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A13348 A very necessarie and profitable booke concerning nauigation, compiled in Latin by Ioannes Taisnierus, a publice professor in Rome, Ferraria, & other uniuersities in Italie of the mathematicalles, named a treatise of continuall motions. Translated into Englishe, by Richard Eden. The contents of this booke you shall finde on the next page folowyng Taisnier, Jean, 1508-ca. 1562.; Eden, Richard, 1521?-1576. 1575 (1575) STC 23659; ESTC S101247 53,484 76

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R. and L M Q Then by the fourth of the fyrste the triangle F G E. shal be of equall sydes and also of equall angles to the triangle F G R. Furthermore Q M is equidistant G R. by common science by R G. of the fyrst the angle F Q M. equal to the angle F R G. and the angle F R G. equal to the angle F M Q. and wheras the angle F R G. is cōmon to eyther of them then by the 4. of the syxt the same or al one shal be the proportion R G. to Q M. as is of G F. to M F. But as is G F. to M F. so is G F. to M L. Wherefore by N. of the fift G F. so hath it selfe to M L. as G R. to Q M. But by the 16. of the same M L. to Q M. hath it selfe as G F. to G R. Wherefore M L. equall M Q. whiche M Q. I diuide by equall in the poynt X by 10. of the fyrst wyl doo as before Then by the reasons aforesayde of the same the portion F X G. shal be equall to the trigon A B H. and the whole Superficies F G. N X. shal be equall to the whole trigon A B C. whiche is proposed The contrary appeareth thus Let be graunted a Superficies conteyned of two paraboll lynes as F N G. and F X G. proposing for example to fynde a superficiall of ryght lynts trianguler equal to the graunted superficies I drawe fyrst F G. Then after by 44. of the second of Apollonius Pergeus I find the Diameter of the parabol F N G. whiche is M N. whiche I draw to N L. to be equall M N. Then I drawe F L. which shal touch the parabol F N G. in the poynt F. by 33. of the first of the same Then from the poynt G. I draw a lyne G E. equidistant frō the Diameter M N L. by 31. of the fyrst of Euclide whiche I drawe vntyll it ioyne togeather with F L. the whiche doubtlesse shal be done by the second of the firste of V●tellio The poynt of the concourse or ioyning togeather is E. then I diuide F E. into three equal portions by the 11. of the syxth of Euclide in the poyntes S. and T. which poyntes I ioyne with the poynt G. by the lynes F G. and G R. Nowe shall there be three angles all equall to them selues by 38. of Euclide After this I constitute a Trigon B H C. equall to the Trigon F S G. by this meanes I drawe foorth H C. to the equalitie G S. by the 4. of the first of Euclide Then at the poynt H. I designe an angle B H C. equall to the angle F S G. by 23. of the first of Euclide and by 3. of the first of the same I drawe H B. vntyl it be equall F S. Afterwarde I ioyne B C. by a lyne Then by 4. of the first the tryangle B H C. shal be equall to the triangle F S G. and shal be equal to the portion F N G. by 17. Archimedes De Quadratura parabolae by the helpe of the first conception of Euclide I do the like of the portion F G X to whom by an equall triangle O P R. Then I drawe P Q equally distant O R. and R V. equally distant O P. by 31. of the firste of Euclide Then by 41. of the same O P R. shal be halfe of the superficies O V. Now then I somwhat protract C H. then vpon B H. I constitute a superficiall of equidistant sides hauyng an angle B H A. by 44. of the first of Euclide twyse assumpted the Diameter of the which superficies be A P B. Then by 41. of the same with the first conception of the Trigon A B C. shal be equal of the superficies F G N X. graunted which is the intent FINIS Exod. xxxv Bezaleel and Ahaliab Of this instrument reade the Cosmolabe of Besson An instrument in motion agreeyng with the motion of heauen Anno Dom. 1584. Lib. 3. Ca. 18 The inuention of a Shyp which can not be drowned A perpetual or continuall motion Michael Angelo Fiue kindes of Lode stones Lode stone male and female The best Lodestone of Hewe colour Lode stone s●●d for the weight of si●uer One lodestone draweth another Lode stones m●d●cin●● 〈◊〉 for the 〈◊〉 The stone Theamedes putteth iron from it Iron nayles drawen out of Shippes by the stone Art in manye thyngs passeth and amendeth nature The stone Magnes is knowen by colour vertue weyght and equalitie Colour Vertue Equalitie Howe to finde the poles by the stone A question of attraction of humours c. Scammonea and chole● A vire or a needle How the stone draweth ●ron or ariueth it away Agent and patient The stone diuided in the mydde●t From whence the stone hath his vertue The North starre is not the Pole. Euery part of this stone respect 〈◊〉 some part of heau●●● The greatest miracle in naturall thinges Denticles 〈◊〉 litle 〈…〉 that it 〈◊〉 the 〈◊〉 Calculus a litle rounde stone or small weyght lyke a pellet or plomm●● A strang experiment practised The ryuers of Tagus Danubius M●rueylous swiftnesse of a shyp Swyfte spe●●● after m●●nyng prayer Another experience of swift sayly●● The differēce of sh●ppe● in sa●●●ng The prop●●●●●● in ●●aming of shyppes ●●nes and 〈◊〉 It is easier to adde to inuentions then to inuent The newe ryuer from Antwerpe to Bruxels A no●●●le experiment The water intendeth to ●●●bus form● Why t●e water 〈◊〉 about ouerflowe the lande An experimēt The dr●wning of certayne ●●gio● This experiment may be proued with a great bell An other example of the foresayd experiment A secrete knowen is no more a miracle Ignorance causeth admiratiō Whirlepooles deuouryng Shyppes The lyke of earthquakes ●●●me and vndermin●ng The spirite of De●●gorgon To make said water fres●e There is a better way Eyght p●in●●●s of ●●u●n for 〈◊〉 and res●●●yng A right Horizon is when both the poles lye in the Horizon that is to them only which dwell vnder the Equinoctiall Poyntes of equall vertue in moouyng the water of the sea The aspectes whiche the Moone maketh with the Sunne euery moneth The Sunne Moone beyng in con●●●ction what effect●●s they ha●● in mo●●●● the w●●●● the sea A quarter of heauē is three signes A tyme wherin is neyther ebbyng nor flowyng The Moone being in ●●artile aspect or at the firste with the ●●arter some what effectes it causeth in ebbyng and flowyng A very litle ebbyng or flowyng Eyght daies ●●ter 〈…〉 A long tyme of flowyng The Moone being in opposition with the Sunne what effectes they haue in moouyng the water of the sea The Moone 〈…〉 The Moone beyng in the last quarter causeth the same effectes as in the first A briefe collection of all the premisses Ebhyng and flowyng begin not alwayes at one houre Great motio is of the water in the coniunction of the Sunne and Moone Greatest motions in opposition of the Sunne and Moone Smal motions of the water without determinate time alwayes in the quadratures of the Sunne and Moone Note The Moone foloweth the Sunne in rysing When flowyng s al e 〈◊〉 ●●ares after Sunne rysing Ebbyng after noone The Moone rysing before the Sunne Note A general obseruation for the beginnyng of ebbyng and flowyng Note In what Horizon this discourse taketh place The beginning 〈…〉 of 〈…〉 I he begynnyng of eb●●● 〈◊〉 by re●● 〈◊〉 the 〈◊〉 ch●●● Two flowyngs in one day and none in the nyght Note The ●●●●●enes ●f other 〈…〉 ●●●e cause 〈…〉 in ●●l by 〈◊〉 and 〈…〉 And lyk● 〈…〉 Narownesse of places may cause disorder Thomas de Aquino Motiō of the bodies 〈…〉 and siluer The 〈◊〉 of fyre Motion of heauen 〈◊〉 The greater body the quicker motion The greater fire the swyfter motion Perspectiue errour of Vitellio Archimedes Motions violent and naturall Apollonius Pergeus
¶ A very necessarie and profitable Booke concerning Nauigation compiled in Latin by Ioannes Taisnierus a publike professor in Rome Ferraria other Vniuersities in Italie of the Mathematicalles named a treatise of continuall Motions Translated into Englishe by Richarde Eden The contentes of this booke you shall finde on the next page folowyng ¶ Imprinted at London by Richarde Iugge Cum priuilegio OMNIA DESVPER R. I. ❧ The Table 1 OF the marueylous nature and vertue of the Lode stone called in Latin Magnes where they be found and howe to knowe the best 2 Of continual motion by the sayd stone Magnes 3 Of the due proportion of whatsoeuer Ship and the disclosyng of certayne Mathematicall secretes 4 Of ebbyng and flowyng with their diuersities and the causes thereof 5 Demonstrations of proportion of motions local confutyng the opinion of Aristotle therein ❧ To the ryght woorshipfull Syr Wylliam Wynter Knyght Maister of the Ordinaunce of the Queenes Maiesties Shippes and Surueyor of the sayd Shippes Richarde Eden wysheth health and prosperitie IT is nowe about twelue yeeres paste gentle Maister Wynter since the curtesie and fauour which long before I founde at your hande mooued me no lesse for the good wyll that I haue euer borne you and your vertues to excogitate or deuise somethyng within the compasse of my poore abilitie that myght be a witnesse as it were a seale to testifie both that I haue not forgotten your gentlenesse also howe desyrous I am to pay the debtes of freendshyp which then I promised you also attempted to perfourme But beyng at that tyme preuented by meanes of my sodayne departyng out of Englande with my good Lorde the Vidame with whom I remayned for the space of ten yeeres vntyll the calamities of that miserable countrey with losse of goods and danger of lyfe hath dryuen me home agayne into my natiue countrey Where fyndyng my selfe at some leysure and desyrous to passe foorth parte of my tyme in some honest exercise which myght be profytable to many domagable to none and a meanes to geat me newe freendes the olde in my so long absence in maner vtterly wasted I chaunced in the meane tyme to meete with my olde acquayntance and freend Richard Iugge Printer to the Queenes Maiestie who had many yeeres before printed the Booke of Matten Curtes of the Art of Nauigation by me translated out of the Spanyshe tongue Whereof hauyng with him some conference he declared that he woulde prynt that booke agayne yf I woulde take the paynes to deuise some addition touchyng the same matter that myght be ioyned thereto At whiche tyme hauyng with me in the Latine tongue these bookes here folowyng printed whiche I brought with me out of Fraunce I soone agreed to his honest request to translate them into Englyshe Whiche beyng accomplyshed this onely remayned accordyng to the common custome to consecrate and dedicate the same to some worthie personage whose fame auchoritie and dignitie myght defende them from the euyll tongues of such as are more redie rather to reprooue other mens dooynges then to doo any good them selues And therfore gentle Maister Wynter knowing your aucthoritie and fame in well deseruyng and honorable seruice vnto your Prince and Countrey to be suche as all men thynke so well of and so greatlye esteeme to whom rather then vnto you may I dedicate this booke of Nauigation In consyderation whereof and the hope that I haue in your approoued curtesie fauourably to accept this dedication as proceeyng from one that desyreth nothyng more then to doo you seruice and remayne in your grace I shall thynke my trauayle wel bestowed and sufficiently recompenced yf it shall please you to accept the same as thankfully as I wyllyngly offer it vnto you For yf there be any thyng in me wherein I maye by good reason please my selfe it is cheefely this that I haue euer loued and honoured men of singuler vertue or qualitie in what so euer laudable Art or Science euen of those whereof I mee selfe haue litle knowledge as are Geometrie Astronomie Architecture Musicke Payntyng feates of Armes inuentions of Ingens and suche lyke Of the whiche this our age maye seeme not onely to contende with the Auncientes but also in many goodly inuentions of Art and wyt farre to exceede them For not to speake agaynst all the marueylous inuentions of our tyme what of theirs is to be compared to the Artes of Printyng makyng of Gunnes Fyre woorkes of sundry kyndes of artificial Fyres of suche marueylous force that mountaynes of moste harde rockes and stones are not able to resyst their violence but art by them broken in peeces and throwen into the ayre with suche violence that neyther the spirite of Demogorgon or the thunderboltes of infernal Pluto can doo the lyke What shoulde I here speake of the woonderfull inuentions of Fartalio in his booke De Arte maiori or of many other wherof Vannucius Beringocius wryteth in his booke entituled Pytotechnia As touchyng which terrible inuentions and the lyke although some men be of opinion that they were inuented by the instigation of the deuyll for the destruction of mankynde yet other weyghyng the matter more indifferently thynke that the inuention of Gunnes hath been the sauyng of many mens lyues because before the vse of them men were not woont so long tyme to lye batteryng in the besiegyng of Townes or Fortresses but in short space to come to hande strokes and to soughten feeldes to the great slaughter of great multitudes And seeyng that nowe our enimies the Turkes and other Infidels haue the vse of these deuylyshe inuentions as they name them it may be thought requisite for vs agaynst suche deuylles to vse also the lyke deuylyshe inuentions lest refusyng the same and geuyng place to euyl we shoulde wyllyngly suffer the kyngdome of the deuyll to triumphe ouer vs not otherwyse able to resyst and much lesse to ouercome so puissant and horrible enimies except besyde al hope myght aryse in our defence some newe Moyses or Elias or the Priestes of Iericho whiche onely with the noyse and sounde of Hornes or Trumpettes ouerthrewe the walles of the towne Neyther wyl the example of Dauid and Goliath or of Samson and the Philistines serue our turne at this tyme although I beleeue that the arme of the Lorde is not weakened yf there lacked not a Moyses with his rodde and woorthie Assystentes which myght helpe to holde vp his weerye arme But to returne to speake of ingens and ingenious inuentions whiche inuented and vsed to the glorie of God and defence of his people against the furie and tyrannie of Infidelles they may as woorthyly be called the gyftes of God as were the inuentions and Art of them that buylded eyther the Temple of Hierusalem or the Arke of God And yet is it there wrytten of those Artificers that God gaue them the spirite of knowledge and cunnyng in suche Artes. And therefore I thynke it may also be sayde without offence
attraction of the fal draweth downe with it sodainly the Ship or Shippes whiche at that tyme approcheth neare vnto the place of that whyrelepoole Furthermore anye ignoraunt man woulde hardly beleeeue that the salt water of the sea maye be made freshe and potable to be dronke whiche neuerthelesse maye be doone naturallye as hath been often prooued dyuers wayes Some doo this as is wrytten in Gemma Philosophica puttyng the salte water in a vessell playstered or crusted ouer with cleane Waxe whiche distyllyng through the strayte and narowe pores thereof leaueth the salt which for his grosnesse can not passe therby The same may be done better by a Canon or Pype fylled with grauell or litle stones and that the salt water powred thereon may diuers times passe through that Pype into an other vessell ¶ Of the Flowing and Reflowing that is increase and decrease of the Sea with the causes therof more exactly then hytherto hath been declared by any WHeras heretofore mention hath ben made of the sea and flowyng of waters and diuers other motions it may be conuenient to adde hereunto the sayinges and wrytynges of the most expert and learned man Fredericus Delphinus Doctor of artes and phisicke and publique professor of Mathematical sciences in the famous vniuersitie of Padua touchyng the flowyng reflowyng or increase and decrease otherwise also named accesse and recesse that is commyng and goyng or ebbyng and flowing of the water of the sea Which flowyng and reflowing some do also name the false rest or quietnesse or inordinate motion of the water of the sea And albeit diuers learned men haue intreated of this matter yet forasmuche as some of theyr wrytynges are somewhat darke and not easie of all men to be vnderstoode I haue thought it necessarye partly out of theyr wrytinges and partly by mine owne industrie more clearly largely to entreat hereof that the same may be the better vnderstoode of all men A figure shewyng the beginning of the day increase at the Sunne rising and the beginning of the day decrease in the midday and the beginning of the night increase at the Sunne setting and the beginning of the night decrease at midnight Secondaryly is also to be knowen that there be in heauen eyght poyntes for the flowyng and reflowyng or increase and decrease of the sea of the whiche foure are strong and foure weake Of the weake two are weake for the flowyng and two for the reflowyng Weake for flowyng are the poynt of the East and poynt of the West whiche are the begynnyng of the two quarters of flowyng Weake for reflowyng are the poynt of the South or mydday and the poynt of mydnyght whiche are the begynnynges of the two quarters of reflowyng and these foure poyntes are distant the one from the other by a quarter of heauen Of the strong poyntes two are strong for flowyng and two for reflowyng Strong for the flowyng are the middle poynt betweene the East and the South in the daye quarter of flowyng beyng distant from the East .45 degrees and from the South lykewyse And the middle poynt betweene the West and mydnyght in the nyght quarter of flowyng ●●yng distant from the West 45. degrees and from mydnyght lykewyse Poyntes strong for the reflowyng is the myddle poynt betweene South and West in the day quarter of the reflowyng beyng distant from the South .45 degrees and from the West lykewyse And the myddle poynt betweene midnight and the East in the quarter of the nyght reflowyng beyng distant from mydnyght .45 degrees and from the East lykewyse And as the weake poyntes are distant one from the other by a quarter of heauen so are also the strong poyntes distant the one from the other by a quarter of heauen to them that haue a ryght Horizon It is thyrdly to be knowen that beside the aforesayde eyght poyntes to suche as haue a ryght Horizon there be many other poyntes equipollent or of equall vertue And suche be all the poyntes of heauen equally distant from the foure principal poyntes of heauen whiche foure principall poyntes are the poynt of the East poynt of the West poynt of the South and poynt of mydnyght or from the foure strong poyntes of heauen whiche is all one yet in quarters of contrarie operation For all suche poyntes are equipollent or of equall vertue in moouyng the water of the sea but in a ryght Horizon it is otherwyse as shal appeare hereafter It is fourthly to be knowen that the Sunne and Moone euery moneth are togeather in one signe degree and minute And this so beyng is called the Coniunction of the Moone with the Sunne From thence for the space of eyght dayes or there about the Moone is departed from the Sunne by her proper motion by a fourth part of heauen and this departyng is called the fyrste quarter of the Moone with the Sunne From thence in fourteene dayes or thereabout she is departed from the sunne by an other fourth parte of heauen and so by the halfe of heauen and this distance is called the opposition of the Moone with the Sunne or the ful Moone From thence to .21 dayes or thereabout she is departed from her opposition with the sunne or full Moone by an other fourth part of the heauen commyng towarde the Sunne and this distance is called the seconde qu●●●ature of the Moone with the Sunne and then the Moone is distant from the Sunne by a fourth parte of heauen as it was distant in the fyrste quarter and so commeth neare to Coniunction with the Sunne From thence at thyrtie dayes or thereabout the Moone is agayne with the Sunne in coniunction as it was fyrst Fyftly and lastly is to be knowen that the Sunne Moone both togeather euery naturall day whiche is the tyme of .24 houres to the mouyng of the fyrst moueable are the causes of flowyng and reflowyng or increase and decrease of the water of the sea twyse These declarations premised and wel kept in memorie let vs declare howe the Sunne and Moone both togeather euery naturall day to the moouyng of the fyrste moueable are the causes of the flowyng and reflowyng of the sea For yf these declarations be well helde in memorie and especially the quarters of heauen in whiche is the flowyng and the quarters of heauen in whiche is the reflowyng and whiche are the strong poyntes for the flowyng and strong poyntes for the reflowyng and whiche be the weake poyntes for the flowyng and the we●ke poyntes for the reflowyng these I say beyng kept in memorie al the narration of the mouyng and false quietnesse of the sea shal be cleare and manifest Fyrst of all as touchyng the flowyng and reflowyng of the sea to the mouing of the first moueable it is to be knowen that when the Sunne and Moone are ioyned togeather which coniunction is called Nouiluniun that is the new Moone when they be moued to the moouyng of the fyrste moueable called Primum mobile
Moone departeth from her coniunction with the Sunne and is not come to her first quadrature with the Sunne and is betweene the coniunction and fyrst quadrature and when the Moone shall come to her coniunction with the Sunne then agayne al the dispositiō before declared shal returne in al poynts in lyke maner as is sayde Therefore this motion of the water of the sea whereof we haue spoken is a motion folowyng the motion of the Sunne Moone to the motion of the first moueable For yf you shall wel consyder that we haue sayde of the flowyng and reflowyng that is increase and decrease or accesse and recesse of the water of the sea you shall vnderstande that the begynnynges of suche flowyng and reflowyng and lykewyse the rest and quietnesse chaunce diuersly in the houres of the day and the nyght For they come not euer in the same houres of the day as is manifestly knowen to suche as obserue suche flowyng and reflowyng or false rest or quietnesse of the water of the sea And therefore by the aforesayde dooth appeare that the water of the sea hath motion of flowyng once in the day and once in the nyght and lykewyse of reflowyng once in the day and once in the nyght It is manifest also that the flowyng doth not begyn euer the same houre of the day or nyght but at diuers houres and lykewyse the reflowyng Also the tyme of flowyng or reflowyng proceedeth inordinately when the Moone is in her quadratures with the Sunne that is in the first or seconde There chaunceth sometymes great increase of waters sometyme lesse sometymes meane when the Moone shal be in any other place from the sunne beside these foure That is to meane in the coniunction or opposition or her first quadrature or second with the Sunne And as are sometymes increases of waters greater lesse and meane euen so are the decreases in lyke maner The greatest concourses and motions of waters are when the Moone is in coniunction with the Sunne also the greatest flowynges and reflowynges Lykewyse in opposition of the Moone with the Sunne and greater then in the tyme of the coniunction of the Moone with the sunne For the superior bodyes by their motion light geue their influence into these inferior bodyes And so much more as they haue of lyght so much more stronglyer they worke and because in oppositiō of the Moone with the Sunne the Moone is ful of light her light is toward vs therfore is it reasonable that then should be caused greater flowynges and reflowyngs then in her coniunction with the Sunne Neuerthelesse because that in her coniunction with the Sunne the Sunne Moone are both vnite together and their vertues therfore also are great encreasynges and decreasyngs of waters because both their vertues are vnite as I haue sayde but yet greater in the opposition then in the coniunction for causes before rehearsed The Moone beyng in her quadratures with the Sunne the water of the sea hath no determinate tyme of flowyng or reflowing and then are the lesse concourses of waters least flowing and reflowyng And suche motion of the sea the Venetians call De fele and then the water of the sea hath no determinate begynnyng of flowyng or reflowyng but is mooued inordinately in dyuers maner sometyme commyng and sometyme goyng The cause of this diuersitie is because the Sunne the Moone where so euer they shal be in moouyng to the water equally or as it were equally haue contrarietie in what so euer poynt they shal be For in what so euer poynt the Sunne shal be the Moone shal be in the point of opposite vertue contrary to the place of the Sunne or neare And when the Moone shal be without the sayde foure places then the water of the sea shal begynne to come or goe And when the Sunne and Moone shal be in equall poyntes of vertue of the quarters of contrary operation the concourses of waters shal be so muche the greater in howe much the Moone shal be nearer to her coniunction with the Sunne or to the opposition and so much the lesse in howe muche the Moone shal be nearer to the quadratures lykewyse also the flowynges and reflowynges shal be so muche the greater For yf the Moone shal be betweene her coniunction with the Sunne and the fyrst quadrature then the Moone to the mouyng of the fyrste moueable dooth folowe the Sunne in his rysyng and then shal be the begynnyng of the day flowyng of the day after the rysyng of the Sunne about three of the clocke or before that is to meane when the Sunne shal be so muche aboue the Horizon on the part of the East in the day quarter of flowyng howe muche the Moone vnder the Horizon on the same parte of the East in the nyght quarter of reflowyng because then the Sunne Moone shal be of equall force because they shal be in the poyntes of equal vertue in the quarters of contrary operation and the begynnyng of the nyght flowyng shal be in the nyght after the fal of the Sunne that is when the Sunne shal be so muche vnder the Horizon on the same parte of the Weast in the day quarter of flowyng howe muche the Moone vnder the Horizon on the same parte of the Weast in the day quarter of reflowyng And the begynnyng of the day reflowyng shal be in the day after noone when the Sunne shal be so muche after noone in the day quarter of reflowyng howe muche the Moone before noone in the day quarter of flowyng And the begynnyng of the reflowyng of the nyght shal be in the day after mydnyght that is when the Sunne shal be so muche after the poynt of mydnyght in the nyght quarter of reflowyng howe muche the Moone before hym in the nyght quarter of flowyng And yf the Moone be betweene the fyrste quadrature and the opposition the Moone yet in her rysyng foloweth the Sunne and then shal be the begynnyng of the day flowyng in the day after noone about euenyng that is a litle before or after that when the Sunne shal be so muche aboue the Horizon on the parte of the Weast in the day quarter of reflowyng howe muche the Moone aboue the Horizon on the parte of the East in the day quarter of flowyng and the begynnyng of the nyght flowyng shal be in the day before day that is about mornyng before or after that is when the Sunne shal be so muche vnder the Horizon on the parte of the East in the nyght quarter of reflowyng howe muche the Moone vnder the Horizon on the parte of the Weast in the nyght quarter of flowyng and the begynnyng of the day reflowyng shal be in the day before noone when the Sunne shal be so muche before the poynt of noone howe much the Moone after the poynt of mydnyght And the begynnyng of the nyght reflowyng shal be in the nyght before mydnyght