is a well that sheweth the Sommer solstitiall because that place is vnder the circle of the Tropike of Cancer and the Sunne seemeth to stand directly ouer that place at mydday of the solsticiall whereby the well is then very cleere and hath in it no shadowe at all as the Poet
respiration and life of men and other beastes As concerning which samâ— thinke that the Ocean Sea is higher then the earth and aske the question why the Sâ—a couereth not the whole earth and why the earth is not sunke in the water To this it may be a sufficient aunsweare that it hath so pleased the wyll of Gâ—d according to the saying of the prophet Dâ—uid Terminum posuisti quem non transgredietur neque conuertetâ—r operirâ— terram That is Thou hast appoynted limits which it shall not passe neyther shall it returne to couer the earth Besyde the wyll of God which is the cheefe and sufficient cause thereof we say that nature fayleth not in her necessaries For she sometime admitteth a litle inconuenience to auoyde a greater euill as when heauie things which natuâ—ally should descend doo not only not descende but rise vp And aâ— also soâ—â—time it chaunceth that fyre descendeth and wâ—ter aryseth to fyll the voyd or emptie places least any where should be fouâ—d voyd or emptie which nature so greatly abhoâ—reth Tâ— this puâ—pose nature foreseeing the kindes of many things that could not elsewhere liue then on the earth neither bee conserued wâ—thin the water as men and other earthly beasts determâ—â—ed before to mâ—ke the earth not perfectly round contrary to the nature thereof whereof it foloweth that it is not altogeather couered of the water And as sayth Origen the earth remayneth discouered of water that it might bring foorth fruites trees and plantes As touching the conuex aforesayde the water and earth discouered are conteyned vnder the concauitie of the ayre which is diuided into three Regions as the lowest hyghest and middlemost The lowest is hote by reason of the reflection or rebounding of the beames of the Sunne stryken backe by the earth The highest also is hote by participation of the fyre and nearenesse thereunto The myddle region is colde as is manifest by the snowe and hayle engendred in the same The ayre neare vnto the region of the fyre which is pure heate doth neither burne nor lighten because it hath no combustible matter and so hath it power and not acte It is neare vnto and reacheth the circle of the Moone which compasseth it about The heauen or circle of the Moone is next vnto the heauen of Mercuri and Mercuri vnto Venus Venus vnto the Sunne the Sunne to Mars Mars to Iupiter Iupiter to Saturne which is next and reacheth vnto the heauen of the Starres called the Firmament because that in it are all the Starres except the Planets firme and fyxt as a knot in a table The knowledge of the Planets was had by seuen sundry motions they haue among themselues and by their course not vnifourme to that of the Starres of the eyght heauen because that sometimes the Planets appeare vnto vs ioyned togeather and sometimes diuided The Christaline heauen compasseth about or conteyneth within it the heauen of Starres This Christaline heauen is transparent and pâ—rspicuous as cleare water or glasse that may be seene through by reason of the cleerenesse and pure substaunce thereof It is by an other name called the heauen of water whereof holy Scripture speaketh saying Aquae quae supra caelos sunt laudent nomen Domini That is to say Let the waters that are aboue the heauens prayse the name of the Lord. It was created for the conseruation of corporall things and to temper the heate engendred of the moouing of the fyrst moueable which being so great of body that it not onely compasseth all the Elements but also all the inferior heauens is mooued so swiftly that it dayly perfectly mooueth all the aforesaid Spheres And least by reason of the great heate thereof caused by his swyft motion it should consume inferior things God ordeyned this Christaline heauen that the coldnesse thereof might temper the extreame heaâ—e of the other This Christaline heauen reacheth vnto the fiâ—st moueable heauen called Primum mobile Aâ—d this reacheth to the Emperiall heauen which is the twelfth called Emperium by reason of his cleerenesse and respleâ—â—â—â—â—â— Tâ—â—â— is 〈…〉 aâ—â— is moâ—t pâ—â—fect The Philosophers had no knoâ—ledge heereof Bâ—â— we beleeue by holy Scripture that such a heauâ—n there is and the same to be the habitation of Aâ—gelles and Spirituall creatures It is also called Coelum Coelorum that is The heauen of heauens because it conteyneth and includeth within it all the other heauens It is of greater cleerenesse then all the other heauens and was created immediatly with the Angelles In this also remayneth the humanitie of Iesus Christ our GOD and in dignitie aboue it It conteyneth three holy orders or principalities called Hierarchias Wâ—ereof the fyrst is called Supercelestâ—all and hath in it alâ—o three orders Seraphims Câ—eruâ—ims anâ— Thrones The second is called Celestiall and conteyneth Dâ—minations Principates and Potestates The third called Subcelestiall conteineth Uirtutes Archangells and Angelles And to coâ—clude it hath aboundance of all goodnesse and perfect felicitie with priuation or want of all euill The heauen also geueth influence of constancie stedfastnesse and durabilitie to things agaâ—nst the fluxabilitie and inconstancie of the other heauens the order whereof doth appeare in the demonstration followyng The vi Chapter of the immutabilitie or immobilitie of the Earth THE Pythagorians and other auncient naturall Philosophers as sayth Aristotle were of opinion that the earth did mooue yet not by a ryght foorth motion but circulerly about the middest of one place The which errour both Aristotle himselfe and the Astronomers doâ— confute and reprooue by euident causes and manifest demonstrations For circuler motion is proper to the heauens And as the earth differeth from them in nature so likewise in moouing And although it be so that the earth may naturally mooue by certayne of his partes yet to mooue in the whole and without the circuite of his Sphere it is impossible being founded and established vppon his owne center the which of it selfe is naturally immooueable for as much as in it the reason of all heauynes consisteth Whereas otherwise euery part that is mooued should ascend contrary to the nature of all heauie things Bâ—t there is found nothing heauie that doth not naturally enclyne directly to the center of the earth and would actually descend thyther if it had no impediment of some other thing to resist it and when it toucheth there or is come thyther would still rest and remayne there And heereby it foloweth that the earth being founded vppon his owne center is not mooued The wâ—ich thing the Prophet Dauid also affyrmeth saying Fundasti terram super stabilitatem suam that is Thou foundedst the earth vppon his stabilitie The vij Chapter of the roundnesse of the Earth and Water THAT the Earth is rounde it appeareth by manifest euidence For if it were playne or flatte the dawning of
altitudes And if the Carde haue no graduation you shall take with the compasse in the trunke of the leagues seuen spaces of 12. leagues and a halfe which are 87. leagues and a halfe And these must be deuided into fiue partes which come foorth at 17. leagues and a halfe for a part and the foure partes taken with the compasse make foure degreés and deuided into foure partes euery part is a degrée and is marked thus ° And yf you wyll make the degreés at 16. leagues and two terces or more you shall geue to euery degreé so much space as the leagues comprehend This graduation must be begun from some one cape whose altitude of the Pole is well knowen And the whole Carde being thus graduate you must begin the number of the degrées from the Equinoctiall lyne one two thrâ—e c. toward the one Pole and the lyke toward the other so that to the knowne Cape may answeare the number of his altitude And so shall you doo to the whole Carde Also the Equinoctiall lyne shall be marked in his proper place And in lyke maner shal you marke the Tropikes according as they are in y e sphere But forasmuch as in Spayne Cape saint Uincent is the principall they begin there to make graduation number it in 37. degreés And from thence towarde the Pole Artike the degrées doo encrease And from thence towarde the Equinoctial line they deminish and from that lyne to the pole Antartike they encrease againe as we haue sayd as is conteined in the Carde and as appeareth in this demonstration following And if the paterne haue neyther leagues nor degreés you must take or know the altitudes of two Capes that are North and South of the degreés and the difference of the degreés of the eleuation that is from the one Cape to the other ye shall deuide all that space in so many partes and so eche one parte shal be seuenteéne leagues and a halfe as answereth to one degreé Or accordyng to the opinion of the leagues of the roundnesse of the earth as we haue sayde as touchyng this in the eyghteénth Chapter of the fyrst part In Spayne they vse with the compasse to take the space that is from Cape saint Uincent to the myddest of the greatest Ilande of Berlinga whiche they account threé degrées so that after seuenteéne leagues and a halfe for a degreé they are 52. leagues and a halfe and so much do they put in this space Other put fiftie leagues accompting after syxteéne leagues and two terces for a degrée and in this maner they make of leagues degreés and of degrées leagues The sayling Cards haue no certayne bignesse limitted them because they onely represent the description of the water and earth and not the quantitie and for this cause some are paynted in great space and other in lyttle They that are in great space are more manyfest and more precise and these the Maryners call Cards of the lâ—rgest pricke or draught Some desire rather to haue them in lesse space because they are brieffer and conteyne much in litle roome and these thâ—y call Cardes of the lessâ— prycke And if for any consyderation aforesayde you desire to reduce any Câ—rde from the greatest pricke to the least or contrarywyse yâ—u must paynt onely the coast and Ilands on a paper in maner as you did in the ruled Carde of the lynes or wyndes I say let it be drawen vpon paper for destroying or rasing the paterne And when it is traced onely with ynke then vpon that draught shall you drawe certayne ryght liâ—es equidistaunt made all by one compasse according to the length of the Carde and other lynes that may cut them in ryght angles and lykewyse equidistaunt and of the same compasse that the fyrst are These two orders of lynes shall deuide all the superficiall part of the Carde into perfect squares or quadratures And it is to be noted that the nearer the lynes are ioyned togeather and the squares the leâ—se so muche the more perfectly may it be reduced and more easily Then shall you take another paper greater or lesse then the Carde accordyng to the poynt that you desyre to reduce it vnto and in the length and breadth thereof you shall deuide so many spaces as are betweene the lynes of the other paper and yf it bee greater the squares shal be greater and if lesse lesse To keâ—pe order in the correspondence of the squares which shal be a great lyght to translate the one from the other you shall number the orders of the squares as those of the longitude by the â—ronte or vppermost part and those of the latitude by the syde as well in the one paper as in the other conformable also those of the front from the left hand to the ryght and those of the side from aboue downeward Then beholde the coast how it goeth by the squares of the first paper and likewise the tracting or drawing in the squares of the seconde in the selfe same order and proportion as it is there and so shall it remayne reduced to the poynt whiche you desyre And this shal serue for a paterne to set in the ruled Carde Heere foloweth the maner of the translating of the Card from one fourme into another greater or lesse Here foloweth a similitude of the Mariners Carde ¶ The iii. Chapter of the vertue and propertie of the Lodestone called in Latine Magnes and in Spanish Pâ—edraymon THe Lode stone as writeth Cardinall Cusanus hath substance vertue and operation His verâ—ue is engendred of his substance essence or being and of his essence vertue proceedeth this operation and effect in such sort that this stone communicating his vertue to iron by reason thereof causeth the iron to moue although betweéne the one and the other be a cuppe or plate of syluer or a table or any other lyke thing The attractiue or drawing force of the Lode stone causeth the nature of iron to be and rest in it and that so fyrmely and quietly that being naturally heauy and ponderous it descendeth not because his nature resteth not in hym self but is vnite with the nature of the stone which seémeth to extende it selfe and as it were to cast â—oorth a liuely spirit of enchaunting vertue Insomuch that as we sée by experience by the sayde vnion it not onely distributeth his vertue to one iron but that iron likewyse to another and that other againe to another and so foorth vntill of many ryngs or lynkes of iron be made a chayne Saint Augustine as he writeth in his bookes De ciuitate Dei did maruayle that he sawe an iron mooue it selfe vpon a vâ—ssell by mooâ—ing the Lode stone vnder the vessel It is called Magnes because the inuentour or fynder therof was so named who as Plinâ—e writeth keéping cattell in East Iâ—dia had his shoes soled with plates of iron and iron nayles such as they
must be put a square grayne or stubbe which on the inner part may come playne with the halfe circle on the vtter part may câ—me forth a litle where shal be nâ—yld a square peéce of Laton of the breadth of the halfe circle This graine or stubbe being so nayled with the péece must haue in the middest a hole so small as may receiue a litle pinne and by the center of this hole must passe a line which shal trauerse all the grayne And this lyne shall serue to put the sunne which the hole representeth in the degrée of the signe where it is This halfe circle where it goeth in the circumferences of the rundels for the houres must â—e fyled on the one side vnto the line that is in the myddest to marke it and shew the number of it For the placyng or settyâ—g of this instrument you must cut a gyrdle or ryng of laton as thick as the plate and of the breadth of a fyâ—ger or litle lesse and so large that of it may be made a circle somewhat bigger then the plate so that the plate and the Meridian may easily be conteyâ—ed within it This circle shal be called the Horizon which must be deuided into foure quarters In lyke mâ—ner must be mâ—de two semicirculer péeces the ends of them must be nayled or sothered in the poynts that deuide the quarters of the circle and deuide the one from thâ—ther in two equal parts making right spherical angles And in this ioynt of these two peéces must be nayled or sothered a Mastâ—â— the which at the one end is deuided into two braunches or forks Then shal you make a base or foote for the same which in the vppermost part thereof shall haue a concauitie or holownesse where may be set a sayling compasse or a neédle touched with the Lode stone and couered ouer with a glasse And on the highest edges of this base the two braunches of the Mastel shal be made fast and this base with the Mastel the halfe circle and the circle shal be all one peéce which â—halbe called the seate or frame of the instrument The Horizontal circle in the ends of one halfe circle must haue two holes in the which may enter the Axis that are made in the ends of the lyne of East West Also you must take good heéde when you sother or make fast the Mustel in the base that the North and South of the plate or Horizon come with the North and South of the néedle that is beneath hauing euer respect how much the neédle doth vary from the Meridian by Northeasting or Northwesting In the ioynt of the two halfe circles vpon the Mastel must be a poynt called the index or shewer whâ—ch shal shew in the halfe circle sothered in the place on y e neâ—ther part the degrées that the Pole is raysed aboue the Horizon For the perfection of this instrument it shal be conuenient to set the Horizon very playâ—e and equal at the time of the operation or practising with the instrument and this may be done in two maners Whereof the one is hanging by a fine threéde at the center of the plate a plomet made somewhat poynted at the neather ende so that the Horizon standing playne leuel the poynt of the plomeâ— may â—al vpon the poynt of the index and this maner is good for the land But for the Sea you shall sother the Horâ—zon two Axâ—s little stubbes or endes comming foorth These shal be put in the two opposite holes of a circle of mettall made somewhat strong and this circle must haue other two stubbes lykewyse comming foorth and equally distant from the two holes These must be sothered or nayled in two holes of another circle in like maner and the other circle with other two stubbes inclosed in a boxe If then the boxe stand euen and leuel the poyse or waight shall cause the Horizon to stande leuell although the Ship sway or roule from side to side The vse of this instrument is in this maner When you desyre to knowe the paralel in whiche you are and the houre that is put the lyne that trauerseth the graine in the degree of the signe in the which the Sun is which you shal knowe by the â—able of the place of the Sunne in the seconde Chapter of the second parte and set the North and the South of the plate with the North and South of the néedle Then turne the moueable Meridian against the Sunne the foote of the instrument standing fast and rayse it or put it downe in the plate vntill the beame of the Sunne enter in at the hole of the graine and fall in the center of the plate and standing so behold the index and how many degreés it sheweth from the Meridian so much is the altitude of the Pole Then looke where the moueable Meridian sheweth in the rundel of the houres and there shall you sée the houre that is Heere foloâ—eth the demonstration ¶ The xii Chapter of the leagues that are runne for a degree according vnto diâ—ers courses IN the sixth Chapter I promised to geue a rule to knowe the distaunce from one paralel to another sayling by whatsoeuer lyne or wynde except the East and West for the whiche is to bée vnderstoode that the Nauigation or course from one place to another according to the Cosmographers ought to be by the arke of the greater circle for that by this maner shal be the shortest course and this greater circle they deuide into 360. degreés and al the distances that are froÌ„ one place to another they accompt by the degreés minutes of this circle and so sayling from North to South to one degreé of the variation of the height of the Pole shal answeare another degreé of the greater circle in the superficiall part of the water and land And therefore sayling by whatsoeuer other line vntill the Pole doth vary one degreé of altitudes we shall haue gone more then one degrée of the greater circle and the degreés that aunsweare to euery lyne or winde you shall seé in the demonstration folowing which hath two paralel lynes whiche are East and West and the lyne that cutteth them in ryght angles which commeth foorth of the center from the quarter of the circle that is made is North and South and then shall you seé by this order all the other wyndes halfe wyndes and quarters of wyndes reduced to one quarter For the selfe same accompt serueth for Northeast and Southwest and Northwest and Southeast and so of the halfe windes quarters of winds that are equally distant from the line of the North and South and so this quarter shall serue for all the 32. wynds of the compasse Without this quarter harde by the lyne you shall finde two numbers wherof the first shal be of the degreés minuts of degrées of the great circle which is