whiche they shoulde carrie victualles and other prouisions agaynst the course of the ryuers And therefore in fauour of the common wealth I haue inuented these kynde of Shyppes that I may hereby as by my seale confyrme the good wyll I beare to our posteritie Nowe therefore it may suffice to haue sayde thus muche of this swyfte motion whiche I haue prooued with myne owne strength and haue sufficiently declared the framyng and vse thereof wherevnto it shal be easye for all men to adde more accordyng to the excellencie of their wyttes and experience For in all sciences it is easyer to adde to inuentions then to inuent Consyder nowe what commoditie this may bryng to the Brabantines saylyng from Antwerpe to Bruxels in the newe ryuer For that which they attempt dangerously with great vexation and shoggyng in waggons by foule and tedious iourney often wette to the skyn for the space of one whole day maye by water be doone more conueniently in the space of foure or fyue houres euen agaynst the ryuer and wynde And leste the reader shoulde seeme to refute our sayinges whyle he thynketh those thynges whiche he esteemeth for miracles to exceede the limittes of nature I wyll shewe manifestly by one Demonstration howe a man may descende into the bottome of anye water or ryuer his body remaynyng drye as here before I haue affirmed that I sawe in the famous Towne and kyngdome of Toleto before the Emperour Charles the fyfth and infinite other But here muste fyrste be consydered that naturally the water or sea as other Elementes intendeth to Sphericall forme and with his globosite or rysing ouerpasseth moste hygh mountaynes But agayne here shall ryse an other doubt to the vnexpert That is If the sea be hygher then the lande howe is it then that it dooth not drowne and couer the earth Whereunto I aunsweare that the dryenesse of the earth maye so long resyste the moystenesse of the water vntyll it receiue or imbibe to muche moystenesse whiche may thus be naturally prooued Fyll a cuppe or other vessell with water or wyne to the brymme so that the fulnesse thereof maye seeme to swell as though it woulde ouerflowe the brymme of the cuppe Then may you yet put therein many peeces of golde without sheddyng of one droppe of water But yf the extremitie of the brymme be once wette immediately the water ouerfloweth because the dryenesse of the vessell dooth participate the moystenesse of the water whiche is yet better prooued in maner as foloweth Take a certayne quantitie of water and sprynckle it by droppes vppon a drye or dustie cable so shall the droppes partly shewe a Sphericall and swellyng forme remaynyng But yf the table before be neuer so lyttle wette with water the droppes sprynckled thereon shall flote abrode and keepe no Spherical or rounde forme by reason of the moystnesse whiche the table had before receiued of the water It hath also oftentymes chaunced that certayne Townes and landes haue ben drowned by ouerflowyng of ryuers neare vnto them Neuerthelesse howe muche so euer suche waters increase and ryse there is no daunger vntyll great showres fallyng from heauen doo thorowly wette the banckes rampertes or calseys of suche riuers For when they as we haue sayde be thorowly imbibed with moystenesse they cause the ouerflowyng and breache whereof foloweth the ouerflowyng and drownyng of the region and this may suffise for aduertisement Nowe therefore I come to the experience aforesayde shewed at Toleto by two Greekes who takyng a chaulderon of great capasitie and the mouth turned downewarde and so hangyng it in the ayre by ropes they fasten certayne postes and boordes or shelues in the myddest of the chaldron where they place them selues with the fyre Thē to make it hang stedfastly and equally they compasse the circumference brymme or border thereof with leaden plommetes on euery syde equally and made of equal weyght least any part of the circumference of the mouth of the chaldron when it is equally and softly let downe into the water shoulde sooner touche the water then the whole circumference For so shoulde the water easyly ouercome the ayre inclosed in the chaldron and resolue it into moysture But yf by due proportion the chaldron thus prepared be fayre and softely let downe into the water the ayre inclosed in the chaldron by resistance of the water shall violently make hym selfe place not admittyng the water to enter So the men there inclosed shall so long remayne drye in the myddest of the water vntyll successe of tyme doo by respiration debilitate and consume the inclosed ayre turnyng it into grosse humiditie ingrossed by the coldnesse and moystnesse of the water but yf in due tyme the chaldron be softly and equally drawen out of the water the men shal remaine drye and the fyre not extinct whiche also may thus be prooued Take a cuppe of glasse of a certayne quantitie the circumference of the mouth wherof shal be broder then the circumference of the bottome In the mouth let be fastened a little sticke tying thereto a threede On the stycke fasten a little candle of waxe whose lyght may come onely to the myddest of the cuppe least to muche nearenesse of the water myght suffocate the candle Then proportionally as in the former experiment put the cup with the burnyng candle into a vessel ful of water in due tyme drawe it out softly and equally so that no part of the mouth of the circumference therof be drawen out before the whole or sydelye so shall the candle remayne alyue as it was before Then be naturall and Mathematicall Demonstrations Let not therefore the ignoraunt condemne our wrytynges before they knowe what maye be doone by experience It is nowe then no more a miracle when it is knowen to be naturall And thus is it in all other Sciences and experimentes whiche the common people thynke to be impossible As the lyke in growyng of certayne fruites trees and herbes by art so helpyng nature that they may spring and growe before their naturall tyme euen in the harte of Wynter It seemeth also a miracle to the common people that in the tyme of moste temperate season and great calmenesse on the sea Shyppes behelde faste immoueable in the myddest of the sea and sodaynely swalowed into the bowelles of the earth whiche neuerthelesse is doone naturally in maner of an earthquake and by lyke natural cause The reason whereof is that the ayre as a moste lyght Element inclosed in the bowelles of the earth striuyng euer naturally to the circumference of the earth as vnto his owne region But the pores of the earth beyng stronglye stopped and the ayre thereby agaynst his nature forcibly inclosed stryueth by violence to brust foorth and so cleauyng the earth in the bottome of the sea and great abundance of water fallyng into the breache euen from the hyghest parte of the sea in that place with swalowyng
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
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 begynnâ—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 froÌ„ 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
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 â—â—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 quâ—â—â—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 weâ—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
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 Autumnaâ—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
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 coÌ„mon 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 froÌ„ 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 Vâ—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 sâ—â—d for the weight of siâ—uer One lodestone draweth another Lode stones mâ—dâ—cinâ—◠〈◊〉 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 choleâ— A vire or a needle How the stone draweth â—ron or ariueth it away Agent and patient The stone diuided in the myddeâ—t From whence the stone hath his vertue The North starre is not the Pole. Euery part of this stone respect 〈◊〉 some part of heauâ—â—â— The greatest miracle in naturall thinges Denticles 〈◊〉 litle 〈…〉 that it 〈◊〉 the 〈◊〉 Calculus a litle rounde stone or small weyght lyke a pellet or plommâ—â— A strang experiment practised The ryuers of Tagus Danubius Mâ—rueylous swiftnesse of a shyp Swyfte speâ—â—â— after mâ—â—nyng prayer Another experience of swift saylyâ—â— The differeÌ„ce of shâ—ppeâ— in saâ—â—â—ng The propâ—â—â—â—â—â— in â—â—aming of shyppes â—â—nes and 〈◊〉 It is easier to adde to inuentions then to inuent The newe ryuer from Antwerpe to Bruxels A noâ—â—â—le experiment The water intendeth to â—â—â—bus formâ— Why tâ—e water 〈◊〉 about ouerflowe the lande An experimeÌ„t The drâ—wning of certayne â—â—gioâ— 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 admiratioÌ„ Whirlepooles deuouryng Shyppes The lyke of earthquakes â—â—â—me and vnderminâ—ng The spirite of Deâ—â—gorgon To make said water fresâ—e There is a better way Eyght pâ—inâ—â—â—s of â—â—uâ—n for 〈◊〉 and resâ—â—â—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 conâ—â—â—ction what effectâ—â—s they haâ—â— in moâ—â—â—â— the wâ—â—â—â— the sea A quarter of heaueÌ„ is three signes A tyme wherin is neyther ebbyng nor flowyng The Moone being in â—â—artile aspect or at the firste with the â—â—arter some what effectes it causeth in ebbyng and flowyng A very litle ebbyng or flowyng Eyght daies â—â—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 〈◊〉 â—â—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 ebâ—â—◠〈◊〉 by reâ—◠〈◊〉 the 〈◊〉 châ—â—â— Two flowyngs in one day and none in the nyght Note The â—â—â—â—â—enes â—f other 〈…〉 â—â—â—e cause 〈…〉 in â—â—l by 〈◊〉 and 〈…〉 And lyk◠〈…〉 Narownesse of places may cause disorder Thomas de Aquino MotioÌ„ 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
description of it shal seeme vnto you somewhaâ— obscure you shall not ascribe it altogether to my declaration but partly to the subtiltie nouiltie of the thyng It is in fourme of a square pyller sharpe toward the top in maner of a Pâ—ramiâ— of the height of almost three cubites ouer or aboue it in maner of a couer is a flat or playne rounde plate of gylted copper garnyshed with sundry colours on whose other part is expressed the whole course of the Planets and whose dimention or measure is somewhat shorter then a cubite and is within turned or mooued with certayne litle denticle wheeles an immouable circle comprehendyng the hyghest border or margent and diuided with the spaces of xxiiii houres within it in the hyghest turnyng rundel the twelue signes are discerned by three degrees Further within are seene eyght runde is in maner all of one greatnesse Of these two obteyne the myddle poynt the one fastened in the other so that the lowest beyng somewhat bygger representeth the Sunne and the hygher the Moone From the Sunne a beame commyng to the circle sheweth in it the houres and in the Zodiacke the monethes dayes and number of degrees and also the true and halfe motion of the Sunne From the Moone also procedeth a pâ—â—ne or wyre whiche beneathe or downwarde in the border or margent of the greatest rundell sheweth the houres and passyng by the center of the Epicicle of the Moone and extendyng to the Zodiacke sheweth the halfe motion of his Planet Another also rysyng from thence and cuttyng the border of the center of the Moone that is of the Epicicle sheweth her true place whereby art seene the slownesse swyftnesse al motions and courses coniunctions also and ful Moones About these are syxe other rundels of the whiche one whom they call the head and tayle of the Dragon sheweth the Eclipses both of the Sunne and Moone The other are attributed to the Planets from euery of whiche proceede two payâ—â—es assigning the motions as we haue sayd of the Moone but they also goe backwarde whiche chaunceth not in the Moone whose Eclipse is mooued contrarywyse And thus the reason of coniunctions departynges and latitudes is manifest in all There is also an other border lyke vnto a Zodiacke cutting or diuidyng vpwarde or aboue those syx litle rundels whereof we haue spoken being the rundels of the Planettes whereby appeareth the degrees of the East signes and the spaces of the dayes that is to say at what houre the Sunne riseth by the whiche euery of the Planettes are carried in their rundels or circles by course in the day tyme to the East and in the nyght to the West Agayne contrarywyse the greatest rundel of al draweth with it al the Planettes in the nyght to the East and in the day to the West in the space of .24 houres At which to agree with the motions of heauen both reason and experience doo confyrme And therfore ought ye not to marueyle yf these thynges seeme incredible to many For as sayth the wyse Prouerve fayth is slowlye geuen to great thynges for euen we scarsely beleeue our owne eyes when we see suche thynges And therefore whereas in tyme past I read that suche a lyke instrument was made by Archimedes my fayth yet fayled me to geue credite to so great an Aucthour which thyng neuerthelesse this our Florentine hath perfourmed The worke doubtlesse beyng of such excellence that all prayse is inferior to it and can not therfore for the woâ—â—thynâ—sse thereof be otherwyse praysed then to say that it passeth all prayse The Artificer him selfe also being a man of such integritie of maners that the sunne is nothing inferior to the excellencie of his wyt in so much that he may seeme a man sent from heauen where be learned the makyng of this heauen by the example of the other Hytherto Policianus Of the lyke instrument Roger Bacon also maketh mention in his sayde booke of the marueylous power of Art and nature affyrmynge the same to be woorth a kyngdome to a wyse man But for as muche as the subiect whiche I haue nowe in hande is cheefely touchyng inuentions parteinyng to Shyppes and the Art of Nauigation I thynke good to speake somewhat of the inuention of a certayne Italian wryter named Leonardo Fâ—oâ—ananti who in his booke entituled Specchio discientia vniuersale doeth greatly glory in the inuention of Shyppes whiche can not peryshe eyther on the sea or the lande affyrmyng that the lyke was neuer inuented since the creation of the worlde But I feare me lest vayne glorie of discoursyng in the Italian tongue hath caused him more then needes to commende his owne inuention as for the moste parte is the maner of the Italian writers Therfore committing the iudgement hereof to men of greater experience and knowledge in these thynges I wyl onely translate his woordes whereby in the booke before named he describeth the sayde Shyppe in this maner Take beames of Fyrre or Pyne tree which of their owne nature can neuer goe downe or syncke or abyde vnder the water and with these beames frame an eâ—â—â—ne Machina yf I may so call it of the length of three score foure and of the breadth of twentie foote and of the heyght of syxe foote laying the fyrste ranke in length and the other trauerse or ouerthwarte and the thyrde agayne in length fasâ—â—onyng the sore parte lyke vnto other Shyppes and in lyke maner bryngyng the poupe or hynder parte to good fourme then with suche irons as â—pparteyne bynde it and strengthen it in suche maner that it can not breake And vpon this frame or fundation buylde your Shyppe of suche fashion as you thynke best c. It were here too long to rehearse with what proude woordes and ostentation he magnifieth this inuention But whether this frame or engine shoulde be bylden vpon the keele or bottome of the Shyp or otherwyse I commit it to them of better iudgement as I haue sayde But wheras it may for this tyme suffice to haue wrytten thus muche of these thynges I wyll make an ende with onely a brâ—â—te rehearsal of the inuention and encrease of the Art of Nauigation After that the Art of Nauigation was founde euery man began to chalenge vnto hym the dominion of the sea there to dwel and kepe warre euen as on the land Minos as wryteth Strabo was the fyrst that ruled on the sea whiche neuerthelesse other ascribe to Neptunus who fyrst founde the Art of Nauigation and was therefore as wryteth Diodorus appoynted by Saturnus to be Admiral of the fyrste Nauie and thereby the posteritie afterwarde ascribed to him the gouernaunce of the sea and named him the God thereof After whom the Cretenses euer were esteemed most expert in the Art of Nauigation But as wryteth Pliuie boates were fyrst inuented and with them was the fyrste saylyng in the Ilandes of the redde sea vnder kyng Erythra as also witnesseth Quintilian saying If none had proceeded
most furious wyndes what so euer they be euen also in deepest wynter and greatest sourges of waters Neyther is it marueyle yf this be incredible to the vnexpert For the common people counteth that for a miracle which the expert Mathematitians knowe to be naturall and easie for yf it shoulde be propounded to the ignoraunt people that anye man myght in the myddest of the waters and fluddes descende to the bottome of the ryuer of Rene his apparel remaynyng drye no part of his body weâ—te also to bryng with hym burnyng fire from the bottome of the water it shoulde seeme to them a laughing stocke a mockerie and impossible Whiche neuerthelesse in the yeere 1538. in Toleto a citie of Spayne in the most swyft riuer Tagus in the whiche golde is founde runnyng agaynst the course of the Sunne none otherwyse then Danubius and three other in the world makyng theyr course from the west to the East I with twelue thousand other persons saw in the presence of Charles the Emperour the fyfth of that name Of such other marueylous naturall experimentes I neede not here to speake muche Other there be that dare affirme that a certaine ship was in such sort dryuen with violent wyndes and furious seas with so swyfte a course that the Pilote standyng in the keele of the shyp neare vnto the mast shootyng an arrowe out of a crosse bowe the arrowe fel downe before his feete and came not so farre as to the forepart or forecastle of the shyp I haue hearde also of credible men that a certayne Pilote Cantabrian lying at anker at Antwerpe on a certayne Sunday after mornyng prayer departed with full sayles and prosperous wyndes vntyll he came to the coast of Saint Iames in Compostella And immediately returnyng with lyke prosperous wyndes came agayne to Antwerpe in the same shyp the Sunday next folowyng The whiche I denye not but may be done yet not without great daunger of shipwracke especially in the returne the winde beyng at the South Also in the yeere .1551 I had experience of a most swyft motion For from Drepan of Sicilia and Trinacria the porte of the galles of Maltha nowe being in place of the Rhodes otherwyse called of Saint Iohn in Ierusalem a certayne shyp without euer strykyng sayle in .37 houres arryued at Naples And yet are these places distant in latitude almost fyue degrees besyde some part of longitude whiche on the earth correspondeth or amounteth to foure hundred and fyue myles These motions are caused by violent fluddes and outragious wyndes The lyke also may be doone agaynst the furie of wyndes and violence of fluddes when neede shal be for expedite cariage of vitayles by sea and euen in places where it is harde to come to lande and this with small labour as hereafter I wyll playnely declare by Demonstration but oftentymes most expert Pilotes and sea men do marueyle that saylyng in shyppes of the selfe same makyng weyght content or capacitie framed also of the seife same shypwryght furnished with equall sayles and all other thynges apparteining yet to be of such diuers swiftnesse that the one can not kepe equal course with the other Which marueiling douhtlesse proceedeth of ignorance and lacke of knowledge of the due proportion of the frame of al sortes of shippes that is to meane the deapth breadth heyght and length named by the maisters latitude longitude altitude and profunditie The which yf they be vnknowen to the maister Carpenter or Shypwryght two shyppes can neuer be so directed by equall course but that one shal be swyfter then another as I playnely obserued in the expeditions of Arsenaria or Thunes or Agolette in which amongst in maner innumerable shyppes and especially Galleys and foystes were scarsely two or one of the same quantitie heauynesse greatnesse and capacitie dryuen all with one wynde and equall sayles that kept equall course one with another And this doubtlesse onely by reason of the different proportion of the framyng makyng or architecture Of the ryght and due proportion of what so euer Shyppe IN the framyng of any maner of shyppe the proportion of length breadth heyght and deapth ought most cheefely to be exactly obserued lest the ignorance and negligence of these consyderations shoulde hynder the swyfte course and cause daunger of shypwracke The due proportion therefore of shyppes is that fyrste the longitude or length of the shyppe or vessell what so euer it be more or lesse ought to be diuided into .300 equall partes as appeareth in the figure folowyng Of the whiche partes .30 must be assigned to the heyght or depth for the tenth part of the whole requisite longitude or length and to the latitude or breadth shall corresponde the partes of the sayde longitude .50 or the syxth part of the longitude The matter also or tymber of the Shyp must be lyght lest too muche heauynesse of the matter shoulde hynder the swyfte course And this proportion of Shyppes or other saylyng vesselles of whatsoeuer shape or frame is most conuenient and no lesse necessary As for Scafes Shyppes of burden Galleis double triple or quadruple that is to say of two three or foure men to an Ore. Also for Foystes Pinaces Brigantines Espions and suche lyke Of the framyng and Architecture of the aforesayde Shyp I HAVE often tymes attempted by Mathematical reason howe and in what maner a commodious fashion of Shyppes or other lyke vesselles may be inuented with smal labour and litle cost which may in short tyme stryue against the course of whatsoeuer strong fluddes or ryuers as Rhene Danubie Mosella Scalda and almost infinite suche other boylyng and ouerflowyng through the abundance of great showres molten snowes and furious wyndes and this especially for the commoditie of transportyng victualles and suche other necessaries In consyderation wherof the proportion fyrst obserued and the sayde Shyp or vessell almoste finished then must be made three holes from the Kele towarde the forecastle or foremoste part of the Shyp as appeareth in the fygure by the letters ABC In which holes in tyme of the course certayne engines of strange and marueylous inuentions may be fastened In the poupe or hynder parte of the Shyp maye be prepared after the maner of Germanie a litle Stoue or whotte house where the Passengers maye commodiously rest Nowe the Shyp beyng thus prepared the bottome thereof must be dressed with tallowe and not with tarre that it may mooue the swyftlyer Thus hauyng absolued the frame and proportion of the sayde Shyp the rest of Mechanicall or handicrafte woorke we leaue to the Carpenters and Shypwryghtes To what vse suche kinde of Shyppes or vesselles may be applyed IT chaunceth often tymes and especially in winter that certayne floods and riuers ouerflowen with to much abundance of waters doo with their violence refuse all nauigations that may be made agaynst their course to the great domage and hurt of the Inhabitantes of many Townes and Cities to the
from the East to the South because the vertues both of the Sunne and Moone be vnite togeather and both these Luminaries are moued continually to the moouyng of the first moueable by the quarter of the day flowyng whiche is from the East to the West the day flowyng or increase of the sea is continuall And whyle they are moued froÌ„ the South to the West because they are moued continuall by the day quarter of the reflowyng the reflowyng styll continueth And whyle they are moued from the West to mydnyght because they are then moued by the quarter of the nyght flowyng the nyght flowyng is agayne continuall And whyle they are moued from mydnyght to the East because they are then moued by the nyght quarter of reflowyng the nyght reflowyng is agayne continuall And thus twyse in the naturall day is the flowyng or increase and twyse the reflowyng or decrease of the water of the sea It is agayne secondarylye to be knowen that when the Moone after her coniunction with the Sunne by her proper motion is departed from the Sunne towarde the East accordyng to the order of the signes goeyng towarde her fyrste quadrature with the Sunne whiche the Venetian Pilottes call il Quartirune euer before the Moone by her proper motion come to that first quarter whiche is the distaunce of the Moone from the Sunne towarde the East accordyng to the order of the signes by a quarter or fourth part of heauen when the Sunne is so muche aboue the Horizon of the East parte in quarter of the day flowyng howe muche the Moone is vnder the Horizon of the same parte of the East in the quarter of the nyght reflowyng because then the Sunne is so muche distant from the strong poynt of the flowyng aboue the Horizon as the Moone is distant from the strong poynt of the reflowyng vnder the Horizon they are equipollent and of equall vertue therefore then is neyther flowyng nor reflowyng of the water of the sea but the water seemeth to stande And then the Venetians saye L'aqua è stanca But when the Sunne by the motion of the first moueable commeth neare to the strong poynt of flowyng whiche is aboue the Horizon in the day quarter of the flowyng the Moone by the same motion of the firste moueable departeth so muche from the strong poynt of the reflowyng whiche is vnder the Horizon in the nyght quarter of reflowyng commyng towarde the weake poynt of the East flowyng And then because the Sunne is nearer to the strong poynt of flowyng whiche is aboue the Horizon in the day quarter of flowyng then is the Moone in the strong poynt of reflowyng whiche is vnder the Horizon in the nyght quarter of the reflowyng the reflowyng is weakened and the flowyng is fortifyed and then the water of the sea begynneth to flowe And howe muche more the Sunne approcheth to the strong poynt of the flowing which is aboue the Horizon in the day quarter of the flowyng so much more the Moone is departed from the strong poynt of the reflowyng whiche is vnder the Horizon in the nyght quarter of the reflowyng approchyng to the weake poynt of the East flowyng and therefore the flowyng continueth But when the Sunne by motion of the first moueable commeth to the strong poynt of the flowyng whiche is aboue the Horizon in the day quarter of the flowyng then the Moone is departed from the strong poynt of the reflowyng whiche is vnder the Horizon in the nyght quarter of reflowyng and is made neare to the weake poynt of the East flowyng and therefore the flowyng yet continueth But when the Moone shall come to the weake poynt of the East flowyng shee then to the mouyng of the first moueable is moued by the day quarter of flowyng approchyng to the strong poynt of flowyng whiche is aboue the Horizon And the Sunne because it is distant from the Moone lesse then a quarter shall lykewyse be moued by the same day quarter of flowyng approchyng to the weake poynt of the South reflowyng And therefore because both are mooued by the day quarter of the flowyng the flowyng shall continue And when the Sunne by the moouing of the fyrst mooueable commeth to the weake poynt of the South reflowyng because then the Moone is nearer to the strong poynt of the flowyng whiche is aboue the Horizon then the Sunne to the strong poynt of the reflowyng whiche is aboue the Horizon in the day quarter of the reflowyng the flowyng shall continue And when the Moone shall come to the strong poynt of the flowyng in the daye quarter of flowyng the Sunne shall not yet be in the strong poynt of the reflowyng in the day quarter of the reflowing because that the Sunne is distant from the Moone lesse then a quarter but wyll come to it and then the Moone shall depart from the strong poynt of the flowyng and shal be lesse distant from it then the sunne from the strong poynt of reflowyng and therefore the flowyng shall yet continue vntyll the sunne be so muche beyonde the South toward the West in the day quarter of reflowyng howe much the moone on this syde the South towarde the East in the day quarter of the flowyng And then the sunne shal be so muche distant from the strong poynt of the reflowyng whiche is aboue the Horizon beyonde the South in the day quarter of the reflowyng howe muche the moone from the strong poynt of the flowyng whiche is aboue the Horizon before the South in the day quarter of flowyng And incontinent the Sunne and the moone shal be equipollent or of equall strength therfore shal be no flowing nor restâ—wing as we haue sayd before And when he sunne by the motion of the fyrst moueable shall come to the strong point of reflowing in the day quarter of reflowyng the moone by the same motion of the fyrst moueable shal be departed so muche from the strong poynt of flowyng in the day quarter of flowyng commyng towarde the weake poynt of the South reflowing and then the moone shal be more distant from the strong poynt of flowyng then the sunne from the strong poynt of reflowyng And so the sunne shal be stronger then the moone and therefore then shall begynne the reflowyng and shall continue accordyng that the sunne shall approch to the strong poynt of the reflowyng in the day quarter of reflowyng and the moone shal be departed from the strong poynt of the flowyng in the quarter of the day flowyng And when the sonne shal come to the strong poynt of the reflowing the moone shal be departed from the strong poynt of the flowyng and therefore the reflowyng shall yet continue And when the moone shall come to the weake poynt of the South reflowyng the sunne shal be departed from the strong poynt of the reflowyng in the day quarter of the reflowyng commyng toward the weake poynt of the West flowyng Yet shall the sunne be lesse distant from the strong poynt of
the reflowyng then the moone from the strong poynt of the flowyng and therefore the reflowyng shall yet continue And when the sunne shall come to the weake poynt of the West flowyng the moone shal be neare to the strong poynt of reflowyng which is aboue the Horizon in the day quarter of reflowyng and shal be lesse distant from it then the sunne from the strong poynt of the flowyng whiche is vnder the Horizon in the nyght quarter of flowyng because she is distant from the sunne lesse then a quarter or fourth part of heauen therefore the reflowyng shall yet continue vntyll the sunne shal be so much vnder the Horizon on the West part in the quarter of the nyght flowyng howe muche the moone is aboue the Horizon on the same part of the West in the day quarter of reflowyng And because then the Sunne shal be so much distaunt from the strong poynt of the flowyng whiche is vnder the Horizon on the Weast parte in the nyght quarter of flowyng as the Moone from the strong poynt of reflowyng whiche is aboue the Horizon on that parte of the Weast in the day quarter of reflowyng then the Sunne and the Moone shal be equipollent that is of equal strength and vertue and so shal there be neyther flowyng nor reflowyng But when the Sunne by the moouyng of the fyrst mooueable shall come to the strong poynt of the flowyng whiche is vnder the Horizon in the nyght quarter of the flowyng the Moone by the same moouyng of the fyrst mooueable shal be departed as much from the strong poynt of reflowyng whiche is aboue the Horizon in the day quarter of reflowyng And then the Sunne shal be lesse distaunt from the strong poynt of flowyng in the nyght quarter of the flowyng then the Moone from the strong poynt of reflowyng in the day quarter of reflowyng and therfore the Sunne shal be stronger then the Moone and then agayne shall begynne the flowyng and shall continue as is sayde before vntyll the Sunne be so muche beyonde mydnyght towarde the East in the nyght quarter of reflowyng howe much the Moone on this syde mydnyght toward the Weast in the nyght quarter of flowyng and then the Sunne shal be so muche distaunt from the strong poynt of the reflowyng as the Moone from the strong poynt of the flowyng and then incontinent the Sunne and the Moone shal be of equal strength and there shal be nother flowyng nor reflowyng But when the Sunne by the moouyng of the fyrst mooueable commeth to the strong poynt of the reflowyng in the nyght quarter of reflowyng the Moone by the same moouyng of the fyrst mooueable goeth backe is departed as muche from the strong poynt of the flowyng 〈◊〉 night quarter of the flowyng comming to the weake poynt of midnight reflowyng And then the Sunne shal be lesse distaunt from the strong poynt of the reflowyng in the nyght quarter of the flowyng then the Moone from the strong poynt of flowâ—ng in the nyght quarter of flowyng and then shal the flowyng be weakened and the reflowyng strengthened and the water of the sea shall then agayne begyn to reflowe whiche reflowyng shal continue as is sayde before vntyll the Sunne be so muche aboue the Horizon on the East parte howe muche the Moone vnder the Horizon on the same parte of the East And then the Sunne shal be so muche distaunt from the strong poynt of the flowyng whiche is aboue the Horizon in the day quarter of the flowyng howe much the Moone from the strong poynt of the reflowing whiche is vnder the Horizon in the nyght quarter of the reflowyng and then the Sunne and Moone agayne shal be of equall strength and there shal be nother flowyng nor reflowyng Then daylye that is to say in euery naturall day shall returne the lyke change to this aforesaid vntil the Moone by her proper motion shall come to her fyrste quadrature with the Sunne which the Pilottes or Mariners Venetians cal il Quartirone as I haue sayde before And when the Moone shall come to her fyrste quadrature with the Sunne then when the Sunne shal be in the weake poynt of the East for the flowyng the Moone shal be in the weake poynt of mydnyght for the reflowyng and then the Sunne shal be so muche distaunt from the strong poynt of the flowyng which is aboue the Horizon on the East parte in the day quarter of the flowyng howe muche the Moone from the strong poynt of reflowyng which is vnder the Horizon of the same part of the East in the nyght quarter of the reflowyng and so the Sunne and the Moone agayne shal be of equall force and power and there shal be nother flowyng nor reflowyng notable but onely smal encreasyng and diminishyng And when the Sunne by the motion of the fyrst mooueable shal come to the strong poynt of the flowyng whiche is aboue the Horizon on the East part in the day quarter of the flowing the Moone by the same motion of the fyrste mooueable shall come lykewyse so muche to the strong poynt of the reflowyng whiche is vnder the Horizon on the same parte of the East in the night quarter of the reflowyng and continually to the diurnall or day motion the Sunne shal be distaunt so muche from the strong poynt of flowyng whiche is aboue the Horizon in the day quarter of the flowyng howe muche the Moone from the strong poynt of reflowyng whiche is vnder the Horizon in the nyght quarter of the reflowyng and continentlye the Sunne and Moone shal be agayne of equall power vntyl the Sunne by the moouyng of the fyrst mooueable shal come to the strong poynt of flowyng whiche is aboue the Horizon And then lykewyse the Moone shal come to the strong poynt of reflowyng whiche is vnder the Horizon because these poyntes are distaunt one from the other by a quarter of heauen as the Sunne and Moone are distaunt from them selues by a quarter of he And when the Sunne by the motion of the fyrste mooueable shall departe from the strong poynt of the flowyng whiche is aboue the Horizon in the day quarter of the flowyng commyng towarde the weake poynt of the South reflowyng the Moone by the same motion of the fyrste mooueable shall lykewyse departe as muche from the strong poynt of the reflowyng whiche is vnder the Horizon commyng towarde the weake poynt of the East flowyng and the Sunne shal be contynually distaunt so muche from the strong poynt of flowyng whiche is aboue the Horizon howe much the Moone from the strong poynt of reflowyng whiche is vnder the Horizon vntyll the same come to the weake poynt of the South reflowyng and then the Moone lykewyse shall come to the weake poynt of the East flowyng And the Sunne and the Moone in all this tyme shal be of equall strength and incontinently shal be nother flowyng nor reflowyng notable and shal be after the same manner whyle the Sunne to the motion of the fyrste mooueable
shal be mooued from the South to the Weast because then the Moone by the same motion of the fyrste mooueable shal be mooued from the East to the South And lykewyse whyle the Sunne shal be mooued from the Weast to mydnyght because then the Moone shal be mooued from the South to the Weast And lykewyse whyle the Sunne shal be mooued from mydnyght to the East because the Moone shal be mooued from the Weast to mydnyght And so in all the tyme of one reuolution of heauen whiche is one daye naturall of foure and twentie houres the sea shall neyther flowe nor reflowe sensiblye but shall seeme to stande because the Sunne and the Moone in all the tyme of that reuolution of heauen shal be euer of equall power without any notable difference And this chaunceth about the eight day after the coniunction of the Moone with the Sunne And this false quietnesse of the water of the sea the Venetians cal Acquae de fele and vse this manner of saying Da gliotto à inoue Lacqua non si moue From the eyght day to the nienth the water mooueth not When the Moone shal be departed from the Sunne beyond the fyrst quadrature goyng towarde her opposition with the Sunne then euer vntyll the Moone shall come vnto her opposition with the Sunne when the Sunne shal be so muche aboue the Horizon on the East part in the day quarter of the flowyng how much the Moone is vnder the Horizon on the same part of the East in the nyght quarter of the reflowyng the Sunne shal be so muche distaunt from the strong poynt of the flowyng whiche is aboue the Horizon in the day quarter of flowyng departyng from it by the motion of the fyrst mooueable and commyng to the weake poynt of the reflowyng howe muche the Moone from the strong poynt of the reflowyng whiche is vnder the Horizon in the nyght quarter of the reflowyng commyng to it by the same motion of the fyrste mooueable And then the Sunne and Moone shal be agayne of equal power and there shal be neyther flowyng nor reflowyng And when the Sunne by motion of the fyrst moouable shal come to the weake poynt of the South reflowyng the Moone by the same motion of the fyrst mooueable shall approche or come neare as muche to the strong poynt of the reflowyng whiche is vnder the Horizon in the nyght quarter of the reflowyng and then the Moone shal be nearer to the strong poynt of the reflowyng whiche is vnder the Horizon in the nyght quarter of the reflowyng then the Sunne to the strong poynt of the flowyng whiche is aboue the Horizon in the day quarter of flowyng because the Moone shal be stronger then the Sunne And according that the Sunne by the motion of the fyrst mooueable shal approch to the weake poynt of the South reflowyng the Moone by the same motion of the fyrst moouable shal approch as much to the strong poynt of the reflowyng whiche is vnder the Horizon And so the reflowyng shall continue vntyll the Sunne come to the weake poynt of the South reflowyng And when the Sunne by the motion of the fyrste mooueable shall departe from the weake poynt of the South reflowyng and shal be mooued by the day quarter of the reflowyng approchyng to the strong poynt of the reflowyng the Moone by the same motion of the fyrste mooueable shall departe as muche from the strong poynt of the reflowyng whiche is vnder the Horizon in the nyght quarter of the reflowyng and she shal be also mooued by the quarter of reflowyng as the Sunne commyng to the weake poynt of the East flowyng because the Sunne and the Moone are distaunt betweene them selues more then by a quarter of heauen And so both shal be mooued by the quarters of reflowyng and therefore the reflowyng shall continue vntyll the Sunne shal be so muche beyonde the South towarde the Weast in the day quarter of the reflowyng howe muche the Moone on this syde the South towarde the East in the day quarter of the flowyng And then the Sunne shal be so muche distaunt in the strong poynt of reflowyng in the day quarter of reflowyng departyng from it by the motion of the fyrste mooueable towarde the Weast howe muche the Moone from the strong poynt of flowyng whiche is aboue the Horizon in the day quarter of the flowyng commyng to it And so the Sunne and the Moone shal be of equall force and then shal be neyther flowyng nor reflowyng And when the Sunne by the motion of the fyrste mooueable shal be departed from the strong poynt of the reflowyng which is aboue the Horizon in the day quarter of the flowyng commyng to the weake poynt of the Weast flowyng the Moone by the same moouing of the fyrst moouable shall approch as much to the strong poynt of the flowyng whiche is aboue the Horizon in the day quarter of the flowyng and then the Moone shal be nearer to the strong poynt of the flowyng in the day quarter of the flowyng then the Sunne to the strong poynt of the reflowyng in the day quarter of the reflowyng and so the Moone shal be stronger then the Sunne and then shal begynne the flowyng And as the Sunne shal cōtinually be departed from the strong poynt of reflowyng in the day quarter of the reflowyng so the Moone continually shal approche to the strong poynt of flowyng in the day quarter of the flowyng and so the flowyng shall continue And when the Sunne shal come to the weake poynt of the Weast flowing the Moone shall yet mooue by the day quarter of the flowyng because the Sunne and the Moone are distaunt one from the other more then by a quarter of heauen and then the Moone shal be nearer to the strong poynt of flowyng in the quarter of the day flowing then the Sunne to the strong poynt of flowing whiche is vnder the Horizon in the nyght quarter of the flowyng and therefore the flowyng shall continue And when the Moone shall come to the weake poynt of the South reflowyng the Sunne shall passe the weake poynt of the Weast flowyng approchyng to the strong poynt of the flowyng whiche is vnder the Horizon in the nyght quarter of the flowyng and then the Sunne shal be nearer the strong poynt of the flowyng which is vnder the Horizon in the night quarter of the flowyng then the Moone to the strong poynt of the reflowyng which is aboue the Horizon in the day quarter of the reflowyng and so the Sunne shal be stronger then the Moone and therefore the flowyng shall continue And when the Sunne shall come to the strong poynt of flowyng whiche is vnder the Horizon in the nyght quarter of the flowyng the Moone shall not yet be in the strong poynt of the reflowyng whiche is aboue the Horizon in the day quarter of the reflowyng because the Moone is distaunt from the Sunne more then by a quarter of heauen and therefore the flowyng shall yet continue vntyll
the nyght quarter of reflowing toward the weake poynt of the East flowyng the Sunne by the same mouyng of the fyrst moueable shall approche as muche to the strong poynt of flowyng whiche is vnder the Horizon on the West part in the nyght quarter of flowyng commyng to it And then because the Moone shal be more distant frō the strong poynt of reflowyng then the Sunne from the strong poynt of flowyng then shal begyn the flowyng because the Sunne shal be stronger then the Moone And howe muche more the Moone shal be distant from the strong poynt of reflowyng in the nyght quarter of reflowyng so much more the Sunne shall approch to the strong poynt of flowing in the night quarter of flowyng and so the flowyng shall continue and when the Moone shall come to the weake poynt of the East flowyng the Sunne shall yet be in the nyght quarter of flowyng because the Sunne is distant from the Moone more then by a quarter of heauen and the Sunne shal be nearer to the strong point of flowing in the night quarter of flowing then the Moone to the strong poynt of reflowyng which is in the night quarter of reflowing and so the flowing shal yet continue vntyl the Moone be so much aboue the Horizon on the East parte howe muche the Sunne vnder the Horizon on the same parte of the East And then the Moone shal so much be distant from the strong point of flowing whiche is aboue the Horizon in the day quarter of flowyng departyng from it by the motion of the first moueable towarde the weake poynt of the South reflowyng howe muche the Sunne from the strong poynt of reflowyng which is vnder the Horizon in the night quarter of reflowyng commyng to it by the same motion of the first moueable And then the Sunne the Moone shal be of equall force and there shal be neyther flowyng nor reflowyng and the first disposition shall returne agayne and suche flowyng and reflowyng shall continue euery natural day in this maner vntyll the Moone shall come to her quadrature with the Sunne And when the Moone shal be in the seconde quadrature then the water of the sea shall neyther flowe nor reflowe but shall seeme to be at rest as it was in the first quadrature in the which in the whole reuolution of heauen the Sunne and the Moone were euer of equall strength for the causes there declared for the same are the causes of the seconde quadrature which are also of the fyrst and is about .21 dayes And this quietnes or stay of the water of the sea as is sayde before the Venetians call Acqua de fele and vse this saying Da vent ' uno à venti due l'acqua non va ne su ne giu From the .21 to .22 the water goeth neither vp nor downe And when the Moone by her proper motion shall passe this seconde quadrature proceedyng to her coniunction with the Sunne then the Moone shal be distant from the Sunne lesse then the fourth parte of heauen And then when she shal be so muche aboue the Horizon on the East parte in the day quarter of flowyng as the Sunne vnder the Horizon on the same parte of the East in the nyght quarter of reflowyng then the Moone shal be so muche distant from the strong poynt of flowyng which is aboue the Horizon in the day quarter of flowyng commyng to it by the motion of the fyrste moueable howe muche the Sunne from the strong poynt of reflowyng whiche is vnder the Horizon in the nyght quarter of reflowing going from it by the same motion of the fyrste moueable towarde the weake poynt of the East flowyng and then the Sunne and the Moone shal be of equall power and there shal be neyther flowyng nor reflowyng And when the Moone by the motion of the fyrst moueable shall come to the strong poynt of flowyng whiche is aboue the Horizon in the day quarter of flowyng the Sunne by the same motion of the first moueable shall depart as muche from the strong poynt of reflowyng whiche is vnder the Horizon in the nyght quarter of reflowyng toward the weake poynt of the East flowyng And then because the Moone shal be lesse distant from the strong poynt of flowyng whiche is aboue the Horizon in the day quarter of flowyng then the Sunne from the strong poynt of reflowyng the Moone shal be stronger then the Sunne and therefore then shall begynne the flowyng and howe much more the Moone shall approche to the strong poynt of flowyng so muche more the Sunne shal be distant from the strong poynt of reflowyng approching to the weake poynt of the East flowing and therefore the flowyng shall continue And when the Sunne by the mouyng of the fyrste moueable shall come to the weake poynt of the East flowyng because the Moone shall yet be in the day quarter of flowyng for that she is distant from the Sunne lesse then a fourth parte of heauen she shal be lesse distant from the strong poynt of flowyng whiche is aboue the Horizon in the day quarter of flowyng then the Sunne from the strong poynt of reflowyng whiche is vnder the Horizon in the nyght quarter of reflowyng therefore the flowyng shall yet continue And when the Moone shall come to the weake point of the South reflowyng the Sunne shal be aboue the Horizon in the day quarter of flowyng and shal be nearer to the strong poynt of flowyng then the Moone to the strong poynt of reflowyng whiche is after mydday or the South in the day quarter of reflowyng because the Sunne is distant from the Moone lesse then the fourth parte of heauen and therefore the flowyng shall continue vntyll the Moone be so muche beyonde the South towarde the West in the day quarter of reflowyng howe muche the Sunne before the South towarde the East in the day quarter of flowyng And then the Moone shal be so muche distant from the strong poynt of reflowyng in the day quarter of reflowyng commyng to it by the motion of the firste moueable howe muche the Sunne from the strong poynt of flowyng in the day quarter of flowyng departyng from it by the same motion of the firste moueable and so the Sunne and the Moone shal be of equall force and there shal be neyther flowyng nor reflowyng And when the Moone by the motion of the firste moueable shal approch to the strong poynt of reflowyng in the day quarter of reflowyng the Sunne by the same motion of the first moueable shall goe backe and depart as muche from the strong poynt of flowyng in the day quarter of flowyng and then the Moone shal be nearer to the strong poynt of reflowyng in the day quarter of reflowyng then the Sunne to the strong poynt of flowyng in the day quarter of flowyng and so the Moone shal be stronger then the Sunne and therefore shall begynne the reflowyng and the flowyng and reflowyng shall continue in the same maner as is sayde When the