IT is a common prouerbe that in stones, woodes, and hearbes, consy­steth great vertue: which saying is doubtlesse most manifest by the day­ly experience of this stone, beyng founde in sundry places of India, it is sayde also that it was founde in Spayne by one named Heracleon (as witnesseth Nicander) whyle in keepyng of cattell, Fiue kindes of Lode stones. the iron nayles of his showes and pyke of his staffe, cleft fast to the stone. Of the which Magnes, are fiue kinds as Sotacus wryteth. That is to wyt: one of Ethiopia. An other of Macedonia. The thyrde is founde in Echio of Beotia. The fourth about Troades of Alexandria. Lode stone male and fe­male. The fyfth of Magnesia Asiae. The difference of the stone is, whether it be male or fe­male. The next difference, is in coloure: for that which is founde in Macedonia and Magnesia, is ruddishe and blacke. That of Beotia, is more ruddish thē blacke. That of Troades is blacke, and of female kinde, and therefore without vertue. The best Lodestone of Hewe colour. Lode stone s [...]d for the weight of si [...]uer. The worst of Magnesia Asiae, is whyte, and draweth not iron, and is lyke vnto a punice stone. They are proued the best which are most of blewe or heauenly colour. That of Ethiope is most praysed, and (as Plinie sayth) is solde for the weight of siluer. This is found in Zimri, a sandie region of Ethiope, where is also founde Hae­matites Magnes, of blooddy colour, appearyng lyke blood yf it be grounde, and also lyke saffron, whiche in drawyng of iron, One lodestone draweth ano­ther. is not of like vertue to the Hematites Magnes of Ethiopia, whi­che draweth vnto it another Magnes. All these be profitable for medicines of the eyes, eche of them accordyng to their portion, and do specially stay Epiphoras (that is) droppyng of the eyes. Lode stones m [...]d [...]cin [...] [...] for the [...]. And also beyng brunt or made in powder, they heale burninges. And not farre from the same place of Ethiopia, is a mountayne [Page] whiche bryngeth forth the stone called Theamedes, The stone Theamedes putteth iron from it. which put­teth from it, and refuseth iron. I haue often prooued the vertue and power of the stone Magnes, by the needle whiche is in some Dialles, by the attraction thereof, moouyng it selfe from syde to syde, and rounde about. Although the stone were vnder a table, yet doeth the needle, being aboue the table, naturally folow the moouyng of the stone. It is therfore no marueyle yf there be great vertue in stones, Iron nayles drawen out of Shippes by the stone. woodes, and herbes. It hath also been prooued, that Shyppes compact with iron nayles, saylyng by the sea of Ethiope, and by tempest dryuen to lande, to certayne capes or landes endes, haue by these stones been eyther drawen to the bottome of the sea, or els the nayles beyng drawen out by the vertue of the stone, the Shyp hath fallen in a thousande peeces. And therefore the discreete and ware Cantabrians, most expert Mariners, saylyng by the sea of Ethiope, frame their Shyppes with pynnes and hoopes of wood, to auoyde the dan­ger that myght chaunce of lyke occasion.

WE intende nowe to speake of moste swyft motion, which to the cōmon sorte of men seemeeth incredible, for that the same maye be doone by saylyng in a shyp or other vessell, a­gaynst what so euer moste outragi­ous course of any fludde or ryuer, and agaynst 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: A strang ex­periment prac­tised. 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 we [...]te, & also to bryng with hym burnyng fire from the bot­tome of the water, it shoulde seeme to them a laughing stocke, a mockerie, The ryuers of Tagus & Da­nubius. 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, M [...]rueylous swiftnesse of a shyp. 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 [Page] men, that a certayne Pilote Cantabrian, lying at anker at Ant­werpe, on a certayne Sunday after mornyng prayer, Swyfte spe [...] after m [...]nyng 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, Another expe­rience of swift sayly [...]. 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 shalbe 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, The differēce of sh [...]ppe [...] in sa [...]ng. 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. The prop [...] in [...]aming of shyppes. 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 shalbe swyfter then another, as I playnely obserued in the expe­ditions of Arsenaria, or Thunes, or Agolette: [...]nes and [...]. in which amongst in maner innumerable shyppes, and especially Galleys, and [Page] 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.

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.

Therfore, for the more easie vnderstandyng of these two ma­ners of motions of the water of the sea, folowyng the moouyng of the Sunne and Moone, to the mouing of (primum mobile) the fyrst moueable, is fyrst to be knowen, Diuisiō of [...] ­uen and the H [...]i [...]. [...] [...] ­u [...]n into two partes. that whersoeuer a man is on the earth, his Horizon (as I haue said before in my treatise of the sphere) euer cutteth or diuideth to him the heauen into two halfes, & the one halfe of heauen is euer aboue his Horizon, and the other halfe beneath. And whereas in the halfe of a sphericall or rounde body, are conteyned two quarters, two quarters shall

[Page] euer be aboue his Horizon, & two beneath. Those that are aboue the Horizon, are called diurnall or day quarters: & they that are vnder the Horizon, are called nocturnall or nyght quarters. Of these foure quarters of heauen, are two in the which is made the flowyng or increase of the water of the sea: and other two in the which is made the reflowing or decrease of the sea. The quarters in the which is made the flowing, is the quarter whiche is from the East to the South aboue the Horizon, whiche is the quarter of the day accesse, or increase of the day: and the quarter opposite or contrary, which is from the West to midnight vnder the Ho­rizon, is the quarter of the nyght accesse. The quarters in which is made the reflowyng or decrease, is the quarter which is from the South to the West aboue the Horizon, which is the quarter of the recesse of the day: and the quarter opposite, which is from mydnyght to the East vnder the Horizon, is the quarter of the recesse of the nyght. &c.

Secondaryly, is also to be knowen, Eyght p [...]in [...]s of [...]u [...]n for [...] and res [...]yng. that there be in heauen eyght poyntes for the flowyng and reflowyng, or increase and decrease of the sea: of the whiche, foure are strong, and foure weake. Of the weake, two are weake for the flowyng, and two for the reflowyng. Weake for flowyng, are the poynt of the East, and poynt of the West, whiche are the begynnyng of the two quarters of flowyng. Weake for reflowyng, are the poynt of the South or mydday, and the poynt of mydnyght, whiche are the begynnynges of the two quarters of reflowyng: and these foure poyntes are distant the one from the other, by a quarter of heauen. Of the strong poyntes, two are strong for flowyng, and two for reflowyng. Strong for the flowyng, are the middle poynt betweene the East and the South in the daye quarter of flowyng, beyng distant from the East .45. degrees, and from the South lykewyse: And the middle poynt betweene the West and mydnyght, in the nyght quarter of flowyng, [...] ­yng distant from the West 45. degrees, and from mydnyght lykewyse. Poyntes strong for the reflowyng, is the myddle poynt, betweene South and West, in the day quarter of the re­flowyng, beyng distant from the South .45. degrees, and from the West lykewyse: And the myddle poynt betweene midnight [Page] and the East, 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. 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, The aspectes whiche the Moone ma­keth with the Sunne euery moneth. is called the Coniunction of the Moone with the Sunne. From thence for the space of eyght dayes, or there about, the Moone is departed from the Sunne by her proper motion by a fourth part of heauen: and this departyng is called the fyrste quarter of the Moone with the Sunne. From thence in fourteene dayes, or thereabout, she is departed from the sunne by an other fourth parte of heauen, and so by the halfe of hea­uen: and this distance is called the opposition of the Moone with the Sunne, or the ful Moone. From thence to .21. dayes or thereabout, she is departed from her opposition with the sunne or full Moone by an other fourth part of the heauen, commyng towarde the Sunne: and this distance is called the seconde qu [...]ature of the Moone with the Sunne, and then the Moone is distant from the Sunne by a fourth parte of heauen, as it was distant in the fyrste quarter, and so commeth neare to Con­iunction with the Sunne. From thence at thyrtie dayes, or thereabout, the Moone is agayne with the Sunne in coniunc­tion, as it was fyrst.

Fyftly and lastly, is to be knowen that the Sunne & Moone, both togeather euery naturall day (whiche is the tyme of .24. [...] houres, to the mouyng of the fyrst moueable) are the causes of flowyng and reflowyng, or increase and decrease of the water of the sea twyse. These declarations premised, and wel kept in memorie, let vs declare howe the Sunne and Moone both togeather euery naturall day; to the moouyng of the fyrste moueable, are the causes of the flowyng and reflowyng of the sea. For yf these declarations be well helde in memorie, and espe­cially the quarters of heauen in whiche is the flowyng, and the quarters of heauen in whiche is the reflowyng, and whiche are the strong poyntes for the flowyng, and strong poyntes for the reflowyng, and whiche be the weake poyntes for the flowyng, and the we [...]ke poyntes for the reflowyng: these (I say) beyng kept in memorie, al the narration of the mouyng, and false quiet­nesse of the sea, shalbe 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, The Sunne & Moone beyng in con [...]ction, what effect [...]s they ha [...] in mo [...] the w [...] the sea. 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) 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 frō 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, A quarter of heauē is three signes. 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, A tyme wher­in is neyther ebbyng nor flowyng. 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 [Page] 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 shalbe 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 shalbe 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, [Page] before the South in the day quarter of flowyng: And inconti­nent, the Sunne and the moone shalbe equipollent or of equall strength, & therfore shalbe no flowing nor rest [...]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 y ^e day quarter of reflowyng, the moone by the same motion of the fyrst mouea­ble, shalbe 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 shalbe more distant from the strong poynt of flowyng, then the sunne from the strong poynt of reflowyng: And so the sunne shalbe 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 shalbe 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 shalbe 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 shalbe 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 shalbe neare to the strong poynt of reflowyng, which is aboue the Horizon in the day quarter of re­flowyng, and shalbe 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 shalbe 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 [Page] then the Sunne shalbe 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 shalbe 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, shalbe departed as much from the strong poynt of reflowyng, whiche is aboue the Hori­zon in the day quarter of reflowyng: And then the Sunne shalbe 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 shalbe 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 shalbe 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 shalbe of equal strength, and there shalbe 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 y ^e weake poynt of midnight reflowyng: And then the Sunne shalbe lesse distaunt from the strong poynt of the reflowyng, in the nyght quarter of the flo­wyng, then the Moone from the strong poynt of flow [...]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 [Page] (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 shalbe 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 shalbe of equall strength, and there shalbe 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. The Moone being in [...]ar­tile aspect, or at the firste with the [...]ar­ter, some what effectes it cau­seth in ebbyng and flowyng. And when the Moone shall come to her fyrste quadrature with the Sunne, then when the Sunne shalbe in the weake poynt of the East for the flowyng, the Moone shalbe in the weake poynt of mydnyght, for the reflo­wyng: and then the Sunne shalbe 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 shalbe of equall force and power, A very litle ebbyng or flowyng. and there shalbe 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 shalbe 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 [Page] Moone shalbe 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 shalbe 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 shalbe of equall strength, and incontinently shalbe nother flowyng nor reflo­wyng notable, and shalbe after the same manner whyle the Sunne to the motion of the fyrste mooueable, shalbe moo­ued from the South to the Weast, because then the Moone by the same motion of the fyrste mooueable, shalbe moo­ued from the East to the South: And lykewyse, whyle the Sunne shalbe mooued from the Weast, to mydnyght, because then the Moone shalbe mooued from the South, to the Weast: And lykewyse, whyle the Sunne shalbe moo­ued from mydnyght to the East, Eyght daies [...] ­ter [...]. because the Moone shal­be 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 [Page] reuolution of heauen, shalbe 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 shalbe 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 shalbe 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 shalbe 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 shalbe agayne of equal power, and there shalbe 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 shalbe 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 shalbe 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 [Page] 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 shalbe 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 shalbe 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 shalbe mooued by the quarters of reflowyng, and therefore the reflowyng shall continue, vntyll the Sunne shalbe 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 shalbe 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 shalbe of equall force, and then shalbe neyther flowyng nor reflowyng. And when the Sunne by the motion of the fyrste mooueable, shalbe 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 shalbe 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 shalbe 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 [Page] 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 shalbe 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 shalbe 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 shalbe stronger then the Moone, and therefore the flowyng shall continue. A long tyme of flowyng. 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 Sunne be so muche vnder the Horizon on the Weast parte, in the nyght quarter of the flowyng, howe muche the Moone aboue the Horizon on the same parte of the Weast, in the day quarter of the reflo­wyng and then the Sunne shalbe so muche distaunt from the strong poynt of the flowyng, whiche is vnder the Horizon in the nyght quarter of the flowyng, commyng to the weake poynt of midnight reflowyng, howe much the Moone from the strong poynt of reflowyng, whiche is aboue the Horizon, in the day quarter of the reflowyng commyng to it: and therefore the Sunne and the Moone shalbe of equal strength, and then shalbe neyther flowyng nor reflowyng. Afterwarde, when the Sunne [Page] by the motion of the fyrste mooueable, shalbe distaunt from the strong poynt of the flowyng, whiche is vnder the Horizon on the Weast parte, in the nyght quarter of the flowyng, commyng towarde the weake poynt of mydnyght reflowyng, the Moone by the same motion of the fyrste mooueable, shall approche as muche to the strong poynt of reflowyng, whiche is aboue the Horizon, in the day quarter of the reflowyng commyng to it. And so the Moone shalbe nearer to the strong poynt of reflo­wyng, then the Sunne to the strong poynt of flowyng, and ther­fore the flowyng shall begynne, and shall continue in maner (as is sayde) vntyll the Sunne be so muche beyonde mydnyght, toward the East, in the nyght quarter of reflowyng, howe much the Moone before mydnyght towarde the Weast, in the nyght quarter of flowyng: and then the Sunne shalbe so much distaunt from the strong poynt of reflowyng, in the nyght quarter of reflowyng, goyng backwarde from it towarde the foresayde weake poynt of the East flowyng, howe muche the Moone from the poynt of the strong flowyng, in the nyght quarter of the flowyng commyng to it: and then the Sunne and the Moone shalbe of equall force, and there shalbe neyther flowyng nor reflowyng. And when the Sunne by the motion of the fyrst mooueable, shalbe departed from the strong poynt of reflowyng, vnder the Horizon, which is in the nyght quarter of reflowyng, commyng towarde the weake poynt of the East flowyng, the Moone by the same motion of the fyrst moouable, shal approch as much to the strong poynt of flowyng, which also is vnder the Horizon, in the nyght quarter of the flowyng commyng to it. And because then the Moone is nearer to the strong poynt of flowyng, whiche is in the nyght quarter of flowyng, then the Sunne to the strong poynt of reflowyng, whiche is in the nyght quarter of reflowyng: then shall the flowyng begynne and continue in manner aforesayde, vntyll the Sunne be so muche aboue the Horizon on the East parte, 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. And because the Sunne shalbe so much distaunt from the strong poynt of flowyng, whiche is aboue the Horizon, [Page] in the day quarter of flowyng, commyng by the motion of the fyrst mooueable, towarde the weake poynt of the South reflo­wyng, howe muche the Moone from the strong poynt of reflo­wyng, whiche is vnder the Horizon, in the nyght quarter of re­flowyng, commyng by the same motion of the fyrst mooueable towarde it, they shalbe of equall force, and so shalbe neyther flo­wyng nor reflowyng. And in this maner, the flowyng and re­flowyng shall continue in euery naturall day, vntyll the Moone shall come to her opposition with the Sunne.

The Moone being in oppo­sition with the Sunne, what effectes they haue in moo­uyng the wa­ter of the sea.And when the Moone shall come to her opposition with the Sunne, then when the Sunne shalbe in the weake poynt of the East flowyng, the Moone shal lykewyse be in the weake poynt of the Weast flowyng: and then shal the flowyng begyn, and shall continue as long as the Sunne shalbe mooued to the moouyng of the fyrste mooueable, from the weake poynt of the East flowyng, by the day quarter of the flowyng, to the weake poynt of the South reflowyng. And the Moone then in al this tyme, shalbe mooued lykewyse to the moouyng of the fyrste mooueable, from the weake poynt of the Weast flowyng, by the nyght quarter of flowyng, to the weake poynt of mydnyght re­flowyng: and then the flowyng shall ceasse, and the reflowyng begynne, and continue as long as the Sunne at the moouyng of the fyrste mooueable, shalbe mooued from the weake poynt of the South reflowyng, by the day quarter of reflowyng, vnto the weake poynt of the Weast flowyng, and the Moone in all that tyme shalbe mooued lykewyse to the moouyng of the fyrste mooueable, from the weake poynt of mydnyght reflowyng, by the nyght quarter of reflowyng, vnto the weake poynt of the East flowyng: and then the reflowyng shall ceasse, and the flo­wyng shall begynne agayne, and shall continue as long as the Sunne shalbe mooued to the motion of the fyrste mooueable, from the weake poynt of the Weast flowyng, by the nyght quarter of the flowyng, vnto the weake poynt of mydnyght re­flowyng. And then the Moone in al that time, by the same moo­uyng of the fyrst mooueable, shall lykewyse be mooued from the weake poynt of the East flowyng, by the day quarter of the flo­wyng, vnto the weake poynt of reflowyng: and then the flowyng [Page] shall ceasse, and the reflowyng begyn, and shall continue as long as the Sunne, by the mouyng of the first moueable, shalbe mo­ued from the weake poynt of mydnyght reflowyng, by the night quarter of the reflowyng vnto the weake poynt of the East flowyng. And then the Moone in all this tyme by the same motion of the fyrste moueable, shalbe moued lykewyse from the weake poynt of the South reflowyng, by the day quarter of the reflowyng, vnto the weake poynt of the West flowyng: and then the reflowyng shall ceasse.

And when the Moone shall passe her opposition with the Sunne by her proper motion, The Moone [...]. goyng to her seconde quadrature with the Sunne, then when the Moone shalbe so muche aboue the Horizon on the East part in the day quarter of flowyng, how muche the Sunne vnder the Horizon on the same part of the East in the nyght quarter of the reflowyng, because then the Moone shalbe so much distant from the strong poynt of flowing wh che is aboue the Horizon in the day quarter of flowyng, how muche the Sunne from the strong poynt of reflowyng, whiche is vnder the Horizon on the same parte of the East in the nyght quarter of reflowyng, then the Sunne and the Moone shalbe of equall power, and therefore shalbe neyther flowyng nor re­flowyng. And when the Moone by motion of the fyrste mo­ueable, shalbe departed from the strong poynt of flowyng, which is aboue the Horizon in the day quarter of flowyng, commyng towarde the weake poynt of the South reflowyng, the Sunne by the same motion of the fyrste moueable, shall approche as muche to the strong poynt of reflowyng, whiche is vnder the Horizon of the nyght quarter of reflowyng, commyng to it: and then because the Sunne shalbe lesse distant from the strong poynt of reflowyng, whiche is vnder the Horizon on the East parte in the nyght quarter of reflowyng, then the Moone from the strong poynt of flowyng, whiche is aboue the Horizon on the same parte of the East in the day quarter of flowyng, the re­flowyng shall beginne and continue. And when the Moone by the motion of the firste moueable, shall come to the weake poynt of the South reflowyng, the Sunne shall yet be vnder the Horizon in the nyght quarter of reflowyng, because the Sunne [Page] and the Moone are distant frō them selues more then by a quar­ter of heauen, and then the Moone to the mouyng of the firste moueable, shalbe moued by the day quarter of reflowyng, as al­so the Sunne in lyke maner by the nyght quarter of reflowyng, commyng to the strong poynt of reflowyng in the day quarter of reflowyng, and so the reflowyng shall continue. And when the Moone shall approche to the strong poynt of reflowyng in the day quarter of reflowyng, the Sunne shall approche to the weake poynt of the East flowyng, in the nyght quarter of re­flowyng, and shalbe further distant from the strong poynt of flowyng, whiche is aboue the Horizon, in the day quarter of flowyng, then the Moone from the strong poynt of the reflow­yng, whiche is lykewyse aboue the Horizon in the day quarter of reflowyng: and so the reflowyng shall continue, vntyll the Moone be so muche beyonde the South towarde the West in the day quarter of the reflowyng, as the Sunne before the South towarde the East in the day quarter of flowyng: and then the Moone shalbe so farre distant from the strong poynt of reflowyng in the day quarter of reflowyng, howe muche the Sunne from the strong poynt of flowyng in the day quarter of flowyng: and so the Sunne and the Moone shalbe of equall force, and there shalbe neyther flowyng nor reflowyng. And when the Moone by the motion of the firste moueable, shall depart from the strong poynt of reflowyng, commyng towarde the weake poynt of the West reflowyng, the Sunne by the same motion of the firste moueable, shall approche as muche to the strong poynt of flowyng, in the day quarter of flowyng: And then because the Sunne shalbe nearer to the strong poynt of flowyng, whiche is in the day quarter of flowyng, then the Moone in the strong poynt of reflowyng, whiche is in the day quarter of reflowyng, the flowyng shall begynne and continue accordyng that the Moone, to the mouyng of the fyrste moue­able, shalbe departed from the strong poynt of reflowyng, in the day quarter of reflowyng, commyng towarde the weake poynt of the West flowyng: and the Sunne shall approche to the strong poynt of the flowyng, in the day quarter of the flow­yng commyng to it.

And when the Moone to the mouyng of the fyrste mouea­ble, shall come to the weake poynt of the West flowyng, the Sunne yet by the same motion of the first moueable, shall moue by the day quarter of the flowyng, because the Sunne and Moone are distant the one from the other more then by a quar­ter of heauen: & the Sunne shalbe more neare to the strōg poynt of the flowyng, in the day quarter of flowyng, then the Moone to the strong poynt of reflowyng, in the day quarter of reflow­yng, and therefore the flowyng shall continue. And when the Sunne shal come to the weake poynt of the South reflowyng, y ^e Moone shalbe vnder the Horizon on the West part in the nyght quarter of the flowyng, and shalbe nearer to the strong poynt of the flowyng, whiche is vnder the Horizon in the nyght quarter of the flowyng, then the Sunne to the strong poynt of reflowyng, whiche is aboue the Horizon in the day quarter of reflowyng: And therefore the flowyng shall yet continue, vn­tyll the Moone be so muche vnder the Horizon on the West parte, in the nyght quarter of the flowyng, howe muche the Sunne aboue the Horizon on the same part of the West in the day quarter of the reflowyng. And then the Moone shalbe so muche distant from the strong poynt of flowyng, vnder the Ho­rizon in the nyght quarter of flowyng, commyng towarde the weake poynt of mydnyght reflowyng, howe muche the Sunne from the strong poynt of reflowyng aboue the Horizon, in the day quarter of reflowyng commyng to it: and so the Sunne and Moone shalbe of equall strength, and then shalbe neyther flowyng nor reflowyng. And when the Moone by the motion of the fyrste moueable, shall departe from the strong poynt of flowyng vnder the Horizon, in the nyght qu [...]ter of flowyng, commyng towarde the weake poynt of mydnyght reflowyng, the Sunne by the same motion of the firste moueable, shall ap­proche as muche to the strong poynt of reflowyng, whiche is aboue the Horizon, in the day quarter of reflowyng commyng to it: And then the Sunne shalbe nearer to the strong poynt of reflowyng, whiche is aboue the Horizon, in the day quarter of reflowyng, then the Moone to the strong poynt of flowyng, whiche is vnder the Horizon, in the nyght quarter of flowyng [Page] And therefore then shall begynne the reflowyng, and shal conti­nue accordyng that the Moone shall departe from the strong poynt of flowyng, whiche is vnder the Horizon in the nyght quarter of flowyng, approchyng vnto the weake poynt of myd­nyght reflowyng, and the Sunne shall approche to the strong poynt of reflowing, which is aboue the Horizon in the day quar­ter of reflowyng. And when the Moone by the motion of the first moueable, shall come to the weake poynt of mydnyght re­flowyng, the Sunne shal yet be aboue the Horizon on the West part in the day quarter of reflowyng, commyng by the motion of the first moueable, to the weake poynt of the West flowyng, because the Sunne and the Moone are distant one from the o­ther more then by a quarter: And then the Sunne shalbe more distant from the strong poynt of flowyng, whiche is vnder the Horizon on the West part in the quarter of the nyght flowyng, then the Moone from the strong poynt of reflowyng, which also is vnder the Horizon on the part of the East in the night quarter of reflowyng. And therefore the reflowyng shall continue vntyll the Moone be so muche beyonde mydnyght towarde the East, how much the Sunne before mydnyght towarde the West: and then the Moone shalbe so farre distant from the strong poynt of reflowyng in the nyght quarter of reflowyng, goyng from it by the motion of the firste moueable, and commyng to the weake poynt of the East flowyng, howe muche the Sunne from the poynt of flowyng in the nyght quarter of flowyng, commyng to it by the same motion of the firste moueable: and so the Sunne and the Moone shalbe of equall force, and then shalbe neyther flowyng nor reflowyng. And when the Moone by the motion of the first moueable, shalbe departed from the strong poynt of re­flowyng, whiche is vnder the Horizon, on the East parte of 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 shalbe more distant frō the strong poynt of reflowyng, then the Sunne from the strong poynt of flowyng, then shal begyn the flowyng, [Page] because the Sunne shalbe stronger then the Moone. And howe muche more the Moone shalbe 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 shalbe 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 shalbe of equall force, and there shalbe 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 shalbe in the seconde quadrature, The Moone beyng in the last quarter, causeth the same effectes as in the first. 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 shalbe distant from the Sunne, lesse then the fourth parte of heauen. And then when she shalbe 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 shalbe so muche distant from the strong poynt of flowyng, which is aboue the Horizon, in y ^e 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 shalbe of e­quall power, and there shalbe 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 shalbe 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 shalbe 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 shalbe 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 shalbe 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 [Page] 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 shalbe aboue the Horizon, in the day quarter of flowyng, and shalbe 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 shalbe 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 shalbe of equall force, and there shalbe 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 shalbe 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 shal­be 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 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. A briefe col­lection of all the premisses. 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. [Page] 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.

Ebhyng and flowyng begin not alwayes at one houre.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 shalbe 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.

Great motio is of the water in the coniun­ction of the Sunne and Moone.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: Greatest mo­tions in opposi­tion of the Sunne and Moone. 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 y ^t then should be caused greater flow­ynges and reflowyngs, then in her coniunction with the Sunne. Neuerthelesse, because that in her coniunction with the Sunne, [Page] 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, Smal motions of the water without de­terminate time alwayes in the quadratures of the Sunne and Moone. 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 shalbe in moouyng to the water equally, or as it were equally, haue contrarietie in what so euer poynt they shalbe. For in what so euer poynt the Sunne shalbe, the Moone shalbe in the point of opposite vertue, contrary to the place of the Sunne, or neare.

And when the Moone shalbe without the sayde foure pla­ces, then the water of the sea shal begynne to come or goe. And when the Sunne and Moone shalbe in equall poyntes of ver­tue of the quarters of contrary operation, the concourses of wa­ters shalbe so muche the greater, Note. 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 shalbe nea­rer to the quadratures, lykewyse also the flowynges and reflo­wynges shalbe so muche the greater. The Moone foloweth the Sunne in ry­sing. For yf the Moone shal­be 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 shalbe 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 flo­wyng s al e [...] [...]ares after Sunne rysing. when the Sunne shalbe 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 shalbe of equall force, because they shalbe in the poyntes of equal [Page] vertue in the quarters of contrary operation, and the begyn­nyng of the nyght flowyng shalbe in the nyght, after the fal of the Sunne (that is) when the Sunne shalbe 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: Ebbyng after noone. And the begynnyng of the day reflowyng shalbe in the day after noone, when the Sunne shalbe 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, shalbe in the day af­ter mydnyght (that is) when the Sunne shalbe 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 shalbe the begynnyng of the day flowyng, in the day after noone, about euenyng (that is) a litle before or af­ter, that when the Sunne shalbe 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, shalbe in the day before day (that is) about mornyng, before or after (that is) when the Sunne shalbe 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, shalbe in the day before noone, when the Sunne shalbe so muche before the poynt of noone, howe much the Moone after the poynt of myd­nyght. And the begynnyng of the nyght reflowyng, shalbe in the nyght, before mydnyght, when the Sunne shalbe 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 shalbe betweene the opposition of the Sunne, and her seconde quadrature with the Sunne, then the Moone in her [Page] rysyng, goeth before the Sunne, The Moone rysing 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, shalbe in the day about three of the clocke, before or after (that is) when the Sunne shalbe 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 shalbe in the nyght, when the Sunne shalbe 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, shalbe in the day after noone, when the Sunne shalbe 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, shalbe in the day, when the Sunne shalbe 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 shalbe betweene the seconde quadrature, and her coniunction with the Sunne, then the Moone also in her ry­syng shall goe before the Sunne: and then shalbe the begyn­nynges of flowyng and reflowyng in the same houres, Note. 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 shalbe 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 shalbe in the night, about mornyng, before or after, when the Sunne shalbe 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. [Page] But the begynnyng of the day reflowyng, shalbe in the day be­fore noone, when the Moone shalbe 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 shalbe in the nyght be­fore mydnyght (that is) when the Moone shalbe 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, A general ob­seruation for the beginnyng of ebbyng and flowyng. 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, Note. on the parte of the East or Weast. And euery reflowyng by respecte to the Meridian, or to the poynt of myd­day, or mydnyght.

In what Ho­rizon this dis­course taketh place.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 shalbe 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, The beginning [...] of [...]. 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, I he begyn­nyng of eb­ [...] [...] by re­ [...] [...] the [...] ch [...]. 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 shalbe 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 [Page] 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 shalbe 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 shalbe 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, Two flowyngs in one day, and none in the nyght. 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 shalbe 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 shal­be after noone (that is) about euenyng, then the begynnyng of suche flowyng shalbe 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 shalbe be­fore mydnyght, it shalbe later and more in the nyght, then in re­gions [Page] 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 shalbe after myd­nyght, that is, towarde the day, then suche begynnyng of flo­wyng in the crooked Horizon, shalbe sooner (that is) in fewer houres of the nyght (that is) more before the day, or before the rysyng of the Sunne, then shalbe 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 shalbe 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 shalbe 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, Note. it is ma­nyfest, that howe much the nearer we shalbe 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 shalbe nearer vnto the standings or stayinges of the Sunne (cal­led Solstitium) or the longest daies, & longest nightes, so much greater and more certaine shalbe 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) shalbe about the Sunne or Moone, The [...]enes [...]f other [...], [...]e cause [...] in [...]l by [...] and [...]. And lyk [...] [...]. 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, Narownesse of places may cause disorder. 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 y ^e sea procedeth not in cer­tayne order. And to haue saide thus much of the diuers motions of the wa­ter of y ^e sea, may suffise.

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 with iniuries, to hynder our procee­dinges, and sometimes to make an ende of our disputations with quarrels and strokes. It chaunced in the meane tyme that mention was made of the lecture of Aristotel. And whereas, from the pur­pose, one enuious person moued the question of the Proportions of Locall Motions, I refused to dispute with hym, affirming that he euyll vnderstoode the intention of Aristotel, whom he so esteemed as a heauenly God, that it seemed to hym sacrilege, if any shoulde dissent from his doctrine. But he, malitiously and furiously, affirmed that I dyd rashly condemne Aristotel. I was therefore enforced by [Page] the request of my reuerende Cardinal of Adulphis Florentine, openly to repeate the same, especially for that the reporte of these contentions, was nowe come to the Popes eares, whose request also, I tooke for commaundement. And thereupon (whiche I had not doone before) I declared the errours of Aristotle, in the presence of the reuerende Cardinal Crescentius, and the Bishop of Ponset, men most expert in all kinde of learnyng, and in maner infinite other Au­ditours, before whom (in maner as foloweth) I shewed the errours of Aristotle by wordes and demonstrations. You therefore gentle and indifferent readers, accept this our Demon­stration with fauourable myndes. I repute Ari­stotle for the chiefe of all Philosophers. Yet forasmuche as it is humane to erre, he also myght some­tymes fayle.

FIrst of al, and before we shall touch the poynt of the Demonstration of Proportions of Motions locall, is to be noted, that of bodyes beyng of one and the same kinde, the like and self same is the proportion betwene quantities, whiche is also betweene heauinesse or lyghtnesse, eyther sim­ply, or in respect to other, it maketh no matter. It is yenough, that among them whose proportion we shall consyder by quantitie, among the same lykewyse, we shall vnderstande by heauynesse and lyghtnesse. &c. Let be for example two bodyes of leade, and vnequall, as A. and E. of the which the body A. shalbe triple in quantitie to the body E. for of the multiplication of the body, let no man be deceiued: for many haue thought the sphere to be duplicate, when his Diameter is duplicate, whiche is a great errour, as appeareth by .15. of the twelfth of Euclide. For there is shewed that the proportion of two spheres the one to the other, to be as it were the triplicate proportion of the Diameter of the greater sphere, to the Dia­meter of the lesse. Lykewise also is shewed in .37. of the twel [...], of solid bodyes lyke, and equidistant superficies. Further [...] Albertus Durerus, speaketh sufficiently of this in his .4. Albertus Du­rerus. Cubus is a square [...]re lyke a [...]ye. booke of Geometrie, teachyng the duplication of Cubus, &c. For then the same bodye A. shoulde exceede the body E. in heauynesse in triple proportion. Note therfore the weyght A. and the letter B, and E be signed F. and conceiue in minde the bodye A. to be di­uided into three equal parts, that is to say, C D G. of the which partes, H I K. nowe is it manifest for the presupposition, that euery part of, C D G. in equallitie shal correspond to y ^e body E. and shal waygh by common science, equally F. which yf it were [Page]

not, euery part of A. shoulde not be reputed Homogenie, or all of one lyke substance with the body E. and so shoulde it repugne with the presupposed. Therfore, forasmuch as H I K. togeather is equiualent to B. only by common science, shalbe also (by the 7. of the fyfth) B. to F. the same that is H I K. to the same F. but the weyght of H I K. is triple to F. by whiche reason the pro­position is manifest.

I wyll nowe make Demonstration howe bodyes of the selfe same, or one kinde and figure, equall or vnequal one to the other, in the same middest or meane, by equall space, be moued in one or selfe same time: the which is agaynst Aristotel and all other philosophers that haue not yet seene this proposition. Aristotel first in the .4. of his phisickes. Cap. De Vacuo, where he inten­deth to shewe, that yf Vacuum, or voyde, be graunted, mouyng or motion is taken away, &c. he there sayth thus, We see those bodyes whiche haue more heauynesse or lyghtnesse, so that they be of one figure, to be more swyftly moued by equal space, and by such proportion as they haue the one to the other. And therefore they are so moued, per Vacuum &c. which is proued to be false. Furthermore what S. Thomas sayth touchyng this, Thomas de Aquino. any man that wil, may reade: for no man euer better vnderstood y ^e minde [Page] of Aristotle. But for the examples which Simplicius and A­uerroes geue to the vnderstandyng of this (by two sphericall bodyes of equal quantitie, but of diuers kindes, as one of gold, & the other of syluer) we must not therfore say that they vnderstood this proposition as I wyll demonstrate. For they shoulde haue sayde somewhat of the equalitie of the quantitie of those bodyes, forasmuche as the motion of bodyes equall or vnequall, Motiō of the bodies [...] and siluer. is all one, so that they be all of one figure: as for example, yf there be three spherical bodyes, of the which two be of gold, and the thyrd of syluer, and they of golde be vnequall, and the other of syluer e­qual to one of the golden bodyes: then in the same proportion of tyme, shalbe moued the golden body equall to that of syluer, with the syluer body, in the whiche proportion the syluer body with the go [...]den vnequall, as shalbe declared hereafter.

Furthermore 6. Phisicorum. Cap. 1. in the ende, and in ma­ner through al the .2. Chapter of the same booke, he confirmeth the same: but in the fourth he sayth thus, Whereas euery thyng that moueth, moueth in some other, & in some time, and that mo­ueable is motion of the whole, the same or all one shalbe the di­uisions of the tyme and the mouyng, and of to be moued, and of that which is moued, and also of that in the whiche is mouyng. Afterward he geueth demonstration after his maner: but cap. 7. he wylleth the same, where he intendeth, that in finite tyme, no­thyng may passe into infinite greatnesse. &c. Furthermore Ari­stotle in his fyrst booke, De Coelo, confirmeth the same, saying simply that the reason or consyderation of tymes, is contrary to the reason of weyghtes: as yf halfe a weight be moued in this time, the double is moued in the halfe of this. &c. And this cap. 6. Furthermore cap. 8. of the same booke he sayth, The [...] of fyre. The fire in as muche as it is greater then the earth, so muche the sooner and swyftlyer it commeth to his restyng place. &c.

Also in his seconde booke, De Coelo. Cap. 8. he sayth thus: As in other things, the greater body, is more swyftly moued by his proper course or motion, euen so also in the heauenly circles, &c. Agayne Cap. 13. he affirmeth the same in two places, Motion of heauen [...]. saying that the greater earth, is euer swyftlyer moued.

Item, lib. De Coelo. cap. 2. he sayth thus, If accordyng to [Page] the proportion whiche hath the space C D. the body of B. shalb diuided, all B. in the same tyme shalbe moued by C E. in th whiche tyme parte of B. by C D. of necessitie: wherefore it fo­loweth that B. be moued with swyfter motion then parte of B. Afterwarde he maketh lyke Demonstration, saying thus, The swyftnesse of the lesse, The greater body the quic­ker motion. to the swyftnesse of the greater, hath suche proportion as the greater bodye to the lesse, &c. Agayne in the thyrde, De Coelo. Cap. 5. in the ende he sayth lykewyse, that so muche the more euery thyng is moued, as it is the greater, as also the fire the greater it is, is so muche of swyfter motion, &c. He confirmeth the same also, The greater fire the swyf­ter motion. Cap. 2. and 4. of the same booke, where yet speakyng more clearely, he sayth that the greater fire ryseth vpwarde swyfter then a lesse: and a greater peece of gold or leade, doth swyfter moue downewarde, and the lyke of other heauy bodyes: and more clearely can no man geather the mea­nyng of Aristotle.

Perspectiue & errour of Vi­tellio. Vitel io, in his seconde booke of Perspectiue in the seconde proposition, hath fallen into the same errour. I pretermit his ignorance in that proposition where he thynketh that there is no quantitie insensible: but let this passe with other errours, the whiche at any other tyme shalbe shewed in theyr place. He that wyll reade all other Philosophers, shall see that they all accorde with the mynde and sentence of Aristotle, who also in diuers o­ther places confirmeth the same: but to haue rehearsed these principall places, may suffise, and therefore we wyll nowe come to the Demonstration.

This propounded Demonstration, I wyll shew apparently, that it may the better be vnderstoode. And forasmuche, as Ar­chimedes in his woorke, Archimedes. De insidentibus aquae, hath spoken nothyng of the proportion of motion of Elementes, it is mani­fest that he had not yet searched this proposition: for there was the proper place of this matter. But it is not graunted to any one man to knowe all thynges: and therefore it was very diffi­cult to many to imagine the supposition, whiche I openly ex­pounded in Rome, whereas Archimedes maketh none other Demonstration, but that naturall motion is not caused of any other then of the excesse or proceedyng of a bodye in an Ele­ment, [Page] aboue or vpon the sayde Element, or contrarywyse. &c.