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diversity_n day_n equinoctial_a night_n 376 5 9.6498 5 true
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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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when the Sunne shal be so muche before the poynt of mydnyght in the quarter of the nyght flowyng howe muche the Moone after the poynt of noone or mydday in the day quarter of reflowyng And yf the Moone shal be betweene the opposition of the Sunne and her seconde quadrature with the Sunne then the Moone in her rysyng goeth before the Sunne and then the begynnynges both of flowyng and reflowyng be in lyke maner as they were when the Moone was betweene the coniunction and fyrst quadrature For the begynnyng of the day flowyng shal be in the day about three of the clocke before or after that is when the Sunne shal be so muche aboue the Horizon on the East parte in the day quarter of flowyng howe muche the Moone aboue the Horizon on the Weast parte in the day quarter of reflowyng And the begynnyng of the nyght flowyng shal be in the nyght when the Sunne shal be so muche vnder the Horizon on the part of the Weast in the nyght quarter of flowyng howe muche the Moone vnder the Horizon on the parte of the East in the nyght quarter of reflowyng But the begynnyng of the day reflowyng shal be in the day after noone when the Sunne shal be so muche after the poynt of the South in the day quarter of reflowyng as the Moone before the poynt of mydnyght in the nyght quarter of flowyng And the begynnyng of the nyght reflowyng shal be in the day when the Sunne shal be so muche after the poynt of mydnyght in the nyght quarter of reflowyng howe muche the Moone before the poynt of noone in the day quarter of flowyng And yf the Moone shal be betweene the seconde quadrature and her coniunction with the Sunne then the Moone also in her rysyng shall goe before the Sunne and then shal be the begynnynges of flowyng and reflowyng in the same houres as they be when the Moone is betweene the fyrst quadrature and opposition because the begynning of the day flowyng in the day after noone about euenyng before or after when the Sunne shal be so muche aboue the Horizon on the part of the Weast in the day quarter of reflowing howe much the Moone vnder the Horizon on the same part of the Weast in the nyght quarter of flowyng and the beginning of the night flowing shal be in the night about mornyng before or after 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 aboue the Horizon on the same parte of the East in the day quarter of flowyng But the begynnyng of the day reflowyng shal be in the day before noone when the Moone shal be so muche after the poynt of mydday or the South in the day quarter of reflowyng howe muche the Sunne before it in the day quarter of flowyng and the begynnyng of the nyght reflowyng shal be in the nyght before mydnyght that is when the Moone shal be so muche after the poynt of mydnyght in the nyght quarter of reflowyng howe much the Sunne before the poynt of mydnyght in the nyght quarter of flowyng And hereby it appeareth that as wel the flowyng as reflowyng of the water of the sea begyn not euer in the same houres of the day or nyght for the begynnyng of flowyng is eyther in the begynnyng of the day or begynnyng of the nyght whiche chaunceth the Moone beyng in coniunction or opposition to the Sunne or is before day from the mornynges towarde the day or from the day vntyll foure of the clocke or thereabout or is before Euenyng towarde Euen tyde and from thence to the Cocke crowyng or thereabout whiche chaunceth when the Moone is betweene her coniunction or opposition with the Sunne or anye of the quadratures The begynnyng of reflowyng is eyther at noone or at mydnyght as when the Moone is in coniunction or opposition with the Sunne or is before noone or after or before mydnyght or after as when the Moone is betweene her coniunction or opposition with the Sunne and anye of the quadratures It is apparent also that sometymes the water of the sea hath no determinate or certayne begynnyng neyther order of flowyng or reflowyng which chaunceth the Moone beyng in her quadratures with the Sunne It is manyfest also that al flowyng of the water of the sea is caused by respect to the Horizon on the parte of the East or Weast And euery reflowyng by respecte to the Meridian or to the poynt of mydday or mydnyght Here is also to be consydered that all that is sayde are moste certaynely true in a ryght Horizon but in an oblique or syde Horizon they sometymes fayle as shal be sayde hereafter folowyng It chaunceth as I haue sayde that the water of the sea doth sometime wander or decline from the order aboue prescribed yet commonly and for the moste parte keepeth that due order Such maner of declynyng is after two sortes For there is eyther disorder or errour in the houre of the begynnyng of the motion of the flowyng or reflowyng or in the myddest of the motion that is to meane that they haue greater or lesser courses then at other tymes or otherwyse greater or lesser increases and decreases The errour commyng in the houre of motion may come of three causes As by reason of the situation of the region or by reason of the bodyes supercelestiall or by change of the ayre By reason of situation of regions chaunceth diuersitie onely in the houre of the begynnyng of the flowyng because the begynnyng thereof hath respecte to the Horizon or is by respecte to the Horizon for in the begynnyng of reflowyng is no diuersitie nor errour because the begynnyng of the reflowyng is by respecte to the Meridian circle Agayne by reason of the situation of the region diuersitie chaunceth thus that is that eyther the region is vnder the Equinoctial circle or without it And if it be vnder the circle because they haue a ryght Horizon and the dayes be there euer equall with the nyghtes there at all tymes of the yeere That we haue sayde of diuers houres of the begynnyng of flowyng is certaynely true But regions distaunt from the Equinoctiall because they haue a wyndyng or slope Horizon in them the begynnynges of flowyng are as in regions vnder the Equinoctiall onely in two tymes of the yeere That is to say in the Spryng tyme or Equinoctial Vernal and in the tyme of Autumne or Equinoctiall Autumna●l that is to say About the myddest of the Moneth of Marche and about the myddest of the Moneth of September But in other tymes of the yeere or from the Vernal Equinoctial by the whole Sommer vntil the equinoctial Autumnal it is otherwise because the begynnyng of the day flowyng yf the flowyng be before noone that is about the mornyng it shal be later then it ought to be That is to say more of the day then is in
regions vnder the Equinoctiall and that because that in suche regions the day begynneth sooner or the Sunne ryseth sooner then in regions whiche are vnder the Equinoctiall for the declynyng of the oblique or syde Horizon although these regions be vnder one and the same Meridian But and yf the begynnyng of the day flowyng be after noone that is about euenyng then suche begynnyng shal be sooner then it is in regions vnder the Equinoctial that is to say in fewer houres of the day because that then the Sunne falleth latelyer then in regions whiche be vnder the Equinoctial But the begynnyng of the nyght flowyng yf it be before mydnyght it is sooner in the sayde places or regions that is to say in lesse tyme of the nyght or in lesse tyme after the fal of the Sunne then in regions vnder the Equinoctiall because that then the nyght begynneth to them afterwarde And yf the begynnyng of the nyght flowyng be after mydnyght that is towarde the day it shal be later that is of more houres or more neare the day then is in regions vnder the Equinoctiall because the Sunne ryseth sooner to them then to those that be vnder the Equinoctiall And this diuersitie groweth so much that sometyme it chaunceth to see two flowings in one day and none in the nyght whiche chaunceth for the inequalitie of the dayes with their nyghtes For in howe much the artificiall day shal be longer then his nyght so muche suche diuersitie and errour groweth more euidently Therefore in the longest dayes of the yeere suche diuersitie shall appeare manyfestly But from the Equinoctiall Autumnal by al Wynter vntyl the Equinoctial Vernall it is contrary because the begynn●ng of the day flowyng yf it be before noone that is about the mornyng then shal it be sooner then it shoulde be that is to say in fewer houres of the day then it shoulde be in a ryght Horizon for then the day begynneth latelyer or the Sunne ryseth latelyer to them that haue a wyndyng or crooked Horizon And yf such flowyng shal be after noone that is about euenyng then the begynnyng of suche flowyng shal be later that is more towarde the euenyng or nearer to the fallyng of the Sunne then in regions which are vnder the Horizon For in sayde or crooked Horizon the nyght is sooner and the Sunne falleth sooner then in a ryght Horizon Also the begynnyng of the nyght flowyng yf it shal be before mydnyght it shal be later and more in the nyght then in regions vnder the Equinoctial because then the nyght shal sooner begynne in the crooked Horizon then in the ryght because the Sunne fyrste falleth in the crooked Horizon then in the ryght And yf the begynnyng of the nyght flowyng shal be after mydnyght that is towarde the day then suche begynnyng of flowyng in the crooked Horizon shal be sooner that is in fewer houres of the nyght that is more before the day or before the rysyng of the Sunne then shal be in regions whiche be vnder the Equinoctiall because the Sunne ryseth latelyer then in regions vnder the Equinoctiall And suche diuersitie groweth so muche that sometime shal be two flowynges in the nyght and none in the day And this chaunceth for the inequalitie and encrease of the nyght aboue his day For in howe muche the nyght shal be longer then his day so muche the more groweth suche diuersitie and therefore suche diuersitie shall appeare greatest in the longest nyght of the yeere Wherefore by the aforesayde it is manyfest that howe much the nearer we shal be to the Equinoctial so muche the lesse shall appeare the diuersitie in the houre of the begynnyng of flowyng of the water And how much the Sunne shal be nearer vnto the standings or stayinges of the Sunne called Solstitium or the longest daies longest nightes so much greater and more certaine shal be the diuersitie and shal appeare more manyfestly Furthermore diuersitie chaunceth by reason of the heauenly bodyes and errour not onely in the begynnings of flowyng but also of reflowyng For when anye of the great and luminous Starres as are Venus and Iupiter shal be about the Sunne or Moone they helpe them in moouyng the water of the sea and therefore by this meanes also they haue their due order Lykewyse as we haue sayde by reason of the change of the ayre often tymes chaunceth diuersitie and errour in the begynnynges of flowyng and reflowyng For the violent disposition of wyndes vehemently blowyng as well neare as farre of remooueth the courses of waters from their due order sometyme hastenyng the flowyng and sometyme the reflowyng and sometyme staying or stackyng them lykewyse There chaunceth also errour in the mydst of motion of waters for as wel courses of waters as also flowynges and reflowyngs sometyme keepe not the due motion For as is sayd the disposition of wyndes may either encrease or diminishe their courses Furthermore also the straytenesse or narownesse of places by reason of Ilandes or mountaynes cause great concourses and diuersities in many places For where the sea is strayter or narower there is the stronger course as about the Iland Fuboea Nigropontis and betweene Sicilia and Calabria is greatlye obserued Suche straytes hynder the encrease of waters because lesse quantitie passeth thereby and therefore there the flowynges and reflowynges are lesse And herevpon it chaunceth that in the Ocean sea are greatest flowynges and reflowynges because there are no straytes which may hynder or stay the courses of waters and by that meanes they haue their full and free course and in more certayne order But in our sea Mare Mediterraneum it is otherwyse For what so euer water of the Ocean entreth therein or commeth foorth passeth from the Weast by one onely narowe strayte and therfore it can not in the flowyng be greatly fylled neyther in the reflowyng be greatly emptied And so consequently the motion of the water of the sea procedeth not in certayne order And to haue saide thus much of the diuers motions of the water of the sea may suffise ❧ Demonstration of Proportions of Motions Locall printed rather for the learned Philosopher then the Mariner yet the Mariner may learne many proper conclusions necessarie to be knowen To the godly and not enuious reader Iohn Taisnier Hannonius wisheth health c. WHereas a fewe yeeres past at Rome Ferraria and in other Vniuersities of Italie when Paul the third possessed the Papal dignitie I tooke in hande to reade publique lectures of sciences Mathematike I may testifie without scruple of arrogancie that my lectures were honourably accompanyed with the presence of more then three hundred auditors because that artes Mathematike are there greatly esteemed And therefore after the lecture was finished as is the maner of auditors oftentimes many resorted vnto me departing frō the scholes to demaund further of such doubtes wherof they had not ful vnderstanding In the meane while certaine which enuied my reputation and assertions ceassed not