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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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argument is deriued from the consutation of 2. opinions wherof the one supposeth thàt 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 conne●ities The s●●st●es or aptnes vnto 〈◊〉 is either belonging vnto the di●●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 need●s be some emptie place and a body without a place for elsan regarde of the celestiall o●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 che●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 Solstit●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 d●●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
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