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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
places giuen haue Meridionall Latitude the same Iudgement is to be pronounced of them as of the places vnder Septentrionall Latitude Of the fowerfolde rising and setting of the Starres Chap. 31. THe Poets and for the better parte all other Authors doe periphrasticallye describe the times of thinges worthie the noting by the Starres of heauen either rising or setting In their rising is to be considered the definition the subdioision The definition doth cheiflie consist of the name and of the matter The name in this place signifieth their first apparition vnto the e●e or their Ascension The matter is that according wherunto the rising of a starre is defined to be the apparition of any starre giuen which before could not be be seene as either being vnder the Horizon or hidden by the Sunne beames The subdiuision also offieth 2. considerations 1. That the starres do ascend or rise by the vninersall motion from the lower hemisphere vnto the Horizon either in the morning with the ☉ and then they are said to haue a morning a diurnall a cosmicall or worldly rising os els in the Euening at the ☉ setting and then they are saide to haue an euening a nocturnal a chronicall or acronychall rising 2. That the starres do rise by the 2. motion freed from the ☉ beames either before the rising of the Sunne and then they are saide to haue an Heliacall morning rising which commeth to passe in those starres that are flower then the ☉ or els after the setting of the ☉ and then they are saide to haue an Heliacall euening rising and that is in those starres that are swifter thē the ☉ In the setting of the starres there is also offred the definition and the subdiuision The setting is defined to be the occultation or hiding of any starre giuen either by the depression therof vnder the Horizon or by the ingression thereof into the beames of the ☉ The subdiuision consisteth in their setting and withdrawing from our sight which is done two manner of waies 1. By the first motion they descende from the vpper hemisphere vnto the lower either in the morning which is done cosmically at the rising of the Sunne and that setting as the rising also is referred vnto the ☉ and those fignes of the Zodiake which the ☉ possesseth or els in the euening which is done chronically at the setting of the ☉ and this setting as also the rising is referred vnto all the starres generally 2. By their propre motion at their entrance into the beames of the Sunne either before the sunne rising that is cosmicallye which happeneth onely vnto the starres that are swifter then the ☉ ot els after the setting of the Sunne that is chronically which belongeth vnto those starres onlie that are slower then the ☉ Another more easie and perfect distinction ef the risinges and settinges with the exposition of certen principles which are to be Vnderstoode for the reading of Authors concerning the rising and setting of the Starres taken out of Ptolemee and the later Astronomers Chap. 32. FOr the easier vnderstanding of the Poets and other Authors which by the rising and setting of the starres do circumscribe the times 4. things chieflie are to be knowne 1. The latitude of the place wherof the speach is made which may be gathered out of the Tables of the Regions set downe in all Geographicall writings 2. The place of the ☉ in the Eclipticke at any time which the ancient Recordes do minister where notwithstanding you must note that our age doth differ from former times and that the ☉ in our age doth entre into the heades of the signes sooner almost by 6. daies then in the ancient times 3. What signes are opposite one vnto another viz. ♈ to ♎ ♉ to ♏ ♊ to ♐ ♋ to ♑ ♌ to ♒ ♍ to ♓ 4 The difference of the rising or of the setting The rising is either Heliacall and of the Morning or Acronychall and of the euening The Heliacall or morning rising is either true or apparent The true Heliacall rising is when a starre ioyned with the Sunne doth together and at the same instant arise with him in the morning The apparent Heliacall rising is when the star doth ascende and begin to appeare at the dawning and before the Sunne rising The Acronychall or euening rising is also either true or apparent The true Acronychall rising is when a starre precisely riseth at the very instant of the Sunne setting The apparent Acronychall rising is when after the setting of the Sunne the starre being freed from the beames thereof shall make his first apparence in the twilight The setting of a starre is also either Heliacall or Acronychall The Heliacal setting is either true or apparēt The true Heliacall setting is whē a star at the ☉ rising doth at the same instant set in the opposite part of the world which before was called the morning starre The apparent Heliacall setting is when in the morning somewhat before the ☉ rising the starre is newly seene to set The Acronychall setting is in like sorte either true or apparent The true Acronychall setting is when at the ☉ setting the starre also setteth which all the meane time was called the euening starre The apparent acronychall setting is when after the setting of the ☉ the starre doth not set at the same instant with the ☉ but by reason it is hidden by the beames of the ☉ it appeareth no more vntill the morning that it arise againe Of the Astronomicall rising setting of the signes or as the Greekes call it 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Chap. 33. THe rising the comming vnto the Meridian and the setting of the signes or of any point of the heauē is either poetical or astronomicall The Poeticall or vulgare is when the reason of the apparition or occultation of the signes is onely in their comparison with the ☉ which was handled in the 31. 32. chapters The Astronomicall rising culmination setting of any starre or point of the heauen is that which defineth the proportion of the time and space both when and how great it is wherein the aforesaid thinges are performed either in a right or an oblique sphere In the rising are to be considered the definition and the bipartite diuision The definition is either of the name or of the matter The ascension is called the rising which wee measure by the coascendēt arke of the Equator The matter is that according whereunto it is defined to be the arke of the Equator comprehended between the signe rising or the East part of the Horizon that conteineth the signe the head of ♈ the which arke is to be accōpted according to the orderly succession of the signes The consideration had of the diuision is that either a greater portion of the Equator riseth with the signe then it is said to haue a right ascension because it maketh righter angles with the Horizon or els that a lesse portion of the Equator