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A29742 An account of the rotula arithmetica invented by Mr. George Brown. Brown, George, 1650-1730.; Dary, Michael. Dary's Miscellanies.; Cooke, Francis, fl. 1669. Principles of geometrie.; Georgius, Henisschius. Tables of the astronomical institutions. 1700 (1700) Wing B5019; ESTC R4627 82,687 247

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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 de●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 ♐ 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 nūber 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 comprehēded 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 nūber 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 thē 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 complemēt of the greatest obliquation they must be placed vnder the arctick circle if greater vnder the frozen zone 2. If the
generall reason is ether in respect of their names or their definition They are named by the Greekes 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Tropickes by the Latines Versiles conuersius Vertentes tourning and the Solstitiall paralleles Their definition conteineth their quantitie and their circumference Their quātity is noted either in respect of the other circles these being compted in the number of the lesse circles or in regard of thēselues whereby they are compted equall in asmuch as they are equally distant from the centre of the world beeing separated the one from the other by the double distance of the ☉ greatest declination Their circumference is that round compasse which the ☉ passing throughe the 2 solstitiall points doth describe They are in number 2. the one Septentrionall the other Meridionall The Septentrionall Tropicke is on this side of the Equator in respect of vs which wee call either the Sommer tropicke for that it passeth through the poinct of the Sommer solstice or●ls the tropick of ♋ because it is described through the end of ♊ the beginning of ♋ The Meridionall tropicke is situated on the other side of the Equator and is called either the Winter tropicke as passing through the poinct of the Winter solstice or the tropicke of ♑ because it is drawen through the head of ♑ The offices and commodities of them are in number 4. 1 They shewe the Tropes that is the conuersions or tournings of the ☉ aswel in Sommer happening in our age the 3. and 2. of the Ides of Iune as also in winter the 3. 2. of the Ides of December 2 They shew in euery situation of the sphere both the longest day which is as long as the diurnall Arke of the Tropicke of ♋ conteineth howers and the shortest day which is as long as the space of howers conteined within the diurnall arke of the tropicke of ♑ 3 They poinct out the limits of the course of the ☉ and his greatest declinations which are 23. gr 52. mi. as in the time of Aristarchus Ptolemee or 23. gr 28. mi. as it is now in our time 4 They shew the burnt zone which they separate from the temperate and the midst of the second climate which they call dia-Syenes and Anti-dia-Syenes Of the 2. polare circles Chap. 26. The two poles of the Zodiake carried about by the regulare reuolution of the vniuersall frame describe about the poles of the worlde two circles whereof the generall reason the number and the vse is to be noted The generall reason offereth to our consideration their name their definition and their accidents They are called the Polare circles either because they are described about the poles or by the poles Their definition by the Latines t is made by their quantitie and their circumference and plane Touching their quantity they are in the number of the lesse circles equall in all places Their circumference and plane is described either by lines drawen from the poles of the Zodiake vnto the Axe of the worlde at right angles and hauing by the daily motion a perfect reuolution or els they are described by certen semidiameters drawen from the centre of the earth vnto the poles of the Zodiak and turned about by the diurnall and nocturnall motion The accidentes of the polare circles do determine either their equality for they are paralleles compared either one with another in asmuch as they are equidistant from the centre or compared with the tropicks the Equator or else they determine their distance either from the next tropicke which is 43. gr or from the poles of the worlde which is equall vnto the ☉ greatest declination They are two in number The one Septentrionall the other Meridionall The Septentrionall Polare circle is described by the North pole of the Eclipticke the Meridionall by the South pole thereof The Septentrionall polare circle is called Boreall North of the North winde called Boreas and Arcticke and Septentrionall because of the 2. constellations the one of the greater beare called Arctos the other of the lesse beare called Septentriones which are nigh thereunto The Meridional polare circle is called Australl or Southerne of the South winde called Auster and Antarcticke ●s opposite vnto the Arcticke and Meridionall of the South part of heauen called Meridies Their vse is noted in that they comprehende the cold and frozen zones and the inhabitants of the earth called Perison whose shadowes goe round about them and on either side limite the the distances of the poles The Polare circles otherwise described according to the Grecians Chap. 27. THe polare circles are described either according to the greatest declination of the ☉ or the altitude of the Pole aboue the Horizon The greatest declination of the ☉ by means of the motion of inclination of the eight Sphere is diuerse For it was one in times past and is found to be another now and of such circles the reason is declared in the Chapter before The polare circles described according to the altitude of the pole require the consideration of their definition their varietie their offices and the manner of their description In defining the Arcticke polate circle we say 1. That it is the greatest of those circles which are alwaies in our sight that is of those which we may see at the same instant 2. that it toucheth the Horizon in one point 3. that it is altogether aboue the earth In defining the Antarctick polare circle we say 1. that it is equall and parallele vnto the Arcticke 2. that it toucheth the Horizon in one point 3. that it is altogether hidden vnder the earth The varietie is manifolde according to the didiuersitie of the climates For either they are not at àll as in a right Sphere it happeneth where excluding altogether the polare circles the Grekes recon 3. paralleles onlie or els they are and those sometimes either lesse equall or greater then the tropickes or els they are equal vnto the Equator and the Horizon For by how much the pole shal be higher by so much shal these circles be greater The offices and vse of the Arcticke circle is in that it sheweth the Starres that neuer arise ●nor sette of the Antarcticke circle the con●trary is to be conceiued The meanes of their description is by those Starres that in any Region do touch the Horizon Of the Milkie circle Chap. 28. OF all the circles there is none to be seene beside the Milkie circle which for that the Greekes do recon among the other circles we wil expresse the names the definition the causes thereof and the distinct Starres which make the same The names are diuerse as Galaxia the Milkie orbe or circle the Milkie Zone or milkie waye The Arabians dal it Matarati as it were a broad space or arke that moueth It is defined to be one of the greater circles oblique drawen or stretched toward both the Poles most brightly shining apparent vnto the sense inequall both in
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
doth ascende therewith and then it is said to haue an oblique ascension by reason of the more oblique angles that it maketh with the Horizon The culmination is defined either the passing of some poinct of the Zodiake or of the world by the Meridian circle or else the degrees of the Equator which with the portion of the Zodiake geuen passe through the Meridian The setting of a signe or of any poinct of the heauen offereth 2. thinges vnto our consideration the definition and the diuersity thereof The definitiō is either according to the name or according to the matter According to to the name it is called the descension or setting which wee measure by the arke of the Equator descending therewith According to the matter it is defined to bee the arke of the Equator cōprehended between the signe or poinct setting and the head of ♈ The consideration of the diuersity of settinge is either that a greater part of the Equator descendeth with the signe or poinct of the heauen and then it is said to haue a right or along and slowe descension or els that a lesse portion of the Equator setterh therewith and then it is said to haue an oblique or a short and swift descension Of the diuersitie of ascensions descensions and culminations in a right sphere Chap. 34. THe Zodiake in a right sphere is fitted vnto the equall conuersion of the Equator and together with the partes thereof passeth by the East or the West or the midst of heauen both in the quadrants or quarters and in the signes The quadrants in equall spaces of time do ascend and descend or do passe through the midst of heauen beginninge either at the Solstitiall poinctes namely at the heade of ♋ ♑ and compting to the end of ♍ ♓ or els beginning at the Equinoctiall poincts which are the heads of ♈ ♎ and compting to the ende of ♊ ♐ The signes applied vnto the motion of the Equinoctiall are considered either whole or in partes The signes considered wholly haue relation either vnto the Equator or vnto the Zodiake The signes in their relation vnto the Equator do ascend inequally For some of them doe rise rightly and some obliquely Those that haue right ascension are ♊ ♋ ♐ ♑ with the which there do coascende 32. gr 11. mi. of the Equator Those that haue oblique ascension are ♈ ♎ ♓ ♍ wherewith there doe coascende 27. gr 54. mi. of the Equator and ♉ ♏ ♌ ♒ wherewith there arise 29. gr 54. mi. thereof The signes in their relation vnto the Zodiake or considered seuerally apart haue ascensions either equall or inequall one vnto another They haue equall ascensions that come forth in equall times and they are either opposite in the diameter or equally distant from the Equinoctiall poinctes as are ♓ ♈ ♒ ♉ ♑ ♊ ♐ ♋ ♏ ♌ ♎ ♍ They haue inequall ascensions that neither are opposite nor equally distant from the aforesaid poinctes The signes considered in their parts haue also relation either vnto the Equator or vnto the Zodiake The partes hauing relation vnto the Equator do as before ascend inequally and that either rightly or obliquely The partes hauing right ascensions are comprehended within the foure signes nexte vnto the 2. solstitialles The partes hauing oblique ascensions are conteined within the signes next vnto the Equinoctiall poincts on each side Those partes of the signes that haue relation vnto the zodiake haue their ascensions partly equall and partly inequall Partes hauing equall ascensions are these the first degree is equall vnto the first degree of the opposite signe and the first degree vnto the last of another signe equidistant from the equinoctial poincts Partes hauing inequall ascensions are those in whom neither opposition falleth out nor equidistancie Of the diuersity of ascensions and descensions in an oblique sphere Chap. 35. IN the oblique situation of the sphere we consider either the proportion of the ascensions or of the descensions of the zodiake The ascensions are compared and applyed either vnto the Equator or one with another or vnto the ascensions of a right sphere Beeing compared vnto the Equator they are either equall or inequall vnto the ascensions thereof In their equality they are numbred either in the Northren semicircle from the head of ♈ vnto the end of ♍ or from the head of ♎ vnto the end of ♓ In their inequality they are reconed either in the whole semicircles beginning not in the Equinoctiall poinctes but els where or els the reconing is made in some of their partes In their comparison one with another they are either equall or inequall When they are equall they are reconed in some 2. concordant arkes of the Ecliptick as in ♈ ♓ 14. gr 50. mi. ♉ ♒ 18. gr 51. mi. ♊ ♑ 27 gr 16. mi. ♋ ♐ 36. gr 58. mi. ♌ ♏ 40. gr 57. mi. ♍ ♎ 40. gr 58. mi. in the latitude of 40. gr When they are inequall they are reconed either in parts not equidistant or in the semicircle either ascendent or descendent The semicircle ascendent is from the head of ♑ vnto the end of ♊ and that ascendeth more oblique and swift The descendent semicircle is from the head of ♋ vnto the end of ♐ it ascendeth more right and slow When the ascensions are compared vnto the ascensions in a right sphere they are either lesse or more oblique or greater or righter then the said ascensions in a right sphere The lesse or more oblique fall out in the North semicircle the greater or more right happeneth in the South semicircle the distance betweene the ascensions of each sphere is called the difference of ascensions The descensions of the Zodiake are vnto the ascensions thereof either equal or inequall They are equall either in regard of the moities of the Ecliptick comprehended betweene the equinoctiall poinctes or else according to the equidistant or opposite partes of the Zodiake The descensions of the Zodiake are inequall being compared either vnto the right sphere or vnto the same climate The descensions of an oblique sphere are more oblique then the descensions of a right sphere whereunto they are compared when as the ascensions in an oblique sphere are more right then in a right sphere The descensions of an oblique sphere are more right then the descensions of a right sphere when as the ascensions in an oblique sphere are more oblique then in a right sphere The inequall descensions of the zodiak compared vnto the same climate are to bee noted either in the parts of the Zodiake which descending oblique doe rise right such as are the parts of the descending semicircle or els in the parts of the zodiake which descending right do rise oblique and such are the partes of the ascending semicircle Of the naturall day and of the inequality and difference thereof Chap. 36. OVt of the premisses wee may not vnfitly deriue some matter concerninge the dayes whereof there are two sortes the one