the other foure degrees and nine minutes vnder it And they are deuided by certaine lynes equidistant to the East and West In y e center of this circle is annexed a horne with his seuen stars moueable round about by all the windes And seeing them in heauen how in what wind they are euen so in this figure shal we seé the North starre in what part it is of the degrees high or lowe from the pole that the Pilot or Mariners shall not erre I say that he ought not to put the foreguard in the windes that passe through the center of the figure for it shal be North and South with the pole and not with the starre of the North as it ought to be and so of the other windes And in this maner the starre of the North shall shew in the lynes equidistant from the lesse circle the degreés partes of degreés that it is higher or lower then the pole of the world for the same course differences and variations it maketh in heauen ¶ This figure is after the Astronomers Which affirme that thâ— North starre is four degrees and nine minutes from the Pâ—lâ— Thus being knowen how muche the North starre is vnder or aâ—oue the pole let vs take the altitude thereof and that of if that is vnder the Pole let vs ioyne to his height and as muche of it as is aboue let vs take away and that shall rise thereof shall be the altitude of the Pole aboue our Horizon The xi Chapter of the composition and vse of an instrument by the which without obseruing the South Sunne or mid-day is knowen the altitude of the Pole and the houre that is WE haue geuen rules whereby the Pilotte may knowe in what paralel he findeth himselfe with his Shippe But hee may not knowe this at all houres for as muche as for the altitudes of the Sunne it is necessary to obserue the mid-day iustly and for the altitudes of the North it is necessâ—ry to obserue that the foremost guarde be placed iustly with the North in some of the foure lynes of the eight wyndes And ouer and besyde the rules aforesaide I haue thought good to describe an instrument by the which may be knowen the paralel where the Shippe is and what the houre is at any time of the day by the beames of the sunne Make a rounde plaâ—e of Laâ—on or other conuenient mettall of the Diameter of a spâ—â—ne or more For the greater that it is the more precisâ— shall it beé and make in it two Diameters that may cut themselues in ryght angles vpon the center In the foure extreames or endes of these Diameters leaue foure rounde puncâ—es or poyntes that may serue for axis The one of these Diameters shal be called the axis of the world and the other the lyne of East and West This doone make of the same laâ—on a semicircular peéce of the thicknes of the plate or litle lesse and of the breadth of halfe a â—inger this must stand vpon an edge so that the coâ—â—ex part may come iustly with the halfe of the circumference of the plate to the whiche it must be nayled or sothered in the neather part of the plate the semicircle being raysed that the endes thereof may come with the endes of the axis of the world And this semicircle shal you deuide into â—wo equal partes and euery halfe into 90. degreés beginning from the halfe poynt toward the ende of the Axis of the world which are the Poles In lyke maner shall you makeâ— two circuler peeces of the bignesse of a peâ—ce of foure ryals of plate which thâ—y call rundels for the houres these must be made fast in the plate by the Poles of the worlde whiche may hold or beare them by their cenâ—ers And euery of these rundelles must be deuided into 24. equall parts and although not all yet the vppermost part of the plate And aboue in y e highest point of these diuisions you must write 12. because that there it shall shew the midday or noone And froÌ„ thence the afternoone houres must begin their numbers toward the West part and shall ende 6. houres in the halfe or middest of the ioynt of the circle with the plate In the other ioynt of the other part shall begin 6. of the houres before noone shal ende 12. in the â—ighest poynt You must also make another Semicircular peece of the breadth of a finger this must be playne or flat the concauitie or holownesse thereof equall to the Semicircle of the edge or syde of the plate and in the endes muste haue two holes wherein may iustly enter the poynts that come foorth of the circle for the houres which are the Poles of the world Also this Semicircle must haue two lynes one on the vppermost part and the other on the neathermost whiche may deuide the breadth into two equall parts This halfe circle likewise must be deuided into two equal parts by longitude with a â—â—auersed line which shal be called the Equinoctiall from this lyne to the inwarde part thereof must be counted 13. degreés and a halfe towarde the one part and as muche towarde the other parte of the 90. that euery halfe of the circle conteyneth And at euery part where ende the 13. degreés a halfe make a trauersed line so that from the one to the other may be 47. degreés And in this space shall you drawe certayne lynes equidistaunte with them of the middest that they and the middle lyne may deuide into 4. equall partes the breadth of the halfe circle Then looke in the table of the declinations of the sunne what declination haue the 5. degreés of Aries and that shall you accompt from the Equinoctiall towarde the one part and as much more toward the other making a lyne that may trauerse that of the myddest where that declination doth end and touch in the other two lynes And the same shall you doo at 10.15.20.25 and 30. wâ—ich is the end of Aries and beginning of Taurus and then the lyne shal trauerse al the breadth The like also shall yoâ— doo to Taurus and Gemini then in the spaces write the caractes of the xii signes beginning Aries from the Equinoctial toward the North Pole And then doo Taurus and Gemini end in the greatest declination beginning Cancer in the other part of it Then Leo and Uirgo do end in the Equinoctial where shal begin Libra Scorpio Sagittarius and in the other part Capricornus Aquarius and Pisces shall end in the Equinoctiall where Aries began This halfe circle must haue an opening or open place euen and iust in the middest from the Equinoctial vnto somewhat more then the greatest declinations and must be a litle broder on the inner part then without and not so brode as may come to the two lynes because it would then take away the graduation of the signes And in this open place
of December And heere wyll I not omit to say how in those times at these foure dayes that is to meane in the two Solstitialles and two Equinoctialles were celebrated or dyd chaunce foure marueylous thynges in the worlde For in the spring Equinoctiall which was at the xxv of March the Sonne of GOD was incaâ—nate and afterwarde borne of the Uirgin Marie in the Solstitiall of Wynter whyche was at the xxv of December In the Equinoctiall of Autumne whiche was the xxvii of September was conceyued blessed Iohn Baptist the cryer and precursour of Christ and was borne in the sommer Solsticiall that was the xxiiii of Iune And this is the syxth Moneth whereof Saint Luke speaketh in the Gospell Whiche thyng also Iohn Chrysostome doth veryfie saying that S. Iohn was borne when the dayes beganne to decrease and our Lorde when they began to increase And it may certaynely seeme woorthie to be had in memorie that in the sayde Equinoctiall of the spring Christ suffered Adam was created and loste the estate of innocencye Abel was slayne Melchisedech offered bread and wyne Isahac by Abraham was brought to be sacrificed Iohn Baptist was beheaded at Macherunta Peter delyuered out of pryson Saint Iames beheaded by Herode the good Theefe enioyed Paradise and the bodyes of many Saintes rose wyth Chryste And who so further desyreth more precisely to knowe the entraunce of the Sunne into Aries and into the other principall signes shall in the thyrde parte of thys woorke in the eyght Chapter fynde rules whiche shall bryng hym to the knowledge thereof Bâ—t â—o returne to our tyme I say that thys present yeere of 1545. the Sunne entreth into the fyrste degree of Aries at the tenth of Marche at foure of the clocke at after noone and into the fyrst degree of Taurus the nynth of Apryll 2. houres and 7. minutes and into Gemini the 11. of May 2. houres and syxe minutes into Cancer the 11. of Iune 14. houres 44. minutes into Leo the 13. of Iuly 3. houres 50. minutes into Virgo the 13. of August 9. houres 56. minutes into Libra the 13. of September 4. houres 4. miuutes into Scorpio the 13. of October 7. houres 13. minutes into Sagittarie the 12. of Nouember iust at noone into Capricorne the 11. of December 8. houres 16. minutes into Aquarius the 9. of Ianuarie 2. houres one minute into Pisces the 8. of Februarie 1. houre 30. minutes after midday that is to say from noone 1. houre 30. minutes And that we may in the yeeres to come knowe the day houre and minute in the whiche the Sunne entreth into euery signe we will followe this order Upon the dayes houres and minutes that the Sunne entreth into euery signe thys sayde yeere 1545. we must adde for euery yeere fyue houres and 49. minutes which with the 365. dayes which euery yeere conteyneth shal be the tyme in the whiche the Sunne accomplysheth his Reuolution And because that in the yeere of the Bisextile or Leape yeere is added to Februarie one day more to his 28. which he hath once in foure yeeres from 6. to 6. houres yf we shall take from the computation that whyche we haue geuen hym turning one day backward as shal be in the yeere 1548. and vppon that that remayneth shall returne in the yeere folowyng of 1549. to adde fyue hoâ—res 49. minutes and as much more euery other yeere folowing shal be a certayne rule for euer And it is to note that the degrees and minutes which wee haue touched before are properly for the Citie of Cadiz And yf we desyre to applye them for other Cities or places more Eastwarde then for euery xv degrees that they are distaunt from Cadiz in longitude we must adde one houre And yf for Cities or places more Wâ—stwardâ— in lyke maner for euery xv degrees we must take away one houre by reason of the course of the Sun by his rapte moouing from the East to the West For it is certayne that when with vs in Cadiz it is xii houres of the clocke tâ— them that are xv degrees Eastward from vs it is one of the clock and to them that are from vs xv degrees toward the West it is xi of the clocke Nowe that we haue Rules to knowe the entraunce of the Sunne into the xii signes thereby may we also knowe his entraunce into the foure Câ—â—dinall or principall signes whiche are they that determine and ende the Equinoctialles and Solstitialles whereby are caused the foure tymes of the yeere And forasmuch as the generall chaunge of tymes is by reason of the Sunne who by his comming neare warmeth by hys remayning dryeth with his departure cooleth and by his long tarying away causeth maystnesse we will shew the qualities of the principall windes elements regions humours and ages in one briefe Table and then consequently in an other will we describe the beginning middest and ende of the foure times of the yeere aswell in the monethes as in the heauenly signes The Table of the qualities of the Elementes Qualities Hot dry Hot moyst Cold moyst Cold dry Partes of the yere Sommer Spryng Winter Autumne Principall windes East South West North. Elements Fyre Ayre Water Earth Regions East South West North. 4. Humours Choler Blood Flegme Melancholy 4. Ages Youth Mans state Aged Age. The Table of the foure tymes of the yeere Tymes Beginning Myddest Ende Spryng Marche Aries Apryl Taurus May. Gemini Somâ—er Iune Cancer Iuly Leo. August Virgo Autumne Septemâ— Libra Octob. Scorpio Nouemb. Sagit Wynter Decemb. Capricor Ianua Aquar Februa Pisces The v. Chapter of the Moone and of her motions and properties IN the Chapters past of this seconde parte wee haue entreated of the Sunne and of his motions and effects as the most noble and principall luminarie In this present Chapter we wyll entreate of the Moone which is the second luminarie although in the order of the heauens she is the first and nearest vnto vs of all other Planets or Starres The Mâ—one therefore is a round body of heauenly substaunce solide and darke in respecte of the Sunne hauing no proper light of his owne but is apt to receyue light She is mooued from the West into the East according to the order of the signes euery day 13. degrees litle more or lesse and somewhat more then 10. minutes by the proper motion of the heauen or sphere vpon the Ares and Poles of the Zodiaâ—ke I sayd more or lesse because that ouer and beside the moouing of her deferent or circle which is moued euery day the aforesayd 13. degrees and 10. minutes almost 11. she hath an Eclipse where the Moone is fixed at the motion whereof sometimes she is moued more swâ—ftly and sometimes more slowly Neuerthelesse according to her selfe motion she maketh her course in 27. dayes and almost 8. houres and hauing no light of her owne she is lyghtened of the Sunne as manifestly appeareth
the Meridian Circle THE Meridian is one of the greate Circles imagined to trauerse the sphere by the Poles of the worlde cutting the same in two equall partes by the zenith or verticall poynt It is called Meridian for this effect that wheresoeuer a man becommeth and at what soeuer tyme of the yeere when the Sunne by the moouyng of the fyrste mooueable shall come to hys Mâ—ridian to hym shall it be hygh noone at mydday and is therefore alsâ— called the circle of the mydday It is also to be noted that there are as many Meridians or Meridian lynes as are differences or habitations by longitude so that they that dwell in the East haue other Meridians then they that dwell in the West So that the interposition of the arke of the Equinoctiall betweene the Meridian of one Citie and the Meridian of the other is called the difference of longitude from one Region to another and from one Citie to another as we wyll further declare heereafter The xiiij Chapter of the Horizontall Circle THE Horizon after the Astronomers is a Circle whyche deuydeth that parte of the heauen whyche wee doo see from the other parte whiche wee see not so that the sayde Horizon deuideth the Sphere of the worlde into two equall halfes called Hemispheres The halfe whiche wee doo see is called the Hemisphere superior and it whiche wee see not is called the Hemisphere inferior This Horizon chaungeth to them that mooue for as one doth mooue hys Horizon doth chaunge And heereof it commeth that how many places are vppon the earth and the circumference thereof it is possible there should be so many Horizons The Astronomers suppose the Horizon after two manner of sortes that is to say a ryght Horizon and an oblique or crooked Horizon The ryght Horizon is to them whose zenith or verticall poynt is directly in the Equinoctiall and thys ryght Horizon passeth by the Poles of the worlde and deuideth the Equinoctiall in ryght sphericall angles The other oblique or declyned Horizon haue they vnto whome the Pole of the world doth ryse aboue theyr Horizon This Horizon is also called oblique because it deuideth the Equinoctiall in vnequall and oblique or crooked angles Also it is to bée vnderstoode that the Pole of the Horizon is called Zenith or the verticall poynt of heauen perpendiculerlye or directly ouer our head Whereby is inferred that as much as is the eleuation of the Pole of the world aboue the Horizon so much is the distaunce of the Zenith from the Equinoctiall For the Zenith by all his partes is distaunt from the Horizon by niâ—ntie degâ—eés And all other impediments excluded we may euer seé halfe the heauen And in as much as any shall passe from the Equinoctiall toward the one Pole or the other so much falleth the Horizon vnder or beneath the Pole toward the course he entendeth and likewise as much shall it be raysed aboue the contrary Pole as shall appeare by a demonstration in the ende of this Chapter This Horizon is diuided by the Meridian into two equall partes that is to say the East and West partes of the sayde Horizon The Eâ—st part is where the Sunne and Starres beginne to aryse to vs and appeare in our syght The West part is where the Sunne and Starres doth set and begyn to be hydde out of our syght vnder the sayde Horizon Moreouer it is to beé vnderstanded that there be two manners of the East and West that is to say the true East and West or the vntrue The true East is the poynt in the East part of the Horizon where it doth cutte with the Equinoctiall for when the Sunne is in the poynts of the Equinoctiall then he ryseth in the poynt of the true East And lykewyse is to be vnderstand of the poynt of the true West to be in the West part of the Horizon where the Equinoctiall doth cutte with the sayde Horizon The vntrue East and West is variable accordyng as the Sunne ryseth and setteth dayly in dyuers poynts of the Horizon which is distant from the poyntes of the true East and Wâ—st sometymes more to the Northward and sometymes more to the South The xv Chapter of the foure lesse Circles HAuing entreated of the vi biggest Circles it remayneth to speake of the foure lesse Circles A lesse Circle as we haue sayde before is that whose superficiall diuideth the Sphere into vnequall partes not passing by the Center thereof And of these two are named Tropikes so named of Tropo the Greeke word which signifieth Conuertion because the Sunne comming to any of these Tropikes is conuerted and turneth toward the Equinoâ—tiall These Tropikes are described by the motion of the fyrst moueable with the poynts of the Solstitials The one with the beginning of Cancer and this is called the Tropike of Cancer or Eâ—tiuall or Sommer Tropike The other is described with the beginning of Capricorne and is called the Tropike of Capricorne or Hiemall or Winter Tropike These two Tropikes and the Polaâ— Circles whereof I wyll say more heereafter are called Paralelles so named for that they are equally distant by their circumferences one from an other as well as from the Equinoctiall The Polar Circles are described in this manner so that as the Zodiacke declineth from the Equinoctiall so do the Poles of the Zodiacke decline from the Poles of the world And as the eyght Sphere is mooued at the motion of the fyrste mooueable so shaâ—l the Zodiacke mooue whiche is parte of the Sphere And the Zodiacke being mooued his Poles shall lykewyse mooue aboue the Poles of the world And as the Poles of the Zodiacke are distant from the Poles of the world xxiii degrees and a halfe which is as much as the greatest declination they shal describe certayne circles distaunt from the Poles of the world in the selfe same xxiii degrees and a half These Polar Circles take their name or dominion of that Pole of the world that is most neere vnto them and therefore is the one called Artyke and the other Antartyke The xvj Chapter of the fyue Zones THE auncient Astronomers diuided the Sphere into v. Zones The fiâ—st from the Pole Artyke to the Circle Artyke The second from the Circle Artyke to the Tropike of Cancer The thyrde from the Tropike of Cancer to the Tropike of Capricorne The fourth from the Tropike of Capricorne to the Circle Antartike The fyfth from the Circle Antartyke to the Pole Antartyke Of these fyue Zones they haue certayne knowledge that two of the Poles were vnhabitable for extreame colde and also that the burnt Zone called Torrida Zona whereby the Sunne passeth by the middest of them should be vnhabitable for extreame heate That from the Tropike of Capricorne vnto the Circle Antartyke they called desart because they knew not that it was inhabited And this our Zone that is
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