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day_n degree_n longitude_n minute_n 8,159 5 12.3086 5 true
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A08349 A mathematicall apendix,[sic] containing many propositions and conclusions mathematicall: with necessary obseruations both for mariners at sea, and for cherographers and surueyors of land; together with an easie perspectiue mechanicall way, to deline at sunne dyalls vpon any wall or plane giuen, be it direct, inclyning, declyning, or reclyning, for the horizon, or meridian, in any region or place of knovvne latitude. With other things pleasant and profitable for the weale publick, not heretofore extant in our vulgar: partly collected out of foreigne moderne writers, and partlie inuented and practised by the author. Written by R.N. Gent. Norton, Robert, d. 1635. 1604 (1604) STC 18675; ESTC S119965 19,791 52

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Paralaxis abstracted 3 A Comet or the Moone appearing how to finde the paralax or difference of aspect thereof two seuerall wayes and thereby how farre it is from the Centre or Circumference of the Earth 4 The Paralax and distance from the Earth giuen to finde what Angle it will make in the Centre of the Earth with any other Star that hath no Paralax 5 To find the Longitude by a Comet or the Moone appearing and the difference of tyme from one Meridian to another by comparing it with a fixed Star A Corollarie vpon the same shewing more euident accomplishment thereof by comparing it with the true moouing of one of the Planets 6 A Starre m Heauen propounded to finde the Longitude without the difference of Tyme 7 How to finde the Longitude and Latitude of anie place at once without the difference of time by obseruation of the Coelestiall Luminaries 8 How to finde the Longitude at all times from moment to moment Mechanically And withall to describe all the places of note in a Region or Country on a Map or platte according to their seuerall distances and situations exactlie With the vse of the Protractor A Corollary vpon the same applying it to the Suruey and platting of Land Another Corollary vpon the same Consequence expressing a Mechanicall meanes to find the Longitude at Sea at all times and to keep a perfect Trauerse for a whole voyage An Annotaion shewing an artificiall deuise how the Master or Pylot at Sea may much more exactly make obseruation of the Coelestiall Luminaries with any Instrument then the ordinarie manner can possiblie admitte by reason of the heauing and setting of the Ship The making of the Cosmodelite an excellent Instrument for many Mathematicall conclusions As for the Longitude of places to take any Altitude Latitude or distance in sight for Suruey and platting of Land to make Sun dialls c. inuented by the Author How by the Cosmodelite to delineate a Sun diall on any plane giuen with great facility without arithmeticall calculation Master Robert Smith his inuention to delineat a Sun diall otherwise The making of an artificiall engine whereby with any strength giuen be it neuer so little to eleuate and lift vp any ponderous weight assigned Brief Expositions of the Geometricall and Aftronomicall tearms mentioned in this Treatise Finis Tabulae The first Proposition How to find the Longitudes of places by the daylie Declination of the Sun THe Sunne continually declyning from the AEquator according to the seuerall poynts of the Ecliptick wherein hee properly mooueth sometimes towards the South being in the Meridionall signes and sometimes towards the North Pole beeing in the Septentrionall making his greatest declination on eyther side to be 23. degrees and 28. or thereabouts doth from the noone of one day vnto the noone of the next day so sensibly vary his declination on any one Meridian as that you may easilie find how much hee declyneth from Meridian to Meridian on all the Meridians that may be imagined vpon the face of the whole earth As for example if from the noone of this day vntill the same moment to morrow he shall be found to vary one minute of a degree in his declination vpon one same Meridian imagining then 60. seuerall Meridians on the Earth equally distant one from another it is most certaine that he will make from one of those Meridians vnto the next 1 60 part of a minute which is a second difference of declination and so consequently more or lesse as the same shal happē to be beyond or short of the said Meridian Wherefore if you diuide 360. the degrees of the Equator by 60. the number of the supposed Meridians you shall finde the Quotient to produce 6. degrees the difference of the Longitude which one of them shall be from the next This may be obserued from day to day at all times of the yeare bee it that the Sunne haue greater or lesse declination then the saide minute vnder the assigned Meridian which collected into a Table will be a ready means for to find the Longitude of any vnknowne Meridian The practise to find the Longitude the Table being made is thus Hauing exactly obserued the declination of the Sunne by some perfect Mathematicall Instrument for the hower of Noone then enter the sayd Table seeking there the declination set downe for that day which beeing found the difference of the declination will shew you vnder what Meridian you obserue and are with the difference of Longitude which difference being added or subducted as reason will direct to or from the former giuen Meridian will yeelde the sought vnknowne Longitude Note that the Table may be enlarged not onelie to thirds and fowerths but vnto tenths which will be much better for the more exact expressing of his slowe declination And thus you may finde the Longitude by the daylie declination of the Sunne The second Proposition How to find the Longitudes by Arches of great Circles which passe by the Centres of the fixed Starres and such of the Planets as yeelde no sensible paralax or difference of aspect FOrasmuch as great Circles which passe by the Centres of all the Stars doe expresse in theyr Arches the seuerall distances of all the Planets and fixed Stars considered by two and two And for that the Planets in their proper mouings do ouergoe the Stars of the Firmament It must necessarily follow that their said distances do continually vary either more or lesse and the Angles also subtending them Wherefore if by Astronomicall Tables you obtaine the true place of one of the Planets hauing no Paralax and compare the same with one of the fixed Stars giuen be it Septētrionall or Meridional seeking for euery day hower and minute what Angles the same Planet shall make with the said fixed Star and of such Angles to make a Table it wil be an Artificiall preparatiue to the finding of the Longitudes of places with facility For all the Inhabitants of the Earth according to Ptolomy being in the Centre of the worlde in respect of the fixed Stars and higher Planets it is certaine that all such Stars and Planets will appeare to them all to vary theyr angles continually but chiefely when the Planet shall bee direct and that those Planets which mooue most swiftlie do yeelde more euidently such variation then the slower ♄ and ♃ The Table beeing prepared when you desire to finde an vnknowne Longitude Obserue exactly by Instrument what Angle the same Planet maketh with the saide Starre for which the said Table was made which had seek then in your said Table for the Angle calculated for that moment of time in which you make your obseruation and the difference of the Angles will giue you the difference of the Longitude if any bee between the place of obseruation sought and the place giuen for which the table was made Corollary I. Then it followeth that by the same meanes and with more euident variation of Angles wee may