breadth and in colour The causes are diuers and those either fabulous or naturall The fabulous causes are in number 4. The first is taken from the scorching of the ☉ as if the ☉ had sometimes made his motion there and by his scorching had caused that place to be white The second is drawen from the milke of Iuno that running plentifully out of her pappes painted this circle of that colour The third is fetched from the seate and habitation of strong and valiant men whom the Poets haue placed in this circle The fourth is deâ—iued out of the way of the Gods as if they passed thereby vnto the pallace of Iupiter The naturall causes alleadged although they be many yet are principally but 3. The first by Theophrastus who said that it is that ioyning together wherby the heauen being diuided into two hemispheres is as it were by a certen claye fastened The second by Aristotle who tooke it to be a Meteore set on fire in such sorte as a Comete The third is Astronomicall which affirmeth that it is a girdle caused by many little starres as it were one touching another in the which concurring in that Place the light of the Sunne is diffused The distinct starres that make it are cheiflie these The Arowe the Eagle the bowe of â™ the Altare the 4. feete of the Centaure the ship Argo the head of the Dogge the right hand of Orion Erichthonius or the Wagoner with the Goate on his shoulder Perseus Cassiopeia and the Swanne Of the 5 principall Regions of the worlde commonly called Zones Chap. 29. THe Vniuersall Globe aswell of the heauens as of the earth answerable thereunto is distinguished into certain orbicular tractes which the spaces comprehended betweene the 4. paralleles do make of which tractes we may consider the names the definition the generall nuÌ„ber and their distance one from another Their names are diuerse For they are called either Zones or swadling bandes or girdles or Mashes or coastes They are defined to be the space either of the heauen or of the earth compreheÌ„ded between two lesse paralleles or els included on euerye side with the polare circles Their generall number is twofolde For either they are celestiall and so the causes of the terrestriall or els they are terrestriall of the same proportion with the celestiall The celestiall are either Meane or Extreme or betweene meane and extreme The Meane is that Zone which is included betweene the 2. tropickes and is cut in two equall partes by the Equator The Extremes or polare Zones are those wherof being but 2 the one is called the Septentrionall Zone within the Arcticke circle the other the Meridionall Zone within the Antarcticke circle The Zones between meane and extreme are also 2. whereof the one is Septentrionall comprehended betweene the tropicke of ♋ and the circle Arcticke and the other Meridionall comprehended betwene the tropicke of ♑ and the circle Antarticke The terrestriall Zones haue the same reason with the celestiall aswell in respect of their nuÌ„ber as in regarde of their names The terrestriall Zones are also 5. in number answering proportionallye vnto thé 5. celestiall Zones conically marked out by the 4. celestiall paralleles The terrestriall Zones haue the same reason with the celestiall in respect of their names also For that terrestriall Zone that is vnder the mean celestiall is called meane those which are vnder the extremes or polares are called extremes septentrionall or Meridionall and those which are vnder the Zones betweene meane and extreme haue their name accordingly and are either Northerlie or Southerlie The distance one from another is in this manner the meane or burnt Zone according to the Latitude reconed in the Meridian conteineth 47. gr or 705. miles the extreme intemperate Zones do each of them according to the said reconing conteine as many degrees and miles as the meane the temperate zones betweene meane and extreme do eache of them conteine according to the former reconing 41. gr or 645. miles The difference of the Zones and the manner how all places Vpon the earth may be brought within their compasse Chap. 30. THe difference also of the zones as well celestiall as terrestriall and the reason how all places vpon earth may be referred vnto them is worthie the noting Their difference is to be considered either in respect of their figure or their accidental nature The figure of the meane is vniforme and for the most parte alike The figures of the extremes are either of theÌ„ equall to other yet such as that they seeme rather to carie the shape of circles then of zones The figures of the zones betweene meane and extreme be either of them alike and equall vnto the other yet about the tropicks their figure is limited with a greater compasse then towarde the polare circles The accidentall nature of the zones is that in regarde wherof they are saide to be meane extreme and betweene meane and extreme The Meane or burnt zone is diuided into 2. partes whereof the one is situated vnder the Equator the other about the Tropickes That parte which is situated vnder the Equator seemeth to be temperate and that for three causes 1. By reason of the sodaine and crosse accesse and recesse of the Sunne 2. By reason of the continuall equality of the night and day in that place 3. By reason of the swift carying about of the ☉ by the first motion That parte which is situated vnder the Tropickes is hardlye to be inhabited and that also for 3. causes 1. For the slowe conuersion of the ☉ 2. For the doubled proiection of the Sunne-beames vpon those places 3. For the great increase of the Sommer daies aboue the nights The extreme zones are both of them frozen by reason of the too much colde that falleth out there by meanes of the oblique proiection and reflexion of the Sunne beames The zones betweene meane and extreme are both of them temperate and are diuided into 3. Regions whereof one is situated about the middle parte thereof which we iudge simplie to be temperate by reason of the moderate heate of the ☉ namely from 34. gr vnto 48. gr distance from the Equator the other 2. regions are about the extremes therof the one being about the tropicks and so subiect vnto the intemperate heate of the burnt zone the other nigh vnto the polares and therfore subiect vnto the intemperate colde of the frozen zone The reason how al places vpon the earth may be referred vnto those zones hath two considerations 1. If the places haue Septentrionall Latitude and that lesse then the greatest declination of the ☉ they belong vnto the burnt zone if equall vnto the trop of ♋ if greater and yet not exceeding ♋ gr 30. mi. they belong vnto the temperate zone If the said septentrionall Latitude be equall vnto the complemeÌ„t of the greatest obliquation they must be placed vnder the arctick circle if greater vnder the frozen zone 2. If the
is called ciuile or naturall the other artificiall In the ciuile or naturall day we may consider the definition the distinction and the cause of inequality The definition respecteth either the name or the thing it selfe It is called either naturall as caused by the naturall or regulare motion of the whole or 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 by Prolemee as consisting of the night and day together or els ciuile because all nations naturally do tearm it a day The definition respecting the thing is that according to which it is defined to be the space of 24. howers and certen minutes consisting of light and darkenesse The definition thereof is in respect of the continuance and length of the day and thereof one is called inequall or different also the true and apparent day the Greekes call it 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 irregulare another the equall or meane day The inequall or different daye is the space of 24. howers and so many minutes as are answerable vnto each portion of the zodiak which the ☉ doth daily run ouer The equall or indifferent day is the space of 24. howers and so many minutes as are answerable vnto the quatity of the meane motiō of the ☉ in one day which is 59. gr 8. mi. The cause of the inequality happeneth vnto the true naturall day either in a right or in an oblique sphere The cause of the inequality happening in a right sphere is through the inequall augmentation by meanes either of the Equinoctiall ascensions inequally answering the same by reason of the obliquitie of the zodiak orels of the motiō of the ☉ which about the cētre of the world is inequal The cause of the inqualitye of the day happening in an oblique sphere is through the inequall augmentation apperteining either to the Equinoctiall ascensions inequally answeringe the same by reason of the obliquity aswell of the Horizon as of the zodiake or else to the eccentricke circle of the ☉ wherin the ☉ running doth in equall tymes perform an inequall motion The Artificiall day is handled in the Chap. folowing Of the artificiall day and night and the diuersitie belonging to them both Chap. 37. THe ☉ caried about by the first motion distinguisheth the naturaall day into two partes whereof the one is called the artificiall day the other the artificiall night Concerning the artificial day Astronomy deliuereth the definition and the proportion thereof The definition conteineth the Author and the terme thereof The Author of the artificiall day is the ☉ who caried about by the first motion describeth in the day time a certen arke The terme is either from whence that is from the Easterlie part of the Horizon or by what that is by the verticall meridian or vnto what that is vnto the Westerly part of the Horizon The proportion of the artificiall day is deliuered in so much as apperteineth vnto the length thereof either in a righte or in an oblique sphere In a right sphere it is alwaies equall vnto it selfe and to the night by reason of the equalitie both of the Ascensions for the one halfe of the Equator doth alwaies equally ascend and descend with sixe signes of the zodiake and of the diurnall and nocturnall segments In an oblique sphere the dayes to themselues and to the nights are either equall or inequall The dayes are equall both to themselues and to the nightes in the Equinoctiall by reason of the equality both of the ascensions for looke how great the ascension of the diurnall arke is so great also is the descensiō of the nocturnal of the segments which the ☉ describeth the said segments being incident with the Equator The daies are inequal both among thēselues and to the nightes when the ☉ hath passed the Equinoctiall poincts aswell by reason of the diuersity of the ascensions of the signes as also by reason of the Sunnes inequall describing of the paralleles by the motion of the world The artificiall night geueth vs to consider the definition and the measure It is defined to be the part remaining of the naturall day comprehending the space between the setting of the ☉ and the rising thereof The measure thereof is either equall or inequall The equality of measure falleth out in the right sphere alwaies in an oblique sphere two times in the yeare The inequality of measure hath notwithstāding either a like diuersity in the signes equidistant frō the Equator or alternate in opposite points Of the reason of the equall and inequall howers Chap. 38. HAuing thus set downe the description of the dayes it falleth out nowe to intreat of their partes commonly called howers whereof we must consider the generall reason and the diuision The generall reason attendeth their definition their number and their subdiuision They are defined to be that space of time wherin the 24. parte or 15. gr either of the Equator or of the Eclipticke do fullie arise They are in number 24. belonging vnto euery naturall daye Euery hower is subdiuided into 60. minutes euery minute into 60. seconds c. The diuision of the howers consisteth in this that either they are reconed in the Eclipticke or els in the Equator Those that are taken in the Eclipticke the ascensions whereof do varie are called inequall howers whereof the names the definition and the number are to be noted They are called naturall by Io. de sacro bosco and temporall and artificiall and Planetarie They are defined to be the space of time wherin the moitie of a signe of the Zodiake counted from the place of the ☉ or the opposite thereof doth ascende Their number is as much by day as by night For 6. signes of the Ecl. do alwaies arise aswell by day as by night The howers that are reconed in the Equator which ariseth vniformelie are called equall howers whereof we are in like manner to note the names the definition and the number They are called naturall by many and equinoctiall howers They are defined to be that space of time whe◠in 15 gr of the Equator do fully arise Their number is alwaies inequall sauing in the 2. Equinoctiall seasons For at other times 6. signes of the Equator do not euerye daye completely arise and set Of the diuers accidents of diuers partes of the earth according to the diuerse situation of the Sphere Chap. 39. THe situation of euery place and region on the earth is in the space either of the burnt or temperate or frozen zone The places situated in the burnt zone are either in the meane spaces or betweene meane extreme or in the extremes Their situation that are in the meane spaces differeth from the rest 1. In the 4. sortes of shadowes which they haue viz. Septentrionall Meridionall Orientall and Occidentall 2. In their 4. solstices which they haue two being highest in ♈ ♎ and two lowest in ♋ ♑ 3. In their continuall Equinoctialles 4. In their two Winters and two Somers Those that haue their
on the one side longer from whence are deriued figures long and broade as pillers or cylinders or els they are of other sortes which are infinite from whence diuers formes and kindes of bodies are drawen The regulare bodies conteined vnder surfaces folded one toward another are onely these 5. the Tetraedrons the Hexaedrons the Octaedrons the Dodecaedrons and the lcosaedrons Irregulare bodies are such as inequall surfaces do limit and describe the which surfaces are either turned rouÌ„d or folded one toward another The surfaces turned round and making irregulare bodies are either the sections of circles or els they are inequall right lined figures The sections of circles are either greater then a semicircle wherof the lenticulare bodies are made or els they are lesse then a semicircle and therby are the Onalles made The inequall right lined figures by whose coÌ„uersion the irregulare bodies are made may be of what sorte soeuer wherby diuers kindes of vessels are framed either wanting or exceeding the regulare forme The Irregulare bodies mà de of inequall surfaces folded one toward another may differ infinitely Of the name and definition of the Sphere Chap. 6. IN as much as we make often mention of the Sphere and thereafter do intitle this present treatise the doctrine of the Sphere it shall not be amisse to declare the name and the definition therof The name is vsed in diuers significations 1. It signifieth sometime any solide regulare bodie limited with one surface onely 2. Sometimes it signifieth an instrument that doth instisie the apparences of heauen and conteineth the celestial circles and is otherwise termed a ring or materiall sphere 3. Sometimes it signifieth the whole worlde wherunto all the coÌ„ditions of the sphere may be applied For it is a solide bodie wherin nature abhorreth that any emptines should be giuâ— It hath a sphericall forme running dayly about his owne Axis without intermission It hath a point placed in the midst therof namely the earth The definition thereof as it signifieth any body is by Io. desacro baseo set downe two waies the one after Encl. 11. Elem. the other out of Theodosius The definition thereof taken out of Euclide conteineth the Geometricall description of the sphere For the sphere is described by the fixed and vnmoued diameter and by the aâ—ke of the semicircle which must be fully brought about The definition of a sphere according to Theodosius determineth first the orbiculate forme euery parte whereof is equally distant from the centre secondly the principall partes as the conuexe surface which is but one and the centre that is the point in the midst equidistant from euery parte of the surface and the Axis about which the sphere is tourned and which is limited by the 2 poles viz. The North pole or pole Arctick and the south pole or pole Antarcticke and thirdly the soliditie For it is a complete body hauing all the dimensions The diuision of the celestiall Sphere Chap. 7. THe celestiall sphere according to Io. de sacro bosco admitteth a double diuision according to substance and according to accident The celestiall sphere considered according to the substance is diuided into seuerall orbes in the which we are to note the number and the cause The number is diuersly set downe For the ancientes contenting themselues with 8. orbes only did distinguish them into the orbes of the 7. Planets viz of ♄ ♃ ♂ ☉ ♀ ☿ and ☽ and the firmament of the fixed starres And the later Astronomers vnto the time of Alphonsus into 9. orbes but the Moderne among whom Purbachius was the first added the tenth The cause is considered either in the diuersitie of their number noted both by the former and later Astronomers or in their order The ancient Astronomers noted their diuers number either by the brightnes of the Starres reconing so many orbes as they perceiued to conteine any starres or by the peculiar motion of each seuerall orbe reconing so many orbes as they found simple motions belonging thereunto The later Astronomers for instruction and the better reconings sake added the ninth and the tenth as circles necessarye for the vnderstanding of the motion of the 8. sphere vnknowne vnto the ancient Astronomers The order is proued 1. by the slower motion of the higher and the swifter motion of the lower orbes 2. by the occultation or hiding of the higher starres by the lower 3. by the diuersitie of apect either great or little or insensible The celestial sphere considered according vnto accident that is according to the situation of the heauen or the course of the starres is distinguished into a right or an oblique sphere The right sphere belongeth vnto those that dwell vnder the Equinoctiall who by reason that the poles of the world about the which the starres are carried by the firste moueable haue none eleuation as also for that the Horizon cutteth all the paralleles vnder which the stars do goe at right angles perceiue no reflexion in the diurnall motion of the starres The sphere is said to be oblique wherein the O and the rest of the starres are caryed from the East into the West by an oblique motion and it is Septentrionall vnto those that haue the North pole eleuated and Meridionall vnto those vnder the Southerne eleuation The partition of the whole worlde and the comparison of the celestiall with the Elementall Sphere Chap. 8. THe whole frame of the worlde is made of some certain and those more principall and notable partes wherof there is first the number and the name and then the difference to be considered The number and name is double For the partes are either ethereall or sublunare The aethereall that is the celestial parte without the which Philosophie admitteth nothing to be although the Diuines do adde the third which they call Angelicall and the Platonickes intellectuall is that wherof we intreated in the 7. Chapter The sublunare is that which conteineth the elementall bodies and those either simple as the fire the aer the water the earth or els mixed which are diuerse and innumerable ingendred of the 4. elementes either perfect or imperfect The difference or dissimilitude of the partes of the worlde is that whereby they are distinguished one from another either in respect of their situation or of their dignitie magnitude motion or their office They are distinguished according to their situation For the celestiall parte hath obteined the higher place the elementall the lower Their distinction according to dignitie is noted in the partes conteined by the celestiall Region which partes are bright and immortall and by the elementall region those partes being of their owne nature obscure and decaying or els it is noted in the partes conteyning wherof the one is altogether with out alteration neither increasing nor diminishing the other is continually subiect vnto generation and corruption and is increased and diminished Their distinction according to their magnitude is considered in that the celestiall parte with the great
argument is deriued from the consutation of 2. opinions wherof the one supposeth thà t the motion of the heauen is direct and instnite which if it were the starres should vanishe out of our sight The other that the starres in their setting are quenched and in their rising are lighted againe as Heraclitus affirmed which is absurd both in respect of the motion which is perpetuall and constant in it selfe and of the contrary power which cannot be in the earth as also in regarde of our Antipodes whose West is our East The second argument is drawen from the dignitie thereof For the circulare motion is the most worthye and more perfect then the right motion inasmuch as it breedeth no scission or cutting and is made about the midst of the whole not by displacing the whole bodie but by the onlie vnchangeable succession of the situation of the partes The criculare figure of the Heauen is proued partely by similitude and partely by reasons The similitude is this namely that this sensible worlde is the image of the first Archetype or paterne of the worlde who is without beginning or end The reasons do containe either the commoditie of the circulare figure or the necessitie The commoditie consisteth either in the capacitie or els in the swistnes or aptnes vnto motion The capacitie was sit for the heavens in that they were to comprehend all other things Fot the circulare figure is the grated of alother circumscribed with equall conneâ—ities The sâ—â—stâ—es or aptnes vnto 〈◊〉 is either belonging vnto the diâ—â—nall motion called also the right hand monon nature all vnto the 〈◊〉 storels vnto the second motion which resisteth the former Their asons drawen from the necessitie of the circulare figure are either in respect of the whole world For if the 〈◊〉 were of any other figure there must needâ—s be some emptie place and a body without a place for elsan regarde of the celestiall oâ—bes which gather could not be tarned about by diuerse motions or els they shuld suffer a scission or cutting in sunder not without their greate hurt There is one sarface of the earth and water and that is round Chap. 12. THe earth and the water make one globe and it is proued by causes either generall or speciall The generall causes belong vnto both the elements made vp in one forme and are deriued from 3. heades First from the signification of the worder For both in common speach and in the scriptures it is called Orbis terra the Globe of the earth or the round world Secondly from the Sphericall forme aswell of the Heauen into whose round compasse inasmuch as it is included it cannot be but it must also be round as also of the shadowe that this globe doth cast forth For the Maisters of Perspectiue do teach vs that such is the darke bodie as is the shadowe therof Thirdlye from the naturall descending of the portions either of the earth the saide portions coueting the centre of the Globe and falling vpon the surface of the earth at right angles or els of the water sinking also into the centre of the worlde for the which their discending they gather themselues into a round forme and cannot abide vpon a plane surrace The speciall causes are such as decerne the roundnes of the earth and of the water particularely The roundnes of the earth is decerned two waies The one is according vnto Longitude from the Last toward the West or contrarywise and that either by all the starres which in diuers places do not appeare at the same instant or els cheâ—sely by the ☽ whose Eclipse falleth out at one and the same time but by those in the East reconed one way by those in the West another The other is according vnto Latitude from the Equator towarde each pole gathered by the vnlike eleuation of the Pole and inequall quantitie of the daies both which increase vnto those that goe from the Equator towardes the North or South The roundnes of the water is decerned by tokens deriued from the swelling of the droppes either hanging or throwen vpon the dust or laide vpon the mosse of boughes as also from the swelling of the Sea by meanes whereof the Land cannot be seene from the Shippe belowe although from the maine toppe it may and againe if any shining thing be sastened to the top of a ship saying faire from the shore it deseendeth by little and little according as the Shippe runneth further off and at the last is hidden from the sight The situation immobilitie and magnitude of the terrestriall Globe Chap. 13. THe earth or globe of the earth and water hath situation rest and magnitude The situation as being in the centre or the place of the worlde farthest distant from the extremities thereof is proued by arguments either direct or indirect The direct are deriued from the nature of the broken partes expressed either Physicallye or Astronomically Physically because wheresoeuer they are about the earth we alwates obserue them that of their owne inclination they tende downewarde But the centre is the lowest place Astronomically inasmuch as all the semidiameters of the worlde by which heauy thinges descende are continued through the centre of the worlde and there they cut one another So that where the section is made there must needs be the place of the earth The indirect arguments consist in two suppositions The one that the earth were in the Axis of the motion of the Heauen towardé one side then should be taken away the apparent reason of the middle Heauen the reason of the shadowes Equinoctiall Solstitâ—all and plagall and the reason of the vniuersall Equinoctialles The other supposition that the earth were without the Axis remoued from the poles either to the East or to the Westwarde and then shal be taken away both in the rising and setting the equall quantitie both of the dares shadowes and starres The Rest of the earth excludeth al locall motion either right or circulate The right motion is that which is made from the midst and it is either naturall and peculiar vnto the earth For otherwise it should come to passe that heauy things should ascend or els it is violent some outward thing insorcing it For otherwise it should come to passe that the earth should forsake the centre of the world The earth hath no circulare motion neither from the West to the Eastwarde as some haue thought For if it had all things that are moued in the aer should alwaies be moued to the westward Neither from the last to the Westward by the dâ—â—n nall motion For then it should be an harder matter to trauaile toward the East then toward the west The magnitude of the earth is nothing being compared either with the whole world wherof it is the centre which is proued by Mathematicall instrumentes that agree with the centre of the world For they at one time and through the same sight hole shew two Starres opposite in the
Diameter or els being compared but with the orbe of the ☉ which is proued by the equall spaces of the dayes and nights The measure of the compasse of the earth Chap. 14. THe circuÌ„ference of the Globe of the Earth and water is found out by the rule of foure proportionall numbers in which rule 3. numbers are giuen and the fourth is vnknowne The three numbers giuen which conteine the proportion of a segment of a celestiall circle vnto the like space on the earth are 1. the difference of Latitude 2 the viatorie distance 3. the circumference of the whole heauen By the difference of Latitude is vnderstoode so many celestiall degrees as any terrestrial places are distant asunder The viatorie distance is that terrestriall space of waye that is answerable vnto one degree or any other difference of Latitude and it is found out 3 manner of wayes First by the distance of any two places vpon the earth situated vnder one meridian the said distance being precisely tryed Secondly by the latitude of both places either obserued by instruments or taken out of Tables Thirdlye by subducting the lesse out of the greater for so the difference of latitude shall appeare whereunto the space of way knowen betweene the places geuen shal be answerable Whereby vnto each degree of a great circle in the heauen there are answerable vpon the earth after Ptolemee furlongs 500. passes 62500. greater leagues 15. After Eratosthenes surl 700. pass 87500 leag 21. â…ž The circumference of the whole heauen conteining 360. gr is the 3. number in the proportion 1 for that of a little and of a great globe there is the like reason 2. because the terrestriall meridian hath the same centre with the celestiall The fourth number of the proportion that is the circuit of the greatest circle in the earth hath 2. considerations The first is the maner of the searching thereof and that is first by multiplying the third number that is the circumference of the heauen by the second which conteineth the space of way vpon earth and then by diuiding the product by the first which is the difference of latitude The second consideration is of the quotient or manifestation of the content which according to Prolemee is miles 22550. furl 180000. pas 22500000. greater leagues 5400. according to Eratosthenes miles 61250. furl 252000. pass 61250000. greater leagues 7875. The measure of the Diameter and Semidiameter of the earth as also of the Area and Surface thereof Chap. 15. IN measuring the terrestriall Globe wee conder either the Diameter or the Semidiameter or the Area or the connex surface thereof The Diameter is measured by the proportion thereof vnto the whole circumference by the rule of foure proportionall numbers wherein againe three are geuen and the fourth is vnknowen The three numbers geuen beeing throughlye knowen and vnderstood must be duely placed and they must conteine two things The first is the proportion of the circumference of a circle vnto the Diameter thereof which is tripla sesquiseptima that is to say the circumference is vnto the Diameter as 22. is vnto 7. The second is the greatest circuit of the earth in any measure which was set downe in the 14. Chapter The fourth number of the proportion being vnknowen is the Diameter which is sought first by multiplying the thirde by the second which is 7. diuiding the product by the first which is 22. then by subducting the 22. parte which commeth forth of the diuision of the circumference by 22. out of the circumference diuiding the remainder by 3. whereupon ariseth the content of the Diameter after Ptolemee conteining miles 7159 〈◊〉 furl 57272 〈◊〉 pass 7159090 10 11 greater leag 1718 〈◊〉 After Eratosih mâ—es 19488 7 11 fur 80181 〈◊〉 pass 1948863 〈◊〉 greater leag 2505 〈◊〉 The â—emidiameter is the distance between the conuex surface of the earth and he centre therof which some do imagine to bee the place of helly the said distance is found two waâ—es 1 By the proportion of the circle vnto the Semidiameter which is sâ—â—tuple ouer and beside 1 14 or as 44 is vnto 7. 2 By diuiding the Diameter into two parts by which meanes it shall bee found to conteine after Ptolemec miles 3579 ½ furl 28636 passes 3579545 greater leag 859 1 11 After Eratosthenes miles 9744. furl 40090 ½ pass 974431. greater leag 12â—2 ½ The Area or plane is founde by multiplying halfe the circuit of the earth taken in anye knowen measure by the Semidiameter thereof The conuex surface that couereth the whole earth is founde by multiplying the terrestriall Area or plane by 4. The generall definition and diuision of the circles Chap. 16. IN as much as the surface of the Heauens is spherical and their motion circulare therfore for the better conceiuing of the reasons of the celestial motioÌ„s they are distinguished into certaine circles as partes whereof we are to shew the names the diuision In the names we are to consider their acception and their diuersity being notwithstanding all one in signification The acception of the name Circle is of two sortes Geometricall and Astronomicall The Geometricall acception is when a circle is taken for a plane figure which one line equally distant from the centre doth encompasse The Astronomicall acception is other as it signifieth a circular line or a circumference wanting breadth or else a circulare surface which hath breadth therunto adioyned The diuersitie of names all one in meaning is when circles are called amongest diuers Authors threds compasses orbs segments rings paralleles equidistant lines The diuision of circles is diuerslye deliuered by the Greekes and Latines in three respectes First in respect of the materiall sphere within the which some of the circles are not placed are therefore called extrinsecal sixed and manisold as the Horizons and the Meridians others are placed within the sphere are therfore called intrinsecall moueable and singular as are the two polares the Equator the zodiak the two colures and the two tropickes Secondly in respect of the poles of the world or the twofolde motion of the heauen and in this case the Greekes distinguish them againe into three sortes The first are paralleles in number 5. namely the 2. polares the 2. tropicks and the Equator all which haue the same poles with the world are equidistant on all sides and serue the fyrst or vniuersall motion The second are oblique circles in number 3. namely the Zodiak seruing the second motion the Horizon the milke way all the which lye oblique betweene the poles The thirde are those circles that are drawen through the poles and they are also 3. in number namely the Equinoctiall and solstitiall colure and the Meridian The thirde diuision of circles is in respecte of their quantity according whereunto some circles are called greater and some lesse The greater circles are in number 6. namelye the Equator the Zodiak theâ— Colures the Horizon and the Meridian all which are equall
Equator and true place of the starie It is diuided into the Septentrionall and Meridionall declination The relation that the starres haue vnto the Zodiake is also two folde either according to the Longitude of the Zodrake or els according to the transuerse distance towarde either of the Poles In the Longitude of the Zodiake we are to consider the name and the definition It is called Longitude For that it is recoued longwaies on the circumference of the Eclipticke it is also called the true motion of the Starre It is defined to be the Arke of the Zodiake intercepted betweene the head of ♈ and the section of a great circle passing through the poles of the Zodiake and the true place of the starre In the transuerse distance we are to note the name the definition and the diuision It is called Latitude because it is reconed according to the position that it hath from some one side of the Ecliptick It is defined to be the arke of a great circle drawen through the poles of the Zodiake and the true place of the starre the said Arke being intercepted betweene the Zodiake and the centre of the Starre It is diuided into the Septentrional Latitude when the starres are vnder the northerly signes and into the Meridionall Latitude when they are in the Southerly signes Of the propertion and supputation of the declination of every point of the Eclipticke or the regarde of the partes of the Zodtake vnto the Equator Chap. 20. IN the declination of any point of the Eclipticke 2. thinges are to be obserued the proportion and the supputation In the proportion we may note also 2. things For either they haue none obliquation or els their obliquations are equall Those that haue none obliquation are the head of ♈ and ♎ as being the common intersections of the Equator and the Zodiake Those that haue equall obliquations are such as are equally distant from the Equator and they are either greater obliquations or els the greatest The greater obliquations are those that haue any distance lesse then the greatest from either of the sections and of that sorte there are alwaies foure The greatest obliquations are those that haue the greatest distance from the Equator as the head of ♋ that s the Somer solstice and the head of ♑ that is the winter solstice The supputation is made either by the tables of declinations or of Sines The Tables of declinations are calculated in sundrye places by Astronomers and they consist of the 2. sides the Area and of the two extremities or endes The sides are either at the right hand or at the left that at the left hand to be entred into whe you haue the signe in the toppe of the table and that on the right hand when the signe is in the foote therof The Area is that wherein at the common angle the declination is found The 2. extremities are those that conteine the signes of which extremities the one is called the toppe or vpper parte the other the foot or the nether patte of the table The supputation that is made by the table of Sines is performed by the helpe of the rule of 4. proportion all numbers wherein 3. numbers are giuen and fourth is to be sought out The 3. numbers giuen must conteine the right sine of the whole quadrant or of the semidiameter the right sine of the greatest declination of the ☉ and the right sine of the distance of the point of the Eclipticke giuen from the first section of the Zodiake and the Equator The fourth number produced by multiplitation and diuision is the right sine of the declination sought whose subtended arke declareth the number of degrees Of the 2. circles called the colures distinguishing the Equinoctiall and Solstitiall pointes Chap. 21. FOrasmuch as there are certaine pointes of the Zodiake and the Equator more notable then the rest therfore the Astronomers haue thought good to fit vnto those pointes 2. Circles wherof we may consider the reason of their name their definition their number their figuration or description and their vse They are terméd colures that is imperfect in 3. respectes 1. Because they appeare alwaies incomplete or maymed the which thing notwithstanding semeth to be common with diuers other circles 2. Because they haue some partes that do neuer arise 3. Because they are carried about after an imperfect manner not according to the position of Longitude as the motion of the Heauen is The definition conteineth their magnitude their intersection and their motion As touching their magnitude they are of the number of the greater circles As touching their intersection they cut one another in both the poles of the world at sphericall right angles In their motion they are moued together with the sphere Their number is two wherof the one passeth through the Equinoctiall pointes and the poles of the world and is called either the equinoctial colure or the distinguisher of the Equinoctialls the other passeth through the solstitiall pointes and the poles both of Eclipticke and of the worlde and is called both the solstitiall colure the distinguisher of the Solstices and also the circle of the greatest declinations Their figuration is described by the semidiameter of the worlde whose reuolution being fullye perfourmed through the poles of the worlde and the Equinoctiall pointes maketh the Equinoctiall colure but passing through the poles of the worlde and the solstitial points it maketh the solstitiall colure Their vse is manifolde but principallye in 3. thinges 1. In distinguishing the Equinoctiall and Solstitiall pointes 2. In reconing aswell the quantitie of the greatest declinations of the ☉ by the arke intercepted betweene the Equator and the Eclipticke as the space comprehended between the poles of the worlde and the poles of the Ecliptick which is alwaies equall vnto the arke of the greatest declination 3. For better vnderstanding of the ascensions and descensions of the signes Of the Meridian Chap. 22. THe ☉ carried about by the first motion whē it is at the highest designeth a point of a circle whose definition varietie and office we are to consider The definition taketh holde both of the names thereof and of the matter it selfe It is called the circle Meridian Meridionall and Merinoctiall the circle of the midday and midnight either because it diuideth both the day and the night into 2. equall partes the one ascending the other descending or els because so often as the ☉ according to the first motion is vnder the Meridian it is then either midday or els midnight The matter it selfe is that according whereto it is defined to be one of the greater circles drawen through the poles of the worlde and the verticall point of any place geuen and standing still when the Sphere is moued The varietie of the Meridian by reason of the round figure of the earth is either none at all or manifolde It is none at all either in regarde of reason or of sense It is
situation betweene the meanes and extremes do as the former differ from the rest 1. In the double passage of the ☉ ouer their heads but not in the heads of ♈ ♎ 2. In their foure shadowes and Solstices although not happening at the same time as in former situation Those that haue their situation in the extremes of the burning zone do differ from the other 1. In that the Sunne commeth but once vnto their Zenith 2. in the length of their greatest day which is 3. ho. ½ Those places that are situated within the temperate Zone are either in the extremes or in the meane The extreme spaces are those that are vnder either the trop of ♋ wherof we spake before or the Arcticke circle Those that are vnder the Arcticke circle do differ frō other 1. In that they haue the Zodiake coincident with their Horizon and the pole therof with their Zenith 2. In that the signes do arise vnto them either most swiftlye or most flowelye 3. In the length of one day consisting of 24 howers Those that are situated within the meane spaces of the temperate zone do differ from others 1. In their verticall point which the Sunne neuer cometh vnto 2. In their shadowes which are onlie 3. Those places that are situated within the frozen Zone are either in the meane spaces or in the extremes Those that are within the meane spaces of the frozen zone do differ from other 1. In the interfection of the Zodiake and the Horizon in equidistant pointes 2. In that some portion of the Zodiake is alwaies either aboue the horizon or vnder the same Those that are within the extremes of the frozen zone are either vnder the Arcticke circle whereof we speake a little before or vnder the pole Those that are vnder the pole do differ from other 1. In their Horizon which is all one with the Equinoctiall 2. in their daye which is halfe a yeare by reason that the one moitie of the zodiake doth alwaies appeare aboue the horizon Of the diuersitie of the names of the inhabitantes Chap. 40. THe inhabitants of the earth compared one with another haue diuerse appellations by reason aswell of the shadowes of the ☉ as of the Horizon or paralleles and meridians The shadowes cast by the ☉ vpon the earth at Noone are either infinite or none at all or els they are finite The shadowes that are infinite or equidistant vnto the beame are cast in the frozen zones whose inhabitants are called Periseti that is shadowed round about because their shadowes do goe in compasse round about them Those that haue no shadowes at Noone tide are in the burnt zone whose inhabitants are named either Aseu because when the ☉ is in their Zenith they haue no shadowe at all or els Amphiscii hauing 2 shadowes the one Septentrionall when the Sunne goeth from them toward the South the other Meridionall whē he passeth from them toward the North. Those whose shadowes are finite are named Heteroscii as hauing but one of those shadowes either Septentrionall as in the Septentrionall temperate zone or els Meridionall as in the Meridionall temperate zone whereof Lucane maketh mention As concerning the inhabitants of the world whose comparison one with another standeth vpon the Horizon or the paralleles and Meridians we haue 5. thinges to consider 1. Some of them haue the same sensible Horizon whome Albertus calleth Simul habitantes dwelling together 2. Some of them do dwell vnder the opposite pointes of the same parallele and are called proprelie by the Greekes Pertoeci as if you would say dwellers about of the Latines Transuersi dwellers on the other side 3. Some of them dwell vnder the same parallele but not in the opposite pointes hauing a diuerse Longitude whome Albertus calleth circulare dwellers 4. Some of them dwell vnder the pointes of the same semimeridian equidistant from the Equator hauing a contrarye Latitude and are called Antoeci or Antomi also oblique inhabitantes 5. Some of them do inhabite an equall or also the same parallele but vnder the pointes of the Meridian diametrallie opposite and are called Antipodes Antichthones and opposite The distinction of the Surface of the earth according to the length of the dates Chap. 41. FOr the more exact knowledge of the longest dayes in euery place of the world sensiblie changing them selues the Astronomers haue deuised the distinction of paralleles and of Climates The paralleles offer vnto our consideration their definition and their supputation They are defined to be circles distinguishing the climates and distant one from another at the most but quarters of howers Their supputation is diuerse deliuered by 3. sortes of Geographers 1. By the common Geographers which do distinguishe the space of the earth from 12. gr 45. mi. vnto 50. gr 30. mi. into 15. paralleles attributing vnto eache one of an hower 2. By the Mariners who in like manner do recon 14. paralleles distinguished by quarters of howers from the Equator vnto 45. gr but then they proceede by halfe howers vnto the 19. parallele and then by adding on whole hower they come vnto the 21. prrallele 3. By the more subtile Geographers who make 48. seuerall paralleles from the Equator toward the pole of the world vnto the 66. gr 30. mi of eleuation and from thence augmenting them by dayes they adde 20. more The climates are to be considered in their definition in their diuision in their number and in their magnitude The definition is thus A climate is a space of the earth included within 3. paralleles conteining the difference of ½ an hower Their diuision is either general or particulare Their generall diuision it that in regarde whereof some of them are called Northern climates and some Southerne The Northern climates haue their propre names deriued from the places through the which they do passe The Southerne climates are those that are named by the contrarie Their particulare diuision is that in regarde whereof euery one of them is diuided into 3. paralleles the first the middlemost and the last parallele Their number is knowne through the supputation of the paralleles Their magnitude is inequall aswell in respect of their Longitude as of their Latitude Their Longitude toward the Equator is greater by reason of the greater compasse of circles and towarde the poles it is lesse by reason of their lesse compasse Their Latitude is inequall in respect of the space of degrees that halfe an hower doth conteyne and it is greater about the Equator by reason of the almost equall compasse of the degrees and lesse about the poles by meanes of the narrowe inclination of the roundnesse of the earth Of the light and of the shadowes and their differences Chap. 42. FOrasmuch as there hath bene often mention made of the shadowes it shall not be amisse if we set before your eyes the methodicall description thereof and seeing that contraties are by their contraries made more manifest we will declare the nature of the light and
of the shadowe The nature of the light is shewed by the definition the diuision and the cause thereof It is defined to be the image or the beame of the bright light It is diuided either into the first and principal or the secondarie and reflexed light The first and principall is that which proceedeth directly from the light body and is either perpendiculare or oblique The perpendiculare light is that by the fall whereof right angles are made The oblique light is that which falleth not at right angles The secondarie or reflexed light is that which from one side spreadeth it selfe on al parts without any falling of the beames The cause of the light is either the Elementall bright light whereof here we teach nothing o◠the celestiall The celestiall bright light is that which either causeth the shadowe as that of the ☉ of the ☽ of ♀ or els which hath no power to make any shadow as the light of the of the other Starres The nature of the shadowe is declared by the definition and by the diuision thereof It is defined to be a light diminished or a certen forme of a darke body alwaies contrarie to the body casting the light The diuision thereof is two folde the one drawen from the coastes of the worlde the other from the position of the darke body The shadowe taking the appellation from the coastes of the worlde is of 2. sorts The one is extended toward some coaste and it is either Orientall or Occidentall or Meridionall or Septentrionall The other is perpendiculare or a right shadowe by a perpendiculare which is not extended as it is vnto those that haue the ☉ in their Zenith The diuision deriued from the position of the darke bodie is that in respect whereof one shadowe is called right or extended another reuersed The right shadowe is that which is caused by the darke bodie perpendicularelie erected vpon the terrestriall plane The reuersed shadowe is that which is caused by the darke bodie that is parallele vnto the Horizon Of the Eclipses in generall Chap. 43. OF al the apparēces of the heauen the Eclipse is the principall and therefore we will declare the generall reason of the same by the definition and by the termes thereof The definition is either barelye and planelye propounded or els it is more largely expressed The plane definition thereof is that whereby it is defined to be the taking away or the hindering of the bright light so that it cannot come vnto the eye The larger expression thereof is thus vnto euery Eclipse there belong 3. thinges a bright heauenly light our sight and a shadowy or dark bodie The bright heauenly light was formed by the Creator for the expelling of shadowes and it is twofolde a greater and a lesse The greater is that of the ☉ shining of it selfe The lesse is that of the ☽ casting about as out of a looking glasse her light borowed of the ☉ Our syght is diuerse according to the diuerse position thereof vppon the round compasse of the earth The shadowy or darke bodie is also twofold viz. the bodie of the ☽ the one moitie whereof the ☉ enlighteneth not and the earth whose shadow is alwaies opposite vnto the ☉ The termes of the Eclipse which in this kinde of doctrine the Astronomers do vse are in number three The first is the quantity of the bodie either of the ☉ whose visuall diameter as a chord doth subtende in the Auge of his eccentricke 31. mi. and in the opposite thereof 31. mi. or else of the ☽ whose apparent diameter doth in the Auge of her eccentricke and epicycle subtende 29. mi. and in the opposite thereof 36. mi. The secōd is the quantity of the shadow which the motion of the ☉ through either Absis doth canse to varie aswell in regard of the longitude from the surface of the earth which for the most part conteineth 276. semidiameters of the earth as also in respect of the latitude which also in the place of the ouerthwart crossing of the ☽ is diners both in respect of the ☉ beeing in either Absis and of the ☽ which in her opposition is either in the Auge of her epicycle and then it is 75. mi. or in the opposite thereof and then it conteineth 94. mi. The third is the quantity of the termes eclipsed either of the ☽ which are 15. partes 12. mi. or of the ☉ by reason of the Parallux of the latitude of the ☽ being either about the South and it is 11. gr 22. mi. or about the North being 20. gr 40. mi. The particular description of the Eclipses Chap. 44. THe beames therefore both of the ☽ and of the ☉ may be hindered from shining vpon the earth The beames of the ☽ being borowed may bee hindered by the comming of the earth and the shadow thereof betweene the ☉ and her and that maketh the Eclipse of the ☽ whereof wee may consider the time wherein it happeneth the continuance thereof The time of her eclipse is when shee is at the full when the ☉ being in opposition with the ☽ driueth the shadowe either according to the longitude as euerye moneth it commeth to passe or els according to the latitude whiche falleth out when the ☽ is either within or nigh vnto the Nodi that is the head and taile of the Dragon In the continuance it is to be considered that the staye of the ☽ in her darkening is either long or short The long stay is with her whole bodie when her opposition falleth out precisely in the Nodi The short stay is when she is distant from the Nodi and then her body is darkened either all or halfe or lesse then the halfe Shee is darkened wholly when shee hath her latitude lesse then the semidiameter of the shadow by the quantity of her apparent semidiameter Shee is darkened halfe when she hath her latitude equall vnto the semidiameter of the shadow Shee is darkened lesse then the halfe when she hath her latitude greater then the semidiameter of the shadow The beames of the ☉ are hindered by the interposition of ☽ and that is called the Eclipse of the ☉ wherein wee may haue consideration of the tyme wherein it happeneth the diuersitie thereof and the difference thereof from the Eclipse of the ☽ The time wherein the ☉ is eclipsed is in the new ☽ at which time she seemeth to haue a diametrall coniunction with the ☉ aswell in respect of longitude as of latitude The diuersitie thereof is in that it is eclipsed either wholly or lesse then all The ☉ is wholly eclipsed when the ☽ beeing in visible cōiunction with the ☉ is in the Nodi The ☉ is eclipsed lesse then wholly when as the ☽ being in visible coniunction with the ☉ hath latitude but yet lesse then 35. mi. or els when the semidiameters of the ☉ and the ☽ are ioyned together The difference of the Eclipse of the ☉ from the eclipse of the
compasse thereof doth couer all thinges like a thing without measure and ende but the elementall parte is couered within the compasse of the heauen the diameter thereof conteining the diameter of the earth 23. times Their distinction according to their motion is in that the celestiall parte hath a circulare and a sphericall motion the elementall a right motion more imperfect then the circulare Finally they are distinguished according to their office For of those thinges that are ingendred in the elementall parte the heauen working by a continuall motion is as it were the formall and efficient cause from whence life is deriued and the elementall parte which is subiect vnto passion and alteration is as it were the materiall cause from whence nourishment doth proceede The reason of the sublunare or elementall Region Chap. 9. THe Elementall region which the heauen encompasseth comprehendeth within it the elements wherin we are to consider the definition the number and the situation or order The elements are simple bodies aswell in respect of the mixt bodies which are vnderstoode to be compounded of them as of the simple and least partes as also in respect of the diuision for that they cannot be diuided into bodies of diners kindes if they be giuen pure and without mixture For the vse of liuing creatures and things growing doth make them impure The elements are 4. in number found so to be by sense and by reasons The elements are found to be soure by sense which the Physicians doe sollow First for that more simple bodies cannot be shewed 2 nature hath alotted vnto them certaine places to the end that other things might by thē be bred and nourished 3 nothing els can euidently be shewed wherof other things may be made 4 in liuing cretures there are certain parts agreable vnto the natures of the seuerall elements The Elementes are found to be foure by two reasons the former whereof is drawen from the number of the foure prime qualities and the foure folde possible knitting together of them For heate may be ioyned either with drinesse which two make fire or els with moisture which two do make vp aer and colde may be ioyned with moisture as it commeth to passe in the water or with drinesse as in earth The later reason is taken from the fower folde difference of the right motion For the elements are directly moued either vpwarde or downward Such things as moue vpward as light thinges do are said so to do either simplie as the fire which is the lightest of the rest or respectiuelie as the aer which is lighter then the water or the earth Such things as moue downeward as heanye things do are said so to do either respectiuelie as the water compared vnto the fire and aer or simplie as the earth which is the heauiest of all the rest The situation and order of the Elementes is found either by their motion or els by the communication of their qualities And first by the motion For inasmuch as the fire and the aer do naturally moue vpward the fier shall occupy the highest place the aer an vpper place and for that the water and the earth do naturally moue downward the water shall possesse a lower place and the earth the lowest Againe the order of the Elements is found out by the communication of their qualities for it were vnsit that such things as are merely contrary but such as in some sorte can agree together should be nigh one another The fire therefore shal be ioyned vnto the aer by reason of the heate common vnto them both the aer vnto the water by reason of the common moisture and the earth vnto the water by reason of coldnesse common to them both The two folde differences of the celestiall motions Chap. 10. THe whole frame of the world is caried round about with 2. motions each of them being distinguished from the other in name and in reason The one of them is called the first and vniuersall motion likewise the diurnall or worldlye motion because it bringeth the day vnto the world For in this motion the ☉ and all the celestiall bodies do euery day arise and set they call it also the violent and rapt motion because by the violent swiftnes thereof it carrieth with it the rest of the Spheres The other is called the second and particular motion altogether contrary vnto the former as by which all the particular orbes do resist the vniuersall motion They call it also Sinister motus the motion to the left hand as the former is in like sorte called dexter that is the motion to the right hand The 2. motions are also distinguished according to the reason or the substance in the which they are inherent For they differ the one from the other three waies The first difference is in respect either of the whole For the diurnal motion is common vnto all the celestiall bodies or els of the partes or starres either fixed or wandring which haue a motion peculiar and propre vnto themselues The second difference is either in regarde of the situation of the Axes For the diurnall motion is made vpon the Axe and poles of the world and therfore the Equator diuideth it in the middle but the propre motion is made vpon the Axe and poles of the Zodiake and therefore the Zodiake doth cut it in the middle Or els it is in regarde of the position of the termes inasmuch as the diurnall reuolution is made from the East vnto the west or as Plinte termeth it from the right towarde the lefte hand but the propre reuolution is from the West vnto the East or from the left toward the right hand The third difference is in consideration of the swiftnes For the diurnall motion fulfilleth his course within the space of 24. common howers but the propre motion in diuers distances of time according to the largenes of the orbes namely the orbe of the fixed starres performeth his circle in 36000. yeares of ♄ in 30 of ♃ in 12 of ♂ in 2. yeares of the ☉ in 365. dayes and about 6. houres of ♀ in 384. dayes after Plinie the orbe of ☿ in as many dayes as the ☉ and the orbe of the ☽ in 27. daies 8. howres The circulare forme and circulare motion of the heauen Chap. 11. THe Heauen is circulare in motion and in figure The circulare motion of the Heauen is proued as well by 2. experiments as by 2. argumentes The one experiment is taken from the starres of the 8. orbe which both in their rising setting do alwaies keepe one the same habitude both in regarde of the earth and one to another which thing can agree with none other then a circulare motion about the centre The other experiment is also taken from the starres of the 8. orbe alwaies appearing and retaining in diuers places the same distance from the Poles and onestom another which also agreeth with the circulare motion onelie The first