from the Tropike of Cancer to the Circle Artyke they called inhabited or habitable And to haue more perfect knowledge hereof it is to imagine that the earth is diuided proportionally into fyue Regions or Portions which answeare directly to the sayd fyue Zones as sayth the Poet Ouid in this Uerse Totidemque plage tellure praemuntur That is And so many Regions are on the earth beneath Euery of these Regions or portions of the earth is situate vnder one of the fiue Zones aforesayd But whereas certayne men of aucthoritie haue moued the question whether the earth vnder the Zone from the Tropike of Cancer to the Circle Antartyke is desart or no Ptolomie and the Astronomers affyrme that it is vnpeopled But Aristotle Ouid in the second of his Metamorphoses Plinie also and Iohn de Sacro bosco affyrme the contrary as for the more certaintie thereof we knowe the experience of such as goe and come dayly from those partes Moreouer then this we knowe that that lande is not onely well replenished with people of good corporature and of white colour but the same to be also very rych in Golde For they that sayle to the East Indies touch in the cape of Buena speranza or Caput bone Spei which is in this Zone Likewyse the land of Brasile and the confynes of Rio de la Plata with all the coast vnto the straights of Magalianes euen vnto the 54. degrees of the south part This lande was discouered by Magalianes in the yeere 1520â— or 1521. whereby that is now weâ—l knowen by sight whereof Ptolome had no knowledge by heare say The â—â—rnt Zone called Torrida Zona they also described to be vnhabitable by reason of the greate heate thereof as Aristotle Pâ—inie and in maner all other ancient aucthors affirme whereof the Poet Virgil wryteth thus Quinque tenent coelum Zonae quarum vna corrusco Semper sole rubens torrida semper ab igne Which in the English tongue is thus much to say in effect In Zones fyue the heauens conteyned be Whereof the one with burning Sunne is red Scorching the Earth subiect to his degree That for the heate thereof it is vnhabited Lykewyse Ouide in his Metamorphoses toucheth the same saying Quarum quae media est torrida semper ab igne c. Yet that the burnt zone is inhabited and well replenyshed wyth people that lyue there we knowe so certaynely by the number of them that dayly passe too and fro the Indies of your Maiestie discouered in your most happie dayes that to say any thing to the contrary it should be a manifest errour and therefore is it greatly to be marueyled that certayne wise men haue affirmed these parts to bee vnhabitable whereas neuerthelesse they had knowledge of Arabia Foelix Aethiopia Tabrobana and dyuers other Regions situate vnder the burnt Zone Plinie wryteth that a Ship came from the sea of Percia by the Ocean round about Ethiope and came to the pyllers of Hercules which is now the Citie of Cadiz where at this present I write this briefe treatise They of Guinca Calicut Gatigara and Malaca lyue all vnder the burnt Zone and many of them lyue very long And doubtlesse many things ought to perswade vs that vnder the burnt zone the earth is furnished with all thynges perteyning to the lyfe of man for that in that region or portion of the earth is in maner continuall Equiuoctiall and the coldnesse of the night doth sufficiently temper the heate of the day Agayne they that inhabite vnder that Zone haue two Sommers and two Winters in the yeere whereby is concluded that the auncient aucthours erred not onely in affyrming this Zone to be vnhabitable by reason of the great heat thereof but in lyke maner erred in affyrming the Zone that is betweene the circle Articke and the pole Articke to be also vnhabited by reason of great cold The contrary whereof we may well affyrme knowing as we knowe that Island with part of Gothland Norway Russia and dyuers other Lands are inhabited and well peopled This is the figure and demonstration which foloweth The xvij Chapter of longitude and latitude and of the proportion which the lesse circles haue to the great circle THE Sphere or globe of the earth is also diuided in breadth and in length The breadth which is called latitude is by degrees for from the Equinoctiall to eyther of the two poles is 90. degrees The length which is called longitude is by the degrees of the Equinoctiall which is diuided in â—60 degrees The fyrst degree of longitude doth begin at a certaine Meridian which passeth by the Ilands of the Canares called the fyxed Meridian and the order of the numbring of the sayd longitude is alwayes toward the East By euery degree of the sayd longitude in the Equinoctiall may be vnderstanded a great circle called Meridian to passe eche one of them passyng and meeting the poles of the world so that the sayd great circles or meridians doth diuide euery paralel or lesse circle proportionally into 360. degrees but we must not vnderstand these degrees to be equall that is to say as great in one circle as in another for the greater the circle is the greater is the degree in it and the greater the paralel is the nearer it is vnto the Equinoctiall lyne Euery degree of the Equinoctiall conteyneth in longitude 60. minutes so likewise it is to be vnderstanded of the degrees of latitude which be diuided ech one into 60. minutes of latitude because the degrees and minutes in the great circles doo not differ in theyr bignesse the one from the other but the degrees in the paralels as they are distaunt from the Equinoctiall and come neare to eyther of the two Poles they diminish consequently so that one degree in the paralel of 7. degrees of latitude doth make in quantitie but 59. minutes and 33. seconds of the Equinoctial circle and to one degree in the paralel of 12. degrees of latitude goeth but 58. minutes and 41. seconds of the Equinoctial and to one degree in the paralel of 16. degrees of latitude there goeth 57. minutes and 41. seconds The Table of minutes which euery degree conteyneth in euery of the paralelles G M S G M S G M S G M S G M S G M S 1 59 59 16 57 41 31 51 26 46 41 41 61 29 5 76 14 31 2 59 58 17 57 23 32 50 53 47 40 55 62 28 10 77 13 30 3 59 55 18 57 4 33 50 19 48 40 9 63 27 14 7â— â—2 2â— 4 59 51 19 56 44 34 49 45 49 39 22 64 26 18 79 11 27 5 59 46 20 56 23 35 49 9 50 38 34 65 25 21 80 10 25 6 59 40 21 56 1 36 48 32 51 37 46 66 24 24 81 9 23 7 59 33 22 55 38 37 47 55 52 36 56 67 23 27 82 8 21 8 59 25
hereby that being in coniunction with the Sunne or neare vnto him we see her not lyghtened because the lyght which she then receyueth is onely her vppermost or highest parte whereby she directly beholdeth the Sunne forasmuche as he is in the fourth heauen and she in the first And departing from the Sunne by her propâ—r moouing the Sunne remayneth on the West part Then toward that part we begyn to see a lytle of the part of the Moone lyghtened and so more and more by lytle and lytle as she departeth farther from the Sunne And at thys tyme she hath her hornes or corners towarde the East because the Sunne is in the West During this tyme also she is sayde to increase or that she goeth increasing vnto the opposition whiche we see by the part of her which the Sunne directly beholdeth And so do we see her altogeather lyghtened and call it the full Moone Then passyng from the opposition she commeth nearer the Sunne by lytle and lytle beyng darkened and hyd fâ—om vs and lyghtened onely by her hyghest part and this tyme is calâ—ed the decreasing or wane of the Moone Then also hath she her hornes toward the West because the Sunne is in the East and this vntyll she turne agayne in coniunction with the Sunne and that we see her not lyghtened at all The Moone is lesse then the Starres or other Planets except Mercurie and lesse then the earth And yf any shall affirme the contrary saying that it is written in the fyrst of Genesis that God made two great lyghtes the greatest to geue lyght to the day and the lesse to lyghten the nyght as Dauid also affirmeth To this I answeare that the Moone beyng nearest vnto the earth appeareth vnto vs greater then she should do yf she were further distaunt from vs. And although she be great of lyght receyued as we haue sayde and bigge of body yet is she not great in respect of the other Starres And therefore the words of Genesis aforesayd may be vnderstoode to be spoken in such maner and phrase as holy Scripture often vseth to humble and apply it selfe to the weakenesse of our vnderstanding and grosenesse of our senses The vi Chapter of the coniunctions and oppositions of the Sunne and the Moone THE Sunne and the Moone are mooued vnder the Zodiacke with diuers motions The Moone with a swifter motion then the Sunne foloweth hym ouertaketh him and goeth before him vntill she place her selfe in Diameter with him And when she hath thus ouertaken him so that they are both in one selfesame degree of the Zodiacke then is the coniunction Then departing from him and being in equall degrees of the signes opposite according to the Diameter is the opposition To knowe the times of these coniunctions and oppositions is very profitable and necessarie for Mariners These times may be knowen in two manners One way by the Ephimerides or Almanacke or other tables or Lunaâ—ie instrumentes And by these meanes is knowen precisely the day houre and minute of the coniunction and opposition It may lykewyse be knowen by the rules of computation whiche are the rules that are knowen by memorie although not precisely as by the bookes aforesayde And heere is to be vnderstoode that from one coniunction to another accordyng to the halfe moouings of the Sunne and the Moone there passeth 29. dayes twelue houres and 44. minuts And consequentâ—y from coniunction to opposition and from opposition to coniunction the halfe thereof which is fourteene dayes 18. houres and 22. minutes To knowe theâ—e coniunctions by rules of computatâ—on is presupposed to knowe the golden number and by it the concurrent or Epacte The golden number is the number of nienteene yeeres In which time the coniunctions of the Sunne and the Moone make all their varieties in the times of euery yeere so that yf the coniunction were the twelfth day of Marche in this yeere of 1545. from this yeere in the nienteene yeeres folowing which shal be in the yeere of 1564. the coniunction shall returne to be at the twelfth day of Mâ—â—che It was fyrst called the golden number by the Egyptians who fyrste found the vse thereof and sent it to Rome written in golden Letters To fynde this number it is needfull to know his rootes which is this In the yeere that Christ our Lorde and redeemer was borne whereby we make this accompt the golden number was the number of one which was the yeere of the roote or begiâ—â—â—ng and the fyrst yeere of the byrth of Christ was two of the golden number So that ioyning to the yeeres of our Lord one of the roote or begâ—â—ning and from all take away the nienteene then the rest shall be the golden number And yf you desyre to make computation by a nearer roote take for the roote the yeere of 1500. when nienteene was the golden number and in the yeere of 1501. did begin one of the golden number and so consequently euer taking away the nienteene This present yeere of 1545. we haue seuen of the golden number And in the yeere of 1546. we shall haue eyght c. The golden number being knowen it is necessarie for thys computation of the Moone to knowe the concurrent The concurrent of euery yeere is the number of the dayes passed of the coniunction of the Moone at the beginning of Marche And theâ—e grow of the difference of the Solar yeere to the Lunar As the Lunar yeere hath 354. dayes and the Solar yeere 365. so hauing euery yeere eleuen dayes of difference which are added euery yeere vntyll they come to the number of thyrtie and passyng thyrtie those that do passe are of the concurrent The number of the concurrent of euery yeere is founde in this maner And the better to beare it in memorie you must imagine three places and these commonly are assigned on the thumbe As the fyrst place at the roote of the thumbe the second in the middle ioynt thereof and the thyrd and last in the toppe of the thumbe Then â—n the fyrst place put tenne in the second twentie and in the thyrd thirtie Then by the order of these places shal be compted the golden number As one in the fyrst place two in the second and three in the third returning foure to the fyrst place c. vntiâ—â— the golden number of that yeere for the whiche the concurrent is sought And the number of that place where the golden number endeth must be ioyned with the number of the golden number and that doth amount thereof shall be the concurrent so that it passe not 30. But if it passe 30. then that that is more then 10. is the concurrent of that yeere And heere is to be noted that the yeeres of this computation of the Moone begin at the first day of March and last vntyll the last day of Februarie so that this present yeere of 1545. by computation of the
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
the xii â—ignes The Eâ—uinoctial Colure The Solstitiaâ—â— Colurâ— Thâ— greatesâ— declination of thâ— Zodiacke Definition of the Meridian Circlâ— The mydday or noone Diuers Meridians Definition of the horizon hemisphere or horizon Diuers horizonâ— The ryght and oblique horizon Distance of the zenith from the Equinoctiall how the horizon is deuided by thâ— Meridian The true and vntrue East and VVâ—st The lesse Circles Tropykes Paralelles The Polar Circles The Poles of the zodiacke and Poles of the world The greatâ—â—â— declination of the Sunne The Artykâ— and Antartike The Sphere diuided into fiue zones Zones habitablâ— and vnhabitable The diuision of the earth according to the fiue zones of heauen An errour of Ptolomie and the Astronomâ—â— The land of Brasile The straights of Magalianes The West Indies People of long life vnder the zone Cold Regions habitable Island Gothlandâ— Norway Russia The diuisioâ— of the Sphere by longitude and latitude The degreâ—â— of the Equinoctial circlâ— Myleâ— Furlongs Leagues Grayne Fynger Foote Pase The degreâ—â— of the sea Cardes The diameter of the earth and water Diuision of the earth and water by Climates Diuersities of thyngs in diuers Climates What is â— climate Differencâ— of dayes The space of sâ—â—â—n climates The quantitiâ—â—f the lâ—ssâ— circlâ—â— The Latitude of Climates Dia Mâ—râ—â— Dia Sienâ— Dia Alexandros Dia Rhodos knightes of the Rhodes The Rhodâ—â— taken by thâ— Turke Dia Romes Dia Boristhenes Dia Rifeos The riuer Tanais Stoflerine The Meridian or South Climate A right line An angle 〈◊〉 A circlâ— The circumference of a circle The center of a circle Diâ—meter Seâ—icircle Zenith Eccâ—ntricke Epicicle Auge Opposâ—â—â— of Auge The Sunâ—e is the guyde in Nauigation The moouing of the Sunnâ— vnder the zodiackâ— The Sommer Tropicke Declination of the Sunne The Winter Tropike The cause of increasing and decreasing of the day and nyghtes The moouing of the Sunne in the center of his Sphere To fynde the true place of the 〈◊〉 The equâ—â—ion of the yeâ—re VVhat is the declination of the Suâ—â—e The entrance of the Sunne into the fouâ—â— principall signes The Latinâ— yeere The Eâ—uinoctialles in the yâ—ere of Christâ—s byrth The Solstiâ—â—â—ls â—our notable thyngs To knowe more precisely the entraunce of the Sunne into the foure principall â—ignâ—â— To knowe when the Sunne entreth into euery of the xii Signâ—â— Leape yeâ—râ— Variation of houres by the rapte mouing of the Sunne from the East to the VVest The entrance of the Sunne into the iiii principall signes causeth the chaunge of tyme. The Sunne and Moone are the principal luminaries The Eclipse of the Moone The coniunction of the Moone with the Sunne The Moone receyueth her lyght of the Sunne The aspect of the Moone to thâ— Sunne The increasing and opposition of thâ— Moone The bignes of the Moone The Moone is â—earest vnto the eâ—â—th The motion of the moonâ— The coniunction Thâ— oppositâ— To know thâ— times of oppositions and coniunctioâ—s To know the golden number The rootes of the golden number The concurrent The Solar and Lunar yeeres To fynde the number of the concurrent Epact To know thâ— dayes oâ— agâ— of the Moonâ— To know tâ—â— day of the coniunction To know the place of the Moone in the Zodiacke and what aspectes she hath with the Sunne The description of the Instrument The vse of the Instrument to fynd the truâ— place of thâ— Sunne To fynde the place of the Moone Fiue aspecteâ— of the Planets Coniunction Opposition Trinall quadrine Sextiâ—e To know thâ— place of the Sunne by thâ— rule of memorie To knowe in what degree the Sunne is The Eclipse of â—hâ— Sunne The Eclipse of the Sunne is not vniuersall â—ow â—hâ— Sunne is eclipsed in the whole or iâ— parâ— why the Moone seemeth somtime bigger and sometime lesse then the Sunne The Sunne is Eclipsed in coniunction the Moone in opposition The reuoâ—ution on oâ— the â—ight Sphere The Solâ—r yeere how the Egyptians painted the yeere The quantitie of the yeere The yeere of the hebrues The Greekes Iulius Caesar. Lâ—â—pe yeere Dayes of the yeâ—râ— Beginning of the yeere Ouid. bruma is the stay of the sunne in winter the winter solstitiall and shortest day of the yeere The Creation of the world Exod. xii VVhere the Christians begin the yeere Diuersitie in the number of the yeeres or the date Machomet The date of the Christians The Lunar yeere or moâ—eth Reuolution of the moone The deuisioâ— of the yeerâ— into twelue monethes The Lunaâ— moneth The moneâ—â— of peragratioâ— The moneth of consecutioâ— The mouing of the Suâ—ne and moone in coniunction To know the tydes by the aspectes of the Moone The illumination or change of the Moone Interlunium is the space of tyme in the which neither the olde Moone doth appeare nor the newe Moone is seene The weeke of the Iewâ—s The Romanâ—â— The Christians Ferine signifieth vacant daies or somâ—time holy or fâ—stiuall 〈◊〉 The naâ—â—â—all day The beginning of the naturall day The ende of the naâ—uâ—all day The artificiall day The nyghâ— houres natural and artificiall The hour natural or equal The houre artificial or temperal The day and nyght diuided into foure partes Interpretation of certayne places of the Gospell The night diuided into iiâ—â— quarters Four watches of the nyght how Mariners ought to watch To know the houres of the day by the Sunne The placing of the instrument The fynding of the Meridian lyne The eleuation of the Pole Dyals horizontall and verticall East â—est The Triangle The making of the Dyall houres of the horizontall Dyall Placing of tâ—â— Dyall The Meridian line of thâ— Dyall The making of the vertical Dyall The Guardâ— starres what is mydnyght Noone or mydday An errour The making of the â—nstrument The horne of the seuen starres whiche make the lesse beare To fynde the hour with the instrument The Mariners opinion of â—bbyng and flowing of the sea or tydâ—s Obseruation of the Moonâ— to know the tydes Eyght principall wyndes The Moone causeth the ebbing and flowing of the Ocean Sea The moouing of the Moone The shortning of the tydes An errour The variation of the tydes A Table to knowe thâ— variation of the tydes Signes of faâ—â—â— and sowle weather Some cal these the fiers of S. Elin and S. Nicolas wandring fyers engendred of exhalations and vapours Castor and Pollux what is smoke and flame Exhalations of the land and water Exhalations and vapours engendred in Shyps A shining flye A superstitious opinion of the Mariners A lye of the fryer preachers Psalm 67. Testimonie of auncient aucthours The buildyng of Rome The Romanâ— kyngs One lyght or fyre is an euill signe Two lyghtes Castor and Pollux an errour of the Mariners Psalm 68. why Eolus was fayned god of winds what is winde The foure principall or Cardinall wyndâ—s Luke xvii East Souâ—h west North. Collaâ—erall wyndes Twelue wyâ—des Eyght whole wyndes Diuision of the horizon by the foure principall wyndes Eyght halfe wyndes quarter windes The deuisioâ— of the windâ— xxxii windeâ— in alâ—â— The names of