¶ A very necessary and profitable Book concerning Navigation, compiled in Latin by joannes Taisnierus, a public professor in Rome, Ferraria, & other Universities in Italy of the mathematicals, named a treatise of continual Motions.  
Translated into English, by Richard Eden.  
The contents of this book you shall find on the next page following.  
¶ Imprinted at London by Richard jug.  
Cum privilegio.   publisher's device (?) OMNIA DESUPER R. I  

❧ The Table.  

1 OF the marvelous nature and virtue of the Lode stone, called in Latin Magnes, where they be found, and how to know the best.  
2 Of continual motion by the said stone, Magnes.  
3 Of the due proportion of whatsoever Ship, and the disclosing of certain Mathematical secrets.  
4 Of ebbing and flowing, with their diversities, and the causes thereof.  
5 Demonstrations of proportion of motions local, confuting the opinion of Aristotle therein.    

❧ To the right worshipful Sir William Winter, Knight, Master of the Ordinance of the Queen's majesties Ships, and Surveyor of the said Ships. Richard Eden wisheth health and prosperity.  
IT is now about twelve years paste (gentle Master Winter) since the courtesy and favour which long before I found at your hand, moved me no less for the good will that I have ever borne you and your virtues, to excogitate or devise something, within the compass of my poor ability, that might be a witness, & as it were a seal, to testify both that I have not forgotten your gentleness, & also how desirous I am to pay the debts of friendship which then I promised you, & also attempted to perform: But being at that time prevented, by means of my sudden departing out of England, with my good Lord the Vidame, with whom I remained for the space of ten years, until the calamities of that miserable country, with loss of goods, and danger of life, hath driven me home again into my native country: Where finding myself at some leisure, and desirous to pass forth part of my time in some honest exercise, which might be profitable to many, domagable to none, and a means to get me new friends, the old in my so long absence, in manner utterly wasted: I chanced in the mean time, to meet with my old acquaintance and friend, Richard jug, Printer to the Queen's Majesty, who had many years before, printed the Book of Matten Curtes, of the Art of Navigation, by me translated out of the Spanish tongue. Whereof, having with him some conference, he declared that he would print that book again, if I would take the pains to devise some addition touching the same matter, that might be joined thereto. At which time, having with me in the Latin tongue, these books here following printed, which I brought with me out of France, I soon agreed to his honest request, to translate them into english: Which being accomplished, this only remained, according to the common custom, to consecrated and dedicated the same to some worthy parsonage, whose fame, authority, and dignity, might defend them from the evil tongues of such as are more ready rather to reprove other men's doings, then to do any good themselves. And therefore (gentle Master Winter) knowing your authority and fame in well deserving, and honourable service unto your Prince and Country, to be such as all men think so well of, and so greatly esteem, to whom (rather then unto you) may I dedicated this book of Navigation? In consideration whereof, and the hope that I have in your approved courtesy, favourably to accept this dedication, as proceeyng from one that desireth nothing more than to do you service, and remain in your grace, I shall think my travail well bestowed, and sufficiently recompensed, if it shall please you to accept the same as thankfully, as I willingly offer it unto you. For if there be any thing in me, wherein I may by good reason please myself, it is chiefly this, that I have ever loved and honoured men of singular virtue or quality, in what so ever laudable Art or Science, even of those whereof I me self have little knowledge, as are Geometry, Astronomy, Architecture, Music, Painting, feats of Arms, inventions of Ingens, and such like: Of the which, this our age may seem not only to contend with the ancients, but also in many goodly inventions of Art and wit, far to exceed them. For (not to speak against all the marvelous inventions of our time) what of theirs is to be compared to the Arts of Printing, making of Guns, Fire works, of sundry kinds of artificial Fires, of such marvelous force, that mountains of most hard rocks and stones, are not able to resist their violence, but art by them broken in pieces, and thrown into the air with such violence, that neither the spirit of Demogorgon, or the thunderbolts of infernal Pluto can do the like. What should I here speak of the wonderful inventions of Fartalio, in his book De Arte maiori? or of many other, whereof Vannucius Beringocius writeth in his book, entitled Pytotechnia. As touching which terrible inventions, and the like, although some men be of opinion that they were invented by the instigation of the devil, for the destruction of mankind: yet other weighing the matter more indifferently, think that the invention of Guns hath been the saving of many men's lives, because before the use of them, men were not wont so long time to lie battering in the besieging of Towns or Fortresses, but in short space to come to hand strokes, and to soughten fields, to the great slaughter of great multitudes. And seeing that now our enemies the Turks, and other Infidels, have the use of these devilish inventions (as they name them) it may be thought requisite for us, against such devils to use also the like devilish inventions, jest refusing the same, and giving place to evil, we should willingly suffer the kingdom of the devil to triumph over us, not otherwise able to resist, and much less to overcome so puissant and horrible enemies (except beside all hope) might arise in our defence some new Moses, or Elias, or the Priests of jericho, which only with the noise and sound of Horns or Trumpets overthrew the walls of the town. Neither will the example of David and Goliath, or of Samson and the Philistines, serve our turn at this time, although I believe that the arm of the Lord is not weakened, if there lacked not a Moses with his rod, and worthy assistants, which might help to hold up his weerye arm. But to return to speak of ingens, and ingenious inventions, which invented and used to the glory of God, and defence of his people, against the fury and tyranny of Infidels, they may as worthily be called the gifts of God, as were the inventions and Art of them that builded either the Temple of Jerusalem, or the Ark of God: And yet is it there written of those Artificers, that God gave them the spirit of knowledge and cunning in such Artes. And therefore I think it may also be said without offence, 
Exod. xxxv. Bezaleel and Ahaliab.  that the knowledge of Archimedes, and other men in such commendable inventions, are the gifts of God, for as much as the gifts of God are free, and not bound to any nation or person. And if it may be granted that the spirits of men, or the spirit of God in men, may be divided (as was the spirit of Moses to twelve other) or otherwise that the spirits of dead men may revive in other (after the opinion and transanimation of Pythagoras) we may think that the soul of Archimedes was revived in Besson, that excellent Geometer of our time, whom I knew in France the Master of the engines to the French king, Charles the ninth, under whom that lamentable slaughter at Paris was committed, in the which were slain so many noble men. Which cruelty the said Besson abhorring, fled hither into England, and here died, in the year. 1573. and left in witness of his excellency in that Art, a book in print, containing the forms and portractes of syxtie engines of marvelous strange and profitable device, for divers commodious and necessary uses. Of the which, for as much as three of them, that is to mean, the .54. 57 and 60. be engines chiefly pertaining unto ships, it shall not be from my purpose here to make a brief rehearsal of them. The .54. therefore (as he writeth) is an engine not unlike unto that which in ancient time Archimedes invented for the Syracusians, wherewith a man with the strength of only one hand, by help of the instrument called Trispaston (which in our tongue some call an endless Serve, brought a Ship of marvelous greatness from the land into the sea, in the sight of king Hieron, and an infinite multitude, which with all their force could not do the same. etc. Of the which also, our country man, Roger Bacon, 
Of this instrument, read the Cosmolabe of Besson.  a great Philosopher (and no Nicromancer, as that ignorant age slandered him) seemed to have had some knowledge: For in his book of the marvelous power of Art and Nature, he maketh mention of an Instrument (as far as I remember) no bigger than a man's hand, wherewith one man might draw to him the strength of three hundred men. And I well remember, that at my being in France, I heard credible report, that the Earl of Rocum●●●fe, an Almain, made an engine, wherewith the said king Charles when he was but xvi years of age, lifted from the ground a weight, which the strongest man in the court was not able to remove. Almost the like device we see in the bending of a crossbow. Also at my being in Germany in the city of Strosburge, a worthy and learned Gentleman, Monsieur de Saleno, told me that in that city one had invented an engine of iron, no bigger than a man's hand, whereunto fastening a rope, with a hook of iron, and casting the hook upon a wall, tree, or other place, where it might take hold, he could with that engine life himself up to the wall, or other place. But to return to the other two engines of Besson, pertaining to our purpose. Therefore the .60. figure (as he there writeth) is the invention of an engine, scarcely credible, wherewith by balance and easy motion, beyond the order of nature, a Ship may be so framed and governed, that in the calm sea it shall move forward, and in little wind hasten the course, & in too much wind temper and moderate the same: A thing worth the knowledge to a king, as he saith. Of the third engine, which is the .57. figure of his book, he writeth thus, An Artifice not yet divulgate or set forth, which placed in the pomp of a Ship, whither the water hath recourse, and moved by the motion of the Ship, with wheels and weights, doth exactly show what space the Ship hath gone. etc. By which description, some do understand that the knowledge of the longitude might so be found, a thing doubtless greatly to be desired, and hitherto not certainly known, although Sebastian Cabot on his death bed told me that he has the knowledge thereof by divine revelation, yet so, that he might not teach any man. But I think that the good old man, in that extreme age, somewhat doted, and had not yet even in the article of death, utterly shaken of all worldly vain glory. As touching which knowledge of the longitude, to speak a little more b● occasion now given, it shall not be from the purpose, to rehearse the saying of that excellent learned man, johannes Feruclius, in his incomparable book De ab●●s rerum causis, where in the Preface to king Henry of France, he writeth in this manner. We have put our helping hand to the Art of Navigation and Geography: forbye observation of the hours of the Equinoctialles, we have invented how, in what so ever region or place of the world a man shallbe, he may know in what longitude it is: which certainly we have not taken of the fountains of the ancients, but first, of all other (as I think) have drawn it of ou● rivers, as our own invention. etc. So that (saith be) which way so ever you turn your eyes, you may see that the posterity hath not riotously wasted the inheritance of Arts and sciences, left them by their predecessors, but have greatly increased the same, and invented other: For certainly, the multitude of things incomprehensible, is infinite, and so therefore inventions must needs also be infinite, & without end. And therefore, as touching this thing (saith he) to speak freely what I think, they seem to me to offend as much, which contend that the ancients have invented and comprehended all things, as do they which attribute not unto them the first inventions, so depriving them of their right possession. For whereas now by the benefit of almighty God (who hath given us his Christ, and with him all good things) the light of truth shineth in our understanding by godly inspiration, there is no just cause why we should in such things think us inferior to the ancients. Of which Argument, who listeth may read more in the said Epistle of Pernelius. 
An instrument in motion agreeing with the motion of heaven. Anno Dom. 1584.  And for as much as I have made mention of such inventions, it shall not be from the purpose, to describe the goodly instrument whereof Angelus Policianus in the fourth book of Epistles to Franciscus Casa, writeth in this manner, I have received your Epistle, wherein you signify unto me, that you have heard of the strange engine or instrument Antomaton invented, and made of late by one Laurence a Florentine: in the which is expressed the course and motions of the planets, conformable and agreeing with the motions of heaven: And that (for as much as the report thereof is hardly believed) you greatly desire that I should writ unto you, what certain knowledge I have of that thing, wherein I am ready to obey your request. And although now it be long since I saw it, yet as far as I bear in memory, I will briefly declare the form, reason, and use thereof. And if the description of it shall seem unto you somewhat obscure, you shall not ascribe it altogether to my declaration, but partly to the subtlety & noviltie of the thing. It is in form of a square pillar, sharp toward the top, in manner of a P●rami●, of the height of almost three cubits: over or above it, in manner of a cover, is a flat or plain round plate of gilted copper, garnished with sundry colours, on whose other part is expressed the whole course of the Planets, and whose dimention or measure is somewhat shorter than a cubit, and is within turned or moved with certain little denticle wheels, an immovable circle comprehending the highest border or margin, and divided with the spaces of xxiiii. hours within it, in the highest turning rundel, the twelve signs are discerned by three degrees. Further, within are seen eight runde is, in manner all of one greatness. Of these, two obtain the middle point, the one fastened in the other, so that the lowest being somewhat bigger, representeth the Sun, and the higher the Moon. From the Sun a beam coming to the circle, showeth in it the hours: and in the Zodiac, the months, days, and number of degrees, and also the true and half motion of the Sun. From the Moon also proceedeth a p●●ne, or wire, which beneath or downward in the border or margin of the greatest roundel, showeth the hours: and passing by the centre of the epicyle of the Moon, and extending to the Zodiac, showeth the half motion of his Planet. Another also rising from thence, and cutting the border of the centre of the Moon (that is of the epicyle) showeth her true place, whereby art seen the slowness, swiftness, all motions and courses, conjunctions also, and full Moons. About these are two other rundels: of the which, one, whom they call the head and tail of the Dragon, showeth the Eclipses both of the Sun and Moon. The other are attributed to the Planets: from every of which, proceed two pay●●es, assigning the motions (as we have said) of the Moon: but they also go backward, which chanceth not in the Moon, whose Eclipse is moved contrariwise. And thus the reason of conjunctions, departings, and latitudes, is manifest in all. There is also an other border like unto a Zodiac, cutting or dividing upward or above, those six little rundels (whereof we have spoken) being the rundels of the planets: whereby appeareth the degrees of the East signs, and the spaces of the days (that is to say) at what hour the Sun riseth, by the which, every of the planets are carried in their rundels or circles by course, in the day time to the East, and in the night to the West. Again contrariwise, the greatest rundel of all, draweth with it all the planets, in the night to the East, and in the day to the West, in the space of .24. hours. At which, to agreed with the motions of heaven, both reason and experience do confirm: And therefore aught ye not to marvel, if these things seem incredible to many. For (as saith the wise Proverve) faith is slowly given to great things, for even we scarcely believe our own eyes, when we see such things. And therefore, whereas in time past I read, that such a like instrument was made by Archimedes, my faith yet failed me to give credit to so great an Author, which thing nevertheless this our Florentine hath performed. The work doubtless being of such excellence, that all praise is inferior to it, and can not therefore for the wo●●thyn●sse thereof be otherwise praised, then to say that it passeth all praise. The Artificer himself also being a man of such integrity of manners, that the sun is nothing inferior to the excellency of his wit: in so much that he may seem a man sent from heaven, where be learned the making of this heaven, by the example of the other. Hitherto Policianus. Of the like instrument, Roger Bacon also maketh mention in his said book, of the marvelous power of Art and nature, affirming the same to be worth a kingdom to a wise man. But for as much as the subject which I have now in hand, is chiefly touching inventions pertaining to ships, and the Art of Navigation, I think good to speak somewhat of the invention of a certain Italian writer, named Leonardo F●o●ananti, who in his book, entitled, 
Lib. 3. Ca 18  Specchio discientia universal, doth greatly glory in the invention of ships, which can not perish either on the sea, or the land, 
The invention of a Ship which can not be drowned.  affirming that the like was never invented since the creation of the world. But I fear me, jest vain glory of discoursing in the Italian tongue, hath caused him more than needs, to commend his own invention, as for the most part is the manner of the Italian writers. Therefore committing the judgement hereof to men of greater experience and knowledge in these things, I will only translate his words, whereby in the book before named, he describeth the said Ship in this manner. Take beams of fir, or pine tree, which of their own nature can never go down, or sink, or abide under the water, and with these beams frame an e●●●ne (Machina, if I may so call it) of the length of three score four, and of the breadth of twenty foot, and of the height of six foot, laying the first rank in length, and the other traverse, or overthwart, and the third again in length, fashioning the sore part like unto other ships, and in like manner, bringing the poop or hinder part to good form: then with such irons as ●pparteyne, bind it, and strengthen it in such manner that it can not break. And upon this frame or foundation build your Ship, of such fashion as you think best. etc. It were here too long to rehearse with what proud words and ostentation he magnifieth this invention. But whether this frame or engine should be bylden upon the keel or bottom of the Ship, or otherwise, I commit it to them of better judgement, as I have said. But whereas it may for this time suffice to have written thus much of these things, I will make an end with only a br●●te rehearsal of the invention and increase of the Art of Navigation.  
After that the Art of Navigation was found, every man began to challenge unto him the dominion of the sea, & there to dwell and keep war even as on the land.  
Minos (as writeth Strabo) was the first that ruled on the sea, which nevertheless, other ascribe to Neptunus, who first found the Art of Navigation, and was therefore (as writeth Diodorus) appointed by Saturnus to be Admiral of the first Navy: and thereby the posterity afterward ascribed to him the governance of the sea, and named him the God thereof. After whom the Cretenses ever were esteemed most expert in the Art of Navigation. But (as writeth Pliuie) boats were first invented, and with them was the first sailing in the Islands of the red sea, under king Erythra, as also witnesseth Quintilian, saying, If none had proceeded further than the inventions of our predecessors, we had had nothing in the Poets above Andronicus, and nothing in histories above the Annals or Chronicles of bishops, and had yet have sailed in troughs or in boats. Other have ascribed this invention to divers other nations and persons, as to the troyans and Mysians in Hellesponto, and also that the ancient Britanes made boats of leather or hides, and sailed with them in the Ocean sea. Pliny writeth, that Danaus was the first that brought a Ship out of Grece into Egypt. Some also give the same to Minerva. But most rightfully, the invention both of the Ship, and Art of Navigation, is ascribed to No, who (as writeth Eusebius) was long before Neptune or Danaus. For doubtless (saith he) the Ark of No was none other than a Ship, and the first and only exemplar of the building of all other ships or vessels of sailing. Also the most ancient writer Berosus the Chaldean (as writeth josephus) calleth the Ark of No, a Ship. The same josephus also saith, that the Nephews of No, departing to inhabit divers parts of the world, used many ships. etc. Long after No, the Tyrians were counted most expert in the Art of Navigation: and after them, divers other nations. For whereas no Art is so perfect, but may receive increase, hereof doth it follow, that this Art also hath been greatly augmented, and brought to further perfection by witty inventions of the posterity, even unto our age: whereof, who so listeth to know further more particularly who invented all other parts and instruments pertaining to all sorts of ships, & Art of Navigation, may read the third book of Polidor Virgil, Cap. xv, De Inuentorib. Rer. and Bayfius, de re navali.  
Thus gentle Master Winter, beseeching your worship to take in good part this testimony of my thankful heart (such as it is) I beseech the immortal God to prospero all your doings to his honour, and the benefit of your Country.   

¶ To the right Reverend father in Christ, and honourable Prince, Lord john Gebhard, of the Earls of Mansfelt. etc. Archbishop of Colen, Prince elector, duke of Angaria and Westphalia, high Chancellor of the Roman Empire. etc.  
THE thing which to this day in manner from the beginning of the world, great Philosophers with perpetual study and great labour, have endeavoured to bring to effect, and desired end (most gracious Prince) hath nevertheless hitherto remained either unknown, or hid, not without great damage and hindrance of most expert Mathematicians and Architecteurs, and all other men of like practical faculties: And if any there have been which have attained to the experience of this continual motion, I suppose the same to have been vexed and noted, 
A perpetual or continual motion.  with the va●ne glory of the incomparable painter and graver, Michael Angelo, 
Michael Angelo.  who even at the extreme rendering of the spirit of life, did not vouchsafe to disclose unto his own son the secrets of his art, esteeming it greatly to the reputation of his fame and glory, by this ingrate hiding of his science, falsely to obtain a perpetual memory with such as should succeed him: Or else truly he doubted (as is commonly seen in all manner of doctrine and science) that there should still rise up certain malicious and envious quarrelers, and troublous wits, instigate by an evil spirit, to deface and suppress truth with slanderous tongues, especially against art's Mathematics (of which kind, are Graving, Painting, and such like) which in all ages have ever been subject to this inconvenience of ignorant detractors, except they be defended by the protection and title of favourable princes. And whereas such sciences unto the ignorant seem ridiculus and suspicious, nevertheless in the frame and experience of this continual motion, aught no suspicion to be bad. And forasmuch as the same is very necessary and profitable for the common wealth, I was the bolder through confidence in your highness clemency under the grace and title of the same, to put forth this little book of continual motion. The which how great profit and exercise it may bring to excellent men of what so ever faculty, experience itself shall easily declare. Most humbly desiring your highness, graciously to accept this ray travail with such as are consecrated to the Muses, and employ their labours to the profit of mankind.  
Your highness most humble servant and Orator, john Taisnier Hannonius▪   

¶ Of the nature and effects of the Lode stone, called in Latin Magues.  
IT is a common proverb that in stones, woods, and herbs, consisteth great virtue: which saying is doubtless most manifest by the daily experience of this stone, being found in sundry places of India, it is said also that it was found in Spain by one named Heracleon (as witnesseth Nicander) while in keeping of cattle, 
Five kinds of Lode stones.  the iron nails of his shows and pike of his staff, cleft fast to the stone. Of the which Magnes, are five kinds as Sotacus writeth. That is to wit: one of Ethiopia. An other of Macedonia. The third is found in Echio of Beotia. The fourth about Troades of Alexandria. 
Lode stone male and female.  The fifth of Magnesia Asiae. The difference of the stone is, whether it be male or female. The next difference, is in colour: for that which is found in Macedonia and Magnesia, is ruddishe and black. That of Beotia, is more ruddish than black. That of Troades is black, and of female kind, and therefore without virtue. 

The best loadstone of Hew colour.  
Lode stone s●●d for the weight of silver.   The worst of Magnesia Asiae, is white, and draweth not iron, and is like unto a punice stone. They are proved the best which are most of blue or heavenly colour. That of Ethiope is most praised, and (as Pliny saith) is sold for the weight of silver. This is found in Zimri, a sandy region of Ethiope, where is also found Haematites Magnes, of bloody colour, appearing like blood if it be ground, and also like saffron, which in drawing of iron, 
One loadstone draweth another.  is not of like virtue to the Hematites Magnes of Ethiopia, which draweth unto it another Magnes. All these be profitable for medicines of the eyes, each of them according to their portion, and do specially stay Epiphoras (that is) dropping of the eyes. 
Lode stones m●d●cin●● 〈◊〉 for the 〈◊〉.  And also being brunt or made in powder, they heal burnings. And not far from the same place of Ethiopia, is a mountain which bringeth forth the stone called Theamedes, 
The stone Theamedes putteth iron from it.  which putteth from it, and refuseth iron. I have often proved the virtue and power of the stone Magnes, by the needle which is in some dials, by the attraction thereof, moving itself from side to side, and round about. Although the stone were under a table, yet doth the needle, being above the table, naturally follow the moving of the stone. It is therefore no marvel if there be great virtue in stones, 
Iron nails drawn out of Ships by the stone.  woods, and herbs. It hath also been proved, that ships compact with iron nails, sailing by the sea of Ethiope, and by tempest driven to land, to certain capes or lands ends, have by these stones been either drawn to the bottom of the sea, or else the nails being drawn out by the virtue of the stone, the Ship hath fallen in a thousand pieces. And therefore the discreet and aware Cantabrians, most expert Mariners, sailing by the sea of Ethiope, frame their ships with pins and hoops of wood, to avoid the danger that might chance of like occasion.  

Again, of the nature, knowledge, virtue, equality, quality, and effects of the stone Magnes, or the Lode stone.  
FOR as much as every thing that is good, is so much the better as it is more common: therefore do I intend to communicate unto our posterity, this little work of the nature, effects and miracles of the stone Magnes. The which, although they may seem to the ignorant common people, to exceed the limits of nature, yet to expert men, and Mathematicians, they seem not so strange, notwithstanding that it is almost impossible to manifest all the secrets and miracles thereof: 
Art in many things passeth and amendeth nature.  For whereas Art inventeth, and bringeth to perfection many things which are impossible to nature, it is necessary that he who desireth to do great effects in these things, and the like, be very expert in working with the hand: neither is it sufficient for him to be a perfect Naturalist, mathematician, or Astronomer, for as much as furthermore is required great dexterity of handy work: And for default hereof, it cometh to pass, that in this our age these natural arts lie hid & unknown. This stone is known by colour, virtue, weight, and equality. 
The stone Magnes is known by colour, virtue, weight, and equality. Colour. Virtue. Equality.  The best colour, is like pure iron, shining, mixed with Indian or heavenly colour, & is in manner like iron poolished. This stone is also oftentimes found in certain regions of the North, & is brought from thence into certain parts of Normandy and Flaunders. The experience of the virtue of this stone, is easy. For if it draw unto it a great weight of iron, it is judged to be strong: & the heavier also the better. By equality, it is judged if it be all alike of one substance and colour: but if it be unequal with chaps, & hollow places indented, having read spots here and there, it is unapt to the art of navigation or of continual motion. It representeth the simititude of heaven. For like as in heaven are two points immovable, ending the axiltre of the sphere, upon the which the whole frame of heaven is turned (as may be found by the art whereby Crystal & other stones are poolished:) even so the stone Magnes, reduced into a globous or round form, laying thereon a needle or any other like iron, 
How to find the poles by the stone.  than which way so ever the needle turneth and resteth, thereby is showed the place of the poles. And that this may be done more certainly, it must be oftentimes attempted, and the line showed by the needle, must be observed: for such lines shall cut the one the other in two points, as the Meridian circles join together in the poles of the world.   

The same is gathered an other way.  
This is done more certainly, if in the round stone (as is said)  lodestone be found the place which oftentimes draweth iron, which being found, if then the point do exactly appear, part of the broken needle, must be laid upon the stone, and be so often by little and little transposed, until the style or pin by perpendicle or plummet do directly fall upon the stone. For there on the contrary part, by like manner shallbe found the other pole. A. shallbe the true point, and B. the false,   

The manner to know the one pole from the other.  
Which of the two points aforesaid may answer to the pole Arctic or the North pole, is found in this manner. cause a large vessel to be filled with water, in the which cause the stone Magnes to be laid upon a light board, not deep, much like the covering of a box, so nevertheless that the two points found in the stone may lie equally elevate in  floating lodestone the said box: and so by virtue of the stone, the box shallbe moved to the place where the meridional pole shall extend toward the South, & the other opposite to the North, & shall rest ther. And thus shall it be easy to discern, which of the points answereth to the pole Arctic, & to the pole Antarctic, so that the places of heaven be first known by any means.   

That one stone draweth another.  
HOw one stone draweth another, we will declare hereafter. Lay the one (as is said) upon a board or box in the water, that it may freely float, & hold an other in your hand. If then the North part of the stone, which you hold in your hand, you turn to the South part of that which floateth in the box, or otherwise the South part to the North, the floating stone shall turn toward your hand: and if contrariwise, you turn the like part to his like, that is to say, the South part to the South etc. the floating stone shall fly from you. 
A question of attraction of humours etc. Scammonea, and choler. A vire or a needle.  By this experience is destroyed the reason of certain Physicians, which dispute on this manner. If Scammonea draw unto it choler by similitude or likeness of nature, ergo much more should one Magnes draw another, rather than iron: for that which they assume falsely, we have now taught to be true. The like judgement is of a long slender iron that is rubbed with this stone: for if in the water it be laid on a light piece of wood, or a straw, or such like, so that it may freely float upon the water, the one end of it shall turn to the North, and the other to the South. And if holding the stone in your hand, you turn his North point to the South extremity or end, or contrariwise, the stone shall then draw iron. But contrarily, 

How the stone draweth ●ron or arriveth it away.  
Agent and patiented.   if you turn the like part to the like (as is aforesaid)  two lodestones with poles marked 


A. The North part.  
D. The South part.    it shall fly from the iron, or drive it away. The reason whereof seemeth to be, that the agent doth not only endeavour to make the patiented like unto itself, but also in such sort to unite it with himself, that of them two be made one, as may appear by this reason. Take the stone Magnes A D. of the which A signifieth the North point, and D. the South. 
The stone divided in the midst.  Divide the stone in two parts AB. and C D. put A B. to the water as is said, and by this means you shall see A. turn to the North, and B. to the South. For the breaking or dividing of the stone, diminish not the virtue thereof, so that it be homogeny, that is, in all parts alike. Take therefore A B. for the patiented, and CD. for the agent. Then whereas the agent, in the best manner it may, worketh to conserve the order of nature, it is manifest that D. can not draw C. the South: For although they could by that means be joined, yet should there not so be made one of them two, the parts remaining in their virtue: for if A. should remain North, then D. should be South, which is certain to have the power of the North.  
 depictions of lodestones with incompatible poles 
Impossible.  
Impossible.   
 lodestones with proper poles 
Natural.  Neither contrariwise shall C. draw A. for both are Northly, and so should B be the North which first was South, and D. in like manner: for so should the order of nature be inverted. It remaineth therefore that A shall naturally draw D. & B. shall draw C. For so every way shall remain equal strength of al. 
From whence the stone hath his virtue.  Some ignorant men were of opinion that the virtue of the stone Magnes, cometh not of heaven, but rather of the nature of the place where it is engendered, saying that the mines thereof are found in the North, and that therefore ever one part of the stone extendeth toward North. But these are ignorant that this stone is also found in other places. Whereof it should follow that it should then extend itself aswell to other and divers parts, as to the North. Which thing is false, as is well known by common experience, for it ever moveth to the North in what so ever place it be. Neither is it to be believed, 
The North star is not the Pole.  that the North star of the Mariners is the Pole: for as much as that star is without the Meridian line, and but twice within one revolution of the firmament. But whereas the marvelous virtue of  hollow globe this stone dependeth of heaven, 
Every part of this stone respect 〈◊〉 some part of heau●●●  who would believe that only two points thereof should so have themselves, and not rather that every part of it should not incline to some like part in heaven, as may thus be proved. Let the stone be brought into a Spherical or round form, as is said, and the Poles being found in manner before declared, let it be turned upon two pins, or Turner's instruments, and there be pullyshed, until it be on every part of equal heaviness, which you may well find by often proving: for that part that falleth down is heaviest, which done, fra●●e it a Meridian circle with a Horizon, wherein fasten two other pins, 
The greatest miracle in natural things.  upon the which it may easily move, and direct the Poles most exactly to the Poles of the world, the which if it come well to pass, rejoice that then you have found almost one of the greatest miracles of natural things. For you shall by this means see the Ascendent, the place of the Sun, and the like. etc. at every moment. But if it fall not out according to your desire, you aught not to impute that to the art, but to your own ignorance and negligence. For if you execute all things duly, according to the art, you need not to doubt the success.   

The composition of Instruments by the stone Magnes.  
How by this stone instruments may be framed, by the which may be found the Azimuthes of the Sun and Stars (that is to say, Vertical circles) it shall not be necessary to show, for as much as the same is easily done by the Mariner's Compass, or by the box with the Magnes or loadstone enclosed, and floating above the water with a pin erected, and in the uppermost part divided into 360 parts, after the manner of Astronomy.  
 depiction of magnetic compass   

Of continual motion.  
FRom the beginning of the world, in manner all natural Philosophers and Mathematicians, with great expenses and labour, have attempted to find out a continual motion or moving: yet unto this day have few or none attained to the true end of their desire. They have attempted to do this with divers instruments & wheels, and with quicksilver, not knowing the virtue of this stone. Neither can continual motion be found by any other means, then by the stone Magnes, in this manner. Make a hollow case of silver, after the fashion of a concave glass, outwardly laboured with curious art of graving, not only for ornament, but also for lightness, for the lighter that it is, so much the more easilier shall it be moved, neither must it be so pierced through, that such as are ignorant of the hid secret, may easily perceive it.   

The form of the stone.  
 lodestone with two poles 
The Pole  
The Pole   
It must have on the inner side certain little nails & denticles or small teeth of iron of one equal weight, to be fastened on the border or margin, so that the one be no further distant from the other, then is the thickness of a bean or thick pease. The said wheese also must be in all parts of equal weight, then fasten the Exiltree in the midst; upon the which the wheel may turn, the Exiltree remaining utterly unmooveable. To the which Exiltree again shallbe joined a pin of silver, fastened to the same, and placed between the two cases in the highest part, whereon place the stone Magnes. Being thus prepared, let it be first brought to a round form, than (as is said) let the Poles be found: then the Poles untouched, the two contrary  lodestone device sides lying between the Poles, must be filed and pullyshed, 
Denticles 〈◊〉 little 〈…〉 that it 〈◊〉 the 〈◊〉.  and the stone brought in manner to the form of an egg, and somewhat narrower in those two sides, jest the lower part thereof should occupy the inferior place, that it may touch the walls of the case like a little wheel. This done, place the stone upon the pin, as a stone is fastened in a ring, with such art, th●● the North Pole may a little incline toward the denticles, to the end that the virtue thereof work not directly his impression, but with a certain inclination give his influence upon the denticles of iron. Every denticle therefore shall come to the North Pole, and when by force of the wheel it shall somewhat pass that Pole, it shall come to the South part, which shall drive it back again: whom then again the Pole Arctic shall draw as appeareth. 
Calculus, a little round stone or small weight like a pellet or plomm●●.  And that the wheel may the sooner do his office within the cases, enclose therein a little Calculus (that is) a little  lodestone device 


A. The stone.  
B. The silver plane.  
E. Calculus.    round stone or pesset of copper or silver, of such quantity, that it may commodiously be received within any of the denticles: then when the wheels shallbe raised up, the pesset or round weight shall fall on the contrary part. And whereas the motion of the wheel downward to the lowest part, is perpetual, and the fall of the pellet, opposite or contrary, ever received within any two of the denticles, the motion shallbe perpetual, because the weight of the wheel and pellet ever inclineth to the centre of the earth, and lowest place. Therefore when it shall permit the denticles to rest about the stone, then shall it well serve to the purpose. The middle places within the denticles aught so artificially to be made hollow, that they may aptly receive the falling pellet or plummet, as the figure above declareth. And briefly to have written thus much of continual motion, may suffice.    

❧ Of most swift Motion by art of Navigation.  
WE intend now to speak of most swift motion, which to the common sort of men seemeeth incredible, for that the same may be done by sailing in a ship or other vessel, against what so ever most outrageous course of any flood or river, and against most furious winds what so ever they be, even also in deepest winter and greatest surges of waters. Neither is it marvel if this be incredible to the unexpert. For the common people counteth that for a miracle, which the expert Mathematicians know to be natural and easy: 
A strange experiment practised.  for if it should be propounded to the ignorant people, that any man might in the midst of the waters and floods, descend to the bottom of the river of Rene, his apparel remaining dry, & no part of his body we●te, & also to bring with him burning fire from the bottom of the water, it should seem to them a laughing stock, a mockery, 
The rivers of Tagus & Danubius.  and impossible. Which nevertheless in the year 1538. in Toleto a city of Spain, in the most swift river Tagus (in the which gold is found) running against the course of the Sun none otherwise than Danubius, and three other in the world, making their course from the west to the East, I, with twelve thousand other persons, saw in the presence of Charles the Emperor the fifth of that name. Of such other marvelous natural experiments, I need not here to speak much. Other there be that dare affirm, 
Marvellous swiftness of a ship.  that a certain ship was in such sort driven with violent winds and furious seas with so swift a course, that the Pilot standing in the keel of the ship, near unto the mast, shooting an arrow out of a cross bow, the arrow fell down before his feet, and came not so far as to the forepart or forecastle of the ship. I have heard also of credible men, that a certain Pilot Cantabrian, lying at anchor at Antwerp, on a certain Sunday after morning prayer, 
Swift spe●●● after m●●nyng prayer.  departed with full sails and prosperous winds, until he came to the coast of Saint james in Compostella. And immediately returning with like prosperous winds, came again to Antwerp in the same ship the Sunday next following. The which I deny not, but may be done, yet not without great danger of shipwreck, especially in the return, the wind being at the South. Also in the year .1551. I had experience of a most swift motion. For, from Drepan of Sicilia and Trinacria, 
Another experience of swift sayly●●.  the port of the galls of Maltha (now being in place of the Rhodes, otherwise called of Saint john in jerusalem) a certain ship without ever striking sail, in .37. hours arrived at Naples. And yet are these places distant in latitude almost five degrees, beside some part of longitude: which on the earth correspondeth or amounteth to four hundred and five miles. These motions, are caused by violent floods and outrageous winds. The like also may be done against the fury of winds and violence of floods, when need shallbe for expedite carriage of victuals by sea, and even in places where it is hard to come to land, and this with small labour, as hereafter I will plainly declare by Demonstration: but oftentimes, 
The difference of sh●ppe● in sa●●●ng.  most expert Pilots and sea men, do marvel that sailing in ships of the self same making, weight, content, or capacity, framed also of the seife same shipwright, furnished with equal sails, and all other things appertaining, yet to be of such divers swiftness, that the one can not keep equal course with the other. 
The prop●●●●●● in ●●aming of ships.  Which marveling doubtless proceedeth of ignorance and lack of knowledge of the due proportion of the frame of all sorts of ships: that is to mean, the depth, breadth, height, and length (named by the masters, latitude, longitude, altitude, and profundity.) The which if they be unknown to the master Carpenter or shipwright, two ships can never be so directed by equal course, but that one shallbe swifter than another, as I plainly observed in the expeditions of Arsenaria, or Thunes, or Agolette: 
●●nes and 〈◊〉.  in which amongst in manner innumerable ships, and especially Galleys, and foists, were scarcely two or one of the same quantity, heaviness, greatness, and capacity, driven all with one wind and equal sails, that kept equal course one with another: And this doubtless only by reason of the different proportion of the framing, making, or architecture.  

Of the right and due proportion of what so ever Ship.  
IN the framing of any manner of ship, the proportion of length, breadth, height, and depth, aught most chiefly to be exactly observed, jest the ignorance and negligence of these considerations, should hinder the swift course, and cause danger of shipwreck. The due proportion therefore of ships is, that first the longitude or length of the ship or vessel what so ever it be, more or less, aught to be divided into .300. equal parts, as appeareth in the figure following.   depiction of ship 
Of the which parts .30. must be assigned to the height or depth, for the tenth part of the whole requisite longitude or length: and to the latitude or breadth shall correspond the parts of the said longitude .50. or the sixth part of the longitude. The matter also or timber of the Ship must be light, jest too much heaviness of the matter should hinder the swift course. And this proportion of ships or other sailing vessels, of whatsoever shape or frame, is most convenient, and no less necessary: As for Scafes, ships of burden, Galleys, double, triple, or quadruple (that is to say) of two, three, or four men to an Ore. Also for foists, Pinnaces, Brigantines, Espions, and such like.   

Of the framing and Architecture of the aforesaid Ship.  
I HAVE often times attempted by Mathematical reason, how and in what manner a commodious fashion of ships, or other like vessels may be invented with small labour and little cost, which may in short time strive against the course of whatsoever strong floods or rivers, as Rhine, Danubie, Mosella, Scalda, and almost infinite such other, boiling and overflowing, through the abundance of great showers, molten snows, and furious winds, and this especially for the commodity of transporting victuals, and such other necessaries: In consideration whereof, the proportion first observed, and the said Ship or vessel almost finished, then must be made three holes from the Keel, toward the forecastle or foremost part of the Ship, as appeareth in the figure by the letters ABC. In which holes, in time of the course, certain engines of strange and marvelous inventions may be fastened. In the poop or hinder part of the Ship, may be prepared (after the manner of Germany) a little Stove or hot house, where the Passengers may commodiously rest. Now the Ship being thus prepared, the bottom thereof must be dressed with tallow, and not with tar, that it may move the swyftlyer.  
Thus having absolved the frame and proportion of the said Ship, the rest of Mechanical or handicraft work, we leave to the Carpenters and Shypwryghtes.   

To what use such kind of ships or vessels may be applied.  
IT chanceth often times, and especially in winter, that certain floods and rivers overflown with to much abundance of waters, do with their violence refuse all navigations that may be made against their course, to the great damage and hurt of the Inhabitants of many Towns and Cities, to the which they should carry victuals, and other provisions, against the course of the rivers: And therefore in favour of the common wealth, I have invented these kind of ships, that I may hereby, as by my seal, confirm the good will I bear to our posterity. Now therefore it may suffice to have said thus much of this swift motion which I have proved with mine own strength, and have sufficiently declared the framing and use thereof: 
It is easier to add to inventions, then to invent.  whereunto it shallbe easy for all men to add more, according to the excellency of their wits and experience. For in all sciences it is easier to add to inventions, then to invent. Consider now what commodity this may bring to the Brabantines, sailing from Antwerp to Brussels in the new river: For that which they attempt dangerously with great vexation and shogging in wagons by foul and tedious journey, 
The new river from Antwerp to Brussels.  often wet to the skin for the space of one whole day, may by water be done more conveniently, in the space of four or five hours, even against the river and wind.  
And lest the reader should seem to refute our sayings, while he thinketh those things which he esteemeth for miracles, to exceed the limits of nature, 
A no●●●le experiment.  I will show manifestly by one Demonstration, how a man may descend into the bottom of any water or river, his body remaining dry, as here before I have affirmed, that I saw in the famous Town and kingdom of Toleto, before the Emperor Charles the fifth, and infinite other. 
The water intendeth to ●●●bus form●.  But here must first be considered, that naturally the water or sea (as other Elements) intendeth to Spherical form, and with his globosite or rising, overpasseth most high mountains. But again here shall rise an other doubt to the unexpert. That is: If the sea be higher than the land, 
Why t●e water 〈◊〉 about overflow the land.  how is it then that it doth not drown and cover the earth? Whereunto I answer, that the dryness of the earth may so long resist the moistness of the water, until it receive or imbibe to much moistness, which may thus be naturally proved. Fill a cup or other vessel with water or wine to the brim, 
An experiment.  so that the fullness thereof may seem to swell as though it would overflow the brim of the cup. Then may you yet put therein many pieces of gold, without shedding of one drop of water. But if the extremity of the brim be once wet, immediately the water overfloweth, because the dryness of the vessel doth participate the moistness of the water: which is yet better proved in manner as followeth. Take a certain quantity of water, and sprinkle it by drops upon a dry (or dusty, cable: so shall the drops partly show a Spherical and swelling form remaining. But if the table before be never so little wet with water, the drops sprinkled thereon, shall float abroad, and keep no Spherical or round form, by reason of the moistness which the table had before received of the water. It hath also oftentimes chanced, 
The dr●wning of certain ●●gio●.  that certain Towns and lands have been drowned by overflowing of rivers near unto them. Nevertheless, how much so ever such waters increase and rise, there is no danger, until great showers falling from heaven, do thoroughly wet the banks, rampertes, or calseys of such rivers. For when they (as we have said) be thoroughly imbibed with moistness, they 'cause the overflowing and breach, whereof followeth the overflowing and drowning of the region: and this may suffice for advertisement. Now therefore I come to the experience aforesaid, showed at Toleto by two greeks: who taking a chaulderon of great capacity, 
This experiment may be proved with a great bell.  and the mouth turned downward, and so hanging it in the air by ropes, they fasten certain posts and boards or shelves in the midst of the cauldron where they place themselves with the fire. Then to make it hung steadfastly and equally, they compass the circumference, brim, or border thereof with leaden plommetes on every side equally, and made of equal weight, lest any part of the circumference of the mouth of the cauldron when it is equally and softly let down into the water, should sooner touch the water then the whole circumference. For so should the water easily overcome the air enclosed in the cauldron, and resolve it into moisture. But if by due proportion the cauldron thus prepared, be fair and softly let down into the water, the air enclosed in the cauldron (by resistance of the water) shall violently make himself place, not admitting the water to enter. So the men there enclosed, shall so long remain dry in the midst of the water, until success of time do by respiration debilitate and consume the enclosed air, turning it into gross humidity engrossed by the coldness and moistness of the water: but if in due time the cauldron be softly and equally drawn out of the water, the men shall remain dry, 
another example of the foresaid experiment.  and the fire not extinct, which also may thus be proved: Take a cup of glass of a certain quantity: the circumference of the mouth whereof, shallbe brother than the circumference of the bottom. In the mouth let be fastened a little stick, tying thereto a thread: On the stick, fasten a little candle of wax, whose light may come only to the midst of the cup, lest to much dearness of the water might suffocate the candle. Then proportionally (as in the former experiment) put the cup with the burning candle into a vessel full of water, & in due time draw it out softly and equally, so that no part of the mouth of the circumference thereof be drawn out before the whole, or sydelye: so shall the candle remain alive, as it was before. Then be natural and Mathematical Demonstrations. Let not therefore the ignorant condemn our writings, before they know what may be done by experience. 
A secret known, is no more a miracle.  It is now then no more a miracle, when it is known to be natural: And thus is it in all other Sciences and experiments, which the common people think to be impossible. As the like in growing of certain fruits, trees, 
Ignorance causeth admiration  and herbs, by art so helping nature, that they may spring and grow before their natural time, even in the heart of Winter. It seemeth also a miracle to the common people, that in the time of most temperate season, and great calmness on the sea, 
Whirlpools devouring ships.  ships beheld fast immovable in the midst of the sea, and suddenly swallowed into the bowels of the earth: which nevertheless is done naturally in manner of an earthquake, and by like natural cause. The reason whereof, is, 
The like of earthquakes, ●●●me, and undermining.  that the air as a most light Element, enclosed in the bowels of the earth, striving ever naturally to the circumference of the earth, as unto his own region. But the pores of the earth being strongly stopped, and the air thereby against his nature forcibly enclosed, striveth by violence to burst forth, and so cleaving the earth in the bottom of the sea, and great abundance of water falling into the breach, 
The spirit of De●●gorgon.  even from the highest part of the sea in that place, with swallowing attraction of the fall, draweth down with it suddenly the Ship or Ships, which at that time approacheth near unto the place of that whyrelepoole. Furthermore, any ignorant man would hardly believe that the salt water of the sea may be made fresh, and potable to be drunk, which nevertheless may be done naturally, as hath been often proved divers ways. 
To make said water fresh.  Some do this (as is written in Gemma Philosophica) putting the salt water in a vessel playstered or crusted over with clean Wax, which distilling through the straight and narrow pores thereof, leaveth the salt, 
There is a better way.  which for his grossness can not pass thereby. The same may be done better by a Canon or Pipe, filled with gravel or little stones, and that the salt water powered thereon, may divers times pass through that Pipe into an other vessel.    

¶ Of the Flowing, and Reflowing, (that is) increase and decrease of the Sea, with the causes thereof, more exactly than hitherto hath been declared by any.  
Whereas heretofore mention hath been made of the sea and flowing of waters, and divers other motions, it may be convenient to add hereunto the sayings and writings of the most expert and learned man, Fredericus Delphinus, Doctor of arts and physic, and public professor of Mathematical sciences in the famous university of Milan, touching the flowing & reflowing, or increase and decrease, (otherwise also named access and recess, that is, coming and going, or ebbing and flowing) of the water of the sea. Which flowing and reflowing, some do also name, the false rest or quietness, or inordinate motion of the water of the sea. And albeit divers learned men have entreated of this matter, yet forasmuch as some of their writings are somewhat dark, and not easy of all men to be understood, I have thought it necessary, partly out of their writings, and partly by mine own industry, more clearly & largely to entreat hereof, that the same may be the better understood of all men.  
A figure showing the beginning of the day increase at the Sun rising, and the beginning of the day decrease in the midday, and the beginning of the night increase at the Sun setting, and the beginning of the night decrease at midnight.  
Secondarily, is also to be known, 
Eight p●in●●●s of ●●u●n for 〈◊〉 and res●●●yng.  that there be in heaven eight points for the flowing and reflowing, or increase and decrease of the sea: of the which, four are strong, and four weak. Of the weak, two are weak for the flowing, and two for the reflowing. Weak for flowing, are the point of the East, and point of the West, which are the beginning of the two quarters of flowing. Weak for reflowing, are the point of the South or midday, and the point of midnight, which are the beginnings of the two quarters of reflowing: and these four points are distant the one from the other, by a quarter of heaven. Of the strong points, two are strong for flowing, and two for reflowing. Strong for the flowing, are the middle point between the East and the South in the day quarter of flowing, being distant from the East .45. degrees, and from the South likewise: And the middle point between the West and midnight, in the night quarter of flowing, ●●yng distant from the West 45. degrees, and from midnight likewise. Points strong for the reflowing, is the middle point, between South and West, in the day quarter of the reflowing, being distant from the South .45. degrees, and from the West likewise: And the middle point between midnight and the East, 
A right Horizon is when both the poles lie in the Horizon, & that is to them only which devil under the Equinoctial. Points of equal virtue in moving the water of the sea.  in the quarter of the night reflowing, being distant from midnight .45. degrees, and from the East likewise. And as the weak points are distant one from the other by a quarter of heaven, so are also the strong points distant the one from the other by a quarter of heaven, to them that have a right Horizon.  
It is thirdly to be known, that beside the aforesaid eight points, to such as have a right Horizon, there be many other points equipollent or of equal virtue. And such be all the points of heaven equally distant from the four principal points of heaven, which four principal points are, the point of the East, point of the West, point of the South, and point of midnight, or from the four strong points of heaven, which is all one, yet in quarters of contrary operation. For all such points are equipollent or of equal virtue in moving the water of the sea: but in a right Horizon it is otherwise, as shall appear hereafter.  
It is fourthly to be known, that the Sun and Moon every month, are together in one sign, degree, and minute. And this so being, 
The aspects which the Moon maketh with the Sun every month.  is called the Conjunction of the Moon with the Sun. From thence for the space of eight days, or there about, the Moon is departed from the Sun by her proper motion by a fourth part of heaven: and this departing is called the first quarter of the Moon with the Sun. From thence in fourteen days, or thereabout, she is departed from the sun by an other fourth part of heaven, and so by the half of heaven: and this distance is called the opposition of the Moon with the Sun, or the full Moon. From thence to .21. days or thereabout, she is departed from her opposition with the sun or full Moon by an other fourth part of the heaven, coming toward the Sun: and this distance is called the second quadrature of the Moon with the Sun, and then the Moon is distant from the Sun by a fourth part of heaven, as it was distant in the first quarter, and so cometh near to Conjunction with the Sun. From thence at thirty days, or thereabout, the Moon is again with the Sun in conjunction, as it was first.  
fifthly and lastly, is to be known that the Sun & Moon, both together every natural day (which is the time of .24. 
 hours, to the moving of the first movable) are the causes of flowing and reflowing, or increase and decrease of the water of the sea twice. These declarations premised, and well kept in memory, let us declare how the Sun and Moon both together every natural day; to the moving of the first movable, are the causes of the flowing and reflowing of the sea. For if these declarations be well held in memory, and especially the quarters of heaven in which is the flowing, and the quarters of heaven in which is the reflowing, and which are the strong points for the flowing, and strong points for the reflowing, and which be the weak points for the flowing, and the we●ke points for the reflowing: these (I say) being kept in memory, all the narration of the moving, and false quietness of the sea, shallbe clear and manifest.  
first of all (as touching the flowing and reflowing of the sea to the moving of the first movable) it is to be known, 
The Sun & Moon being in con●●●ction, what effect●●s they ha●● in mo●●●● the w●●●● the sea.  that when the Sun and Moon are joined together, which conjunction is called Noviluniun (that is) the new Moon, when they be moved to the moving of the first movable (called Primum mobile) from the East to the South, because the virtues both of the Sun and Moon be unite together, and both these Luminaries are moved continually to the moving of the first movable by the quarter of the day flowing, which is from the East to the West, the day flowing or increase of the sea is continual. And while they are moved from the South to the West, because they are moved continual by the day quarter of the reflowing, the reflowing still continueth. And while they are moved from the West to midnight, because they are then moved by the quarter of the night flowing, the night flowing is again continual. 
.  And while they are moved from midnight to the East, because they are then moved by the night quarter of reflowing, the night reflowing is again continual. And thus twice in the natural day is the flowing or increase, and twice the reflowing or decrease of the water of the sea.  
It is again secondarylye to be known, that when the Moon after her conjunction with the Sun, by her proper motion is departed from the Sun toward the East, according to the order of the signs, going toward her first quadrature with the Sun (which the Venetian pilots call, il Quartirune) ever before the Moon by her proper motion, come to that first quarter, which is the distance of the Moon from the Sun toward the East, 
A quarter of heaven is three signs.  according to the order of the signs, by a quarter or fourth part of heaven, when the Sun is so much above the Horizon of the East part in quarter of the day flowing, how much the Moon is under the Horizon of the same part of the East in the quarter of the night reflowing, because then the Sun is so much distant from the strong point of the flowing above the Horizon, as the Moon is distant from the strong point of the reflowing under the Horizon, 
A time wherein is neither ebbing nor flowing.  they are equipollent and of equal virtue, therefore then is neither flowing nor reflowing of the water of the sea, but the water seemeth to stand: And then the Venetians say, L'aqua è stanca. But when the Sun by the motion of the first movable, cometh near to the strong point of flowing, which is above the Horizon in the day quarter of the flowing, the Moon by the same motion of the first movable, departeth so much from the strong point of the reflowing, which is under the Horizon in the night quarter of reflowing, coming toward the weak point of the East flowing: And then because the Sun is nearer to the strong point of flowing, which is above the Horizon in the day quarter of flowing, then is the Moon in the strong point of reflowing, which is under the Horizon in the night quarter of the reflowing, the reflowing is weakened, and the flowing is fortified: and then the water of the sea beginneth to flow. And how much more the Sun approacheth to the strong point of the flowing, which is above the Horizon in the day quarter of the flowing, so much more the Moon is departed from the strong point of the reflowing, which is under the Horizon in the night quarter of the reflowing, approaching to the weak point of the East flowing, and therefore the flowing continueth. But when the Sun by motion of the first movable, cometh to the strong point of the flowing, which is above the Horizon in the day quarter of the flowing, then the Moon is departed from the strong point of the reflowing, which is under the Horizon in the night quarter of reflowing, and is made near to the weak point of the East flowing, and therefore the flowing yet continueth: But when the Moon shall come to the weak point of the East flowing, she then to the moving of the first movable, is moved by the day quarter of flowing, approaching to the strong point of flowing, which is above the Horizon: And the Sun, because it is distant from the Moon less than a quarter, shall likewise be moved by the same day quarter of flowing, approaching to the weak point of the South reflowing: And therefore because both are moved by the day quarter of the flowing, the flowing shall continued. And when the Sun by the moving of the first movable, cometh to the weak point of the South reflowing, because then the Moon is nearer to the strong point of the flowing, which is above the Horizon, than the Sun to the strong point of the reflowing, which is above the Horizon in the day quarter of the reflowing, the flowing shall continued. And when the Moon shall come to the strong point of the flowing in the day quarter of flowing, the Sun shall not yet be in the strong point of the reflowing in the day quarter of the reflowing, because that the Sun is distant from the Moon less than a quarter, but will come to it: and then the Moon shall departed from the strong point of the flowing, and shallbe less distant from it then the sun from the strong point of reflowing: and therefore the flowing shall yet continued, until the sun be so much beyond the South toward the West in the day quarter of reflowing, how much the moon on this side the South toward the East in the day quarter of the flowing: And then the sun shallbe so much distant from the strong point of the reflowing which is above the Horizon, beyond the South in the day quarter of the reflowing, how much the moon from the strong point of the flowing, which is above the Horizon, before the South in the day quarter of flowing: And incontinent, the Sun and the moon shallbe equipollent or of equal strength, & therefore shallbe no flowing nor rest●wing, as we have said before. And when he sun by the motion of the first movable, shall come to the strong point of reflowing in the day quarter of reflowing, the moon by the same motion of the first movable, shallbe departed so much from the strong point of flowing in the day quarter of flowing, coming toward the weak point of the South reflowing: and then the moon shallbe more distant from the strong point of flowing, then the sun from the strong point of reflowing: And so the sun shallbe stronger than the moon, and therefore then shall begin the reflowing, and shall continued according that the sun shall approach to the strong point of the reflowing, in the day quarter of reflowing: and the moon shallbe departed from the strong point of the flowing in the quarter of the day flowing. And when the son shall come to the strong point of the reflowing, the moon shallbe departed from the strong point of the flowing, and therefore the reflowing shall yet continued. And when the moon shall come to the weak point of the South reflowing, the sun shallbe departed from the strong point of the reflowing, in the day quarter of the reflowing, coming toward the weak point of the West flowing: Yet shall the sun be less distant from the strong point of the reflowing, then the moon from the strong point of the flowing, and therefore the reflowing shall yet continued. And when the sun shall come to the weak point of the West flowing, the moon shallbe near to the strong point of reflowing, which is above the Horizon in the day quarter of reflowing, and shallbe less distant from it, than the sun from the strong point of the flowing, which is under the Horizon in the night quarter of flowing, because she is distant from the sun less than a quarter or fourth part of heaven: therefore the reflowing shall yet continued, until the sun shallbe so much under the Horizon on the West part in the quarter of the night flowing, how much the moon is above the Horizon on the same part of the West in the day quarter of reflowing. And because then the Sun shallbe so much distant from the strong point of the flowing, which is under the Horizon on the West part, in the night quarter of flowing, as the Moon from the strong point of reflowing, which is above the Horizon, on that part of the West in the day quarter of reflowing: then the Sun and the Moon shallbe equipollent (that is) of equal strength and virtue, and so shall there be neither flowing nor reflowing. But when the Sun, by the moving of the first movable, shall come to the strong point of the flowing, which is under the Horizon in the night quarter of the flowing, the Moon by the same moving of the first movable, shallbe departed as much from the strong point of reflowing, which is above the Horizon in the day quarter of reflowing: And then the Sun shallbe less distant from the strong point of flowing, in the night quarter of the flowing, then the Moon from the strong point of reflowing, in the day quarter of reflowing, and therefore the Sun shallbe stronger than the Moon: and then again shall begin the flowing, and shall continued (as is said before) until the Sun be so much beyond midnight toward the East, in the night quarter of reflowing, how much the Moon on this side midnight, toward the West, in the night quarter of flowing, and then the Sun shallbe so much distant from the strong point of the reflowing, as the Moon from the strong point of the flowing: and then incontinent the Sun and the Moon shallbe of equal strength, and there shallbe nother flowing nor reflowing. But when the Sun, by the moving of the first movable, cometh to the strong point of the reflowing, in the night quarter of reflowing, the Moon by the same moving of the first movable, goeth back, & is departed as much from the strong point of the flowing, 〈◊〉 night quarter of the flowing, coming to the weak point of midnight reflowing: And then the Sun shallbe less distant from the strong point of the reflowing, in the night quarter of the flowing, then the Moon from the strong point of flowing in the night quarter of flowing and then shall the flowing be weakened, and the reflowing strengthened and the water of the sea shall then again begin to reflowe, which reflowing shall continued (as is said before) until the Sun be so much above the Horizon on the East part, how much the Moon under the Horizon on the same part of the East: And then the Sun shallbe so much distant from the strong point of the flowing, which is above the Horizon, in the day quarter of the flowing, how much the Moon from the strong point of the reflowing, which is under the Horizon in the night quarter of the reflowing: and then the Sun and Moon again shallbe of equal strength, and there shallbe nother flowing nor reflowing. Then daily (that is to say, in every natural day) shall return the like change to this aforesaid, until the Moon by her proper motion, shall come to her first quadrature with the Sun, which the pilots or Mariners Venetians, call il Quartirone, as I have said before. 
The Moon being in quartile aspect, or at the first with the ●●arter, some what effects it causeth in ebbing and flowing.  And when the Moon shall come to her first quadrature with the Sun, then when the Sun shallbe in the weak point of the East for the flowing, the Moon shallbe in the weak point of midnight, for the reflowing: and then the Sun shallbe so much distant from the strong point of the flowing, which is above the Horizon, on the East part, in the day quarter of the flowing, how much the Moon from the strong point of reflowing, which is under the Horizon of the same part of the East, in the night quarter of the reflowing: and so the Sun and the Moon again shallbe of equal force and power, 
A very little ebbing or flowing.  and there shallbe nother flowing nor reflowing notable, but only small, increasing and diminishing. And when the Sun by the motion of the first movable, shall come to the strong point of the flowing, which is above the Horizon, on the East part, in the day quarter of the flowing, the Moon by the same motion of the first movable, shall come likewise so much to the strong point of the reflowing, which is under the Horizon on the same part of the East, in the night quarter of the reflowing: and continually to the diurnal or day motion, the Sun shallbe distant so much from the strong point of flowing, which is above the Horizon, in the day quarter of the flowing, how much the Moon from the strong point of reflowing, which is under the Horizon, in the night quarter of the reflowing, and continently the Sun and Moon shallbe again of equal power, until the Sun by the moving of the first movable, shall come to the strong point of flowing, which is above the Horizon: And then likewise the Moon shall come to the strong point of reflowing, which is under the Horizon, because these points are distant one from the other by a quarter of heaven, as the Sun and Moon are distant from themselves by a quarter of he. And when the Sun by the motion of the first movable, shall depart from the strong point of the flowing, which is above the Horizon in the day quarter of the flowing, coming toward the weak point of the South, reflowing, the Moon by the same motion of the first movable, shall likewise depart as much from the strong point of the reflowing, which is under the Horizon, coming toward the weak point of the East flowing, and the Sun shallbe continually distant so much from the strong point of flowing, which is above the Horizon, how much the Moon from the strong point of reflowing, which is under the Horizon, until the same come to the weak point of the South reflowing: and then the Moon likewise shall come to the weak point of the East flowing. And the Sun and the Moon in all this time shallbe of equal strength, and incontinently shallbe nother flowing nor reflowing notable, and shallbe after the same manner while the Sun to the motion of the first movable, shallbe moved from the South to the West, because then the Moon by the same motion of the first movable, shallbe moved from the East to the South: And likewise, while the Sun shallbe moved from the West, to midnight, because then the Moon shallbe moved from the South, to the West: And likewise, while the Sun shallbe moved from midnight to the East, 
Eight days ●●ter 〈…〉.  because the Moon shallbe moved from the West to midnight. And so in all the time of one revolution of heaven, which is one day natural of four and twenty hours, the sea shall neither flow nor reflowe sensibly, but shall seem to stand, because the Sun and the Moon in all the time of that revolution of heaven, shallbe ever of equal power, without any notable difference. And this chanceth about the eight day after the conjunction of the Moon with the Sun. And this false quietness of the water of the sea, the Venetians call Acquae de feel, and use this manner of saying, Da gliotto, à inove, Lacqua non si move. From the eight day to the ninth, the water moveth not.  
When the Moon shallbe departed from the Sun, beyond the first quadrature, going toward her opposition with the Sun, than ever until the Moon shall come unto her opposition with the Sun, when the Sun shallbe so much above the Horizon on the East part, in the day quarter of the flowing, how much the Moon is under the Horizon on the same part of the East, in the night quarter of the reflowing, the Sun shallbe so much distant from the strong point of the flowing, which is above the Horizon, in the day quarter of flowing, departing from it by the motion of the first movable, and coming to the weak point of the reflowing, how much the Moon from the strong point of the reflowing, which is under the Horizon, in the night quarter of the reflowing, coming to it by the same motion of the first movable: And then the Sun and Moon shallbe again of equal power, and there shallbe neither flowing nor reflowing. And when the Sun by motion of the first movable, shall come to the weak point of the South reflowing, the Moon by the same motion of the first movable, shall approach or come near as much to the strong point of the reflowing, which is under the Horizon, in the night quarter of the reflowing: and then the Moon shallbe nearer to the strong point of the reflowing, which is under the Horizon, in the night quarter of the reflowing, then the Sun to the strong point of the flowing, which is above the Horizon, in the day quarter of flowing, because the Moon shallbe stronger than the Sun: And according that the Sun by the motion of the first movable, shall approach to the weak point of the South reflowing, the Moon by the same motion of the first movable, shall approach as much to the strong point of the reflowing, which is under the Horizon. And so the reflowing shall continued until the Sun come to the weak point of the South reflowing. And when the Sun by the motion of the first movable, shall depart from the weak point of the South reflowing, and shallbe moved by the day quarter of the reflowing, approaching to the strong point of the reflowing, the Moon by the same motion of the first movable, shall depart as much from the strong point of the reflowing, which is under the Horizon, in the night quarter of the reflowing, and she shallbe also moved by the quarter of reflowing, as the Sun coming to the weak point of the East flowing, because the Sun and the Moon are distant between themselves more then by a quarter of heaven: And so both shallbe moved by the quarters of reflowing, and therefore the reflowing shall continued, until the Sun shallbe so much beyond the South, toward the West, in the day quarter of the reflowing, how much the Moon on this side the South, toward the East, in the day quarter of the flowing. And then the Sun shallbe so much distant in the strong point of reflowing, in the day quarter of reflowing, departing from it by the motion of the first movable, toward the West, how much the Moon from the strong point of flowing, which is above the Horizon, in the day quarter of the flowing, coming to it: And so the Sun and the Moon shallbe of equal force, and then shallbe neither flowing nor reflowing. And when the Sun by the motion of the first movable, shallbe departed from the strong point of the reflowing, which is above the Horizon, in the day quarter of the flowing, coming to the weak point of the West flowing, the Moon by the same moving of the first movable, shall approach as much to the strong point of the flowing, which is above the Horizon, in the day quarter of the flowing, and then the Moon shallbe nearer to the strong point of the flowing, in the day quarter of the flowing, then the Sun to the strong point of the reflowing, in the day quarter of the reflowing: and so the Moon shallbe stronger than the Sun, and then shall begin the flowing. And as the Sun shall continually be departed from the strong point of reflowing, in the day quarter of the reflowing, so the Moon continually shall approach to the strong point of flowing, in the day quarter of the flowing, and so the flowing shall continued. And when the Sun shall come to the weak point of the West flowing, the Moon shall yet move by the day quarter of the flowing, because the Sun and the Moon are distant one from the other more than by a quarter of heaven: and then the Moon shallbe nearer to the strong point of flowing, in the quarter of the day flowing, than the Sun to the strong point of flowing, which is under the Horizon, in the night quarter of the flowing, and therefore the flowing shall continued. And when the Moon shall come to the weak point of the South reflowing, the Sun shall pass the weak point of the West flowing, approaching to the strong point of the flowing, which is under the Horizon, in the night quarter of the flowing, and then the Sun shallbe nearer the strong point of the flowing, which is under the Horizon, in the night quarter of the flowing, then the Moon to the strong point of the reflowing, which is above the Horizon, in the day quarter of the reflowing, and so the Sun shallbe stronger than the Moon, and therefore the flowing shall continued. 
A long time of flowing.  And when the Sun shall come to the strong point of flowing, which is under the Horizon, in the night quarter of the flowing, the Moon shall not yet be in the strong point of the reflowing, which is above the Horizon, in the day quarter of the reflowing, because the Moon is distant from the Sun more than by a quarter of heaven, and therefore the flowing shall yet continued, until the Sun be so much under the Horizon on the West part, in the night quarter of the flowing, how much the Moon above the Horizon on the same part of the West, in the day quarter of the reflowing and then the Sun shallbe so much distant from the strong point of the flowing, which is under the Horizon in the night quarter of the flowing, coming to the weak point of midnight reflowing, how much the Moon from the strong point of reflowing, which is above the Horizon, in the day quarter of the reflowing coming to it: and therefore the Sun and the Moon shallbe of equal strength, and then shallbe neither flowing nor reflowing. afterward, when the Sun by the motion of the first movable, shallbe distant from the strong point of the flowing, which is under the Horizon on the West part, in the night quarter of the flowing, coming toward the weak point of midnight reflowing, the Moon by the same motion of the first movable, shall approach as much to the strong point of reflowing, which is above the Horizon, in the day quarter of the reflowing coming to it. And so the Moon shallbe nearer to the strong point of reflowing, then the Sun to the strong point of flowing, and therefore the flowing shall begin, and shall continued in manner (as is said) until the Sun be so much beyond midnight, toward the East, in the night quarter of reflowing, how much the Moon before midnight toward the West, in the night quarter of flowing: and then the Sun shallbe so much distant from the strong point of reflowing, in the night quarter of reflowing, going backward from it toward the foresaid weak point of the East flowing, how much the Moon from the point of the strong flowing, in the night quarter of the flowing coming to it: and then the Sun and the Moon shallbe of equal force, and there shallbe neither flowing nor reflowing. And when the Sun by the motion of the first movable, shallbe departed from the strong point of reflowing, under the Horizon, which is in the night quarter of reflowing, coming toward the weak point of the East flowing, the Moon by the same motion of the first movable, shall approach as much to the strong point of flowing, which also is under the Horizon, in the night quarter of the flowing coming to it. And because then the Moon is nearer to the strong point of flowing, which is in the night quarter of flowing, then the Sun to the strong point of reflowing, which is in the night quarter of reflowing: then shall the flowing begin and continued in manner aforesaid, until the Sun be so much above the Horizon on the East part, in the day quarter of flowing, how much the Moon under the Horizon, on the same part of the East, in the night quarter of reflowing. And because the Sun shallbe so much distant from the strong point of flowing, which is above the Horizon, in the day quarter of flowing, coming by the motion of the first movable, toward the weak point of the South reflowing, how much the Moon from the strong point of reflowing, which is under the Horizon, in the night quarter of reflowing, coming by the same motion of the first movable toward it, they shallbe of equal force, and so shallbe neither flowing nor reflowing. And in this manner, the flowing and reflowing shall continued in every natural day, until the Moon shall come to her opposition with the Sun.  

The Moon being in opposition with the Sun, what effects they have in moving the water of the sea.  And when the Moon shall come to her opposition with the Sun, then when the Sun shallbe in the weak point of the East flowing, the Moon shall likewise be in the weak point of the West flowing: and then shall the flowing begin, and shall continued as long as the Sun shallbe moved to the moving of the first movable, from the weak point of the East flowing, by the day quarter of the flowing, to the weak point of the South reflowing. And the Moon then in all this time, shallbe moved likewise to the moving of the first movable, from the weak point of the West flowing, by the night quarter of flowing, to the weak point of midnight reflowing: and then the flowing shall cease, and the reflowing begin, and continued as long as the Sun at the moving of the first movable, shallbe moved from the weak point of the South reflowing, by the day quarter of reflowing, unto the weak point of the West flowing, and the Moon in all that time shallbe moved likewise to the moving of the first movable, from the weak point of midnight reflowing, by the night quarter of reflowing, unto the weak point of the East flowing: and then the reflowing shall cease, and the flowing shall begin again, and shall continued as long as the Sun shallbe moved to the motion of the first movable, from the weak point of the West flowing, by the night quarter of the flowing, unto the weak point of midnight reflowing. And then the Moon in all that time, by the same moving of the first movable, shall likewise be moved from the weak point of the East flowing, by the day quarter of the flowing, unto the weak point of reflowing: and then the flowing shall cease, and the reflowing begin, and shall continued as long as the Sun, by the moving of the first movable, shallbe moved from the weak point of midnight reflowing, by the night quarter of the reflowing unto the weak point of the East flowing. And then the Moon in all this time by the same motion of the first movable, shallbe moved likewise from the weak point of the South reflowing, by the day quarter of the reflowing, unto the weak point of the West flowing: and then the reflowing shall cease.  
And when the Moon shall pass her opposition with the Sun by her proper motion, 
The Moon 〈…〉.  going to her second quadrature with the Sun, then when the Moon shallbe so much above the Horizon on the East part in the day quarter of flowing, how much the Sun under the Horizon on the same part of the East in the night quarter of the reflowing, because then the Moon shallbe so much distant from the strong point of flowing which is above the Horizon in the day quarter of flowing, how much the Sun from the strong point of reflowing, which is under the Horizon on the same part of the East in the night quarter of reflowing, then the Sun and the Moon shallbe of equal power, and therefore shallbe neither flowing nor reflowing. And when the Moon by motion of the first movable, shallbe departed from the strong point of flowing, which is above the Horizon in the day quarter of flowing, coming toward the weak point of the South reflowing, the Sun by the same motion of the first movable, shall approach as much to the strong point of reflowing, which is under the Horizon of the night quarter of reflowing, coming to it: and then because the Sun shallbe less distant from the strong point of reflowing, which is under the Horizon on the East part in the night quarter of reflowing, then the Moon from the strong point of flowing, which is above the Horizon on the same part of the East in the day quarter of flowing, the reflowing shall begin and continued. And when the Moon by the motion of the first movable, shall come to the weak point of the South reflowing, the Sun shall yet be under the Horizon in the night quarter of reflowing, because the Sun and the Moon are distant from themselves more then by a quarter of heaven, and then the Moon to the moving of the first movable, shallbe moved by the day quarter of reflowing, as also the Sun in like manner by the night quarter of reflowing, coming to the strong point of reflowing in the day quarter of reflowing, and so the reflowing shall continued. And when the Moon shall approach to the strong point of reflowing in the day quarter of reflowing, the Sun shall approach to the weak point of the East flowing, in the night quarter of reflowing, and shallbe further distant from the strong point of flowing, which is above the Horizon, in the day quarter of flowing, then the Moon from the strong point of the reflowing, which is likewise above the Horizon in the day quarter of reflowing: and so the reflowing shall continued, until the Moon be so much beyond the South toward the West in the day quarter of the reflowing, as the Sun before the South toward the East in the day quarter of flowing: and then the Moon shallbe so far distant from the strong point of reflowing in the day quarter of reflowing, how much the Sun from the strong point of flowing in the day quarter of flowing: and so the Sun and the Moon shallbe of equal force, and there shallbe neither flowing nor reflowing. And when the Moon by the motion of the first movable, shall departed from the strong point of reflowing, coming toward the weak point of the West reflowing, the Sun by the same motion of the first movable, shall approach as much to the strong point of flowing, in the day quarter of flowing: And then because the Sun shallbe nearer to the strong point of flowing, which is in the day quarter of flowing, then the Moon in the strong point of reflowing, which is in the day quarter of reflowing, the flowing shall begin and continued according that the Moon, to the moving of the first movable, shallbe departed from the strong point of reflowing, in the day quarter of reflowing, coming toward the weak point of the West flowing: and the Sun shall approach to the strong point of the flowing, in the day quarter of the flowing coming to it.  
And when the Moon to the moving of the first movable, shall come to the weak point of the West flowing, the Sun yet by the same motion of the first movable, shall move by the day quarter of the flowing, because the Sun and Moon are distant the one from the other more than by a quarter of heaven: & the Sun shallbe more near to the strong point of the flowing, in the day quarter of flowing, then the Moon to the strong point of reflowing, in the day quarter of reflowing, and therefore the flowing shall continued. And when the Sun shall come to the weak point of the South reflowing, the Moon shallbe under the Horizon on the West part in the night quarter of the flowing, and shallbe nearer to the strong point of the flowing, which is under the Horizon in the night quarter of the flowing, then the Sun to the strong point of reflowing, which is above the Horizon in the day quarter of reflowing: And therefore the flowing shall yet continued, until the Moon be so much under the Horizon on the West part, in the night quarter of the flowing, how much the Sun above the Horizon on the same part of the West in the day quarter of the reflowing. And then the Moon shallbe so much distant from the strong point of flowing, under the Horizon in the night quarter of flowing, coming toward the weak point of midnight reflowing, how much the Sun from the strong point of reflowing above the Horizon, in the day quarter of reflowing coming to it: and so the Sun and Moon shallbe of equal strength, and then shallbe neither flowing nor reflowing. And when the Moon by the motion of the first movable, shall depart from the strong point of flowing under the Horizon, in the night qu●●ter of flowing, coming toward the weak point of midnight reflowing, the Sun by the same motion of the first movable, shall approach as much to the strong point of reflowing, which is above the Horizon, in the day quarter of reflowing coming to it: And then the Sun shallbe nearer to the strong point of reflowing, which is above the Horizon, in the day quarter of reflowing, then the Moon to the strong point of flowing, which is under the Horizon, in the night quarter of flowing Andrea therefore then shall begin the reflowing, and shall continued according that the Moon shall depart from the strong point of flowing, which is under the Horizon in the night quarter of flowing, approaching unto the weak point of midnight reflowing, and the Sun shall approach to the strong point of reflowing, which is above the Horizon in the day quarter of reflowing. And when the Moon by the motion of the first movable, shall come to the weak point of midnight reflowing, the Sun shall yet be above the Horizon on the West part in the day quarter of reflowing, coming by the motion of the first movable, to the weak point of the West flowing, because the Sun and the Moon are distant one from the other more than by a quarter: And then the Sun shallbe more distant from the strong point of flowing, which is under the Horizon on the West part in the quarter of the night flowing, then the Moon from the strong point of reflowing, which also is under the Horizon on the part of the East in the night quarter of reflowing. And therefore the reflowing shall continued until the Moon be so much beyond midnight toward the East, how much the Sun before midnight toward the West: and then the Moon shallbe so far distant from the strong point of reflowing in the night quarter of reflowing, going from it by the motion of the first movable, and coming to the weak point of the East flowing, how much the Sun from the point of flowing in the night quarter of flowing, coming to it by the same motion of the first movable: and so the Sun and the Moon shallbe of equal force, and then shallbe neither flowing nor reflowing. And when the Moon by the motion of the first movable, shallbe departed from the strong point of reflowing, which is under the Horizon, on the East part of the night quarter of reflowing toward the weak point of the East flowing, the Sun by the same moving of the first movable, shall approach as much to the strong point of flowing, which is under the Horizon on the West part in the night quarter of flowing coming to it: And then because the Moon shallbe more distant from the strong point of reflowing, then the Sun from the strong point of flowing, then shall begin the flowing, because the Sun shallbe stronger than the Moon. And how much more the Moon shallbe distant from the strong point of reflowing, in the night quarter of reflowing, so much more the Sun shall approach to the strong point of flowing, in the night quarter of flowing, and so the flowing shall continued: and when the Moon shall come to the weak point of the East flowing, the Sun shall yet be in the night quarter of flowing, because the Sun is distant from the Moon more than by a quarter of heaven, and the Sun shallbe nearer to the strong point of flowing in the night quarter of flowing, than the Moon to the strong point of reflowing, which is in the night quarter of reflowing: and so the flowing shall yet continued until the Moon be so much above the Horizon on the East part, how much the Sun under the Horizon on the same part of the East: And then the Moon shall so much be distant from the strong point of flowing, which is above the Horizon in the day quarter of flowing, departing from it by the motion of the first movable toward the weak point of the South reflowing, how much the Sun from the strong point of reflowing, which is under the Horizon in the night quarter of reflowing, coming to it by the same motion of the first movable. And then the Sun & the Moon shallbe of equal force, and there shallbe neither flowing nor reflowing, and the first disposition shall return again, and such flowing and reflowing, shall continued every natural day in this manner, until the Moon shall come to her quadrature with the Sun.  
And when the Moon shallbe in the second quadrature, 
The Moon being in the last quarter, causeth the same effects as in the first.  than the water of the sea, shall neither flow nor reflowe, but shall seem to be at rest as it was in the first quadrature, in the which, in the whole revolution of heaven, the Sun and the Moon were ever of equal strength for the causes there declared: for the same are the causes of the second quadrature, which are also of the first, and is about .21. days. And this quietness or stay of the water of the sea (as is said before) the Venetians call Acqua de feel, and use this saying: Da vent' uno à venti due, l'acqua non va ne so, ne giu From the .21. to .22. the water goeth neither up nor down.  
And when the Moon by her proper motion shall pass this second quadrature, proceeding to her conjunction with the Sun, than the Moon shallbe distant from the Sun, less than the fourth part of heaven. And then when she shallbe so much above the Horizon on the East part, in the day quarter of flowing, as the Sun under the Horizon on the same part of the East, in the night quarter of reflowing, then the Moon shallbe so much distant from the strong point of flowing, which is above the Horizon, in the day quarter of flowing, coming to it by the motion of the first movable, how much the Sun from the strong point of reflowing, which is under the Horizon in the night quarter of reflowing, going from it by the same motion of the first movable toward the weak point of the East flowing: and then the Sun and the Moon shallbe of equal power, and there shallbe neither flowing nor reflowing. And when the Moon by the motion of the first movable, shall come to the strong point of flowing, which is above the Horizon in the day quarter of flowing, the Sun by the same motion of the first movable, shall departed as much from the strong point of reflowing, which is under the Horizon in the night quarter of reflowing, toward the weak point of the East flowing. And then because the Moon shallbe less distant from the strong point of flowing, which is above the Horizon, in the day quarter of flowing, then the Sun from the strong point of reflowing, the Moon shallbe stronger than the Sun, and therefore then shall begin the flowing: and how much more the Moon shall approach to the strong point of flowing, so much more the Sun shallbe distant from the strong point of reflowing, approaching to the weak point of the East flowing, and therefore the flowing shall continued. And when the Sun by the moving of the first movable, shall come to the weak point of the East flowing, because the Moon shall yet be in the day quarter of flowing, for that she is distant from the Sun less than a fourth part of heaven, she shallbe less distant from the strong point of flowing, which is above the Horizon, in the day quarter of flowing, then the Sun from the strong point of reflowing, which is under the Horizon, in the night quarter of reflowing, therefore the flowing shall yet continued. And when the Moon shall come to the weak point of the South reflowing, the Sun shallbe above the Horizon, in the day quarter of flowing, and shallbe nearer to the strong point of flowing, then the Moon to the strong point of reflowing, which is after midday (or the South) in the day quarter of reflowing, because the Sun is distant from the Moon less than the fourth part of heaven, and therefore the flowing shall continued until the Moon be so much beyond the South toward the West, in the day quarter of reflowing, how much the Sun before the South toward the East, in the day quarter of flowing: And then the Moon shallbe so much distant from the strong point of reflowing, in the day quarter of reflowing, coming to it by the motion of the first movable, how much the Sun from the strong point of flowing, in the day quarter of flowing, departing from it by the same motion of the first movable: and so the Sun and the Moon shallbe of equal force, and there shallbe neither flowing nor reflowing. And when the Moon by the motion of the first movable, shall approach to the strong point of reflowing, in the day quarter of reflowing, the Sun by the same motion of the first movable, shall go back and departed as much from the strong point of flowing, in the day quarter of flowing: and then the Moon shallbe nearer to the strong point of reflowing, in the day quarter of reflowing, then the Sun to the strong point of flowing, in the day quarter of flowing: and so the Moon shallbe stronger than the Sun, and therefore shall begin the reflowing: and the flowing and reflowing, shall continued in the same manner as is said.  
When the Moon departeth from her conjunction with the Sun, and is not come to her first quadrature with the Sun, and is between the conjunction and first quadrature, and when the Moon shall come to her conjunction with the Sun, than again all the disposition before declared, shall return in all points in like manner as is said. 
A brief collection of all the premises.  Therefore this motion of the water of the sea whereof we have spoken, is a motion following the motion of the Sun & Moon to the motion of the first movable. For if you shall well consider that we have said of the flowing and reflowing (that is) increase and decrease, or access and recess of the water of the sea, you shall understand that the beginnings of such flowing and reflowing, and likewise the rest and quietness, chance diversly in the hours of the day and the night: For they come not ever in the same hours of the day, as is manifestly known to such as observe such flowing and reflowing, or false rest or quietness of the water of the sea. And therefore by the aforesaid doth appear that the water of the sea hath motion of flowing, once in the day, and once in the night: and likewise of reflowing once in the day, and once in the night.  

Ebhing and flowing begin not always at one hour.  It is manifest also that the flowing doth not begin ever the same hour of the day or night, but at divers hours: and likewise the reflowing.  
Also the time of flowing or reflowing, proceedeth inordinately when the Moon is in her quadratures with the Sun, that is, in the first or second.  
There chanceth sometimes great increase of waters, sometime less, sometimes mean, when the Moon shallbe in any other place from the sun beside these four: That is to mean, in the conjunction, or opposition, or her first quadrature, or second with the Sun.  
And as are sometimes increases of waters, greater, less, and mean, even so are the decreases in like manner.  

Great motio is of the water in the conjunction of the Sun and Moon.  The greatest concourses and motions of waters, are when the Moon is in conjunction with the Sun, & also the greatest flowings and reflowynges. Likewise in opposition of the Moon with the Sun, and greater than in the time of the conjunction of the Moon with the sun. For the superior bodies, by their motion & light, give their influence into these inferior bodies. And so much more as they have of light, so much more & stronglier they work: 
Greatest motions in opposition of the Sun and Moon.  and because in opposition of the Moon with the Sun, the Moon is full of light, & her light is toward us, therefore is it reasonable that then should be caused greater flowings and reflowings, then in her conjunction with the Sun. Nevertheless, because that in her conjunction with the Sun, the Sun & Moon are both unite together, and their virtues, therefore also are great increasings and decreasings of waters, because both their virtues are unite, as I have said, but yet greater in the opposition then in the conjunction, for causes before rehearsed.  
The Moon being in her quadratures with the Sun, 
Small motions of the water without determinate time always in the quadratures of the Sun and Moon.  the water of the sea hath no determinate time of flowing or reflowing, and then are the less concourses of waters, & least flowing and reflowing. And such motion of the sea, the Venetians call De feel: and then the water of the sea hath no determinate beginning of flowing or reflowing, but is moved inordinately in divers manner, sometime coming, and sometime going. The cause of this diversity is, because the Sun & the Moon, where so ever they shallbe in moving to the water equally, or as it were equally, have contrariety in what so ever point they shallbe. For in what so ever point the Sun shallbe, the Moon shallbe in the point of opposite virtue, contrary to the place of the Sun, or near.  
And when the Moon shallbe without the said four places, than the water of the sea shall begin to come or go. And when the Sun and Moon shallbe in equal points of virtue of the quarters of contrary operation, the concourses of waters shallbe so much the greater, 
Note.  in how much the Moon shall be nearer to her conjunction with the Sun, or to the opposition: and so much the less, in how much the Moon shallbe nearer to the quadratures, likewise also the flowings and reflowynges shallbe so much the greater. 
The Moon followeth the Sun in rising.  For if the Moon shallbe between her conjunction with the Sun and the first quadrature, than the Moon to the moving of the first movable, doth follow the Sun in his rising: and then shallbe the beginning of the day flowing, of the day after the rising of the Sun, about three of the clock, or before: that is to mean, 
When flowing s all e 〈◊〉 ●●ares after Sun rising.  when the Sun shallbe so much above the Horizon on the part of the East, in the day quarter of flowing, how much the Moon under the Horizon on the same part of the East, in the night quarter of reflowing, because then the Sun & Moon shallbe of equal force, because they shallbe in the points of equal virtue in the quarters of contrary operation, and the beginning of the night flowing shallbe in the night, after the fall of the Sun (that is) when the Sun shallbe so much under the Horizon, on the same part of the West, in the day quarter of flowing, how much the Moon under the Horizon on the same part of the West, in the day quarter of reflowing: 
Ebbing after noon.  And the beginning of the day reflowing shallbe in the day after noon, when the Sun shallbe so much after noon, in the day quarter of reflowing, how much the Moon before noon, in the day quarter of flowing: And the beginning of the reflowing of the night, shallbe in the day after midnight (that is) when the Sun shallbe so much after the point of midnight, in the night quarter of reflowing, how much the Moon before him in the night quarter of flowing. And if the Moon be between the first quadrature and the opposition, the Moon yet in her rising followeth the Sun, and then shallbe the beginning of the day flowing, in the day after noon, about evening (that is) a little before or after, that when the Sun shallbe so much above the Horizon on the part of the West, in the day quarter of reflowing, how much the Moon above the Horizon on the part of the East, in the day quarter of flowing, and the beginning of the night flowing, shallbe in the day before day (that is) about morning, before or after (that is) when the Sun shallbe so much under the Horizon on the part of the East, in the night quarter of reflowing, how much the Moon under the Horizon on the part of the West, in the night quarter of flowing: and the beginning of the day reflowing, shallbe in the day before noon, when the Sun shallbe so much before the point of noon, how much the Moon after the point of midnight. And the beginning of the night reflowing, shallbe in the night, before midnight, when the Sun shallbe so much before the point of midnight, in the quarter of the night flowing, how much the Moon after the point of noon, or midday, in the day quarter of reflowing. And if the Moon shallbe between the opposition of the Sun, and her second quadrature with the Sun, than the Moon in her rising, goeth before the Sun, 
The Moon rising before the Sun.  and then the beginnings both of flowing and reflowing, be in like manner as they were when the Moon was between the conjunction and first quadrature. For the beginning of the day flowing, shallbe in the day about three of the clock, before or after (that is) when the Sun shallbe so much above the Horizon on the East part, in the day quarter of flowing, how much the Moon above the Horizon on the West part, in the day quarter of reflowing. And the beginning of the night flowing shallbe in the night, when the Sun shallbe so much under the Horizon on the part of the West, in the night quarter of flowing, how much the Moon under the Horizon on the part of the East, in the night quarter of reflowing: But the beginning of the day reflowing, shallbe in the day after noon, when the Sun shallbe so much after the point of the South, in the day quarter of reflowing, as the Moon before the point of midnight, in the night quarter of flowing. And the beginning of the night reflowing, shallbe in the day, when the Sun shallbe so much after the point of midnight, in the night quarter of reflowing, how much the Moon before the point of noon, in the day quarter of flowing. And if the Moon shallbe between the second quadrature, and her conjunction with the Sun, than the Moon also in her rising shall go before the Sun: and then shallbe the beginnings of flowing and reflowing in the same hours, 
Note.  as they be when the Moon is between the first quadrature and opposition: because the beginning of the day flowing, in the day after noon about evening, before or after, when the Sun shallbe so much above the Horizon on the part of the West, in the day quarter of reflowing, how much the Moon under the Horizon on the same part of the West, in the night quarter of flowing: and the beginning of the night flowing shallbe in the night, about morning, before or after, when the Sun shallbe so much under the Horizon on the part of the East, in the night quarter of reflowing, how much the Moon above the Horizon on the same part of the East, in the day quarter of flowing. But the beginning of the day reflowing, shallbe in the day before noon, when the Moon shallbe so much after the point of midday, or the South, in the day quarter of reflowing, how much the Sun before it in the day quarter of flowing, and the beginning of the night reflowing shallbe in the night before midnight (that is) when the Moon shallbe so much after the point of midnight, in the night quarter of reflowing, how much the Sun before the point of midnight, in the night quarter of flowing. And hereby it appeareth, that as well the flowing as reflowing of the water of the sea, begin not ever in the same hours of the day or night: for the beginning of flowing is either in the beginning of the day, or beginning of the night, which chanceth, the Moon being in conjunction or opposition to the Sun: or is before day from the mornings toward the day, or from the day, until four of the clock, 
A general observation for the beginning of ebbing and flowing.  or thereabout, or is before Evening, toward Even tied, and from thence to the Cock crowing, or thereabout: which chanceth when the Moon is between her conjunction or opposition with the Sun, or any of the quadratures. The beginning of reflowing is either at noon, or at midnight, as when the Moon is in conjunction or opposition with the Sun, or is before noon, or after, or before midnight, or after, as when the Moon is between her conjunction or opposition with the Sun, and any of the quadratures. It is apparent also, that sometimes the water of the sea hath no determinate or certain beginning, neither order of flowing or reflowing, which chanceth, the Moon being in her quadratures with the Sun. It is manifest also, that all flowing of the water of the sea, is caused by respect to the Horizon, 
Note.  on the part of the East or West. And every reflowing by respect to the Meridian, or to the point of midday, or midnight.  

In what Horizon this discourse taketh place.  Here is also to be considered, that all that is said, are most certainly true in a right Horizon, but in an obliqne or side Horizon, they sometimes fail, as shallbe said hereafter following.  
It chanceth (as I have said) that the water of the sea doth sometime wander or decline from the order above prescribed, yet commonly, and for the most part keepeth that due order. Such manner of declining is after two sorts: For there is either disorder, or error, in the hour of the beginning of the motion of the flowing or reflowing, or in the midst of the motion: that is to mean, that they have greater or lesser courses then at other times, or otherwise greater or lesser increases and decreases. The error coming in the hour of motion, may come of three causes: As, by reason of the situation of the region, or by reason of the bodies supercelestial, or by change of the air. By reason of situation of regions, chanceth diversity only in the hour of the beginning of the flowing, 
The beginning 〈…〉 of 〈…〉.  because the beginning thereof hath respect to the Horizon, or is by respect to the Horizon: for in the beginning of reflowing is no diversity nor error, because the beginning of the reflowing, is by respect to the Meridian circle. Again, 
I he beginning of eb●●● 〈◊〉 by re●● 〈◊〉 the 〈◊〉 ch●●●.  by reason of the situation of the region, diversity chanceth thus, that is, that either the region is under the Equinoctial circle, or without it. And if it be under the circle, because they have a right Horizon, and the days be there ever equal with the nights there, at all times of the year. That we have said of divers hours of the beginning of flowing, is certainly true: But regions distant from the Equinoctial, because they have a winding or slope Horizon in them, the beginnings of flowing are as in regions under the Equinoctial, only in two times of the year: That is to say, in the Spring time, or Equinoctial Vernal, and in the time of Autumn, or Equinoctial Autumnal, that is to say, About the midst of the month of March, and about the midst of the month of September: But in other times of the year, or from the Vernal Equinoctial, by the whole Summer, until the equinoctial Autumnal, it is otherwise, because the beginning of the day flowing, if the flowing be before noon, that is, about the morning, it shallbe later than it aught to be: That is to say, more of the day than is in regions under the Equinoctial, and that because, that in such regions the day beginneth sooner, or the Sun riseth sooner, than in regions which are under the Equinoctial: for the declining of the obliqne or side Horizon (although these regions be under one and the same Meridian.) But and if the beginning of the day flowing be after noon, that is, about evening, than such beginning shallbe sooner than it is in regions under the Equinoctial, (that is to say) in fewer hours of the day: because that then the Sun falleth latelier than in regions which be under the Equinoctial. But the beginning of the night flowing, if it be before midnight, it is sooner in the said places or regions (that is to say) in less time of the night, or in less time after the fall of the Sun, then in regions under the Equinoctial: because that then the night beginneth to them afterward. And if the beginning of the night flowing be after midnight (that is) toward the day, it shallbe later (that is) of more hours, or more near the day, then is in regions under the Equinoctial: because the Sun riseth sooner to them, 
Two flowings in one day, and none in the night.  then to those that be under the Equinoctial. And this diversity groweth so much, that sometime it chanceth to see two flowings in one day, and none in the night: which chanceth for the inequality of the days, with their nights. For in how much the artificial day shallbe longer than his night, so much such diversity and error groweth more evidently. Therefore in the longest days of the year, such diversity shall appear manifestly. But from the Equinoctial Autumnal, by all Winter, until the Equinoctial Vernal, it is contrary: because the beginning of the day flowing, if it be before noon, that is, about the morning, then shall it be sooner than it should be (that is to say) in fewer hours of the day, than it should be in a right Horizon: for then the day beginneth latelier, or the Sun riseth latelier to them that have a winding or crooked Horizon. And if such flowing shallbe after noon (that is) about evening, than the beginning of such flowing shallbe later (that is) more toward the evening, or nearer to the falling of the Sun, then in regions which are under the Horizon: For in said or crooked Horizon, the night is sooner, and the Sun falleth sooner than in a right Horizon. Also, the beginning of the night flowing, if it shallbe before midnight, it shallbe later and more in the night, then in regions under the Equinoctial: because then the night shall sooner begin in the crooked Horizon, then in the right, because the Sun first falleth in the crooked Horizon, then in the right. And if the beginning of the night flowing shallbe after midnight, that is, toward the day, than such beginning of flowing in the crooked Horizon, shallbe sooner (that is) in fewer hours of the night (that is) more before the day, or before the rising of the Sun, than shallbe in regions which be under the Equinoctial: because the Sun riseth latelier than in regions under the Equinoctial. And such diversity groweth so much, that sometime shallbe two flowings in the night, and none in the day: And this chanceth for the inequality and increase of the night above his day. For in how much the night shallbe longer than his day, so much the more groweth such diversity: and therefore such diversity shall appear greatest in the longest night of the year. Wherefore, by the aforesaid, 
Note.  it is manifest, that how much the nearer we shallbe to the Equinoctial, so much the less shall appear the diversity in the hour of the beginning of flowing of the water: And how much the Sun shallbe nearer unto the standings or stayings of the Sun (called Solstitium) or the longest days, & longest nights, so much greater and more certain shallbe the diversity, and shall appear more manifestly. Furthermore, diversity chanceth by reason of the heavenly bodies, and error, not only in the beginnings of flowing, but also of reflowing.  
For when any of the great and luminous Stars (as are Venus and jupiter) shallbe about the Sun or Moon, 
The ●●●●●enes ●f other 〈…〉, ●●●e cause 〈…〉 in ●●l by 〈◊〉 and 〈…〉. And like 〈…〉.  they help them in moving the water of the sea: and therefore by this means also, they have their due order. Likewise (as we have said) by reason of the change of the air, often times chanceth diversity and error in the beginnings of flowing and reflowing: For the violent disposition of winds, vehemently blowing, as well near, as far of, removeth the courses of waters from their due order, sometime hastening the flowing, and sometime the reflowing, and sometime staying or stacking them likewise.  
There chanceth also error in the midst of motion of waters, for as well courses of waters, as also flowings and reflowings, sometime keep not the due motion: For (as is said) the disposition of winds may either increase or diminish their courses. Furthermore also, 
narrowness of places may 'cause disorder.  the straightness or narrowness of places, by reason of Islands or mountains, cause great concourses and diversities in many places. For where the sea is straighter or narrower, there is the stronger course, as about the Island Fuboea, Nigropontis, and between Sicilia and Calabria is greatly observed. Such straits hinder the increase of waters, because less quantity passeth thereby, and therefore there the flowings and reflowynges are less. And hereupon it chanceth, that in the Ocean sea, are greatest flowings and reflowynges, because there are no straits which may hinder or stay the courses of waters, and by that means they have their full and free course, and in more certain order. But in our sea, Mare Mediterraneum, it is otherwise. For what so ever water of the Ocean entereth therein, or cometh forth, passeth from the West by one only narrow straight: and therefore it can not in the flowing be greatly filled, neither in the reflowing be greatly emptied. And so consequently, the motion of the water of the sea proceedeth not in certain order. And to have said thus much of the divers motions of the water of the sea, may suffice.   

❧ Demonstration of Proportions of Motions Local, printed rather for the learned Philosopher, than the Mariner, yet the Mariner may learn many proper conclusions necessary to be known. To the godly and not envious reader, john Taisnier Hannonius, wisheth health. etc.  
WHereas a few years past, at Rome, Ferraria, and in other Universities of Italy (when Paul the third possessed the Papal dignity) I took in hand to read public lectures of sciences Mathematic, I may testify without scruple of arrogancy, that my lectures were honourably accompanied with the presence of more than three hundred auditors, because that arts Mathematic are there greatly esteemed. And therefore after the lecture was finished (as is the manner of auditors) oftentimes many resorted unto me, departing from the schools, to demand further of such doubts, whereof they had not full understanding In the mean while, certain which envied my reputation and assertions, ceased not with injuries, to hinder our proceedings, and sometimes to make an end of our disputations with quarrels and strokes. It chanced in the mean time that mention was made of the lecture of Aristotel. And whereas, from the purpose, one envious person moved the question of the Proportions of Local Motions, I refused to dispute with him, affirming that he evil understood the intention of Aristotel, whom he so esteemed as a heavenly God, that it seemed to him sacrilege, if any should descent from his doctrine. But he, maliciously and furiously, affirmed that I did rashly condemn Aristotel. I was therefore enforced by the request of my reverend Cardinal of Adulphis Florentine, openly to repeat the same, especially for that the report of these contentions, was now come to the Pope's ears, whose request also, I took for commandment. And thereupon (which I had not done before) I declared the errors of Aristotle, in the presence of the reverend Cardinal Crescentius, and the Bishop of Ponset, men most expert in all kind of learning, and in manner infinite other Auditors, before whom (in manner as followeth) I showed the errors of Aristotle by words and demonstrations. You therefore gentle and indifferent readers, accept this our Demonstration with favourable minds. I repute Aristotle for the chief of all Philosophers. Yet forasmuch as it is human to err, he also might sometimes fail.   

Demonstration of the Proportions of Motions Local, against Aristotle and all Philosophers.   depiction of weights 
I will now make Demonstration how bodies of the self same, or one kind and figure, equal or unequal one to the other, in the same midst or mean, by equal space, be moved in one or self same time: the which is against Aristotel and all other philosophers that have not yet seen this proposition. Aristotel first in the .4. of his physics. Cap. De Vacuo, where he intendeth to show, that if Vacuum, or void, be granted, moving or motion is taken away, etc. he there saith thus, We see those bodies which have more heaviness or lightness, so that they be of one figure, to be more swiftly moved by equal space, and by such proportion as they have the one to the other. And therefore they are so moved, per Vacuum etc. which is proved to be false. Furthermore what S. Thomas saith touching this, 
Thomas de Aquino.  any man that will, may read: for no man ever better understood the mind of Aristotle. But for the examples which Simplicius and Averroes give to the understanding of this (by two spherical bodies of equal quantity, but of divers kinds, as one of gold, & the other of silver) we must not therefore say that they understood this proposition as I will demonstrate. For they should have said somewhat of the equality of the quantity of those bodies, forasmuch as the motion of bodies equal or unequal, 
Motion of the bodies 〈…〉 and silver.  is all one, so that they be all of one figure: as for example, if there be three spherical bodies, of the which two be of gold, and the third of silver, and they of gold be unequal, and the other of silver equal to one of the golden bodies: then in the same proportion of time, shallbe moved the golden body equal to that of silver, with the silver body, in the which proportion the silver body with the go●den unequal, as shallbe declared hereafter.  
Furthermore 6. Phisicorum. Cap. 1. in the end, and in manner through all the .2. Chapter of the same book, he confirmeth the same: but in the fourth he saith thus, Whereas every thing that moveth, moveth in some other, & in some time, and that movable is motion of the whole, the same or all one shallbe the divisions of the time and the moving, and of to be moved, and of that which is moved, and also of that in the which is moving. Afterwards he giveth demonstration after his manner: but cap. 7. he willeth the same, where he intendeth, that in finite time, nothing may pass into infinite greatness. etc. Furthermore Aristotle in his first book, De Coelo, confirmeth the same, saying simply that the reason or consideration of times, is contrary to the reason of weights: as if half a weight be moved in this time, the double is moved in the half of this. etc. And this cap. 6. Furthermore cap. 8. of the same book he saith, 
The 〈◊〉 of fire.  The fire in as much as it is greater than the earth, so much the sooner and swyftlyer it cometh to his resting place. etc.  
Also in his second book, De Coelo. Cap. 8. he saith thus: As in other things, the greater body, is more swiftly moved by his proper course or motion, even so also in the heavenly circles, etc. Again Cap. 13. he affirmeth the same in two places, 
Motion of heaven 〈◊〉.  saying that the greater earth, is ever swyftlyer moved.  
Item, lib. De Coelo. cap. 2. he saith thus, If according to the proportion which hath the space C D. the body of B. shalb divided, all B. in the same time shallbe moved by C E. in th' which time part of B. by C D. of necessity: wherefore it followeth that B. be moved with swifter motion than part of B. afterward he maketh like Demonstration, saying thus, The swiftness of the less, 
The greater body the quicker motion.  to the swiftness of the greater, hath such proportion as the greater body to the less, etc. Again in the third, De Coelo. Cap. 5. in the end he saith likewise, that so much the more every thing is moved, as it is the greater, as also the fire the greater it is, is so much of swifter motion, etc. He confirmeth the same also, 
The greater fire the swifter motion.  Cap. 2. and 4. of the same book, where yet speaking more clearly, he saith that the greater fire riseth upward swifter than a less: and a greater piece of gold or lead, doth swifter move downward, and the like of other heavy bodies: and more clearly can no man gather the meaning of Aristotle.  

Perspective & error of Vitellio.  Vitelli io, in his second book of Perspective in the second proposition, hath fallen into the same error. I pretermit his ignorance in that proposition where he thinketh that there is no quantity insensible: but let this pass with other errors, the which at any other time shallbe showed in their place. He that will read all other Philosophers, shall see that they all accord with the mind and sentence of Aristotle, who also in divers other places confirmeth the same: but to have rehearsed these principal places, may suffice, and therefore we will now come to the Demonstration.  
This propounded Demonstration, I will show apparently, that it may the better be understood. And forasmuch, as Archimedes in his work, 
Archimedes.  De insidentibus aquae, hath spoken nothing of the proportion of motion of Elements, it is manifest that he had not yet searched this proposition: for there was the proper place of this matter. But it is not granted to any one man to know all things: and therefore it was very difficult to many to imagine the supposition, which I openly expounded in Rome, whereas Archimedes maketh none other Demonstration, but that natural motion is not caused of any other then of the excess or proceeding of a body in an Element, above or upon the said Element, or contrariwise. etc.  

Demonstration.  
And whereas by the 15. of the fifth of Euclides, the proportion of these heavy bodies, is the same which is between O. and G. by the .19. of the fifth aforesaid: the resistance of the mean or middle to O. shallbe quadruple to the resistance to G. The same also do I say of every of the bodies N L K H. It appeareth by common science, that resistance of the mean to the bodies N L K H. is equal to that which is to the body O. but is the same in the which G. by the first conception of Euclides.  
The like reason is also of violent motions, taking the proportion of the moving strengths, and taking away the proportion of the resistance of the half or middle. 
Motions violent and natural.  Also, whereas are two equal angles above the Horizon, or under, but in contrary order to the motion of nature, because violent motion is swifter in the beginning then in the end: and the contrary chanceth in the motion of nature: For with violent motion, the motion of nature is ever somewhat mixed, if horizontally or angulerly it shallbe above or beneath the Horizon: and nature worketh so much, until it bring violent motion unto some end. But if perpendiculerlye violence shallbe made above the Horizon, and toward the place which that body naturally moveth unto, than nature can not strive against or withstand, but that violence doth ever go with it, in respect of the end from whence. Furthermore, by the aforesaid, it is manifest that to be false which Aristotle saith 7. Physic. in the last chapter, where he saith, If A. be that which moveth B. and B. that which is moved, and C. the longitude whereby, and D. the time in which the motion is, that is to say, in equal time and power equal. A. the half of B. shall move by the double of C. and by C. in the half of D. for so shallbe the similitude of the reason. etc. That it is false I will thus demonstrate. Let us first imagine two bodies as before, in any mean or middle homogeny. etc. As let be for example. M. and N. and that M. be double in quantity to the body N and that the weight of N. be all one with the weight of M. And also that the body A FIVE I be equal to the body M. in quantity, & in likeness or kind of the body N. Then by common science, the body A FIVE I shallbe double in heaviness to the body M. And granting that the body M. be double in heaviness above the half, then shall the body A FIVE I be quadruple in heaviness above the said half. Wherefore the resistance taken away, let be left the time in the which the body A FIVE I to the time in the which M. is in proportion subtriple, or in the which the body A FIVE I in the same time shallbe moved the body N. by the aforesaid. Or if in the same time the body N. shallbe moved with the body M. yet the space by the which N shallbe triple to that by which M. For the reason is all one of violent motions. The same shall precisely come to pass, if in the stead of the excess of weight above the half, we shall take the virtue or power moving etc., as before.  
Wherefore it followeth, that it may be done contrary to that which Aristotle saith, and for the same sentence of Aristotle, some have thought that it is impossible that any of the figures of crooked lines, should be found equal to any figure of right line, or the contrary. The which to be possible, I will now demonstrate. For example, let be given a trigon or triangle A B C. for that I say of the trigon, I mean also of all figures of right lines, for as much as they be divisible into triangles, as appeareth by the 32 of the first. And if of those triangles we shall constitute a superficial line of equidistant sides, by 44. of the first, taken as often as need shallbe, which duplicate by the help of 36. of the first, and afterward a Diameter in it, than the half of that superficies, shall have an equal triangle of the taken superficies by the 41. of the first, or by the taken right line by the first conception, I will constitute a superficial of two crooked lines contained equal unto it. I will divide the first Basis or ground A C. by equal spaces into points H. by 10 of the first, and I draw B H. which also I draw forth until H K. be double to B H. by 3. of the first twice assumpted. Then to the half of H K. that is I I direct C 1 and A I I join thereto also A K. and C K. by right lines: then (by the first of the sixth) these triangles shallbe all equal to themselves. After this, I will constitute a superficial of equidistant sides, and of right angles upon what so ever line, which superficies shallbe equal to the Poligonic A B C K. by 44. of the first assumpted, as often as shallbe needful, that superficies is made G D. But in the which I draw the Diameter F E. so that by 41. of the first trigon F G E. shallbe the half of the whole superficies, and by common science equal to the trigon B K C. and triplus to the trigon B H C. now I divide FLETCHER G. by equal in the point M. by 10. of the first, and I protract or draw forth equidistantly G E. by 31. of the first. So do I also of the line M L. dividing it by equal in the point N. by the aforesaid 10. of the first. afterward by 44 of the first twice assumpted of equidistaunt sides, I make a superficies of right angles upon the line M N. equal to the quadrature of the line F M. which may consist of M N. and N O. Furthermore, of M N. transverse or overthwart, and N O. right, I constitute a parabol of a right angle, that it may be of less labour: For this example may suffice by 52. of the first of Apolonius Pergeus, 
Apollonius Pergeus.  the termining line of which paraboll, shall pass by the points F N. and G. by the same, and by 33. of the same F E. shall touch the parabol at the point F. And afterward when the trigon F E G. shallbe triplus, to the trigon B H C. as we have showed before, but also the portion F N G. triplus by the 17. of Archimedes, De quadratura Parabolae. Wherefore the portion F N G. shallbe equal to the trigon H B C. by the first conception in Euclid, added by Campanus. Furthermore, I draw E G. until by the third of the first G R. equal G R. I draw forth also FLETCHER R. and L M Q: Then by the fourth of the first, the triangle F G E. shallbe of equal sides, and also of equal angles to the triangle F G R. Furthermore, Q M is equidistant G R. by common science, & by R G. of the first, 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 whereas the angle F R G. is common to either of them, then by the 4. of the sixth, the same, or all one, shallbe 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 itself to M L. as G R. to Q M. But by the 16. of the same M L. to Q M. hath itself, as G F. to G R. Wherefore M L. equal. M Q. which M Q. I divide by equal in the point X by 10. of the first, & will do as before. Then by the reasons aforesaid of the same, the portion F X G. shallbe equal to the trigon A B H. and the whole Superficies F G. N X. shallbe equal to the whole trigon, A B C. which is proposed.  
The contrary appeareth thus. Let be granted a Superficies, contained of two paraboll lines, as FLETCHER N G. and F X G. proposing (for example) to find a superficial of right lynts trianguler equal to the granted superficies. I draw first FLETCHER G. Then after by 44. of the second of Apollonius Pergeus, I found the Diameter of the parabol F N G. which is M N. which I draw to N L. to be equal M N. Then I draw F L. which shall touch the parabol F N G. in the point F. by 33. of the first of the same. Then from the point G. I draw a line G E. equidistant from the Diameter M N L. by 31. of the first of Euclid: which I draw until it join together with FLETCHER L. the which doubtless shallbe done by the second of the first of V●tellio.  
The point of the concourse or joining together, is E. then I divide FLETCHER E. into three equal portions by the 11. of the sixth of Euclid, in the points S. and T. which points I join with the point G. by the lines F G. and G R. Now shall there be three angles all equal to themselves by 38. of Euclid. After this, I constitute a Trigon, B H C. equal to the Trigon, F S G. by this means I draw forth H C. to the equality G S. by the 4. of the first of Euclid. Then at the point H. I design an angle B H C. equal to the angle F S G. by 23. of the first of Euclid: and by 3. of the first of the same, I draw H B. until it be equal FLETCHER S. afterward I join B C. by a line. Then by 4. of the first, the triangle B H C. shallbe equal to the triangle F S G. and shallbe equal to the portion F N G. by 17. Archimedes, De Quadratura parabolae, by the help of the first conception of Euclid. I do the like of the portion F G X to whom by an equal triangle O P R. Then I draw P Q equally distant O R. and R V equally distant O P. by 31. of the first of Euclid. Then by 41. of the same O P R. shallbe half of the superficies O V Now then I somewhat protract C H. then upon B H. I constitute a superficial of equidistant sides, having an angle B H A. by 44. of the first of Euclid, twice 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. shallbe equal of the superficies F G N X. granted, which is the intent.   
FINIS.