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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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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