THE Art of Navigation wherein is contained all the rules, declarations, secrets, & advises, which for good Navigation are necessary & aught to be known and practised: and are very profitable for all kind of Mariners, made by (master Peter de Medina) directed to the right excellent and renowned Lord, done Philippe, prince of Spain, and of both Siciles.  
And now newly translated out of Spanish into English by John Frampton.  
1581.  
❧ Imprinted at London, by Thomas Dawson, dwelling at the three Cranes in the Vinetree, and are there to be sold.   

¶ To the right worshipful, master Edward Dier Esquire, john Frampton wisheth health, and perfect felicity with increase of honour.  
COnsidering with myself (right worshipful,) that friendship and bounden duty, doth force many times men to do things, which if they were in the free choice of him that doth them, to leave them undone without any conceived discourtesy, not only he would not do them, but also, not asmuch as think of them. This I say that forced by friendship, and also moved by persuasion of certain pilots, and Masters of ships, I determined to translate this book of the art of Navigation, compiled by Master Peter de Medina a spaniard, in the year of our Lord jesus Christ. 1545. And because the work is so principal that in our time, the like in all respects hath not been set forth in our tongue, considering it instructeth, and teacheth all the whole art of Navigation in all points, and is in as like sort necessary for the Mariner, as the accidens is for the Grammarian, the weapon for the soldier, the Tool for the workman, the Guide for the blind, the instructor for the learner: and finally, comparable to a glass, wherein all the course of the world, the Seas, the Winds, the Altitudes of the sun, Moon, and Stars, are to be seen, and known, as far as naturalle reason may extend to. And besides, the pleasure that I minded to do, to the aforesaid persons, who moved me thereunto, as also to satisfy my good and continual desire, which I have, to help, and bring to light this good and profitable art of Navigation, whereby all men that are desirous to know, the secret of this noble art, may profit themselves therewith by reading it in our English tongue, especially the pilots, Masters, and Mariners, considering their lives and livings do stand there upon. And seeing as I believe and trust, they shall gather much fruit thereby, and that by little and little, these sciences shall remain aswell in our countries as in any other whatsoever. And seeing this work so necessary for the common wealth, setting all other private business aside I took in hand to translate this book, being perused and allowed by the chief Pilot, & learned Cosmographers of the famous contractation house of Sevil for the increase & knowledge of matters of Navigation, for the subjects of Spain, which work so excellent tried & approved by the learned: And for this our England so fit, & by me now thus translated out of Spanish into English, I dedicated to your worship before all others, for that I know you to have the art of Navigation inhigh account, & as highly to esteem all men that endeavour the knowledge of the same, beseeching you to accept of my good will and to be a protector of the same work. And so beseeching the almighty, to give your worship long life, and the advancement in this common weal, that the good people wish unto you, that authority may enable you to do, that good, that your good inclination doth naturally move you unto.  
From London this fourth of August. 1581. Your worships to command. john Frampton.   

THE EPISTLE DEDICATORY TO THE right excellent and renowned Lord, Don Philip Prince of Spain, and of both Siciles, etc. Set forth by Master Peter de Medina, the Author of the Art of Navigation.  
THE subjects are accustomed to serve their Lord right excellent and renowned Prince and Lord, with that which seemeth 〈◊〉 them to be most conformable to their will, and so some there be that serve with things that are delightful to the eye, and others to the taste. Others there are which do employ their persons in labours, and also others in divers other matters: And seeing I am desirous to be of the number of those, I sought by what means I might put it in effect, and for that my ability is not sufficient to do● greater service: I determined to make a book of the Art of Navigation, and to offer it in the service of your highness. Two things have moved me to this most mighty Lord. The first is, to see how great service your highness 〈◊〉 receive by the Navigation, at also how great profit cometh thereby to all the common stealth of Christendom. And this being so, it appeareth that by the Navigation, your Royal Senorie is amplified and extented into so great part of the world. And that which is newly discovered is more than five thousand leagues of the Sea coast, where doth contain so many regions, kingdoms, and provinces, where are found so many nations and diversity of people, and many other things in such sort by good reason it is called the new world. So that by means of the Navigation, there hath been brought and is brought into your highness Country of Spain, so many ships laden with Gold and Silver, that the same thereof cannot be accounted. As also such great quantity of sweet Drugs, and other things of great value and price: And this is little in respect, right excellent Lord, of the great number of people which do sail, not only to places known, but also to such as are far of, and unknown, and of such at is no knowledge of, they procure by sailing to seek and know, And seeing how long and dangerous ways they make by Sea, and f●we of them that sail do know what doth appertain to the Art of Navigation▪ The cause is, there are no instructors thereof, nor books whereby they may attain to it, so that your highness may understand, although the Navigation be of such antiquity, and more than three thousand years 〈◊〉 it began, and a thing of such importance, that the life of man goeth thereupon. And who can manifest the number of ships and people, which only do sail out of Spain to all parts of the world, or who can reckon the multitude of people which do consist only upon the Navigation, with their goods, riches, trades, merchandise, and other things: And for all this, there are no masters which do teach this Art, nor knowledge of an● that unto this day have written the manner of sailing: Even so, the most sort of pilots have the use of Navigation, no otherwise but every one following his own opinion and judgement, whereof it happeneth many times in one ship two or three pilots, the one saith according to his reckoning, the ship goeth sailing upon the land, the other sa●eth, according to his reckoning, the land is far of from him, and the cause thereof is, that there wanteth true knowledge of Navigation, and hereby it happeneth many times both ships and people are lost, and others sustain great dangers and losses. All which being by me considered, and chief seeing the Majesty of the Emperor, father unto your highness, and our Lord many times putteth his imperial person unto the danger of the Sea. Wherefore I being desirous to serve your highness in this, and to do good to such as are Sailors, by giving them rules and advises how they may make their Navigation certain without hazard of ignorance, I have framed and devised an Art of Navigation so orderly, that the pilots and other persons which do sail, shall find themselves so able therewith, that of itself, or with very little help, they shall know and very plainly understand that which they treat of, seeing it is so necessary, and so much standeth them upon to know, as a thing which doth import to many their honours, lives, and goods: Truth it is, most mighty Lord, that weighing my strength with the weight of my judgement, and finding myself of small sufficiency, I greatly disputed with myself, if for my small knowledge I should hold my peace, seeing that I knew it to be overmuch boldness to make a work and to direct it to your highness, but animating myself, and trusting in your accustomed clemency and magnanimity, I put myself under the shadow of your favour, and so most humbly beseeching you to receive this my little service with that Royal courtesy that unto others you are accustomed to do. And being perused by your highness, it may win so much favour whereby it may pass safely through all places, yielding great benefit and service unto your highness, as also profit to such as use the Navigation, that thereby they may understand the perfect knowledge thereof.   

❧ A preamble of the author upon the Art of Navigation, wherein is declared the great excellency of the said art.  
Among all other virtues some are so much the greater, by how much it is comunicated of amongst others, whereby the virtue of justice is most perfect among other virtues, for it doth most communicate and participate withal, so that among all arts the art of Navigation is more excellent than others, for it doth not oenly communicate with them, but doth shut up into it, the most principal of them, that is to say, Arithmetic, Geometry, and Astrology. These have excellency among the Mathematicals, by the most true show that is made of their conclusions. And that this art hath his beginning and greatness among other arts, it appeareth by three reasons following.  
The first, by reason of his subtility.  
The second, by reason of his certainty▪  
The third, by reason of his profit.  
For the first, who is sufficient to speak of so great a mystery that a man with a compass, and certain strekes marked in a card, doth know how to go round about the world, and knoweth both by day and night whether he shall come, and from whence he shall departed, and how much he shall go from one place to another, and that he go certainly in his right way, by so long and so large a thing as the sea is, where is no way no sign thereof, it is a mystery very difficult. And so it was considered by Solomon: who saith, that one of the hardest things to be found, is the way of a ship in the sea, for she followeth not any way, nor leaveth any sign where she went, And who is able to speak of so great a secret, that with a round instrument no greater than the palm of a man's hand called Astrolabio, the roundness of the heaven is measured, being so great th●t the understanding of man cannot attain thereunto. And therewith is taken the height of the sun, passing it by a very little and subtle place, being much greater than all the earth and the sea. And it is known how near and how far of it is from us: And in like manner the height of the stars are taken, and by this we are so certainly guided, that so much as one point faileth not. Likewise who can speak of the secret & fineness of the compass, that being made with as much paper as a man's hand, and with certain streekes marked thereon, doth note the winds. And with a little iron put into it, is made an instrument that doth move of itself, with only the natural virtue that a stone hath given unto it, and moving without the help of any thing, showeth where is the East, the West, the North, and the South. And likewise the thirty two winds which the Navigation hath, and this is showeth not only in one place but in all places, and it showeth it so certainly that thereby they do it, and are certain of their purpose and pretence as many as are sailors in the sea. For the second, the certainty of this art is so great, that it seemeth the knowledge of one man not to be sufficient to ordain it, nor yet of many men, more than God provided a special grace and understanding for that purpose, it is proved wherein it happeneth that a pilot cometh sailing, and a storm taketh him three hundredth leagues in the sea, and the day very cloudy, and the night so dark that standing in the poop of the ship, which is the hinder part, he seethe not the forepart of her, and scantly the mast, and making many turns in the seas, running from one part to another, rising and descending, with a vehemency of the winds and strength of the sea, and yet for all this, by the certainty of the art, he knoweth the way that she hath gone, and the place where she is, and being come to the land, she goeth to the port although it be in the night, not seeing the land, likewise it happeneth many times, as the pilor goeth sailing, he findeth a rock or should CC. leagues in the sea from any land, and marketh the place where he is, although he seethe not wherewith to mark it, for he seethe but the heaven and the water, and in it is not any thing wherewithal to mark or make any sign, because all doth move, but marketh it in his card by the land, he seethe in it and according to the art, which the card hath, it is so certain, that he and others both by day & night do know how to preserve and keep themselves from that place going aside from it, because they would receive no hurt, although it be under the water, that nothing of it is seen, whereby is concluded that although the other arts have truth, this hath more by reason of the demonstration so certain, which showeth to keep a man from hurt and danger that he seethe not. For the third, I say there is no art of any that man useth, so profitable nor so good as this art of Navigation is, and this to be true it seemeth well, because by it we have knowledge of diverse and sundry things in the world, and also of the trade with all parts of the world. And if navigation should cease, men should be driven to live straightly, for that they should lack many things which are necessary for the life of man.  
Also here is to be noted, that among all arts which men do use and practise, none is of so great peril and labour as the art of Navigation, and chiefly in these days, seeing it is so greatly increased and well near the hol● roundness of the world is sailed about: it is strange to consider that the ancient writers, neither saw it, no● thought of it, but rather held it for unpossible: it is worthy to be noted, that I have seen many times a Pilot come from the East India, who hath been one year upon the way, and from our India's four or five months, passing such great dangers and troubles that many times they have been at the point of death, and being come home to their natural country, all hath been so forgotten of them, as if it had passed in adream, and so they procure to return with so geart good will, as though they went to a thing of pleasure. I think that covetousness of goods is not the cause thereof, nor any other worldly gain, but I take it to come of the will of God, that although it be a thing so natural to fear death, and great labour, yet all these labours and fears which they pass in the same Navigation, are by them forgotten, for if they should remember and fear them, there is none that would sail on the sea: And seeing the wise pilot that so often times putteth his life in hazard; and not only his own, but in his knowledge is put in trust the lives and goods of many: wherefore if any person will understand the art of Navigation, let him peruse this book and art, and study therein, and he shall find plainly all things set forth necessary for the same, whereby pleasing God he will grant, to his way the end which he desireth.  
The end of the preamble.   

Errors escaped.  

Fol. 1. page 2, line 14. he in. for he is in.  
Fol. 2. page 2, line 36. and in planets. for and in plants.  
Fol. 3. page 1. line 31. prospective. for perspective.  
Fol. 3. page 2. line 2. the ten heavens. for the tenth heaven.  
Fol. 11. page 1. line. 23. the king juba. the king I●b●.  
Fol. 14. page. 1. line 47. one high. for no high.  
Fol. 15. page 1. line 20. the 1. for the first.  
Fol. 30. pag 1. line 22. is taken for one sphera Esphera, for is taken one spera, Esphera.  
Fol. 30. page. 2. line 1. is in auxe for is in his auxe.  
Fol. 34. page 2. line 23. your are distant. for you are so much distant.  
Fol. 45. page 1. line 3. how soever it be. for how great soever it be.  
Fol. 58. page 2 line 9 and of the guards of his moving, for of the guards and of his moving.  
Fol. 58. page 2. line 22. the month of bozina. for the mouth of bozina.  
Fol. 64. page 2. line 3. he be in the head at three. for he be in the head, at three.  
Fol. 69. page 2. line 27. go one any voyage. for go on any voyage.    

¶ The table of the books and Chapters that are contained in the Art of Navigation.  

The first book treating of the world, of his order and composition. 

CAp. 1. What thing the world is, and how it is compounded of the heavens and elements, it declareth the number of the heavens and their moning.  
Cap. 2. Wherein is declared the three movings which the eight heaven hath, & how they are known.  
Cap 3. How the heaven hath a round figure or shape, and by 5. reasons how it was convenient it should be so.  
Cap. 4. Of the nobleness of the heaven and of his colour.  
Cap. 5. Of the tenth heaven called the first movable and of his moving.  
Cap 6. Of the ninth heaven called Christa●ino or heaven of water, it declareth how there is a heaven of water and of his quality.  
Cap. 7. Of the eight heaven which is the firmament or the starry heaven, and of the light of the stars and their greatness.  
Chap. 8. How it is understood that the sun doth enter into the signs, and the cause wherefore they have the name of beasts.  
Cap. 9 What thing a sign is, and what likeness it hath with that which it is compared unto, and what day of the year the sun entereth into every sign.  
Cap. 10. Of the sevens heavens, of planets, and of their movings, and how they make impression, and cause generation and corruption in the lower bodies.  
Cap. 11. Of the elemental region, and how it is divided into 4. elements.  
Cap. 12. How those elements do shut up one another, and why the water doth not cover all the earth.  
Cap. 13. How the earth & the water, both elements do make one round body.  
Cap. 14. How the earth is situated in the midst of the world.  
Cap. 15. How the earth is quiet & moveth not.  
Cap. 16. Of the foundation of the earth, and how it may be said that the earth is the foundation of the world.    
The second book of the sea and his movings, and how the Navigation was invented. 

CAp. 1. What thing the sea is, and wherefore it was called Ocean.  
Cap. 2. How the sea doth appertain to the perfection of the world, and without it the world would perish, and how the water is engendered in it.  
Cap. 3. By what means the water of the sea is salt, and how it is more convenient it should be so, and better for the Navigation.  
Cap. 4. Of the difference of movings which the Ocean sea hath.  
Cap. 5. What the cause is that the sea never overfloweth above her bounds, nor is augmented.  
Cap. 6. Of the excellency of the navigation, and the antiquity thereof.  
Cap. 7. How that by some tokens of the sun and moan shallbe known when will come any tempest.  
Cap. 8. Of the fires and lights that appeareth in ships which do sail when there is any storm.  
Cap. 9 Of other certain signs, whereby may be known when storms will happen in the sea.    
The third book of the winds, their qualities & names, and how we aught to sail with them. 

CAp. 1. What thing the wind is, and of what quality, and how it is engendered.  
Cap. 2. How the wind doth not move right up nor down, nor contrariwise, but his moving is in circle manner of water and earth.  
Cap. 3. wherefore the wind is not always equal alike, but at sometimes more vehement, and at other times calm, and wherefore it moveth to contrary place.  
Cap. 4. Of the wherling of the wind and what is the cause thereof.  
Cap. 5. Of the winds which are named in the cards of Navigation, and of the number of them and their names.  
Cap. 6. How the winds, contained in the cards of Navigation do compass about the roundness of the world for to sail by them.  
A card to sail by, wherein is contained the Navigation of the most part of Europe, Africa, and India's or new world, with the distance of leagues & height of degrees that everything hath.  
Cap. 7. Of the order that the cards of navigation hath.  
Cap. 8. Of the account which the Pilot aught to have of his way when he saileth with a wind that differeth from his course.  
Cap. 9 How the Pilot should know sailing by any manner of course, where the Meridian is.  
Cap. 10. Wherein is largely discoursed this rule above written.  
Cap. 11. How the Pilotte aught to choose his course for the place whether he mindeth to sail.  
Cap. 12. How he aught to prick his card to know the place that the ship is in.  
Cap. 13. How the Pilotte aught to know that his card is just and certain, that there be no error in his Navigation.  
Cap. 14. Of the number of leagues that is counted for a degree in every course of the Navigation.  
Cap. 15. Of the number and measure, and of how many parts every degree is compounded.    
The fourth book of the height of the Sun, & how the Navigation aught to be ruled thereby. 

CHapter. 1. Wherein is declared. 17. chief principles which aught to be known in the height of the Sun.  
Cap. 2. Of the excellency of the Sun, and of his movings.  
Cap. 3. Of the year when the Sun goeth in his circle, and of other manner of years, and how the leap year is counted.  
Cap. 4. What thing a shadow is, and how the shadows aught to be looked on which the Sun maketh for to take his height.  
Cap. 5. Wherein is declared what thing is the height of the Sun, and how it aught to be taken to know the place wherein a man is. 

Here followeth the rules of the height of the Sun.  
THe first rule when the Sun and the shadow goeth toward the North.  
The 2. When the Sun is at the North, and the shadow at South, and the declination and height is more than 90. degrees.  
The 3. When the Sun is at North, & the shadows at the South, and the declination and height is just. 90. degrees.  
The 4. The Sun at the North, and the shadows at South, and the height and declination come not to 90. degrees.  
The. 5. The Sun in the Equinoctial, and the height to be less than 90. degrees.  
The 6. When the height is taken in 90. degrees, and whether there be any declination in the Sun or no.  
The 7. When the Sun and the shadows goeth to the South.  
The 8. The Sun at South, and the shadows at North, and the declination and height are more than 90. degrees.  
The 9 The Sun at South, & the shadows at North, and the height and declination are 90. degrees just.  
The 10. The Sun at South, and the shadows at North, and the height and declination come not to 90. degrees.    
Cap. 6. By the rules of the height of the Sun the degrees are to be learned, a man is of one side or part of the Equinoctial line, more than of any of the other parts.  
Cap. 7. Wherefore all the rules of the height of the Sun are reduced into 90. degrees, more than any other number.  
Cap. 8. Wherefore do we say that a man is from the Sun the degrees that are taken in the Astrolabio, less than 90.  
Cap. 9 How it is understood that a man hath the Sun upon his head.  
Cap. 10. How to know the height of the sun it must be seen whether it be a leap year, or what year it is. 

A rule to know the leap year.  
Tables of the declination or a departing that the Sun maketh from the Equinoctial line, in every day of the 4. years, as well to the North part as to the South.  
A Calendar of the Saints days through the whole year, with a declaration of the principal feasts.  
A rule to know the Dominical letter every year.    
Cap. 11. How that by the Calendar above written, a man shall know the month and the day wherein he is.    
The fift book of the height of the Pools. 

CHapter 1. What thing a pole is, and how among the Poles, the roundness of the world is divided.  
Cap. 2. How the height of the Pole Arctic is to be taken, and the cause wherefore he is taken.  
Cap. 3. How the account is to be understood which is taken of the pole artic, or North.  
Cap. 4. Of the North star, & of the gwards, and of his moving.  
Cap. 5. That according unto the course the gwardes are in, shallbe known how many degrees the North star is under or above the Pole.  
Cap. 6. How the rules of the height of the North star aught to be applied, and how they aught to be added unto, or taken away, according to the place where the gwardes are.  
Cap. 7. Wherein is declared certain doubts that in this moving of the North star may be had.  
Cap. 8. How the height of the North star may be taken, although the gwards be not seen.  
Cap. 9 How the altitude of the North star may be taken, although the Horizon be not seen.  
Cap. 10. A Clock by the North star, whereby is known what hour of the night it is in any time, or place a man is in.  
Cap. 11. How the height of the Pole Antarctic should be taken.    
The sixth book of the compasses to sail by. 

CHapter 1. Of the compasses of Navigation, and of the de●ects they may have, and how they may be amended.  
Cap. 2. How the winds of the compass may be understood, and how the Sun passeth by them every day.  
Cap. 3. Wherein is declared the opinion had of the Northesting, & Northwesting of the compasses.  
Cap. 4. Of the inconveniences that may follow by the north-easting and Northwesting of the compasses.  
Cap. 5. Of the regard or allowance which the compasses of Navigation have, & how it aught not to be given them.  
Cap. 6. Of an instrument whereby the compasses may be marked and known if they be true.    
The seventh book of the Moon, and 〈◊〉 her increasing and diminishing doth serve in the Navigation. 

CHapter 1. What thing the Moon is, and wherefore her light is not always equal but continually it increaseth, or diminisheth.  
Cap. 2. Of the golden number, and how it amounteth from one to nineteen, and wherefore no more not less.  
A rule to know the golden number of every year.  
Cap. 3. Wherein is declared the day & hour that the Moon maketh conjunction in every month of the year for ever.  
Cap. 4. Of the short account or reckoning without any book to know in short time how many days old the Moon is in any month of the year.  
Cap. 5. How by the days of the Moon and the course where the Sun aught to stand, may be known in what hour the tide will come.  
Cap. 6. Wherein is declared more at large the Chapter above, with a show thereof.  
Cap. 7. How that by the hour wherein the conjunction was, shallbe taken out the ●ide, & the regard or allowance that shallbe given to the Rivers.    
The eight book of the days of the year. 

CHapter 1. What thing a day is, and how it is reckoned, and in how many parts it is divided.  
Cap. 2. How that in all the artificial day the Sun riseth and setteth different unto such as devil in the world.  
Cap. 3. How that under the Equinoctial the days and nights are always equal.  
Cap. 4. How the days and nights go always increasing or diminishing unto such as devil out of the Equinoctial line.  
Cap. 5. How that the increasing and diminishing of the day is not equal in all places.  
A Table of the hours and minutes that such as devil in any distance from the Equinoctial line, have in the greatest day of the year.  
Cap. 6. Of the hours and minutes which they have every day of the year in the height of 40. degrees.  
Cap. 7. Of the hours and minutes that the Sun doth rise and set every day in the year.  
The last Chapter, how the Sun doth give his light in equal time of the year, to all such as devil in the world.     
The end of the Table.   

¶ The first book of the world, his order and Composition.  

THe first chapter, what thing the world is, how it is compounded of heavens and elements, the number of the heavens are declared and there movings.  
THe world according to the Philosophers, is universal, for all things, it confesneth therein, the heavens, the stars, the earth, and the sea, with all the other elements, and altogether is called the world. For as Ptolemy saith it is always moving and hath no time of rest: Seeing this universality which we call world, is compounded and ordained into two distinct regions (that is to say) the region Celestial, and the Region elemental  
The first which is the region celestial, is altogether shining, voided, and free from all variation, alteration and corruption. This according to the opinion of some ancient authors is divided into nine heavens (that is to say) seven of the planets, the eight is the firmament where the fixed stars are, the ninth the first movable: of that opinion was Ptolemy the great, and after him Thebit, Alfragano, Albategni, and others which in astronomy did flourish, more the late Astronomers (that is to say) the wise king Don Alonso, john de Liveris, George Purbachio, john de Monte Rey, and others do bring it very probable.  
That upon the ninth sphere there is another tenth, which is the first movable, it is alone, and they prove that there are ten heavens movable by the movings of the eight heaven. Hereof is written upon the first chapter of the sphere, that the late Astronomers saw fixed stars in the heaven to have three movings, which were found in the eight sphere, which are these following one is the first movable, that is to say of the tenth sphere which is the moving of every day, the which in four and twenty hours maketh a revolution from the east to the west and this is made upon the two poles of the world Arctic and Antarctic.  
It hath another moving of the nienth sphere, and is called the second movable, for it is always according too the succession of the signs from the West into the east, against the moving of the first movable, which moving is made upon the poles of the Zodiac, and this according as King Don Alonso sayeth, is called Auge of the fixed stars, the third moving is of himself, and is called the moving of tripidation, or according to the saying of the said King the moving of access and recess of the eight Sphere, and is made upon two little circles in the concavety of the nienth sphere, in the beginning of Aries and Libra equally described in such sort that as to every one of the heavens should not be given more than one moving of itself, and the eight heaven should have three movings.  
Hereof it cometh that two of them are unproper to him but are caused of other two superior heavens, that is to say of the ninth and tenth, upon these ten heavens or movable spheres we put the eleventh, which according to the learned is called the imperial heaven, that is by reason of his great brightness, which always continueth firm in one manner of order, without any moving, and of this there are some reasons, whereby we are persuaded, whereof there are two things noted.  
The first is, that any manner of thing that moveth from a place modueth his place either in all, or in part, so that which doth move moveth into some place, forotherwise it were immovable, therefore any of the movable heavens moveth place either altogether in himself or his parts, therefore he is in some place but not in any inferior sphere, for the place must compass about that which is put into the place, therefore he in a superior sphere. And it is convenient that there be some heaven steadfast and greater, wherein it may move.  
The second reason, is that there is put a difference in the heaven, that is to say, before and after, on the right side and on the leaf, not in respect of as much as toucheth us, but for the nature of the things, So the Philosopher sayeth in the second of the heaven and the world, this cannot be preserved by the movable spheres, the cause is that in the movable Spheres, the part that now is at the right side, shall be at the left. And the part that is now above shall be underneath, as experience showeth, whereupon it followeth, that it is convenient there be a fixed heaven, which in the behalf of the thing, is found the difference that is alleged. This is the imperial heaven, as it is said, which is higher than all other heavens. It hath great dignity, by reason of his brightness, cleanness, establitie, and pureness, here is the Celestial Court, where they devil that are of good fortune, enjoying of GOD, whereas the Apostle sayeth, nor eye hath seen, nor ear hath heard, nor can enter into the heart of man, that which GOD hath made ready for such as love him.   

The second chapter wherein is declared, the three movings which the eight heaven hath and how they are known.  
I Have said in the chapter before that in the eight heaven are found three movings different, and that some Astronomers were of opinion, that there were only nine spheres movable and others had opinion of ten, and because that in this the ancient authors, and the writers do not agreed, I will show you the reasons, that were of these opinions of the which is to be understood, the first, Astronomers maintained that there were only eight heavens. This they obtained by the moving of the stars. For the stars move not of themselves, but in their circles, so saith the Philosopher in the second of the heaven and the world, that the stars are fixed in the circle, as the knot in the table: so that by their movings the difference that is between the planets which move, and the fixed stars are known, these in their movings are known to be different 〈◊〉 one from the other, in swiftness and in slowness and by their place, but the fixed ●ar●es are so many in number that they cannot be tooth prehended.  
The long experience and observation of the Astronomers, attemed to the knowledge that ●n do move together in equal distance and nearness and continually the one doth keep with the other, so that their moving is one so the Philosopher understandeth in the first of the heaven and the world, therefore I say that these Astronomers understood that in the eight heaven was only the continual moving, that is from the East to the Wea●●, and that th● was the 〈◊〉 movable, it seemeth that the said Philosopher did so understand it in the place before alleged, where he saith that all the fixed stars are 〈◊〉 the first indueable, & for this reason, there are so man●e there, and in 〈◊〉 one of the inferiors ●d more but one.  
There was other Astronomers, that were not content to put only eight spheres but they attained to the ninth. And the reason was because they saw the eight heaven to have two movings different, the one is as aforesaid from the East to the West, and the other contrary to it: (that is to say) from the West into the East, and this motion is so slow, that in A hundred years it is scarcely to be perceived.  
This moving Ptolemy declareth in the seventh of the Almagesto, with most strong and certain reasons, so that these two different movings being considered, they came to the knowledge, that the eight heaven was not the first movable, for the first movable hath one only moving of himself most simple, the late Astronomers by their large speculation, found fixed Stars which moved sometimes from the West too the North, And to the South, and more swiftly to the east then too the West, and at other times more swiftly towards the North then too the South, The which Demonstration, because with only two 〈◊〉 aforesaid it could not be determined, they put another third: moving, and this is one of himself which is made in two small circles in the head of Aries and Libra, So that as the tight Sphere hath three movings, it is not only necessary to put the ninth, but also the tenth: the reason is because one simple body, aught to have but one only simple moving, and that is unto him proper and natural, so sayeth the Philosopher in the first of the heaven and the world, if they have any more movings, they are improper to him.  
And seeing that the eight heaven is a simple body, as the Philosopher understandeth it in the same place, it is convenient that of these three movings, one of them be proper and natural to him and the other two improper. Likewise the moving that is not proper to him, unto another is proper and natural. And seeing that it is not an inferior sphere, it is convenient to grant, that upon the eight heaven are other two movings of whom is caused these two movings aforesaid, so that as the Philosopher saith, the eight heaven was the first movable. It is to be understood, that he and the Astronomers of his time, believed that the eight heaven had only the moving of every day. And they came not too the knowledge of the others, because they were not determined upon, but in a very long continuance of time.   

The third Chapter how the heaven hath a round figure and of five reasons whereby it was convenient 〈◊〉 should be so.  
THE wisdom of the everlasting father which treated and di●●●sed all things, ordained that the heaven should be round up these reason's following.  
The first by reason of the similietude.  
The second, up reason of the commodity.  
The third for necessity, Unto the first, touching similitude or likeness, because the sensible world, is made unto the ●●●nesse of the world imaginat●●●, wherein is no beginning nor ending, and for this cause the sensible world hath a form or figure, after the manne● of a sphere▪ in the which cannot be. assigned or marked, beginning nor ending, For the second, of the commodity or profit this is because in all bodies and Super, fimetros, the which are four principally oval Piramidal, Colu●al, 〈◊〉 the Sphere is of gra●ter body and of all figures the round figure or form doth co●teiue most, and seeing that the round body is the greater, it followeth that all things which have that form or shape are profitable in the world.  
The third which is of necessity, for if the world were of another form or shape then round, as like unto a triangle or Quadrangle or of another form it would follow that some place should be ●●●ptie, or some body without a place, therefore an empty place cannot be put according to nature, for nature itself doth abhor it so much, that more easily it consenteth that which is heavy too rise up, or that which is light too descend, than too permit an empty place. So saith the maker of the commentaries▪ rather the heaven will descend found the earth ascend, than nature to permit any thing empty,  
A ristotle bringeth in other two reasons, to prove that the heaven is round.  
The first reason is, that unto the first and noble body is 〈◊〉 the first and most noble figure or shape. The heaven is the most noble and fyrstbodye and the round figure is 〈◊〉 perfect, therefore unto the heaven is due the round hour 〈◊〉 ●ording too reason, for unto every one body nature gave a form propercionably unto his work, even as it appeareth in Beasts and in planets.  
Therefore the proper work of heaven is to● move itself continually like to a circle. It was convenient that it should have a figure or form 〈◊〉 and 〈◊〉 for such a moving, and that is round, wherefore this lacketh the 〈◊〉 which doth let the moving.  
〈◊〉 sayeth, if the world were plain some part of it would be more near to be the● other 〈◊〉 even as that part which is over our ●●ades, whereupon the 〈◊〉 that is there, should be more 〈◊〉 too be then that which is in the east or in the West, than those things which are nearer too us do seem greater to us, so the Star which is in the midst of heaven shall seem greater to us then that which is in the east or in the West, which we see contrary, For the Sun or another Star seemeth greater in the east or in the West, then in the midst of heaven, the cause of this is, not because the Sun or the Star is greater or lesser, nor that he is father or nearer, But for some vapours that riseth up and putteth themselves between our sight and the Sun or the Star, and as these Uapoures are thick bodies they take away the Beams of the Sun▪ or Star from our sight, in such sort, that the thing in his own quantity● cannot be comprehended.  
As it may be likened to a piece of money cast into 〈◊〉 water, that because of the glistering of the Beams or strickes it seemeth to be of greater quantity than it is.  
Even so doth the Sun or star, when the Uapoures are put between them and our sight.   

The fourth Chapter, of the nobleness of the Heaven, and of his colour.  
ARISTOTLE sayeth that the nobleness of the heaven, is understood and considered in the clearness of his shining, in the roundness of his form, in the unity of his equality, in the virtue of his moving, in the height of his situation, which is very far from the centre of the earth, in the diminishing of his quantity, which doth overreach the imagination and measure of reason.  
In nature nothing is like too it, neither comparable to it in virtue, The heaven is none of the elements nor hath their qualities, nor is compounded of them, if it were it should be corruptible, for all thing compounded of the elements, shall be dissolved and corrupted.  
The heaven is ingenerable inaugmentable, it cannot receive strange impressions, it is neither light nor heavy, hot nor cold, dry nor moist, formal or royal, but virtuous, for his virtue and influence doth heat, so sayeth the Philosopher in the first of the Heaven and the World, and so improperly it may be said, it is not to be broken nor penetrable, and likewise improper, thick, or congealed, improperly it hath his colour bright.  
And for as much as the colour: which seemeth to us it hath, is to be understood, that our senses many times deceiveth us, and the sight may sooner deceive us their any other of our senses, for our eyes be of so tender a composition, that any manner of form, sent of any visible thing, we feel grief thereof.  
So sayeth Alacen in the prospectine; the thirty niene rule.  
And Aristotle in the book of Qualitate Visus, whereby I say that nothing above the Moon can be seen, But the Sun, or the Stars, which Stars we see by means of the light that they receive of the Sun.  
But as touching the colour of Heaven, It is to be noted, that it taketh colour in one of two sorts, one is of itself. And so is the second quality, caused of the first, Even as the white, the black, and other colours, In this sort the Celestial bodies have no colours, But in another sort it is taken, that is to say, commonly by all that which the sight doth show, & extendeth itself to that which is bright and piercing, and in that manner the heaven hath his colour, that is to say, shining.   

The fifth chapter of the ten 〈◊〉 called the first movable and of his moving.  
SEeing there hath been declared the number of the heavens there shapes and qualities, I will speak particularly of them, and especially of that which serveth for our purpose, of the which I say it is manifest to our sight that the heavens move, and it is to be understood, that a moving is a passing from one place to another, so that all things which move passeth from one place to another, or from one limet to another, this moving may be in one of these three sorts, by means of a circle or strait way or from above downward, and so contrary. The first of those three, which is the moving in circle manner, moveth not place according to all his quantity, but according to his parts, as it appeareth in a wheel unless it be all moved from one place to another that they make it go round, so they move all his parts, such is the moving of the heaven, so that, which is now in the east afterward shallbe in the west, and although the heaven moveth not place according to all the proportion which it hath, yet it is well moved which in it is moved. And this hath commonly been doubted, if the first movable of the heavens, were moved by one only mover or by many: And if by many how many there are, and in what sort they move it. Of the which it is to be noted that the heavens in the first movable are moved of one mover, and that they are not moved of many, for one only is sufficient, & many would be superfluous, so saith the Philosopher or the first of his natural philosophy, that it is better to put one beginning then many, and a few rather than an infinite number, therefore it is better to put one only mover then many who maketh this first movable: there are diverse opinions, one saith God alone, bringing therefore that which Aristotle saith that the first mover aught to be of an infinite strength-and seeing that God is of an infinite strength and hath created all things of a reasonable strength, it seemeth that God only is he that moveth the first movable. Others there are that proveth that the first mover is a certain intellective which moveth, the which they prove in this manner. If the first mover were God it would follow either that the moving of heaven were done at one instance, or the doings of God be measured with time.  
Therefore it cannot be said that the heaven is moved at one instant, seeing that all Astronomers holdeth and the sight showeth it, that in four and twenty hovers there is one revolution accomplished. N●● the second can be. For the said Philosopher in the fourth of the natural philosophy saith, the everlasting is not in time nor his doings are measured with time, but this is it which most commonly is under stood, that an angel maketh the first moving, and likewise all the other heavens have intellective motion which moveth them in their own movings and here by it appeareth how orderly they move since the time that GOD made them, until the like moving do cease when his will shallbe.  
Therefore I say that the first movable, of the first moving which is of the tenth heaven according to that as hath been spoken of, giveth a turn once in four and twenty hours round about the world, from the east into the west, & with this his moving he catcheth & carrieth with him all the other inferior heavens and maketh them give a turn to the world in the time that he giveth it. Although that their own movings be contrary to this, this is showed because we see that the stars, the sun, the moon▪ and the other planets have their first original, and are created in the east. And by little & little they rise up and ascend until they come to the meridian and so with one accord they descend and come to the west, and always they make this moving in the same four and twenty hours as the tenth heaven doth, so that continually they obey the movings of the first movable.  
And it is to be noted, that for as much as it is said of this forcible moving or catching which the first movable doth, unto the other inferior heavens, it is to be understood that in the Celestial bodies is no forcible moving or violence, nor any resistance or contradiction, but all with one conformity or accord do follows the first moving.  
And so when it is said that the first movable doth catch the other inferior heavens it aught to be understood sound as if he should say the inferior or lower heavens are moved of the higher by an accident, even so as the mariner moveth the ship moving herself, wherein he saileth or as the water in a vessel, the vessel being moved the water also moveth so it is to be understood, that the inferior heavens do move themselves by the moving of the first movable, so by that aforesaid it seemeth that always there may be a doubt saying.  
(A doubt:) how can it be that the tenth heaven moving itself continually without ceasing from the east to the west, that the other inferior heavens moving themselves with him do make their own movings contrary, so that in one self time there is made by one self body different movings.  
A Declaration for the declaration of this, the present example is to be noted, if in the wheel of a mil there were set a flee or an Aunt, although that the wheel doth make his moving very quick and hasty yet the Aunt or Flee may be going at their leisure, and make their moving contrary to that which the wheel doth. As also if the wheel carrieth them round about and in a short space giveth a turn yet they may make an end of their moving at their leisure, so that in this sort the moving which the tenth heaven doth make which is in every four & twenty hours, the inferior heavens although they are moved of him they make their own movings contrary, the which every one of them by himself doth make an end in different times.   

The sixth chapter of the nienth heaven, called Crystalline or heaven of water, it is declared how there is a heaven of water, and of what quality it is of.  
THe ninth heaven called the second movable, which first of all challengeth the moving from the West into the east for his own, because of the ten movable heavens. This is the first, and that most by leisure maketh his moving from the West into east, this is called the Crystalline Heaven or Heaven of water, of the which is written in Genesis the first Chapter. Where GOD said, let the Firmament be made in the midst of the waters, So that the waters remain divided, some above the Firmament and others beneath, the which firmament is the eight heaven. In such sort that of waters which remain above the Firmament is this nienth Heaven, Of this it seemeth there may be a doubt, saying.  
A Doubt, How can there be waters above the Heaven, seeing that naturally water is heavy, and all bodies which are heavy do naturally descend, neither can it be said that GOD hath them there, for any miracle, but by a natural means.  
A Declaration, to this Nicholas De Lyra, answereth in the gloss upon the said article the first of Genesis, where he sayeth that these waters are taken here in a double sense, for those waters which are above the firmament be of a celestial nature, that is to say, of the like quality that the heavens are of, and of their own nature: And those which are under the firmament are of ellymentall nature. This heaven is called the heaven of waters or crystalline heaven, because it hath a piercing light like to water, and clear shining like to crystal, of this nienth heaven, or of the tenth we have no sign, nor there is any in them: nor our sight doth pass the eight heaven where the fixed stars are.   

The seventh Chapter of the eight heaven, which is the firmament or starry heaven, and of the light of the stars, and of their greatness.  
THe eight heaven, which is the starry heaven, is called the firmament by reason that in it are the fixed stars, in such sort as none by himself moveth but altogether, of these it is to be understood, that although we see them bright, yet there is none of them that have any light of themselves, but the Sun giveth light unto them all, for he only hath light and no other body. This light God made the first day, as it is written in Genesis the first chapter. And the text saith that God saw the light and it was good. Saint Austin speaketh of the light that it is a corporal substance, sovereign and simple, multiplied in virtue, and shining with brightness without resistance it is communicable and delightful and therefore among all other body's there is nothing so profitable, so quiet, so virtuous as the light: The light is sprinkled abroad from the heaven to the earth it is the beauty of all visible creatures, and is the cause wherewithal the other bodies or the world be praised, seeing that I say that the stars have no light of themselves, more than that which they receive of the sun. So Albertus Magnus writeth in the second of the heaven and the world, The sixth chapter, where he saith, all the stars of heaven are lightened of the sun, as also the moon, but there is a difference in receiving of their light, & so they differ in receiving their virtue, as they differ in the nobleness of nature in such sort as, some are most pure and most noble, & these, receiving their light at one instant it doth penetrate them, from the superficie which is opposite to the sun even to the other superficie, so that all the stars remain clean and full of light, others also are penetrated with the sun, although that by their nature they decline to some colour, but howsoever it be, the sun doth penetrate them at one instant, & filleth them full of light even as a candle is lighted with fire, and here it is to be noted that in this eight heaven is the Zodiac where the twelve signs are, or the houses of the sun. These signs are compounded every one of a certain number of stars, & besides the signs, there are other 36. images, which are also compounded of stars, so that there are in all. 48, and these stars, which do compound these signs and images are in number. 1021. of these speaketh Alfragano in the third book of the assembling of the stars, that the lest of the fixed Stars to a notable sight is greater than all the earth. And if all the body of the earth were put into the place where the fixed Stars are, although it had light by reason of the great distance, it would be so little that we should not see it, but this authority is not to be understood of the planets, for all of them be not greater than the earth, nor it is to be understood of all the fixed stars, therefore it is to be said of them that are most notable to the sight. For there are some fixed stars so little, that we see them not, there be others also that although we see them by reason they are little, they are not accounted of the Astronomers, but only such as are great and these be not all of one greatness or quantity, but of diverse quantities, and therefore they be divided into six differences. So Ptholomy hath it in his Almagesto, and the king Don Alonso in his tables.   

The eight Chapter, how it is understood, that the Sun doth enter into the signs, and wherefore the signs have the names of beasts.  
IN the Chapter which goeth before, was said that in the eight heaven is the Zodiac where the twelve signs have their place or houses of the Sun, and of this it seemeth that two things may be doubted. (The first doubt) To the first, seeing that these signs or stars are in the eight heaven and the Sun in fourth, how can the sun enter into the signs, seeing there is so great distance between the sun and them, (The second doubt) To the second, if every one of the signs be compounded of stars wherefore do we say that one sign is called Aries, which is as much to say a Ram, and another Taurus, which is asmuch to say a Bull. And likewise of others: seeing that in the heaven there is not any beasts. (The first declaration) To the first, although it be true that the signs be in the 8. heaven, & the Sun in the fourth, it is to be understood that the moving which the Sun maketh in all the year is, that he moveth himself under the stars of the signs, and so when we say that the Sun is in such a sign, it is understood that then he moveth himself under the stars of that sign, as also any of us may stand under any sign or under the Sun, And the distance that is from the one to the other doth not let it. (2. Declaration) To the second, it is so, that in the heaven are no beasts, but these are so named by reason of the effects which the Sun worketh, being in every one of the signs which do follow and answer by property or likeness to one of these beasts, and by demonstration of such an effect, it compareth itself to the likeness of such a beast, or to another thing that it is likened unto, as in the chapter following is declared, that the Sun entering into every one of these signs, doth cause divers effects. Therefore it is to be noted, that of these twelve signs four of them are movable, four fixed, four common. The movable are Aries, Cancer, Libra and Capricorn, these signs are called movable, for the sun entering into every one of them, it is said, that the disposition of the air doth vary and not continued in one estate, and likewise the Sun entering into Aries, it moveth from winter into summer, and entering into Cancer, it moveth from Summer into Estio, and entering into Libra it moveth from Estio to Otonno which is harvest time. And entering into Capricorn it moveth from Otonno or harvest time into winter. The fixed signs are Gemini, Virgo, Sagitarius and Pisces, they are called fired, for the Sun entering into any of them, it is said, that the time and the disposition of the air doth continued in his own estate, They which are common, are Taurus, Leo, Scorpio, & Aquarius, they are called common signs, for there appertaineth to them some thing of the movable and of the fixed, and so the common in part is movable, and in part is fixed.   

The ninth Chapter what a sign is, and what likeness it hath with that whereunto it is compared, and what day of the year the Sun entereth into every sign.  
I Have said, that the signs of the Zodiac have names of beasts, by reason that the effects which the Sun doth work by entering into every one sign, they have likeness or property, with that beast or with that thing whereof the sign beareth name; And because I thought good to declare this at large. I will show what thing a sign is, and how many manner of ways it is taken, and the likeness that every sign hath with that wherewith it is compared, and in what day of the year according to the common opinion, the Sun entereth into-every sign, For the first is to be noted, that a sign according to the saying of Sacro busto, is a pyramid of four sides, whose seat is that superficie, which we call sign, the sharpness thereof is towards the centre, the signs are those stars, that the Astronomers were accustomed to contemplate on, looking on their light or brightness, whereby they knew what wether would come, and many were accustomed to behold them, and thereby they foresaw the qualities of the summer, winter, and other times of the year. For the principal stars in their risings and in their setting, do show the qualities of the times, A sign is also taken by one part of the Zodiac, the which the sun doth pass, after he hath gone thirty degrees from his moving. And because the sun in one year doth pass the zodiac, which hath three hundredth and threescore degrees, therefore the signs or houses of the sun are twelve, so saith Ptholomy in the second Quadri Partiti, that the signs are twelve, answering to the twelve parts of the earth, therefore of these signs. The first is Aries, and the reason why this sign is first named before the others, is because that some holdeth, that in the first degree of this sign, the sun made his moving the first day that he began, & that day he was in the equinoctial: and also for because the sun entering into this sign making heat, bringeth forth moisture, by the which it is a lively moving of generation, This sign is called Aries, by similitude even as a sheep is weak in one part of the body, and is strong in the other, so entering the sun into this sign the 11. of March, in the first part is a little hot, and in the last with greater strength his heat is felt.  
The 2. sign is called Taurus, to under stand, that as the Bull is a strong beast, so entering the Sun into this sign the eleventh of April, it heateth with more strength than before.  
The third sign is Gemini of this is understood▪ that the sun entering into him the eleventh of May, with his virtue of heating engendereth.  
The Iour●h sign is Cancer, into the which the sun is entered the eleventh of june, it is marked like a Crab.  
The fifth sign is the figure or shape of a Lion, which is a strong beast, choleric and full of anger, so that the Sun entering into this sign the fourteenth of july, it bringeth a strong heat.  
The sixth sign is Virgo, by the which is noted, even as the virgin is barren and doth not engender, so the Sun entering into this sign the fourteenth of August, the earth is barren and bringeth not forth any thing by reason of the great heat.  
The seventh sign is Libra, marked by a pair of Balance of like equality, to understand, that the Sun being entered into this sign the thirteenth of September, the day is equal with the night.  
The eight sign is marked with a Scorpion, which is a Beast, that with the tongue he flattereth, and with the tail he poisoneth, so when the Sun is entered into this sign the fourteenth of October, the first part thereof is temperate, but the last is cold.  
The ninth sign is Sagitarius which is a beast offensive, so that the Sun entering into this sign the thirteenth of November, offendeth with cold and snow.  
The tenth is Capricorn, wherein is understood that even as the Goat from the lower part goeth up to that which is high, so the Sun entering into this sign the fourteenth of December, from the lowest part of our hemisperio beginneth to go to that which is high.  
The. 11. sign is Aquarius, marked by a man that sheddeth water for to show, that entering the Sun into this sign the 11. of january, he sendeth to the earth water & moisture. The. 12. sign is Pisces, marked by 2. fishes in the water, which is cold & moist, to show that entering the sun into this sign the 12. of feburary the weather is cold and moist. Of the aforesaid it may be known, the diversity of the effects, that the sun maketh in every sign. But it is to be noted that this doth happen to such as do devil from the equinoctial towards the north or pole arctic, for such as inhabit towards the pole antarctic, the sun being gone forth of the equinoctial, doth make contrary effects to them, so that when we have summer they have winter, in such sort that the order of the signs in the Zodiac is not conformable or agreeable to all for if unto us cometh forth first Aries before Taurus, to them cometh forth first Taurus before Aries, & in like sort of the other signs as in the material sphere is plainly showed.   

The tenth Chapter, of the seven heavens, of the planets, and their movings, and how they have impression, and cause generation and corruption in the inferior bodies.  
SEeing that the eight heaven hath been treated of, and of the stars & signs that are in it. It is convenient to speak of them seven inferior heavens which are named by the planets, of the which it is to be understood that of the seven heavens. The first is Saturn▪ the second is jupiter, the third is Mars, the forth is Sol, the fifth is Venus, the sixth is Mercury, & the seventh Luna, more near unto us, than any of the rest, these seven planets are called stars, which are movable not because they err, but because their movings be not uniform nor agreeable, these do move the elements & do corrupt the things that are corruptible they bring cloudy weather, and raiseth up the waves of the sea, they move tempests, and causeth flowers to grow, and the heavens & planets have natural virtue to 'cause these effects, the works of these planets are divers according to the variation of the countries & regions, & thereby their impressions are printed in beasts, birds, and plants, and in men they incline more to one then to other. But although they do to incline & move, they do not constrain nor bind by force, But rather as Ptolemy saith, the wise man is lord over the stars He is wise that followeth not sensuality, but reason, every of these planets have a sphere of his own, wherein he moveth in circle wise, And the superior circle moveth round about so near to the inferior, that between the one and the other is no space nor any thing empty. so that these heavens do shut one with another, & they are near together in such sort, that any thing how little or small soever it be, cannot put itself between the one and the other, as it appeareth in the elements, that between the one and the other their is no place empty: so that we see between the water & the earth, or between the air and the water, or between the fire and the air, remain no place, that any thing may be put between: more it is to be noted, that although the heavens are so joined together, & near one to the other, that this joining together do not let them of their moving, so that they move very distinctly in different times the one from the other, without any let of their moving or standing still one only point in such sort, that the tenth heaven maketh his moving in twenty and four hours, & the ninth heaven that is near unto him, in forty nine thousand years, and likewise the eight heaven doth make his moving in thirty & six thousand years, and another in seven thousand, and the seventh heaven which is next to him maketh an end of his moving in thirty years. These are things which do teach us the greatness and power of the master & maker of such works, unto whom the said works giveth praise, so did the royal Prophet consider in the eighteen Psalm where he saith, The heavens do show and manifest the glory of the Lord, and in another place, Lord the heavens shall confess thy great marvels, from the beginning thou madest the earth, & the heavens are the works of thy hands. And it is to be noted that every one of these heavens have two movings one is the first movable, which is made from the east into the west, turning again into the cast as it is declared: The other moving which is proper to every one, is made by a circle obliqne, contrary to the first, that is to say, from the west into the east: Of this is to be noted, that according to the opinion of Francis Capuano, it was necessary that in the heavens were two contrary movings, one in the first movable, and another in the lower spheres, and this for two reasons, The first is, because the first movable doth move so swift, and with so great haste, that scarcely his moving can be considered, seeing that in twenty and four hours he passeth all the space that he doth occupy, which causeth, that he carrieth with him, all the lower heavens, and the fire, and the measured region of the air, as it is written, in the first of the Metheoros, so that if the eight & nienth sphere and the heavens of the planets did not move unto the opposite part, with a contrary moving, the said first moving would not only move unto the Celestial Spheres, and to the fire, but would move all the air, water, and earth round about, with his daily moving, and there would remain nothing quiet nor firm. The second reason is because the stars with their moving do cause influence in the inferior, and so they make impression as they move, but if every one did move, according to their only moving, that is to say, from the Cast into the West, so that if they moved altogether with one uniformity, they would bring forth one equal and uniform effect, the which should be an inconvenience. For that only generation is not sufficient, but it is convenient, that there be corruption, and so it was convenient, that all the Spheres, should modue in their daily moving, round about the earth once in a natural day, because all of them may communicate with us their impressions: and likewise that they move in the second moving in the Zodiac, coming together, and dividing themselves one from another to make that the effects should be different. Aristotle sayeth, in the second of generation, that the moving of the Stars in the circle, obliqne, that is to say, in the Zodiac is cause of the diversity of effects, And so the Sun in the summer coming near unto us, causeth generation, & likewise in Otonno, or Harvest time, and in the winter going ●rom us causeth corruption.   

The eleventh Chapter, of the Region elemental, and how it is divided into four elements, and why it is not divided into any more or less.  
IN the Chapters before written hath been declared the order of the heavens, their number & movings, therefore I will now speak of the elements, how they are ordained and divided, of the which it is to be understood, that the elements are four and no more, by reason, that first of all they have four qualities, and it may be said, that they join in six kind of ways. Let us see if all six be possible. One joining is hot and cold, another moist and dry, the third hot and dry, the fourth hot and moist, the fifth moist and cold, the sixth cold and dry. The two first be not possible, because there cannot be two contraries in one subject. The four which remain are possible, in the which the active one with the other joineth with the passive. These four do constitute the four first essentias which are called elements, And this is by reason of their first simple bodies, even as it seemeth in their qualities. That is to say, in the fire, in the air, in the water, and in the earth, because we see that the fire is hot and dry, the air hot and moist, the water cold and moist, the earth cold and dry, by the which difference of qualities of the first bodies, they are parted in the same manner. All these elements do moon, by the higher moving except the earth which is immovable. So saith Albertus the great in the first of his Metheoros, the fourth Chapter, it is necessary that we say the moving, which we see from the inferior, that is to say, the moving of the elements proceed of the superior, even as of his own cause, but it must be understood of the superior elements the which in their continual moving, they move in circle manner, only the earth which is most lowe, remaineth without moving, not only circular neither yet strait.   

The twelfth chapter how the elements, do compass about one another, and wherefore the water doth not cover all the earth.  
THese four elements, that before are spoken of aught to be understood that the one doth compass about the other in this manner, the earth is in the midst of all, like to a point or Centre of the world, near unto the which is the water, and upon the water and the earth is the air, and upon the air, the fire, and the element of the fire is upon the air Albenruys proveth it in the fourth of the heaven and the world in his thirty two commentary: where he saith, we see that all fire moveth upward and is elevated upon the air, therefore as his moving is not infinite it is convenient that it come to one place where it is natural, and there it is conserved, whereupon it is concluded that the fire is above the air, it is proved by an example in this sort. If there be any that have not seen the sea but seethe how all rivers go to demain in one pla●● as their movings the not infinite, it is necessary to conclude and appoint some place, where the waters may join, And this plate is the sea, so it is convenient to grant that upon the air is a place in the hollow part of the roundness of the moon, where the 〈◊〉 is gathered together. Therefore I say that these Elements either of them do compass in roundness equally from every part of the earth, saving the water in that part of the earth, which is discovered, for the breathing and life of all living creatures, of this it is to be noted according to the saying of Albertus the great, that the water did cover all the earth, and also he saith in the second of the Metheoros the third treaty the second chapter, we see the order of the elements are in such sort, that always the joining of the one is in the hollowness of the other, & this is by reason his roundness doth gird him thereunto, and because this is natural, and sometimes it was so, that at sometime the earth was covered with water, and all bodies naturally have one proper place, whereby it is convenient, that all be filled, for otherwise there would be some thing superfluous in nature, so it is evident, that the proper place of the waters is the superficie of the earth, for always they move by that place.  
Also when at any time two elements do not agreed in any quality, commonly it is called simbol, wherewithal the one doth join with the other.  
Therefore it is necessary, that there be some mean that they communicate and join together, and seeing the earth and the air have no simboll, it is convenient, that they join together by means which is the water that hath a simboll with both, and so it is showed that according to nature all the earth was covered with water: Of this may be asked what is the cause, why the roundness of the elements, failed more in the water then in the others: it is answered that GOD did make nothing in vain but always worketh for the best.  
Therefore as God by his only grace and will made man, and all other things, I leave this part of the discovery of the earth, that man and Beasts might be conserved in their own likeness.  
Of this have passed many questions, this is certain that GOD of his omnipotency made it. And so it is written in Genesis the first chapter, that God said let the waters come together, that are above the heaven, and let the earth be seen dry.   

The thirteenth Chapter, how the earth and the Water, both Elements, make one round body.  
IT is to be noted, that these two Elements, Earth and Water, both together do make one round body, Of this speaketh john de Sacro ●usto in the first chapter of the Sphere, The earth is round, which is showed by the signs and the other Stars, which rise not, nor go down equally to all men wheresoever they be. But first of all they rise to them that be in the east part, rather than to them that are in the west, and why they appear to one rather then to the other, the roundness of the earth is the cause thereof, & that to be true, that the stars are seen to some rather than to others, it appeareth by the eclipse, for one self eclipse of the moon, which we see at the first hour of the night, they which are in the east parts do see them in the third hour of the night, whereby it seemeth, that it was first night, and the sun was first set to them, before it was set to us, the ●ause is, the roundness of the earth, & that the earth is round from the north unto the south, and so contrariwise it showeth itself, for unto those which are towards the north, appeareth always some stars, which are near to the pole artic, & the other stars which are near to the pole antartik are never seen. But if any went from the north towards the south or midday he might go so far, that the stars which he saw first might be laid under the horizon that he should not see them, and how much more he came towards the south, so much less he should see the stars of the north, and then he should see the stars of the south, that first he could not see, as contrariwise, it would happen to such as went from the south to the north, and the cause of this is the roundness of the earth, likewise if the earth were plain from the east to the west, so son or equally, the stars would rise unto those in the east parts as to those in the west, whereby it seemeth false, by the first reason.  
Item if the earth were plain from the north to the south, or by the contrary, the stars that one should see should never be set from him wheresoever he should go, the which is false, by the second reason, for if in any manner of wise the earth do seem plain, unto the sight of men, it is for the great quantity that it containeth, in respect of our sight. And if any should say that the mountains and valleys do let the roundness of the earth. To this is understood, that the mountains have not any proportion that should let the earth to be round And if there be any thing in that sort they be as the nails of a wheel, that very little or nothing do let his roundness, but note that in one of two manner of ways a round thing may be spoken of, the one is by rule, that is to say, when the lines which are straightly carried from the centre to the circumference, be equal, in this sort the earth is not perfectly round. In another sort it is said to be round irregular, that is, when all parts are not of equal distance from the midst, so is the roundness of the earth. And seeing it hath been declared how that the earth is round. I say that the water is likewise round which is proved by the reasons aforesaid.  
Also it is proved, that such as sail by the Sea, for to discover the Land, they always go up to the top of the Ship, which is the highest part, and happeneth to see the Land from thence, and from no other place, And this is by reason of the roundness which the water hath.   

The fourteenth chapter, How the earth is situated in the midst of 〈◊〉 world.  
ALFRAGANO saith, in the fourth difference, if the earth were not in the midst of the world it would not be of equal distance from every part of the heaven. But Euclides bringeth in the first of the Elements, that it standeth in the midst, and is equal in distance from all parts, and proveth so, for if the earth were not in the midst, it would reach more to the east part, or too the West. And for a similitude, when the Sun or other Star, were in that part, it would reach more near to the earth, than it it were in the other part, & so they would seem greater: Which is false, for we see that all people which are vp● on the face of the earth the stars seemeth to them of one self quantity in what part of the heaven soever they be, be it in the middle heaven, in the east or in the west. And the cause of this is, by reason the earth is of equal distance from the Sarres, it followeth therefore that it is in the midst of the Firmament.  
Item if the earth by any of his parts, were more near to the heaven in one place then in another, he that were in that part upon the face of the earth, which were nearer to the heaven, should not see the half heaven.  
This is against Ptolemy, and all the Philosophers, that do say, that wheresoever a man standeth there riseth always with him six signs, and other six setteth with him, and the half heaven is seen of him, and the other half is hid from him, so that equally they are distant from the heaven.  
Sacro busto sayeth, that by the self same sign or show is proved, that the earth is but a point in respect of the Firmament, for if the earth were of any quantity in respect of the heaven, it would not happen that the half heaven should be seen.  
And for the better understanding thereof, Imagine this, if any plain superficie were put upon the Centre of the earth, the which should divide the earth into two equal parts. And also the firmament itself.  
Then the eye of him that were in the Centre of the earth, should see the midst of the Firmament, And the self same eye standing upon the face of the earth, should also see the midst of the firmament, of this is gathered, that the quantity of the earth is insensible in respect of the firmament.   

The fifteenth Chapter, how the earth is quiet and moveth not.  
THAT the earth is unmovable and quiet, to is proved by two reasons, the first is, that being a hole natural body and altogether heavy, it goeth to the place most low, which is the Centre and midst of the Firmament, and there it remaineth. So saith the Philosopher in the fourth of the natural Philosophy and in the first and fourth of the Heaven and the world.  
The second reason is to consider, how that the earth standeth in the midst, and if it should move and depart from the midst, it would rise up, the which would happen to it naturally or violently, not naturally, because his natural moving is to the midst, and so his moving contrary to the midst is not natural to it, than it should be with violence. But it cannot be with violence, because there is no body to be found that should do violence to so great a body, in greatness and weight, where it is to be concluded, that it is always queit and moveth not.  
The same proveth Albertus the great, in the second of the heaven and the World, in the third Treaty and the. 8, chapter where he saith, the order of the stars do learn the earth to be quiet, and placed in the midst, for as the moon is ordained to be under the Sun, if the earth were not in the midst and fixed, it would not happen 〈◊〉 the part of the circle of the signs, the Sun and the moon to be opposite to the head and tail of the Dragon, and likewise the Astrolabios, and other instruments of the Astronomers should be false, and by them would never be found the courses and computations of the stars, as by the said iustruments our senses do attain unto, for always they would happen to be diverse and different, for from the earth the circles of the heaven should not be equally seen. All the which we have proved be Geomitrie and Astronomy. It is to be considered that God made heaven and earth, and all that therein is, he put the earth fixed in the midst, because the heaven and the stars should compass it about with their moving, where the divine power doth sustain it in the nuddest, even as a point. Of this is written, The Lord saith, I have hanged, the earth in one knot founded upon his stabillitie.   

The sixteenth Chapter of the centre of the earth, and how it may be said that the earth is the centre of the world.  
THE Centre of the earth may be understood in three manner of ways, The first as touching the greatness of the Centre, The second of the weight of the centre. And the third of the maze or assembly of the centre, the which assembly or maze is in the midst of the firmament, This being had, four things are to be noted. The first is, that in the land is not one self centre of greatness and of weight, for the earth is deformedly weighty, for that the one part is covered with water, & the other part is discovered. The second, that the centre of the weight of the earth is not in the midst of the firmament, for if you imagine to divide the earth into 2. equal parts, then the part that is covered with water would surmount the other. The third is that the Centre of the greatness of the earth, and the Centre of the firmament, are not one. For that the earth is not equally covered with water. Of the which there followeth, that in the earth we may imagine, three centres really distinct, The first, is the centre of the greatness of the earth, The second the centre of the weight, The third the midst of the firmament, The fourth reason that the, centre or point of the maze or assembly of the water and earth is in the midst of the firmament. This is because the like assembly is a weighty body, and without let, and so the centre touching his weight is in the midst of the world, for that he is weighty by nature, whereby it may be said that the earth is in the midst of the firmament, for that it is a part of the maze, which maze is in the midst of the world.   
¶ The end of the first book.   

¶ The second Book of the Sea, and of his movings, and how the Navigation was invented.  

The first Chapter what thing the Sea is, and wherefore it is called Ocean.  
THe Sea is the proper place of the waters by reason of the similitude of his form. There the waters do engender & are sutained. And according as Albertus the great understandeth it, the rivers come forth of her and return to her again. So he saith in the third of his Metheoros the twelfth chapter, we see that all rivers run into the Sea, and from the Sea they return and come forth, that they may run again, whereby it sevieth, that the Sea is the end and beginning of the waters. It is called the Ocean Sea, for the swift and continual moving where with it moveth: for that, Oikis in Greek is as much to say hasty or swift. The Greeks and Latinists do name it by this name, and therefore this name hath continued common: or else it is called Ocean Casi Cianeus, because it girdeth or embraceth the ends of the earth, & by reason of the diversity of the countries, it taketh divers names, as the Indian sea or Percian sea. etc.  
The Sea hath no colour, being looked upon, when one is near it: for our sight remaineth not upon the superficies of the water, but descendeth down and being looked upon a far of it hath the colour of heaven, & being moved of the winds it hath the form of divers colours. And it is to be noted, that the Sea for seven days riseth increasing, and is that which we call springtides, & other seven she decreaseth. Of these flowings and ebbings. Aristotle bringeth the causes to he natural, in the second of his Metheoro●: and besides that, Hipocrates, in his book of air and water saith that there is a proper cause in Astronomy, that is by the natural virtue of the moon, upon the waters, so likewise we see that all shell fish with the increasing of the moon do increase, & with the decreasing do decrease: for as the moon riseth above the Horizon and with his beams toucheth the sea, moveth a stitring up, whereby it causeth her flowing and ebbing and to cast out into her river or coast all dead bodies or unclean things that are in her.   

The 2. Chapter how the sea appertaineth to the perfection of the world, and without her the world would perish, and how the water is engendered in her.  
THe sea appertaineth too the making of the world and to her perfection, & the world, should not be perfect without her: for if there were no beginning of the waters there should be no simple waters. And if there were no simple waters there would be no mixed waters, and so there would be nothing of that which is engendered of the water, and if there were no water there would be no bodies, as there are continually, and things which cleeveth together, whereof it followeth, that if the waters had not a beginning the generation would be destroyed, And so consequently all the world. Also if there were no beginning of the waters there would not be a joining together of the contraries which are possible, and so nature would dye in that which were necessary, and the work would cease in the act. Then it would happen, not having a beginning of the waters the work of nature would cease, and so the world would perish, where it concludeth, that the sea is necessary for the sustentation of the world. And Aristotle in the second of his Metheoros, saith, that the waters in the sea do engender in the North, which is as much to say, as the greatest part of the water of the sea doth engender in the north. This Albertus the great declareth in the second of his Metheoros, chapter six, saying that the sea runneth from the North into the South, and the cause is that the north is higher than the south and the reason wherefore it is higher, is, because that with the cold of the north there is more water engendered, then that which can contain in the distance and height of the rivers, and in the south the water consumeth and is wasted with the heat of the sun, and for this cause in the north, one water pusheth out another, to the place which is lower than itself: And so accidentally it moveth, from the place of his generation. For as it is moist, it runneth until it come to be detained in some dry place. The reason why the water is so consumed in the south parts is, because the sun always moveth in his circle, Excentrik so that his centre is not in one place of the earth, in such sort that if the Diameter of the circle of the Sun were paste by both centres, that is to say, his own, and that of the earth, the greater part of the diameter should be towards the one part, and the lesser towards the other, in respect of the centre of the earth: And so it is showed by reason of Geometry, that the greater length of the diameter is near unto the twenty degrees of Gemini in this our time, and the lesser length is in the twenty degrees of Sagitarius which is a sign opposite to Gemini, whereof it appeareth that the sun cometh much nearer to the earth in the south parts then in the north parts. And so by reason of his near coming, he heateth in such sort, that he consumeth the water and burneth the earth, the which he doth not in the north parts.   

The third Chapter, wherefore the water of the Sea is salt, and wherefore it is most convenient and better for the Navigation.  
EXperience showeth that the water of the Sea is salt, and so saith Albertus the great, that it is called sea, by reason it is bitter or salt, And the Sea to be salts it seemeth to be against his natural kind, wherefore, seeing that the sea is the beginning of the waters, and his own place, and the waters which engender in her, and those which enter into her forth of the rivers are fresh, it seemeth that with more reason the sea should be fresh, and not salt. Also as it is certain that God made all things to the best, it seemeth to be better, that the sea were fresh then salt. To this answereth Albertus the great in the second of his Metheoros, in the third treaty and fifteenth Chapter, where he saith that matter that causeth the sea to be salt is. According to the truth, there are two kinds of vapours, that is to say, hot and moist, and hot and dry, and in the sea one of these doth rise from the superficies, & the other riseth from the bottom, This is by reason of the heat of the sun, and of the stars, which are an efficient cause of these vapours, and for the vapour of the water it is very subtle, between these two, and therefore being risen into the air is consumed of the sun, and the vapour of the earth remaineth, or more properly his exhalation dispersed, extended, & mingled in the water. As it appeareth by an example in the meat digested, that the thin substance thereof, is raised up and extended, into the members and is that which nourisheth, and the gross substance remaineth, and also that which is undigested: even so doth the vapour of the earth remain gross, and extendeth into the substance of the water of the sea, and the coldness of the water compassing it round about, casting into it coldness, and with the coldness it burneth, by reason they be two contraries together, they are made stronger than before, for the heat of the salt exhalation, being come forth of the depth of the sea, by virtue of the Sun fortifieth itself, with his contrary, which is the cold, and so overcometh the like heat which is that as is required in the generation of a salt fast, as the Philosopher hath it in the second of his metheoros the first chapter speaking in this matter, of this there is a similitude, that if a freshwater were passed through ashes it would make it salt, the like is of the water of the sea, in the time it was made salt, and because that some say, there is a pure element insubstance, and the element of the water is in the sea, and that in the midst of the sea, the water is simple and without taste, wherefore hath it not there an objection of contrariety. This seemeth to me not to be so, for the heat of the Sun, and the stars, are sufficient to make exhalations come forth of the bottom of the sea, which being mingled with the coldness and moisture of the water caused a salt taste in the highest part of the water: As well & with more reason they will make it in the midst or in the bottom of the sea, and so I hold with Aristotle, and with Constantine a great Astronomer, that there is now no element pure, & for as much as the water is salt, it is more convenient & better for the navigation, than the fresh, that is because the salt water is more heavy and gross than the fresh. And that it is so, Albertus the great saith in this manner, that the salt water is more heavy and thick then the fresh, it is gathered by many experiences, of the which one is. If the fresh water be mingled, with salt and made a strong mixture in such sort that all the salt be melted in the water, and in to it is cast an egg fresh laid, it will swim above the water, by reason of the thickness that the water hath which is done with the mixture of the salt, and if the said egg be put in fresh water it will sink, it is said that it must be a new laid egg, for if it be old or cracked, it will sink. And by the same reason is showed, that the ships do rather sink in fresh water, then in that which is salt for the fresh rather divideth itself and riseth up rather then that which is salt.   

The fourth Chapter of the different movings which the Ocean sea hath.  
IT hath been declared, in the. 2. chapter of this 2. book, that a great part of the water of the sea doth engender in the north, and from thence it runneth to the south, and this is one of the movings which the water of the sea hath: we do likewise see that the sea when it floweth moveth towards one part and when it ebbeth it moveth to the contrary, having such order, that where it began first to flow▪ there it beginneth first to ebb, whereby it seemeth that the water of the sea hath contrary movings one from another, and besides this we see that the rivers run to the sea, and also the sea cometh up by them, and this seemeth marvelous in nature: for the water naturally goeth downward, as a body which is heavy, as it is, and if the rivers be higher than the sea, the sea should not go up into them, and if the Sea be higher than the rivers they would not run into the sea, whereby with reason it may be doubted, saying. (A Doubt,) what is the cause seeing that all the waters of the sea, being one body have so many different and contrary movings, so that some waters are moving towards one place, and some towards another, whereby it may be said either that the sea moveth itself in these movings by chance, and without any order, or that she is moved by different movings or movers (A declaration,) To these doubts Albertus magnus answereth, in the second of the Metheoros the sixth chapter of the third treaty where he saith, absolving all the difficulties, which are put, touching these movings of the sea, we say with Seneca that there is no other cause of the course of the waters, to one place or other, but the places which are high or low, (except that only moving, whereby the sea ebbeth or floweth,) for in this it followeth the circle of the moon, as we teach in another place: And that the saying of Seneca is true, it is proved because the waters of the sea do come flowing to all parts of the world, that is to say, to the east, and to the west, to the north & to the south. And▪ likewise they go ebbing from all the said parts. And therefore the Sea hath no part proper where his flowing and ebbing doth begin, so that by accident the water moveth itself from one place to another, unless it be down right, for because this moving cometh not to it by any accident but by proper essence, consequently to his form.   

The fifth Chapter wherefore the Sea never overfloweth, nor is augmented nor made greater.  
IT may be asked what is the cause, seeing that in the sea there is so much water engendered, and continually entereth into her so many rivers and fountains, wherefore she never overfloweth nor is augmented. To this is some cause the which Albertus th● great bringeth in the second of his metheoros where he saith, the sea receiveth no augmentation nor yet maketh itself greater, for because she is a natural receiver of all the waters, and is their quiet place. And the place cannot overflow, with the coming in of the thing which by nature aught to be in this place: for the place aught to be conformable with that which it shutteth into it according to nature, so that the sea is able to receive into it all the rivers. And for the entrance of them neither to overflow nor to augment itself. Likewise it overfloweth not by reason that the Sea is so great that the rivers in the respect of her are nothing, for there is not any thing in them able to augment it▪ The third reason is because the heat of the sun and the blowing of the winds do consume so great part of the water, that although it engender continually in the sea and continually the rivers enter into her: yet in such order God disposed it that it: neither decreaseth nor increaseth. And so it may be said that which is written in job, Lord thou didst appoint her a precinct, that she should not break it. And it is to be noted, that in the flood of Noah. The holy scripture saith in Genesis the seventh chapter, that the water did ●ise up fifteen cubits upon the most high mountain that is under the heaven, so that all the earth was coveted with water. But although that this increasing of the waters were so great, the sea did not overflow nor did cover the earth, by going forth of her limmet and precinct. But the great increase of waters came for two causes, one was that the windows & clouds of heaven were opened, and it reigned forty days and forty nights very leisurly. The second was that the fountains and rivers of fresh water did run so much that all the earth was covered as it is said, so that all living things which were upon the earth did perish (except Noah and all that were in the ark) But the rain being ceased, the said text saith, that God sent such great winds, that they consumed the water, & returned the earth to his own perfectness.   

The sixth Chapter of the excellency of the Navigation, and of the antiquity thereof.  
WIth reason it may be said that the navigation hath great excellency seeing that God was the first that commanded to make a ship or instrument to go upon the water: so it is written in Genesis the sixth chapter where is said that God commanded Noah to make a ship or ark of timber. This Ark had. 300. cubits in length. and 50. in breadth, and 30. in height, of these cubits, there are diverse opinions what length they were of, some say after the manner of Geometry, others say common, with more reason it seemeth they were in manner of Geometry, because they should be greater, for it was convenient that in the ark there should be 〈◊〉 for that which should be put there in.  
S. Isidore writeth of the navigation in the Ethimologias that the Lydians were those that first found out the making of ships, but these did not attain to more knowledge then to join one timber with another, and were well caulked and nailed, they sailed in them not departing far from the land, after that Epaminundas, the Greek made an end to put ships to sail in perfection, and so in the wars of Peloponeso there was found that notable captain, Bias with ships, carrackes, and Galleys.  
In the third of the kings in the; 10. chapter is read that Solomon king of Jerusalem sent two ships to Tharsis. and every three year they went and came from whence they brought gold silver, works of ivory, and apes.  
julio Solino saith that all the sea towards the south, which doth compass Africa about behind and from the India to Spain was sailed, and of this he bringeth testimony of the king of Inba for the confirmation & argument thereof he maketh mo●tion of Islands, and of a certain people the manne●s and confines of the places & the spaces of them Plato in the .32. book, in the dialogue of Tim●o, saith that from an Island called the colunnes or pillars of Hercules, which is at the mouth of a strait there was failing to a firm land, which contained greater than all Africa & Asia; whereby it appeareth that before the time of Plato was sailing from the Island of Cadiz, which is at the mouth of the strait of jebralter unto the land of the India's which we now have.  
Pliny writeth, that governing the things of the empire of Tiberius Caesar there did appear in the coast of the sea of Arabia signs of ships that the Spaniards had lost. Cornelius Nepote giveth knowledge that in his time one that was called E●do● 〈◊〉 from the latin king sailing by the sea of Arabia, and likewise saith that he saw one Ce●● Antipatro that called with merchandise from Spain Ehiopia. In the time of Augustus' 〈◊〉 most pa●● the north Ocean seas were sailed round about. All 〈◊〉 unto the cape of the land of the 〈…〉. Reyhold Seleuco and Anthioco say that the rivers of the Caspian sea were sailed and known with the armies of those of Macedonia: As also they sailed all the north parts from one place to another. Pliny himself useth the testimony of Cornelius Nepote who affirmeth that the king of the Swevians or Esquicaros gave to Metello Celeri chief consul of France certain Indians the which sailing from the India with merchandise were driven into Almain with tempest of weather. Likewise it is read in Othon that in the time of the jermain emperors certain ambassadors of the India were found in the rivers of Almain which were driven thither with great winds, & if was not doubted that they came from the region towards the cast, which could not be if it be as some do think that the north seas be frozen Pope Pio the 3. saith that in the book he wrote of Geography and reason doth manifest, & show the the sea in old time was sailed seeing that the men of old time did put names unto the rivers of the Ocean sea, which doth compass about the farthest parts of the earth, of the great number & multitude of ships that was mould time some authors have written. Homer. saith that in the host of the Greekes which came unto Troy were 1180. ships, likewise Diodorus saith that Xerxes king of the Persians brought in his against Gretia, 700000. men of his own, & 300000. of his friends, and when became to the Sea called Pontico, he made in the sea a bridge of ships whereby he passed with his people so that the ships being together, reached from the land of Asia unto that of Europa, which is at the lest a league of sea.   

The 7. chapter how by some signs of the sun & of the moon may be known when storms will come.  
MAny times there happeneth to be in the Sea tempests of winds & waters which do cause great storms whereof followeth to such as are sailors death or losses of ships and goods or other great troubles: therefore here I mind to declare the signs as I found them written by the which the said tempests or storms may be known & being foreseen or known they may do les hurt. This pleased V●rgil greatly, who saith, that many hurtful battles of winds do come upon the ignorant: it is trade of Democrito the Philosopher, that a brother of his being reaping in time of great heat, who was called Damaso, the said Philosopher said unto him, that he should reap no more, but should gather together that he had reaped, & keep it, for shortly would come a great tempest of wind, that would carry it away from him, And so a few hours being past. It followed as the Philosopher had said, after declaration made of signs or prognostication of the tempests or storms, there shall be first noted, those which are showed in the Sun.  

The signs of the Sun.  
Pliny in his natural history the eighteenth book Chapter forty five showeth that if the Sun when it riseth be clear and not cloudy, foreshoweth a fair day, if it seem yellow, it foreshoweth rain with hail. It when the sun doth rise it seemeth hollow, it foreshoweth rain and wind, if when the sun doth rise there be clouds before it, and show red, and part of the said clouds are dispersed abroad towards the north and part towards the south it signifieth winds with great rain: If when the Sun riseth & setteth do appear any streekes gathered together near it, if foreshoweth rain:  
If before the Sun rise do appear upon it round clouds it foreshoweth great cold, this is if after Sun rising they go towards the south, but if they go towards the west it signifieth fair weather.  
If clouds do compass the Sun round about the less light and clearness they give signifieth, the greater tempest, and it will be the greater if her roundness do seem doubled.  
If in the rising of the Sun do appear red, clouds lying over the sun being brought thither by any manner of wind it signifieth that the self same wind will blow, but if it be a southerly wind it betokeneth rain.  
If when the Sun riseth if be compassed about with clouds, from that part where the roundness doth discover, it is to be looked for that the wind will come, but if it discover all, it signifieth equally fair weather.  
If when the Sun riseth she extend her beams far of, by the clouds and in the midst it seemeth empty, foreshoweth rain.  
If before the sun come forth she show her becames it foreshoweth water and wind.  
If when the sun shall let, her circle be white, it foreshoweth some tempest that night, and if it be very hot, there will be wind.  
If when the sun doth set, her round body doth seem black or thick of the part which is most discovered, it will blow much wind.   

The signs of the Moon.  
Seeing there hath been declared the signs of the sun, for to know the tempests or storms that are to come I will speak of the things which are to come, that the moon showeth.  
In A●gypt they keep holy day, the fourth day of the moon the which if she seem shining with a clean brightness it foreshoweth a very fair day, and if she show red it betokeneth much wind, if black it signifieth rain, if in the fifth day her horns be not sharp & small, but great and broad, it foreshoweth rain.  
If the moon be strait and show herself upward it signifieth winds & chiefly when this is in the fourth day.  
If the moon being four days old, & her roundness be of an Alborne ●ulle● it signifieth great winds, the author hereof is Var●o.  
Pl●nie saith that if in the fourth day of the moon she be upright it betokeneth tempest in the sea: unless that all round about her she hath a circle very clear.  
If at the full moon in the midst of her she be clear if showeth a token of fair weather, or if she be of an alborne colour or like to a rose colour it foreshoweth winds, if she be black it foreshoweth rain.  
When at her rising she rise with the upper part of her horn black about, at the decreasing of the moon, it will rain, and if likewise her horn be black beneath round about before the full moon it also foreshoweth rain.  
If the moon being at the ●ull have a circle round about her of that part which doth show most bright, will the wind come.  
If at the first appearing of the moon that is to say when she is new, the bornes of her do show great it signifieth tempest. And it shall be the greater if before the fourth day the wind do not blows at the west.  
If at the sixteenth day of the moon the seem to be of a great colour of flame it foreshoweth tempest.    

The eight Chapter of the fires and lights, which do appear in ships that do sail when there is torment or tempest in the Sea.  
IT happeneth to such as do sail when there is storms in the sea when it seemeth that they should be lost that all night they see upon the mast or yard or in some other part of the ship a certain fire or clearness, the which some sailors call, S. Edmund, which aught not to be so taken, seeing that it is not as they think, therefore I say that these fires or lights are a certain impression in the air which the Greeks call Pili Deuces, & is so called by means of the grossness of the humour which goeth from the earth & fighteth with the coldness of the might, & so it gathereth itself together and congealeth in the first region of the air, and when his exhalation findeth any body whereunto to cleave, it kindleth and holdeth itself fast to it until it be consumed and wasted. This fire burneth not.  
And Pliny in his second book of the natural history, the thirty seven chapter, saith that when these fires be two they be called Pollux & Castor and it is a good sign, and when it is but one it is called Helena, and it is an evil sign.  
These fires are also seen in the land. And they have been seen in the camps upon the pikes which the soldiers carry, and upon the dead bodies.  
And Pliny saith also that they have been seen upon the heads of men, and of beasts, And so did Virgil affirm that it appeared upon the head of lulio Escanio: In the camps of the wars these fires do appear as well because of the continual fumes, as also because of the heat of many people: In the ships they engender of the fume of the said ship and of the heat of the people gathered together into little room, and of the Mariners and people in the ship, which in the storms with the great moving they have, do engender heat: this is when there is disposition that the rising up of the vapour, should make impression in the air, as before is said: And Plini● said that one only fire is no good sign.  
This is because when there are two it seemeth that in the air is abundance of gross smoke and signifieth that it is sufficient to consume the matter of the tempest.  
Peter de Castroboll, upon the second of the Metheoros saith, that whensoever these fires are seen in a tempest, it is a good sign, for it noteth fair weather. Likewise it happeneth, that there are great storms, & none of these fires are seen, and in small storms they see sometime one or two, so that the sayle●s should have no devotion unto these fires to believe that Saint Edmund is there, for it is a natural thing.  
And therefore every one with his devotion aught to commend himself too GOD, that he keep them, and bring them forth of that Storm, and put them in the port of salvation.   

The ninth chapter of other certain signs, wherein shall be known when storms will come in the sea.  
IN the seventh chapter of this second book I have declared some signs of the sun & the moon whereby may be known when storms of wind and rain will come, as it is declared: and because these storms are things, that unto such as sail is very convensent they should know, and prevent: it seemed well to me to add this present chapter in the which, I will also declare other five signs or prognostications, which I find written, that aught to be looked on and known of the sailors, which are these following.  
The first is when in the high places or in the woods there is heard a noise of wind, and abroad it is not heard it signifieth storms of wind.  
The second when the waves of the scaswel and give great falls or strokes in the bays of the sea being with great noise or rattling, signifieth storms in the sea: of these 2. Pliny is the author in the eigteenth book of the natural history.  
The third, if the sea being calm doth make a nosse within itself signifieth great winds: of this speaketh Virgil in the tenth of Ac●eados and Lucano.  
The fourth when the Porpisses of the sea go leaping upon the sea, and show themselves upon the Waves is a sign of storms, And that the wind will come from that place that they come, This S. Isidore bringeth in the twelfth of the Etimologias.  
Of the fifth, Virgil, saith, in the Georgians that when the Sea Meowes or Gulls do leave the sea and go to the dry land it signifieth storms in the Sea.   
¶ The end of the second book.   

¶ The third book of the Winds, and their qualities, and names, and how one should sail with them.  

The first chapter what thing the wind is, and what quality it is of, and how it engendereth.  
FOR the declaration of the nature of the wind, for the diversity of the doubts that are of it, some say it is the air and it moveth: others say that it is water: others that it is a vapour of the earth: and others, that it is some great celestial body, or other, that with great force and violence doth push forward the air.  
And this cannot be determined, if his nature be not considered in that which principally it is. The which I say that the wind is a vapour of the earth that riseth up and stretcheth even to the highest part of the air and strongly thrusteth forth the air.  
This vapour is hot and dry, and by his subtlety doth pierce the air: for as the wind is of a subtle vapour in his kind, and being subtle and light, it is natural to rise up & so it riseth up, & of the subtlety of the vapour of the earth, he is made, and from thence he descendeth, & in his descending he showeth that the vapour moveth itself unto a high place & as he is come to that place is made wind, and so he descendeth blowing. And it is to be understood, that the vapour riseth not so high as the superior part of the air, which is called Estus, but riseth up to the cold part, & there as Algazel saith with the cold, he waxeth thick and descendeth of the which it seemeth, that the vapour whereof the wind is made, is not congregated with the inward cold as some say, but with the outward cold of the place, by the which as Algazel saith, he is letted that he come not to the superior part of the air. Likewise it is proved, that the vapour is raised up with heat, and for this, if the heat of air round about do help him, it heateth the more: for the ●●ner heat is helped by the outward heat, & so if it were not for the cold of the place, he would neither wax thick nor blow.   

The 2. Chapter, how the wind moveth not right from above downward: nor contrariwise, but his moving is in circle of water and earth.  
FUrther for the moving of the wind, it is to be noted that it moveth not from above downward, nor from beneath upward but it month in circular or round manner, of the water and the earth: so saith Albertus the great in the treaty of winds, chap. 12. all winds commonly move their blast & moving in circle manner, in such sort, that they move not up unto that which is high nor descendeth to that which is low: but moveth by the round superficial of the earth, and water in the air in circular manner, as appeareth by the clouds: that with the winds go up & descend down from the East, into the West: even like to the moving of the stars. Where it is to be understood, by the doctrine of the Astronomers, that there are some stars, which move the winds, as lupiter, that moveth northerly winds: & the sun moveth Easterly winds: and Mars moveth the blast of Southerly winds: & the Moon moveth, Westerly winds. This is as it were a beginning, as every manner of cause, by his own means induceth to one effect, & therefore it is convenient that the effect do imitate the moving of the cause. And seeing that the star●es do move in circular manner, it is convenient that the wind should move like a bow upon his Horizon. In like manner it is said, when the signs do cause winds to blow, because there are three signs, which have hot and dry qualities, which are these, Aries, Leo and Sagitarius: and this is called the triplicity of the fire. And these are called Easterly signs, because they move the winds of the East part. There are other three signs, which have cold and dry qualities. These are Taurus, Virgo, and Capricorn: and this is called triplicity of the earth, these signs are called Meridionales, because they move the Southerly winds continually. There are other 3. signs, which have their qualities hot and moist: these are Gemini, Libra, & Aquarius: & this is called the triplicity of the air. These are called occidental or Westerly signs, because they move the winds of the West part. There is another fourth triplicity of the other 3. signs, which are Cancer, Scorpio, & Pisces, And this is called triplicity of the water: for because his property is cold and moist, and these signs do move the Northerly winds, & that humour which they have in his property, they 'cause to abound in the times so attributed in those bodies, where they are engendered. Of the aforesaid, it is concluded: that the winds do move themselves in roundness of the water and earth like to the moving of the stars, and not right going upward nor descending. For the vapour is elevated with the heat, and is expelled with the cold, which congealeth him, and so it is convenient, that the wind descend not right down, for the heat that riseth up, but that it be by one side in the circuit of water and earth. And this reason Aristo●le giveth.   

The 3. Chapter, wherefore the wind is not always alike: but at sometime bloweth hard, and at other times calm: and wherefore it moveth to his opposite.  
WIth reason might be asked two doubts concerning the wind, which are these: (the first doubt.) What the cause is wherefore when the wind beginneth his blast, it is not equal, but sometimes hard, and other times more calm. And sometimes it ceaseth, and other times it turneth to blow, so that it bloweth not continually after one sort. (the second doubt.) The second is, wherefore the wind moveth to his opposite, for so we call it when from the east he goeth to the west: And from the north to the south, and likewise contrary, of this it seemeth that there is no reason, because the Uapour which is the root of the wind either followeth his moving which is to be elevated because he is hot, and according as it is strait so it aught to go upward, or follow his matter which is earthly, & at it is strait, aught to descend. Likewise what doth make the wind to move more to one side then to the other, rather than to move itself strait so that the east likewise should move itself towards the north, or towards the south, as towards the west, and likewise of the other winds. Item all things which are engendered in one place naturally move not unto the place opposite: so that if the easterly wind be engendered in the east, and the northerly wind in the north, they aught to move to their own place, and not to the place opposite. By the which it is to be said that the winds moving of themselves to their opposite is violent, and against nature, or the matter of the winds is marvelous & unknown to us. (The first declaration.) The first is to be understood that as the matter of the wind, which is the vapour of the earth, riseth up by little & little, maketh a weak & little moving: But as he is increased in great quantity: so with a great force he descendeth and maketh a strong wind. Also the wind bloweth not continually alike because the matter which riseth up is not always equal nor is equally put forward, for the cold is more or less, & the vapour not equally congealed. And therefore the wind at one time bloweth hard, and at another time soft, (The. 2 declaration.) The 2. is to be understood, that the wind to move to his opposite is for two causes. The 1. is as Alpetragio saith, the stars do move in circle manner; & so the wind doth imitate the circle moving, The 2. as Albertus saith, that it is more natural, because the vapour is engendered of heat, & is expelled & thrust out of the cold, & the cold is behind the heat, & therefore is thrust out to his opposite, so that he cannot go upright for the cold that is in the air nor can descend, for the heat that riseth up, nor can return backward for the cold which is behind him: and therefore it is necessary, that he move in circle manner to his opposite, & as much as that which is said that nothing moveth forth from the place of his generation it is to be noted, that which is of the nature of air, moveth itself to the place of air, and the air hath place in all parts, and the vapour hath the nature of air as much as appertaineth to his seldom moving so that he moveth not forth of his place.   

The 4. chapter, of the whirling of the wind, and how it is caused.  
IT hath been spoken before that the moving which the wind maketh is moving himself to his opposite by the roundness of the water & earth, & not going upright nor descending, as it hath been proved, & experience in the navigation doth show it: and seeing that it is so it may be asked what is the cause that many times the wind maketh his moving right from beneath upward. This we see that the wind raiseth up from the ground the dust and the straw, and carrieth them upright one heigh which is commonly a whirlwind, and this is as well caused or done in the sea as in the Land. And in the Sea it is made well near like a right sleeve, & by it the water riseth upward, as many times it is seen▪ Whereby it seemeth that the wind hath likewise a strait moving, that is to say from beneath upward, as the moving in roundness before is declared. To this is to be noted that this moving, which the wind maketh is not natural to it, but accidental and violent: for because it is done by force, by meeting together in this manner: when one wind cometh from one part, and another from another part contrary, & the strength of the one, doth meet with that of the other as every one of them hath no free running, by the let of the wind he findeth contrary: then he that is strongest thrusteth forward the other, and so they put themselves into roundness, and make a whirlwind until they be divided. This appeareth by an example in the water when it runneth, that if it find another body that doth make any resistance, it maketh a whirling, moving it in roundness: even so the wind as it findeth resistance of another wind or of some mountain, or of any like thing, that doth resist his course, it cannot go forward. Therefore he maketh that round whirling. and this causeth in the Sea many times that ships be sunk down under the water, when they found themselves under such a whirlwind or spout: for the water which the wind raiseth, doth overwhelm & drown them. Likewise when there are movings of contrary winds, they 'cause to rise up storms in the Sea, which the sailors many times may know before hand considering and beholding the moving of the clouds if they be contrary and different to the wind that is beneath. For when it is so, it is a token that contrary winds do run abroad, of the which continually the superior doth overcome: because he is of more strength & swiftness then the inferior.   

The fifth chapter, of the winds, of the cards of navigation, of their number, & names.  
AND seeing there hath been treated of the winds, what things they are, & how they are engendered and move, In this I will speak of the winds that are marked in the cards of navigation, their number, & how they have their names according to the ●se of the sailors. Of the which it is to be understood that the winds of the cards which we call courses, do show forth 32. names of winds, which are practised in the navigation, & no more nor less: & the reason wherefore this number is given, is because the roundness of the world, is imagined to be divided into 32. parts, & in every one of these is assigned one wind, & is given to him a whole name, or half, or a quarter, according to the part where it seemeth to us that he cometh; as hereafter shall be declared. And to understand, this is to be noted, that this roundness of the world hath 4. principal regions. These 4. parts are named and known by 4. winds, which are east, west, north, south. The east is also called solan●, it groweth under the equinoctial line, it is also called lecuamte, because the sunn● riseth there, and beginneth to appear in the morning. This wind is called in the navigation east. The second principal wind riseth of the Occident, under the equinoctial line, it is called poniente, because the sun setteth there, or hideth himself in the evening. It is also called, favonio, and in the navigation it is called west. The 3. principal wind is called, Cierco and groweth under the pole artic, he is also called, Aquilonall, and Septemtrionall, Aquilonal because he groweth in the part of Aquilon Semptentrional by the 7. stars of the Vrsa minor. This wind in the navigation is called north. The fourth wind is called Meridional he cometh forth under the pole antarctic, he is called Meridional: for when he is come to the sun, there he maketh unto us the midst of the day. And in the Navigation this wind is called South. These Winds are marked in this manner.  
These four winds have other four Colaterales, and are compounded of the taking a name of half the name of every one in this manner.  
The 1. is marked between the north and the east, and taketh name of both, and therefore is called North-east.  
The second is between the east and the south, and is called southeast.  
The third is between the south and the west, and is called south-west.  
The fourth is between the west & the north, and is called northwest, and is marked in this manner.  
These 8. winds are called in the navigation, whole winds or principals, among the which there is to be marked other 8. which are called half winds not because they have less force than the 1. but because they are described among those 8. winds afoesaid, the which also do take their names of the 2. winds Colaterales and are called in this manner.  
The first is described between the north and the North-east, and taking 〈◊〉 of both of them is called North north-east.  
The 〈◊〉 called east, North-east, because he standeth between the east and the North-east.  
The third is east southeast, because he is between the east & she southeast.  
The 〈◊〉 is south Southeast, because he 〈◊〉 between the south and the southeast.  
The fifth is south south-west, because he is between the south and the south-west.  
The sixth is west south-west, because he is between the west & the south-west.  
The seventh is west northwest, because it is between the west and the northwest.  
The eight north northwest, because it is between the north and the north west.  
And they are ordained in this manner.  
Among these xuj. courses of winds & half winds, are marked other sixteen which are named quarters, and they are put in this manner, every one of the eight principal winds hath two quarters, gathered forth of them, and every one of them doth take the name of the winds nearest to him, in this manner.  
The north hath two quarters, which is by the part of the North-east, and is called North and by east, & that which is by the part of the northwest is called north and by west.  
The North-east hath other 2. & that which standeth towards the north, is called North-east and by north, and that which standeth towards the 〈◊〉 is called North-east and by east.  
The east hath other two that which is towards the part of the North-east is called east & by north, & th●● which is towards the 〈◊〉 of the so●th is called east and by south▪  
The southeast hath two quarters, that which is towards the east part, is pacled southeast and by east, & that which is towards the south part, southeast & by south.  
The south hath two quarters, that which is towards the east, is called south and by east, and that which is towards the West is called south and by west.  
The south-west hath other 2. the which is towards the part of the south is called south-west and by south, and the which is towards the west, is called south-west and by west.  
The west hath two quarters, that which is towards the south-west is called west and by south, & that which is towards the part of northwest is called west and by north.  
The northwest hath two quarters, that which is towards the part of the west is called northwest and by west, & that which is towards the part of the north is called northwest and by north,  
They are ordained in the manner following.  

The .32. ●indes ●n the compass.    

The sixth chapter, how the winds of the cards whereby the sailors do sail do gird or compass about the roundness of the world for to sail by them.  
SEeing there hath been declared, the winds of the cards of navigation, their names, & differences: I will speak in what manner and order these winds do compass about the roundness of the world, to know how to sail by them. Of this is to be noted, that this round body of water and earth, hath in roundness three hundredth and threescore degrees. Therefore he that is in any part or place, and would sail towards the North. All inconvenience being taken away, shall sail with the wind at South, & with no other. It is to be understood, sailing before the wind. Although that he not having the wind at South: But some other wind sailing by the bowling: may go rising up by other courses, making boards, one board unto one wind, & another board unto another: until he come to the place where he pretendeth to go. Likewise, he that will sail from the north to the south, must be with a Northerly wind, or in the manner aforesaid.  
The navigation of the east or west, is in this manner: a ship departeth from the Island of Saint Thomas, or as they call it Saint Thome, which is under the equinoctial, and would go round about the world, if in case, that it might be sailed: this ship if she should sail toward the east, her way should be in this manner, from the said Island or place where she departed, she shall sail with west, 180. degrees, & if from thence she will return to the place from whence she departed, by the same course that she went, she shall return with east the same way: but if she go forward on her way, you shall understand, than all the roundness will serve you, the west wherewith you departed, until you come to the point where you came forth, in such sort that in a place where a man is, a circle being imagined, which girdeth the world, all this circle is sailed with one wind, but if from the half circle, or before or after he will return by the way that he went, he shall return with the wind contrary. For it is to be understood, that from the place that a man departeth until the half circle be ended, he goeth departing from the place, from whence he came, and the other half he returneth towards it again, as the figure following showeth it.  
I say that one departeth from A. to go toward C. and goeth by B. in A. which is the place from whence he departeth: the wind beginneth, & being come to C. which is his opposite, if he return from thence to go to the same B. the wind which is contrary, will serve him. But if he go sailing from C. to D. and from D. to A. you shall understand that with the wind he began to sail by, he shall go all the roundness, until he return, where he came forth. The same account, shall be made, if you begin to sail towards the West, and that which hath been said of the navigation by the equinoctial, the same must be kept by any manner of circle, whatsoever.  
And it is to be noted, that only from the East and West, there are circles or courses greater and lesser: the greater circle passeth by the Centre, and the lesser passeth not by the Centre. But all circles greater or lesser, have three hundredth and sixty degrees of length, but in the leagues that every degree hath, there is difference of more & less, even as the circle standeth near to the equinoctial, or to the poles. But the winds which must serve the turn aught to be of the greater circles and none of them of the lesser circles. The navigation by the other winds is in this sort. If one sailing towards the North-east, gave a turn about the world, going always by the same course, he shall return by the south-west, from the place where he departed: and the same will be done by the contrary. And in the rest let the account be kept as before hath been declared. The same do I say by the navigation towards the southeast, that he shall return by the northwest. And for an example of this, let it be asked: if two ships be in one port, and one departeth towards the north and the other towards the south, these ships if they shall meet, and if they do meet for to go equal way how much shall every one of them sail? I say that these may meet, and that sailing by these courses, when every one of them have gone .180. degrees they shall be together. And in like manner, this account is to be kept departing by other courses. And so it is to be understood, that whensoever two ships or more do go forth of one port, and do sail by different courses, when every one of them have gone 180. degrees, they shall return and join in the place opposite, from whence they departed: this is because as it is said, that all the winds of the navigation be of the greater circles, for all of them do pass by the centre, & so every one going the half circle which is the said. 180. degrees shall find himself in the point opposite from whence he came forth.   

The seventh chapter, of the order of the Cards of Navigation.  
AMong the instruments which are necessary for the navigation, one is the card: for without it good navigation cannot be made, seeing that in it the Pilot or sailor doth see the place where he is, and the place whether he pretendeth to go, & seethe the height of degrees that every place hath, so that he knoweth if he shall go forth right, or if he shall go rising or descending: he seethe also what wind or winds will serve him in his course, and where he shall leave one and take another: he also seethe the distance of the way which he shall go, how many leagues it hath, and so he ordaineth in all things that which is best and convenient for him. But it seemeth that with reason there may be had a doubt in the cards wherewith the navigation is made▪ And say that they be not certain nor true for this cause following. (A doubt,) This being proved that the world is a round body, and not only the heavens, but also every one of the elements, so that the water whereby we sail is round, and the wind wherewith it is sailed moveth itself in roundness & this being so we see that the cards of navigation be not made round but plain: Therefore from the round to the plain is great difference, as appeareth by this present figure,  
If two ships should depart from A. unto C. and the one of them went by B. and the other by D. so great difference will be of the way that the one maketh to the other by how much the distance is from the B. unto the D. & seeing that the way which by the sea is sailed is from the A. unto C. by D. because the water is round, & the cards doth not show it to be so, but it showeth it in plain manner which is from A. unto C. by B. whereby it seemeth that the way which the ship maketh, is half more than that which the card showeth. Seeing the ship goeth it in circle manner, and the card showeth it by diameter, & the diameter hath but only the third part and one seventh part of the circumference. Likewise the aforesaid seemeth to be so: because the round body is greater than all other bodies, and as the world is a round body, there is no other figure so great, that may be compared to it: and so the card which is made in plain, cannot be equal with the round. Also the courses of the navigation, as they are put in the cards in every hundredth leagues: they depart one from the other twenty leagues, in such sort that from the place where the ship doth departed unto the xc. degrees which doth amount to 1575. leagues. An these leagues they departed one ship from another, or one course from another 315. leagues. And seeing there are 32. courses, the world, that is to say, the earth & the water should have in roundness, ten thousand & fourscore leagues: this is false, because this roundness hath 360. degrees of 17. leagues, and a half, every degree, which doth amount to 6300. leagues and no more. Of all the aforesaid, it seemeth that the cards of navigation because they are made in plain: should be false and unperfect. (A declaration.) To this is to be noted▪ that the cards of navigation are true and altogether perfect: and the art wherewith they are made and ordained, doth contain all certainty▪ And answering to the first is: that the navigation which the ship doth make in roundness, and the card doth show in plain: is to be understood, that the same quantity or distance of way, that every part hath in roundness, the self same is reckoned and given in plain: aswell in the land, as in the water, by marking in the leagues and degrees the distance that every thing hath in roundness, without taking from it any thing. And this may well be done, for although that one body be round, there may be given to it the self same proportion and greatness in plain, as Ptholome setteth it forth in the plain sphere. And jordan in the treaty which he made of the same matter. This seemeth to be by an example in an apple, that although it be round, the length & breadth that his roundness hath, may be put in plain form: even so in the cards of navigation, although in their figure or shape they be not round, yet in the accounting of the way, they give and hold in equality with the round: And the round body to be greater than another body. It is to be understood, that those bodies being equal in circumference, for not being equal, another figure may well be greater than the round. And for as much as I say, of the courses of the cards. It is likewise to be understood, that these be ordained in Geometry, & because it is so singular among the Mathimaticals, they cannot be false as those Authors which I have spoken of do show. And if by a point of the card there are found more Leagues in the courses then the world hath: This is not hurtful to the card, for this art and show of the courses, is not only for this number of six thousand and three hundredth Leagues which the world hath: but for any manner of number, so that although the world had a hundred thousand leagues, or had a thousand, the self same would serve those courses in one number as in another: as it appeareth, that such as sail one hundredth leagues do go in their way as well as those which go unto the East India, which sail five thousand. And as Magalanes sailed, and such as went with him in the year 1521. when the strait was discovered, which of Magalanes is named, that then sailing from Spain, they gave a turn about the world: of that as is said, it appeareth plainly, that the cards of navigation are so well ordained, that their agreement and perfection is a thing marvelous: seeing a thing so great as the earth and the Sea is, being marked in so little room as a Card is, and do so much agreed, that it doth not miss one ●otte to sail the whole world thereby.   

The eight Chapter, of the account which the pilot aught to have in his way when he saileth with a wind different to his course.  
SEeing there hath been declared the order which aught to be used, if the roundness of the world were sailed: In this I will speak of shorter voyages or wa●es, and such as are more commonly sailed by sea from one place to another. And how the pilots & sailors should know to keep a good account, & give reason of their navigations, whether soever they go: for the which I say, whensoever the pilot will sail, he aught principally to look upon 3. things.  
First of all, the place where he is, and the place whither he mindeth to go, & to know the distance, that is from the one place to the other.  
The second, in what height of degrees he findeth himself, and in what height the place is which he mindeth to go unto.  
The third is, to know the wind or winds that shall serve him in his navigation, all the which he may see & know in his card.  
And this being known, let him look if he have a wind that is convenient for his navigation, and having it let him proceed upon his voyage as weather, & time will permit him. And it is to be noted, that many times it happeneth that for the navigation which should be made, the wind serveth not according to the course, which the ship should go: And therefore it is sailed with another wind which is different.  
Likewise it happeneth, that as a ship goeth sailing, there cometh such weather, that causeth her to go forth of her right way: and take her course by another, by the which how much more she goeth, so much the land the they go to seek changeth itself into different courses of the compass. This is because the ship goeth not her right course to the place, whither she pretendeth to go: so that the self same place, varieth or changeth itself from one cour●e into another. And likewise sometimes it waxeth near, and other times far of.  
And when it is so, that the pilot saileth with a wind, different to that which is convenient for his course, and sailing would know in what point or course, the land whither he mindeth to go, lieth from him: and how many leagues he hath from him to it, in the figures & accounts following, he shall find it: the which shall profit him to know the certain place where he is, and thereby he shall know how to choose the true course, (when weather serveth him) for to return to the certain place whither he mindeth to go, which is to be understood in this manner. I say that you will sail to a land, which being seen in your card, and the place marked where you are: You shall found the it is from you towards the North or South, or any other course, and so sailing towards one place, you run towards another: and put the case that the land whether you pretend to go, be from you towards the North, so that you should sail with the wind at South, & because this wind bloweth not, you sail with another wind: Therefore if the navigation be by the first coarse more near to the wind itself, in the first figure you shall find marked this first course, and near to it the leagues which you shall go for to get the land, whither you pretend to go towards all the courses of the compass: as also how many Leagues the land is of from you, and in the manner that the navigation is declared by this course, so all others are declared.  
And when in sailing you have not the proper wind which should serve, mark by the wind which you have, how many points it is of from the proper wind, wherewith you should sail, and seek it in one of the figures, that is here put, which shallbe one of them marked with the cross, & near to the figure where the like wind is, you shall find three accounts, these accounts serve in this manner.  
In the first account, you shall find how many leagues you shall go by the course where you sail.  
In the second account is the course where you have the land whether you pretend to go, (I will say) that having gone those leagues which there are declared you shall come unto the land, which you seek after by the course that is there marked: the which you shall know what course it is, by the number that he hath, seeking the same number in the figure that is next to it.  
In the third account, you shall find how many leagues you are distant of the same land whether you go, so that having gone the leagues of the first account you shall have the land whether you go at the course which standeth in the second: And you shall be from the same land the leagues that are marked in the third account.  
This being known, three things are to be noted.  
The first, because here cannot be put any rule for the number of the leagues that are from the place where you are unto the place where you pretend to go: because at one time there will be more distance then at another time.  
Therefore this account is taken out for the number of a hundredth leagues, I will say that the place where you are unto the place whether you will go, is a hundredth leagues of way. And it is to be noted, that although this account, do serve for this number of a hundredth leagues, it serveth likewise for any other number of leagues, that the way hath, in this manner, if the way be of 200 leagues you shall go it twice as much as the numbers of the first account do show: And then you shall have the land whether you go in the course which is marked in the second account, and you shall be from the said land, twice as many leagues of them which are accounted in the third account: and if the way be of 300 leagues you must go thrice as much as the numbers of the first account show so that of every hundredth leagues, which is increased of the way you shall give as much more number of that which is in first and third account, & then you shall have the land at the same courses or points, which are marked in the second account, and if in the way be fifties, or more or less you shall give a half, a third, a fourth, or a fifth, or according as the number is.  
The second is, that in the figures which are put here, the navigation goeth marked by the winds of the one part of the compass: and by the other part of the course where you shall find the land.  
This is to be noted that the same account is when you shall fail by the part where the courses go, and so it serveth for all parts.  
The third is, that towards the wind that these figures do show forth right, shallbe given the name of the proper wind wherewith you should sayle●  

¶ When you shall sail by the first course. I.  
 Leigues of the way. Courses. Leagues of distance. l. 1 l. lx seven. 2 xl lxx. vi. 3 xx viii l●xx. 4 xx v xx. 5 xx two. xx. iiii. 6 xx. xx. viii. 7 xx. c. 8 xc. two c. 9 xx. v. c. x 10 xx. v. c xv. 11 xx. vi c. xx. 12 xl c. xl. 13 l ●●●●●. v 14 c  

¶ When you shall sail by the second course. TWO  
 Leagues of the way. Courses. Leagues of distance. xxx. 1 lxxii. l iii 2 l i lxx. 3 xl two. lxx two. 4 lx two. lxx 5 xl. xcv. 6 xxx. c 7 xl. c iii 8 xl c xv. 9 xl two. c xxx. 10 lx. c xl iii 11 lxx. c lxxx. 12 c. cc lxxx two. 13 cc.     

¶ When you shall sail by the third course. III  
 Leagues of the way. Courses. Leagues of distance. xx v 1 lxxx. xl v 2 lxx. lx 3 lx lxx 4 l viii lxxx i 5 l viii. xc 6 lx. c 7 lx. c x viii 8 lx v c xxx v 9 lxxx. c lxv. 10 c cc x v 11 c xl v ccc lx. 12 cc xc  

When you shall sail by the fourth course IIII  
 Leagues of the way. Courses. 〈◊〉 of distance. xx 1 lxxx v xl 2 lxx v l viii 3 lxx lxx 4 lxx xc. 5 lxx c 6 lxx v c x 7 lxxx c xl 8 c c lxx v 9 c v cc xxx v 10 c lxxx ccc lxxx 11 ccc x     

¶ When you shall sail by the fifth course. V  
 Leagues of the way. Courses. Leagues of distance. xc 1 xc xl 2 lxxx l v 3 lxxx lxx 4 lxxx xc 5 xc. c x 6 c c xxx v 7 c x v c lxxx 8 c xl v cc x 9 cc xx v ccc lx 10 cccc xx v  

When you shall sail by the sixth course VI  
 Leagues of the way. Courses. Leagues of distance. xx 1 xc. xl 2 xc. l v 3 xc lxx v 4 c c 5 c x c xx v 6 c xx v c lxx 7 c lx cc l 8 cc xx d x 9 cccc lxxx v     

❧ When you shall sail by the seventh Course. VII.  
 Leagues of the way. Courses. Leagues of distance. xx. 1 xcv. xl i 2 xcv. lx. 3 cv. lxxx. 4 c x. c x. 5 c xxxv. c l v. 6 c lxv. cc xl. 7 cc xl. cccc xc. 8 cccc lxxx.  

❧ When you shall sail by the eight Course. VIII.  
 Leagues of the way. Courses. Leagues of distance. xx. 1 c. xl. 2 c x. lxv. 3 c xx. xcv. 4 c xxx. v. c xl. 5 c lxxv. cc xxxv. 6 cc l viii. cccc lxx. 7 cccc lxxx.     

❧ When you shall sail by the nienth Course. IX.  
 Leagues of the way. Courses. Leagues of distance. xx. 1 c iii xlv. 2 c xv. lxxx. 3 c xl. c xxv. 4 c lxx. ccv. 5 cc l. ccccxlv. 6 cccclxx.  

❧ When you shall sail by the tenth Course. X.  
 Leagues of the way. Courses. Leagues of distance. xx. 1 c x. l v. 2 c xxx. c 3 c ix two. c lxxx. 4 cc xl. cccc xl. 5 cccclxx.  

¶ When you shall sail by the eleventh course. XI.  
 Leagues of ●he way. Courses. Leagues of distance. xxx. 1 c xx. lxx. 2 c l. c xl. 3 cc x. ccc xxx. 4 ccc cx.  

¶ When you shall sail by the twelfth course. XII.  
 Leagues of ●he way. Courses. Leagues of distance. xxx. 1 c xx. c 2 c lxxx. cc xc. 3 ccc lxx.  

❧ When you shall sail by the thirteenth Course. XIII.  
 Leagues of the way. Courses. Leagues of distance. l. 1 c xl. c xc. 2 cc ixxx.  

❧ When you shall sail by the fourteenth Course. XIIII.  
 Leagues of the way. Courses. Leagues of distance. c. 1 c xc.  
AND for the better declaration of the rules above written, this present figure is to be noted in the which I say, that you find yourself, in the point, A. And the land whither you will go, you have it, I put the case at the North, in the point B. and there is from you to it an hundredth leagues, so that your way should be from A. unto B. that is to say, sailing from the south towards the North, and because you have not this wind, you sail by the first course, and the account being put in the first rule, doth teach you, that if you go fifty leagues by this first course: that the Land, which you had first towards the North, you shall have it at North and by East (you sailing by the course of North, & by west) and there shallbe from you to it fifty Leagues, and if you go by the same course sixty seven Leagues, than you shall find it towards the North north-east, and then it will be from you to it forty leagues. And if you sail seventy six leagues, you shall have it towards the North-east and by north, and there will be from you to it twenty eight Leagues. And so in the rest, this rule teacheth you how many leagues should be sailed for to get to the land whether you go to all these courses. The second figure and rule is, when you shall sail by the second course distant from the proper wind: in the which you shall found the account that shallbe kept in that way. And the third for the third course, and so for all the rest: and it is to be noted, that to this wind at North, which was put for an example, shallbe given the proper name of the wind, whereby you should sail, and to the others the names of the winds, that are next to him.  
Also it is to be noted, that always it must be considered what distance is from the place where your are, unto the place whither you mind to go, whereby you may make the account, even as before is declared.   

The ninth Chapter, how the pilot shall certainly know sailing by any manner of course where the Meridian is.  
AND seeing that in the rules before written hath been declared how the Pilot shall know wheresoever he shall sail, and to what point or course of the compass he hath the land whither he goeth, and how many Leagues the land is from him. Here I will speak, that departing from one place for to sail to another by any manner of course, you shall know how much you departed from that Meridian wherein you were, and know the Meridian, wherein you find yourself: for this is a thing most necessary in the navigation, the height or altitude only excepted. And because this rule of the Meridian, may be the better understood, you shall note this example. I say that eight ships being in one port, and they go forth sailing, the one from the North to the South, the second by the first quarter, the third by the second: and so all the other by different winds, when every one of these ships have gone one degree, or two, or more, being equal in degrees: they shallbe East and West all of them one with the other, although not equal in way, for the one hath gone much more than the other, in such sort, that that which hath sailed by the second course hath gone more way, then that which sailed the first, & the third more than the second, and so of the rest: by how much they go from the first, so much the more way is to be gone to raise up, or to descend a degree. This is caused by reason of the obliquity of the courses as more largely shallbe declared in the 14. Chapter of this third book, and this being known (I say for to know) how far a man is from the Meridian, from whence he departed, imagine that his navigation should be by the same Meridian: that is to say, from the North, to the South, or from the South to the North: and that he saileth by the first, the second the third, or fourth course, or by any of the other: according as the course lieth whither you mind to sail, to one place, or to an other. And this is to be understood in the fourteen courses colaterales, from the North to the South, or from the South, to the North, according as in the first figures which are put here doth appear: for because for the other 14. courses Colaterals, from the East to the West, in the second figure or fable they are declared: therefore I say, when you shall sail by any of the 14. courses heretofore declared, two things must be considered. The first in what height of degrees you were, when you were in them, and in what height you do presently found yourself in: and look how many degrees of difference are from the one to the other. The second is to look by what course you have come unto the place where you are, and this being known, look into the account hereafter written in the first table, and in it you shall find how many Leagues you have departed from the Meridian, which you had in place from whence you departed.  
An example. I say, that you departed from the point of these first marked figures following, & so you were in 20. degrees of height, & after that, taking your altitude, you found yourself in 15. degrees, or in 25. in such sort, that you found to have raised or destended five degrees, and this was sailing by the fourth course, whose name you shall know looking on the fourth where he is marked in the figures which are here put, & the course being known & agreed with the which you have sailed, look in the table which is next in the 4. course at the five degrees, and you shall find that you have gone from the Meridian from whence you departed 87. leagues. And for the better understanding of this rule, imagine that from this point of the twenty degrees, where you were, or from any other place from whence you departed, that when from thence you departed, there departed, likewise another ship from the same point sailing by the same Meridian, and that when you had gone the five degrees she likewise had gone other five, in such sort that you have her East and West with you, and so it is to be understood that these 87. leagues are of distance from you to this ship, because you are so far distant of that Meridian, And so knowing the distance which you have from the Meridian, where you departed, forthwith you shall know the Meridian wherein you are, and in this sort imagine that any manner of course that you shall sail, by any of these that are marked here under in the two first figures, you have this ship East and West with you, and this shall be your guide for to know how far distant you be from the Meridian where you were, this is by seeing how many leagues you have raised or descended, and the course whereby you have sailed, and being sought in the figures and table following, by it you shall know the Meridian certain wherein you are.  


The Navigation by those courses Colaterales from the North to the South.  
  

The Navigation by those courses Colaterales from the South to the North.  
   

A Table of the navigation from the north to the south, or from the south to the north.  
When you shall sail by the first course  
Degrees, i two. iii iii v. vi. seven. viii. ix. x Leagues. 3 7 10 14 17 21 24 28 31 35  
When you shall sail by the second course.  
Degrees i two. iii iiii. v. vi. seven. viii. ix. x. Leagues. 7 15 22 30 37 45 52 60 67 75.  
When you shall sail by the third course.  
Degrees. i. two. iii iiii. v. vi. seven. viii. ix. x. Leagues. 11 23 34 46 57 69 80 92 103 115  
When you shall sail by the fourth course.  
Degrees i two. iii iiii. v. vi. seven. viii ix. x Leagues, 17 35 52 70 87 105 122 140 157 175  
When you shall sail by the fifth course.  
Degrees. i. two. iii iiii. v. vi. seven. viii. ix. x, Leagues. 26 53 79 106 132 159 185 212 238 265  
When you shall sail by the sixth course.  
Degrees i two. iii iiii. v. vi. seven. viii. ix. x. Leagues. 42 85 127 170 212 255 297 340 382 425  
When you shall sail by the seventh course.  
Degrees. i. two. iii iiii. v. vi. seven. viii. ix. x. Leagues. 85 171 256 342 427 513 598 680 769 855   


¶ The Navigation by the courses Colaterales from the east to the west.  
  

The Navigation by the courses Colaterales from the west to the east.  
   

A Table of the navigation from the East to the West, or to the contrary  
When you shall sail by the first course.  
Degrees. i. two. iii iiii. v. vi. seven. viii. ix. x. Leagues. 85 171 256 342 427 513 598 680 769 855  
When you shall sail by the second course.  
Degrees. i. two. iii iiii. v. vi. seven. viii. ix. x. Leagues. 42 85 127 170 212 255 297 340 382 425  
When you shall sail by the third course.  
Degrees. i. two. iii iiii. v. vi. seven. viii. ix. x. Leagues. 26 53 79 160 132 159 185 212 238 265  
When you shall sail by the fourth course.  
Degrees. i. two. iii iiii. v. vi. seven. viii ix. x. Leagues. 17 35 52 70 87 105 122 140 157 175  
When you shall sail by the fifth course.  
Degrees. i. two. iii iiii. v. vi. seven. viii. ix. x. Leagues. 11 23 34 46 57 69 80 92 103 115  
When you shall sail by the sixth course.  
Degrees. i. two. iii iiii. v. vi. seven. viii. ix. x. Leagues. 7 15 22 30 37 45 52 60 67 75  
When you shall sail by the seventh course.  
Degrees. i. two. iii iiii. v. vi. seven. viii. ix. x. Leagues. 3 7 10 14 17 21 24 28 31 35    

The tenth Chapter, wherein is declared, more of this rule before written.  
FOR it is not only necessary to know the navigation which is made from the north to the south, and so contrary: but also that which is made from the East to the West, or from the West to the East (that is to say) by these courses their Colaterales. Therefore I have put the demonstrations & table before written, of the which is to be noted the same order that is in the Navigation from the North to the south, or from the south to the north as it hath been declared. (The which is) when you go sailing you shall mark in how many degrees of height you find yourself in, and after that when you turn to take the said altitude, you shall mark how many degrees you have risen or descended from the place from whence you departed. And this being known look upon the figures before written, the course whereby you have sailed, and if it be the first the second or third, or any of the others, and the course being known seek it in the table, & in the same course look the number of that degrees which you have gone, and near to the degrees, you shall find the leagues which you have sailed. I speak of an example, that taking your altitude you found yourself in 30. degrees, and after that you found yourself in thirty two, or in thirty eight in such sort you rose v p or descended two degrees, and you sailed by the third course.  
Therefore look in the table in the third course at the second degree, and you shall find that you have gone fifty two leagues, and in this order you shall know the rest.  
And note that in these tables, there are not put more numbers than unto ten degrees. (The reason is) that whilst these be a sailing by any manner of course, there will be place to take the altitude, and being taken, to mark the place, and from thence to begin the account as well rising as descending, and in this sort you shall go making a point in your card, and know the certain place where you are.   

The eleventh chapter, how the Pilot aught to choose the course which is convenient according to the place he mindeth to sail unto.  
THE Pilot or any other person that mindeth to sail, before all things he aught to consider of the way that he mindeth to go, and so to choose the course or courses which are necessary, according to the way which he mindeth to make, and for this put before you a certain rule, and this in any manner of place where a man standeth, is a point or beginning where the courses or winds of the navigation do proceed and come forth. Therefore the Pilot aught to look in his card the place where he is, & the place whether he mindeth to go unto, and this being known, he aught to seek for the course that may go most right to it from whence he doth departed unto the place whether he mindeth to go, and if there be a course that will carry him strait from one place to the other, let him put the forepart of his ship into it as his compass will show him, and by that course let him follow his way, as long as weather will serve him.  
And when there is no course that goeth the right way, let him seek with the compass the course that is most agreeable unto him, which is it that will bring him lest out of his way to the place whether he mindeth to go, and by the said course let him follow the degrees or leagues which are of distance, until he find another that goeth more right to the place, and in this let the Pilot have great care, to see how much way every course serveth him, and where he shall leave that way and take another, and that he keep a good reckoning & knowledge of the way that he maketh as much as is possible, and at all times when need requireth to make a point in his card and move his course, let him do it keeping always a good reckoning of his way, and this to continued until he find a course that may carry him directly to the place that he desireth. And the Pilot in the beginning aught not to keep himself towards the courses that are nearest adjoining to him where he is, but unto those that are nearest to the place whether he goeth. And it would do well to prick his card often, and provide diligently upon his course: & let the Pilot note, that for to choose the course the right way as he aught to do, he hath need to know precisely the Meridian wherein he is: for not knowing it there may follow great error, as by this example appeareth.  
If one ship go sailing, the Pilot maketh her to be in the point. A. and would go seeking for B, and in truth his point was the C. it is evident by reason he is ignorant & without knowledge of the Meridian believing that he sailed from A. unto B. his navigation was from C. unto D. And therefore it seemeth that so much as is erred in the knowledge of the place where the ship is, as much more she is distant from the place that she goeth to seek: and this is one of the causes, whereby the Pilots do find themselves in great error in their navigation, and lose much time, and other inconuententies happen to them. Therefore let the Pilot take this for a good advise, in long ways to keep for himself a book of account of his navigation, where he should be put in remembrance of the wind that serveth him every day, and in what sort and so how much the singleness may be, that his ship maketh, looking by his clock how many leagues he may run every hour: and you shall understand, that the most which she can run is four leagues in an hour, and three leagues in an hour is a great tun, and in one hour two leagues is reasonable, and and in an hour to run a league and a half or sometime but a league. It must be well looked unto, and great advise must be had in this, for it will profit much to prick the card to know the Meridian, and thereby to choose the true course as it is said.   

The twelfth chapter, how you should prick your card to know the place, wherein the ship is.  
ONE of the things that the Pilot aught to know perfectly, is to prick his card very precisely, for it is very necessary for good navigation. Therefore when the pilot will prick his card for to know the place where he is, he aught first of all to look in his card, the place from whence he departed in what height of degrees it is in, according as he shall find by the graduation which the rard hath, and let him look also in how many degrees of height he findeth himself in according as he took it, and this being known let him take his two compasses and put the point of one of them in the place from whence he departed, & the other point of the same compass let him put in the course or wind which he hath had, and take the other compass and put the one point in the degrees of height which he hath found, seeking them in the graduation of the card, and the other point of this compass in the wind East, and West that is nearest, and make these compasses to run the one unto the other not taking away the two points which come upon the winds, (that is to say) the one, is it which the ship hath gone, and the other the East or West and coming in this manner where jointly you shall join the two points of both compasses, the one which was put in the place from whence the ship departed, and the other in the height or altitude where in ye found yourself. In this point is the place wherein the ship is, & to know if this point be certain make the proof in this manner. Look in the point where you find yourself in, and from thence with the compass measure how many leagues are from it to the place from whence you departed, & this being known, look into the wind that brought you how many leagues is to be reckoned for a degree, according as you shall find in the fifteeneth chapter of this third book, & being seen how many degrees you have raised or descended from the place where you departed, unto the place where you make yourself to be, you shall reckon the leagues that these degrees do amount unto, and if the leagues of the degrees be just with the leagues that you find of your way, your reckoning is good, and if the reckoning be not agreeable the one with the other, look wherein the error is, for because that these two sums or reckonings should come just. And if the place where you find yourself be just in altitude with the place from whence you departed, here is no rule that can instruct you justly that which you have sailed, but by judgement that which your ship may go, according to the days & hours that she hath sailed, and according to the weather she hath had, and so the reckoning is made little more or less. But let the pilot ●●atke that ●● this account or reckoning of little more or less, aught to be considered the currents or tides that may be in your way, for the many times the wind and tide are one way, & when it is so the ship runneth more way than the Pilot thinketh: at other times the winds & tides are contrary in such sort that as much as the wind carrieth so much the current or tide retaineth or keepeth back, & for this cause you aught to consider that if the wind do cast the ship to one part & the currents to another, the race of the ship will be in that part where is less strength or power, & if the wind & the currents be equal the race of her will be of the side where the current is. Let the pilot consider the falling down or holding up that the ship may make, and so let him make the account that is convenient. This advise is to be had when he pricketh his card by squareness or by fancy, which is by reckoning the singleness that the ship hath made, and arbitrar or indg how much way it may be that she hath gone in every one, and by what course, of all these the Pilot must keep a good reckoning in his navigation as much as in him lieth.   

The 13. chapter, how the Pilot aught to look that his card be just & certain that there be no error in his navigation.  
IN the chapter before hath been declared the manner that the Pilot or sailor should have in the pricking of his card & know the place where he is, & be cause my intent is to declare how the sailors should know to make their navigations with out peril or danger, as well of the ignorance of the rules & instructions of the navigation, as also to know the defects of the cards & instruments wherewith they govern themselves by the sea.  
I say let the Pilot or any other person that shall sail, be well advised that the card which he shall prick, and order his navigation by, be just & true, as well in the courses as in the setting down of the coast in such sort that every one thing be in his proper place both true & certain as well in the course as in the altitude. So that the error or defect of the card be not occasion that in navigation you err, and you must note that among the cards of navigation that until now have been used in the way of the Indians of his majesty, there are many which have 2 graduations different one from the other, in such sort that from one graduation to the other is more than 3 degrees of difference, these cards are false and in the navigations that by them are made may follow much hurt and great inconvenience by reason of the difference, that these 2. graduations have between them, because their difference doth cause that all the courses that reach from one graduation to the other are false, being seen from the place where they begin unto the place where they make an end. The reason is, that as they begin in one graduation, and make an end in another, that is different from that: so the said courses do make the self-same difference, & so the way that is sailed by them, shallbe erred, & you shall not found the place that you do seek by it: seeing that the ports, bay, Islands, & shooldes, & the other things of the cards, where these said courses do begin, being looked on where they end, they be forth of their own places & true altitude, making it equal with the altitude where the navigation began. Also looking in every course of the card, the distance of leagues, that are from one place to another, or from one port to another, I say, from the place where the course began, unto the place where it endeth: and these Leagues being taken with the compass, & the Leagues being seen which are reckoned for a degree in every course of the navigation shallbe found, that the leagues of the courses be not agreeable with those leagues, which are of the distance of the way. This is in the courses that do reach from one graduation to another: the which is caused by reason of the difference that the two graduations have: so that by these said cards cannot be made any good navigation, seeing that they in themselves do vary: likewise because they have 2. equinoctial lines, and many other errors, all the which I have made declaration of before. The Counsel royal of the Indians, of his Majesty, whereupon it hath been commanded that the said cards be not used by reason they have two different graduations, and therefore are false and erroneous as it is said. Therefore I say, that the Pilot or sailor aught to look well that the card whereby he doth sail, be of one only graduation: I will say if they have two graduations or more: let them be equal or uniform and not different, the one from the other. And likewise the other instruments, let them be certain and true, that they 'cause no error, whereby may follow hurt and danger, as it is most certain that with false instruments it may and doth oftentimes happen.   

The fourteenth Chapter, of the number of the Leagues, which are reckoned for a degree in every course of the navigation.  
FIrst, before I declare the number of the leagues, that aught to be given to every degree in every one of the courses of navigation; it is convenient to speak here what is the cause wherefore to the roundness of the world, from the East to the West, or from the North to the South, was given to every degree, 17. leagues and a half, and no more. And in the other courses, although they be equal: with these are reckoned more leagues for a degree then in them. To this is to be noted, what degree is taken in one of two sorts, is to be understood a degree of the roundness of the world, or a degree of elevation or height of the pole. For the first which is a degree of roundness, in this all the degrees of the courses or winds be equal, for all the winds are as the greater circles in the sphere, & as it hath been declared, they have three hundredth and sixty degrees of longitude, and for that cause is given to every degree of roundness seventeen leagues and a half: but in the second manner, which is the degrees of the elevation of the pole, these are different unto those of the roundness. For if in sailing towards the north going 17. leagues & a half, the pole is raised a degree, when you sail towards the North-east, although you go these 17. & a half, you have not raised the pole ● degree: but it is necessary that you go by this course 24. Leagues and a half, for every degree of elevation of the pole, and like in all the rest of the courses, by how much every one is more strait from the pole unto the Line: so many more Leagues, or less shall be gone for every degree of elevation of the pole, so that the roundness wherewith the world is girded, is not to be looked on in all the courses of the navigation. But do you also look how much should be gone by every course for to raise up or to put down every degree of the height of the pole, because this altitude of the pole, is to be reckoned from the half of the world, which is from the Equinoctial line: for that from thence they begin to reckon the degrees, as well for the part of the North, as for that of the South, so that in the cards of navigation, are put the coasts and all the rest that are marked in it according to the degrees that every thing is distant of the said line: in such sort, that sailing by any manner of course, from what place a man is in, towards the Equinoctial, or from the said Equinoctial or any other part, by as much as the course is more strait or crooked, by so much they shall reckon more or less leagues in every degree in this manner.  
 

The Equinoctial line.  
I put the case, that two ships be in the point A. which is a port towards the North, six degrees distant from the Equinoctial, and both of them do departed from thence towards the said line, & the one departeth with North, & the other with North-east towards the south-west: It is certain, that she which carrieth the wind at North, sailing by the same course from the North towards the South after she hath gone a hundredth & five leagues which are the said six degrees, by that course she shallbe in the Equinoctial: And the other that saileth with North-east towards the south-west, by reason that that wind goeth more leaning towards the said line, the way is longer to her. And so although that in the altitude she goeth not down more than six degrees, but for to come to the Equinoctial she shall go one hundredth forty seven leagues, by the which she hath every degree by this course 24. leagues & a half: so that only from the North, to the South, and from the East to the West, & contrariwise every degree hath 17. leagues & a half, but in the other courses every degree hath the leagues following.  
The second course hath a hundredth and eight leagues divided into six degrees, which cometh forth every degree 18. leagues.  
The third course hath a hundredth and fifteen leagues and a half, so that every degree hath nieneteene leagues and a terce.  
The fourth course hath a hundredth twenty six leagus, so that every degree hath 21. leagues.  
The fifth course hath a hundredth forty seven Leagues, so that every degree hath 24. leagues and a half.  
The six course hath a 189. leagues, so that every degree hath 31. leagues and a half.  
The seventh course hath two hundredth seventy three leagues, so that every degree hath forty five leagues and a half.  
The eight course hath five hundredth thirty five leagues, so that every degree hath eighty and nine leagues.    

 
The fifteenth Chapter, of number, and measure, and of how many parts a degree is compounded.  
IT is written in the book of wisdom, that God made all things in number, weight, & measure, therefore without knowledge of the numbers we can know nothing, of the time, of the hours, or of the movings, or other things, by the which it seemeth that without knowledge how to reckon we cannot know any thing.  
There are two sorts of quantities, or numbers: one is continual, another is divided or discrete: The continual is in 3. sorts, that is to say, towards the length only like to a line, and this is called quantity lineal: Another is continued in length, & breadth, but not deep, & this is called superficial: The third is continued in length, breadth, & depth, & is called corporal, or set together. The quantity divided or discrete, is when we say, one, two, three, &c: whereby it seemeth by the diversity of the numbers are understood divers meanings of writings, & so he that knoweth them not, aught not to be called a man. Plato saith, for this cause is man so wise a creature, because he knoweth the manner how to accounted: for the which he had written at the door of his Academia, that who could not make a reckoning or account, should not enter in, to hear him. The measures, & the reasons for them & their properties have sprung of Geometry: for Geometry is a science of measure, the which doth contain lines, superficies, and bodies, as appeareth in any circle three square, four square, & other figures, of Geometry: many Authors have written, and principally Euclides, the father of hippocras. Plurtarch saith, that Archimedes made an artificial thing by Geometry, with the which, Marcellus a captain of the Romans, having besieged the city of Syracula, in Sicilia with the said artificial thing Archimedes took out the ships of Marcellus, that were in the Sea, by raising them up into the air, he put them within the City: this science is called Geometry, as Saint Isidore saith, for the distribution of lands and fields: Geometry properly is of the corporal things for that all corporal things have their proper measure.  
And of the spaces or distances that are from one province or city to another, which are measured by Escadios, miles, Leagues, & Degrees: And this measure whereby that all may be alike in equality is ordained in this manner.  
Four grains of Barley do make one finger.  
Four fingers one hand.  
Four hands one foot.  
Five foot maketh one pace.  
An hundredth twenty five paces maketh one Escadio.  
Eight Escadios which are a thousand paces, do make a Mile.  
Three Miles do make a league.  
Seventeen leagues and a half do make a degree.  
Every degree hath lx. minutes.  
Every minute 60. seconds.  
Every second 60. thirds.  
And so unto tenths.  
The reason why this account is divided into this number of 60. more than into any other. Ptholome declareth in the first of the Almagesto, the ninth chapter: where he saith, that that Astronomers, sought a number, that hath many numbers in proportional parts, which we call parts, Alicotas, and there cannot be given any other number under sixty, for that this number may be parted into many divisions and numbers, as in two times thirty, in three times twenty etc.   
The end of the third Book.   

¶ The fourth book of the height or altitude of the Sun, and how the navigation aught to be ruled thereby.  

The first Chapter, wherein are declared 17. Fundamental principles, which aught to be known in the Altitude of the Sun.  
ONe of the things most subtle and of greatest understanding contained in the Art of navigation, is the altitude of the sun: for it showeth truly the way, that he which saileth, maketh, or shall make in such sort, that if he hath made any error in his voyage: by this altitude he knoweth it: and so by reason that it is a thing so excellent and subtle, the ancient writers in old time did highly esteem of the practise thereof, chief that great Ptholome, & other singular authors, for the which they used divers instruments as the Astrolabio, & the 3. rules, and others.  
This altitude is so effectual for good navigation, that those which do sail to far countries, cannot make their navigations: if this should lack. For among all the rules and advises that I have declared in this art, and will declare as well touching the altitude of the North as of others which serve in the navigation: This altitude 〈◊〉 the sun hath excellency among all others, because he is as a proof of Arithmetic, that soeweth the errors which are in the numbers: so that by the altitude of the sun, being precisely taken, the Pilot may know the want or lack that hath been in his navigation. And because this altitude of the Sun is a matter delicate and subtle as I have said. In this fourth book, I will treat thereof as plainly as possible I can, showing the rules by Text, and giving them their declaration & true understanding, that they aught to have. And likewise giving to every one an example and demonstration that they may be the better understood, and for this shallbe noted 17. fundamental beginnings, which are these following.  

Altitude.  
Degree.  
Horizon.  
Zodiac.  
Equinoctial line.  
Declination.  
Circles.  
Tropikes.  
Part of the North.  
Part of the South.  
Longitude.  
Latitude.  
Parelius.  
Meridian.  
Hemisphera.  
Zenith.  
Centrum.   
Altitude is the degrees which the sun or the ●ole do raise themselves above the Horizon. Likewise an altitude is understood by those degrees, that any city, port, Island, etc., are distant from the Equinoctial line. A degree is one part of three hundredth and sixty: wherein the world is divided, it hath seventeen Leagues and a half of way, by the longitude which is the length or breadth of the water and earth.  
Horizon is a circle which we do imagine upon the uppermost part of the earth: in the which our sight is fixed, which is as far as our sight canreach, and by this circle half the heaven is divided which we see, from the other half which we see not.  
Zodiac is a circle really situated in the eight heaven, under the which the sun moveth itself in all the year. This Zodiac divideth the Equinoctial line, into two equal parts: the one from the Equinoctial line by the part of the north, & the other by the part of the South, by every part of these it hath 180. degrees, so that the Zodiac hath 360. degrees.  
The Equinoctial is a s●rcke or circle imagined by the half of the world from the East into the West in equal distance from both the poles, so that from the Equinoctial unto every one of the poles are ninety degrees. It is called Equinoctial, because the sun passing by it causeth Equinoctio, which is as much to say, the day and the night to be equal.  
Declination is the distance which the sun by his own moving maketh from the Equinoctial line, 6. months of the year to the North part, & 6. months to the South part.  
Circles are the way whereby the poles of the Zodiac do move in roundness from the poles of the world. These do take their names of the said poles: and so they are called circle Arctic, and circled Antarctic, these circles are distant of the said poles of the world, 23. degrees, and 33. minutes.  
Tropicos or Tropikes are 2. circles where the sun last of all doth come once in a year. One unto the part of the North, and the other unto the part of the South. It is called the tropic of Tropos which is a greek name, and is as much to say as conversion, for the sun being come to every one of these tropics converteth herself and turneth back.  
The part of the North is taken for half the world, which is from the Equinoctial line unto the Pole arctic.  
The part of the South is the other half of the roundness of the world, which is from the Equinoctial line unto the pole antarctic.  
Longitude or length, is understood by the way from the East into the West, or from the West into the East, for that this is the length of the world.  
Latitude or breadth is the way which is taken from the North to the South, which is from one pole to the other, for this is the breadth of the world.  
Parelius is a way imagined to go strait by the heaven, or by the Sea, or by▪ the land, from the East into the West, or from the West into the East, with, outcomming near to the Equinoctial line, or to the poles more in one part then in another.  
The Meridian is a line, which is imagined from one pole of the world to the other, right over our heads, and when the sun cometh to this line, it is the midst of the day unto such as inhabit under it.  
Hemisphera is as much to say, the half sphere▪ and it is to be understood, that all the world is one Sphera Esphera, and is taken for a round thing, and because the world is round, it is called Sphera, and seeing that in what place soever a man is, he seethe the half of Heaven: This half of the Heaven, which we see, we call Hemisphera.  
Zenith is appoint imagined in the heaven very precisely put over our head, & from this point or Zenith to any manner of place of our Horizon are 90. degrees.  
Centre is a point in the midst of the sphere imagined, & so in the midst that from it to the superficie, all the lines that from forth right shallbe laid, shallbe equal: and from any part of the superficie to this point is to descend, and from it to the superficie is to rise up.   

The second Chapter, of the excellencies of the sun, and of his movings.  
SAint Ambrose saith▪ in the Exameron, that the sun is the fountain of light, the fairness of the day, the ornament of heaven, the measure of time, the virtue and strength of all things which are borne, and according as the Philosopher saith, is cause of all generation and corruption. It is of a very great quantity, so much that Ptholome saith in the Almagesto and Alfragano, in the difference 22. that the sun in an hundredth sixty & six times greater than the earth, his moving is more swift than any arrow, and we do not see him move by reason of his great brightness which is of more strength to be seen, than our sight can see: And to our judgement he goeth by leisure. But the quantity of the way being known which he goeth, his lightness is innumerable: so that for the great distance that is from us to him, we cannot determine his moving. And it is to be noted, that the sun hath two movings contrary, which are one forcible, and the other proper: the forcible moving is it that we see that every day he maketh a forcible going by the first movable, & in every 24. hours, he goeth round about the world from the East into the West. The other moving which is natural, with proper to himself, worketh contrary to the first, that is to be understood from the West into the East, in his circle Excentrico: the which moving, he maketh in three hundredth sixty and five days & six hours, & less a little quantity: And this moving he maketh in this manner, from the eleventh day of March, that the sun passeth by the line Equinoctial until the eleventh day of June, the sun goeth rising up, by the part of the North, and so putting himself from the said line, the eleventh day of June, he cometh to the tropic of Cancer, and in this rising up that he maketh these three months he departeth from the said line twenty three degrees and thirty three minutes: which is his greatest declination, or distance that he maketh from the said line; and from the twelfth of June, unto the thirteenth of September, the sun descendeth from the said tropic unto the line: and from the fourteenth of September, unto the thirteenth of December: the sun descendeth by the part of the South from the line to the tropic of Capricorn, from whence he departeth other twenty three degrees, and thirty three minutes, which is likewise his greatest declination of that part: and from the fourteenth of December, unto the tenth of March, the sun goeth using up from the tropic of Capricorn unto the line: so that of the twelfmonthes of the year, six of them, the sun goeth from the line to the part of the North, and the other six to the part of the South. And all the moving which the sun maketh, is from one tropic to another: in the which are 47. degrees, and 6. minutes. This is the latitude of the Zona, which the ancient Writers called Torrida, which is as much to say, toasted, because always the sun maketh his moving by her within these Tropikes, without going worth of them at any time.  
And it is to be understood, that the time which the sun goeth toward the part of the North, and the time he goeth toward the part of the South, Is not equal, for the sun goeth toward the part of the North, a hundredth eighty and seven days, and he goeth towards the part of the South, a hundredth sixty and eight: where it appeareth that the sun goeth more time of the year unto the part of the North, then unto the part of the South. The cause is, because this circle Excentrico: wherein the sun maketh his moving, is so shut into the Sphera, that of one part he cometh more near to the firmament, then of the other, for the which cause be is described forth of the Conter of the world.  
The part of this circle that cometh more near to the firmament, is called auxe, which is as much to say elevation, and this he doth, when he cometh to the tropic of Cancer, and that when he is most distant is called opposite of auxe, and this is when he cometh to the tropic of Capricorn: so that when the sun is in Auxe, he is more near to the firmament; and when he is in his opposite, he is more near to the earth, in such sort that in the Summer the sun goeth far from the earth, and in the Winter, is more near to the earth. This is to be understood in respect of us in the Winter 〈◊〉 respect of such as inhabit towards the parts of the South in Summer. The Cardinal Peter de Aliaco proveth, that aforesaid in the twelfth question, in the first article of the second notable, where he sayeth that the sun maketh his moving, being come to the end of Gomini, is in the Auxe: of his Excentrieo, and in the end of Sagitarius is in the opposite.  
This seenteth by the demonstration that Ptholome putteth in the third distinction of the Almagesto. And seeing that the Centre of the Excentrico of the sun is distant from the Centre of the world, by so much when the sun in his Auxe is more distant from the earth; and when he is in the opposite, he is more near to it. And so it is proved that the sun is more near to the earth in our Winter, then in Summer.   

The third Chapter, of the year called Solar, & other manner of years, & how the leap year is reckoned.  
THE year Solar is the time, wherein the sun passeth the twelve signs of the Zodiac, and returneth where he begun. It is called a year, which is, as if one should say, a ring, or circle, because the sun hath gone his circle, he returneth to the same place where he began.  
The Egyptians as S. Isidore saith, before they had the knowledge of learning, they accustomed to figure the year in a dragon, that bit the tail, but since they had learning and account of the year, they began it in September, because they say that in that moveth the world was made. And the Arabians begin in the same time, the Hebrues begin in the month of March, because it was given to them by law, we begin it in I●nuarie, because then did our 〈◊〉 year begin, which was the birth of the son of justice, Christ our God. And because the sun doth begin to come 〈◊〉 us, In the scripture I find five sorts of years. Anno Solet Anno Lun●● Anno Emergence, Anno Grande, Anno Mundano. The year ●ol●● is it the therefore hath been declared. The year Lunar is the time which doth contain twelve moons, of twenty nine days and a half, which amounteth to th●● hundredth fifty four d●●es unto the which is added the eleven days of the concurrent, because the year Lunar which is of the moon may come with the Solar which is of the sun. 〈◊〉 year Emergente is when there happeneth, a thing very notable, and in the time following is speech thereof, even as they talked in the time of Caesar▪ ●od now of the birth of our Lord Jesus Christ. Anno Grande is as much to far, as a great year, according as the master of the histories saith, that it is a time of six hundred years. Anno Mundano according to Macrobio, is when the Stars and all the Planets will come to the point of our degree where they began their first moving. And this he saith shall be in fifteen thousand years, likewise the other saith that it will come in forty & nine thousand years. But any manner of thing that the philosopher speaketh of in this matter, is according to his own opinion, we aught to hold that the time and the moving of the things and the end of them is in the hand of him that made them of nothing, and unto men doth not appertain to judge nor determine of the time or ending of the world. For the most high providence of the father eternal did put it in his own bosom, as our redeemer Jesus Christ teacheth us, answering to such as asked him the said question, as it is written in the Acts of the Apostles the first chapter, Therefore I say that the year called 〈◊〉 hath three hundredth sixty five ●●●yes and six hours lacking twelve minutes giving to every hour sixty minutes and because in the year are accounted six whole hours of this hath come although the quantity be little, that it is no more but one fifth part of an hour ins every one year, in so many number of years they have not made eleven days of difference in the time, so that these six hours which are accounted in the year besides these said days from four to four years doth amount to twenty four ●oures which maketh & natural day, and so this fourth year bathe three hundredth sixty six days and this is called the leap year, it is also called Bissiesto by the minutes which are as called Bises the which minutes the sun tarrieth in every one sign most than the thirty days Bissiesto is ●●oun●● to say two times six, for because 〈◊〉 of Bissiesto the day that is six days before the kalends of march is 〈◊〉 so that in one only letter of the Calendar there are two days which are the twenty four, and twenty 〈◊〉 of February, that is to say the 〈◊〉 which 〈◊〉 the said letter, and more the day which is increased by the Bissiesto or leap year by the which the leap year in the month of February hath twenty nine days and the other years twenty eight.  
Therefore it is to be seen, when the altitude of the sun is taken to know his declination if it be a leap year, or 〈◊〉, the second, or the third after the leap year as is plainly to be found in the seventeen Chapter, which treateth of the declination, and according to the year, so must the declination of the Sun be sought for.   

The fourth Chapter, what thing a shadow is, & how the shadow which the sun maketh aught to be looked on, for to take his altitude.  
THe shadows are caused when any dark body is opposite to the light, and so the shadow hath an appearance or show of a body, and it is none The shadow flieth away from such as follow it, and followeth such as fly from it. The shadow by how much the sun is higher, by so much it is lesser, and how much the lower, the greater: whereby the shadow of a man is greater in the morning and in the evening, then at the midst of the day, and it is to be noted, that the sun goeth always is one of these 3 places, which is toward the part of the north, or in the equinoctial, or towards the part of the south: & in these three parts to such as inhabit in the world it maketh 5 shadows: (That is to say,) a shadow at the east, a shadow at the west, a shadow at the north, a shadow at the south, & a strait shadow. The shadow at the east, is when the sun doth set. The shadow at the west is when the sun riseth.  
The shadow at north is when the sun cometh to the midst of the day, and he that maketh the shadow is more towards the north than the sun. And the shadow at south is when he that maketh the shadow is more towards the south than the sun there is likewise a strait shadow, when the sun is in our Zen●●● All these shadows, such as dwell within the tropics have. Those which inhabit under the tropics, have 4 shadows, (that is to say) shadow at east shadow at west and those of the tropic of Cancer, have the shadow at north and those of the tropic of Capricorn have the shadow at south: and once in the year a strait shadow, which is when the sun entereth into that tropic. Such as dwell without the tropics have three shadows, at east, and at west, and those of the part of the north, have shadow at north, and those of the part of the south, have shadow at south, and never any strait shadow. But do you note, that although the sun doth make in the year five shadows to such as devil in the world not only in five parts, but in xiii. differences of parts, you may be with the sun and have xiii. differences of shadows, and no more, (that is to say) five when the sun goeth towards the part of the north, and three when he is in the line, and five when he is towards the part of the south, the which by xiii. rules with their demonstrations shallbe noted in this manner.  

When the Sun is towards the north.  
The Sun being towards the north, if the shadows be towardees the north, you are more towards the north than the Sun, and the Sun between you and the line.  
The Sun towards the north, if the shadows be to no part, then are you towards the north as far from the line as the Sun.  
The Sun towards the north, if the shadows be towards the south, you may be towards the north between the Sun & the line.  
The Sun towards the north, and the shadows going towards the south you may be in the Equinoctial line.  
The Sun towards the north, and the shadows going towards the south you may be towards the part of the south, and the line between you and the Sun.   

When the Sun is in the Equinoctial Line.  
The Sun in the Equinoctial if the shadows be towards the north, you are towards the part of the north.  
The Sun in the equinoctial, if the shadows be strait you are in the equinoctial.  
The Sun in the Equinoctial, if the shadows be towards the south you are towards the part of the south.   

When the Sun is towards the south.  
The Sun towards the south, if the shadows be towards the south you are towards the south, and the sun is between you and the line.  
The sun at the south if the shadows be strait you are towards the south as far from the line as the sun.  
The sun at south if the shadows be towards the north you may be towards the south between the sun and the line.  
The Sun towards the south, and the shadows going towards the north you may be in the Equinoctial.  
The sun towards the south, and the shadows towards the north you may be towards the north, & the line between you and the sun.    

The fifth chapter, wherein is declared what thing the height of the sun is, and how it aught to be taken to know the place where a man is.  
seeing there hath been declared the difference of shadows which the sun maketh, or may make by all the year in any manner of place that a man is, the which shadows are necessary to be known. For to know precisely how to take the altitude of the sun, I will speak, what thing the altitude of the sun is, and the manner that must be had, for to take it well. For this is to be noted, that Ptolemy saith in the first of Geographia, that wheresoever a man is, he seethe half the heaven and the other half is hid from him, in such sort that of three hundredth and sixty degrees that the heaven hath in roundness we always see the hundredth and four score which is the half wherein is contained our Hemispherio, so that wheresoever a man is, and in any manner of time, from his head or zenith, unto the horizon are ninety degrees, and so from what place that a man is in even unto the sun, when he riseth in the morning, that he do begin to appear in the horizon are ninety degrees, and how much more the day goeth forward, and the sun goeth rising, so much more he cometh nearer towards our zenith. And this rising up that the sun maketh, is called the altitude of the sun, because he goeth rising, and going up upon the horizon, the which altitude he that shall take him at the midst of the day, let him understand that the degrees that he shall find in his Astrolabio, less than ninety, those should be from him to the sun, for that the sun shall be so many distant from his zenith, which is from the right of his head. Therefore I say to know the altitude that the sun hath every day upon the horizon which the pilot or any otherperson that would take it, ought, first of all to look on five things which are these following.  
The first, that it be taken in the midst of the day.  
The second, that he see to which part of the line, the sun goeth that day.  
The third, to what part the shadows go.  
The fourth, what declination the sun hath.  
The fifth, that he know how to apply the rule that is convenient according to the time and place wherein he findeth himself. Unto the first I say, that the altitude of the sun aught to be taken at the midst of the day justly, this is because until the sun cometh to the Meridian he goeth always rising above the Horizon, and if he be taken before or after he will not be so justly taken, but although that in this be some difference of time being but a little thing before or after, it is no great inconvenience, because the most times it cannot be punctually known when he cometh to the Meridian. Although you look on the clock, the Astrolabio, or any other instrument, but always do you procure to take him at the hour aforesaid.  
To the second, it aught to be seen at what part of the line, the sun goeth, if it be at the north or at the south, considering that the time, which the sun goeth to the part of the north, is from the eleventh of March unto the thirteenth of September, and from the fourteenth of September unto the tenth of March he goeth to the part of the south.  
Unto the third, he that taketh the altitude aught to see to what part the shadows are from him, (that is to say) the shadow of his person, or of the mast of his ship, or of any other thing that is put upright. And so by the shadow he shall know at which part of the line he is, for being known to which part the sun goeth, it may be easily known by the said shadow, towards what part he is of, as in the fourth chapter hath been declared.  
To the fourth, the year aught to be looked unto, if it be a leap year, or the first, the second, or third year after the leap year, and according as the year is, let him look on the month, and day wherein he is: and what declination the sun hath towards the part where he goeth, that is how many degrees and minutes he is distant from the said line.  
To the fifth, that he apply every rule of the altitude in his proper time and place, and this the pilot aught always to procure and know the rules of the altitude, not only the words but the meaning of them for he that only knoweth the rule, and doth not attain to the reason or foundation thereof, as it aught to be understood, it procureth to him many harms, and he knoweth not of what they proceed, and finding himself in the error he putteth fault in the instruments and rules, the fault being in himself, because he understandeth them not.  
And because these rules of the altitude of the sun may be well understood, and that their should be no ignorance in any thing, here shall be put every one with his declaration, figure, and example, in manner following.  

The first rule, when the Sun goeth toward the part of the north, and the shadows goes towards the north.  
THE Sun towards the part of the North, if the shadows be towards the North you be towards the north, and the Sun is between you and the line, see how many degrees you took of altitude and how many doth lack of ninety, and with those which lack, join the declination of that day, and all joined together you are distant from the line towards the north.  
This first rule doth show how you shall know the altitude of the sun, when he goeth towards the north, and he that taketh the altitude is more towards the north then the sun, and so he saith.  
The Sun towards the part of the North, is as much to say, that when you do take the altitude of the Sun in any day of the six months, that he goeth from the line unto the part of the north.  
If the shadows be towards the North, if in this day that you take the altitude of the Sun the shadows be from you towards the north.  
You are towards the North and the Sun is between you and the line, in such sort that by the shadows you do know that the Sun is between you and the line, at such time as when they are in this manner.  
Behold how many degrees you take of altitude, these degrees are those that you take the sun in your Astrolabio, therefore look on these degrees how many they are.  
And how many lacketh for ninety, is to be understood upon those that you found of Astrolabio, look how many they are, which do lack for to come to ninety, And with those which lack, as if you had taken fifty, there lack forty: and if you had taken 65. there lack 25. Therefore with those forty, or twenty, or more or less, join the declination of that day, which are those degrees & minutes which the sun is distant from the line, as you shall find in the declination of the said day, And all put together, that is to say, the declination of the sun, & the degrees which lack for nienty, and that which this shall sum or amount unto, you are distant from the line towards the North.  

An Example.  
The sixth day of April, I taking the altitude of the sun, the shadows were from me towards the North, and I took the sun in sixty degrees of Astrolabio, there lacked 30. for 90. with these 30. I joined 10. degrees, which the Sun had this day of declination, which did amount to forty degrees, so much was I distant from the line towards the part of the North. The reason is, for because in the month of April, the sun goeth towards the part of the North, & as the shadows were from me towards the North, I knew that I was more towards the North, than the sun, therefore the sun being taken in sixty degrees, the thirty which lacked for ninety, was I distant of the sun.  
This is because always, when that I shall take the altitude of the sun, those degrees that I shall find in my Astrolabio, less than ninety, the self same am I distant from the sun, and the same day, the sun was distant from the line, ten degrees, which was his declination, so that from me to the sun, were thirty degrees, & from the sun to the live, ten which make forty: so much was I distant from the said line.    

The second rule, that when the sun is towards the North, and the shadows towards the South, the declination and altitude are more than ninety degrees.  
IF the sun be towards the North, and the shadows be towards the south, join the declination with the altitude, and if they pass ninety degrees, those which are more, you are distant from the line towards the North, and you are between the sun and the line.  
In the first rule hath been declared that when the sun is towards the part of the North, & he that taketh the altitude is more towards the North than the sun whereby the shadows go from him towards the North. This rule is, when the sun goeth towards the self-same part of the North, and he which taketh the altitude, the shadows go from him towards the South in this manner. The sun towards the North, the time which the sun goeth towards the North, hath been declared. Therefore in this time, If the shadows be towards the south, the south joineth the declination with the altitude, which is as much to say, look on the degrees and minutes, that this day hath of declination, and join them with the degrees, that you take the sun in your Astrolabio, and if they do pass of ninety degrees, if altogether the declination of the sun, and the altitude which you took, were more than ninety degrees.  
Those which were more, you are distant from the line towards the North. It is to be understood, that if the altitude and declination were nienetie five degrees, you are distant of the line, five degrees: and if they were an hundredth, you were distant ten degrees: and so are to be reckoned those which are more than ninety.  
And then are you between the sun and the line. The which you shall know because the shadows go from you towards the South, and because the altitude & dedination did pass of nienetie degrees.  

An Example.  
The twenty day of May, I took the sun in 80. degrees, this day he had of declination twenty and one degrees, I joined the declination and the altitude, & they amounted to an hundredth and one degrees, so that they be eleven degrees more than nienetie. These eleven was I distant from the line towards the North, between the sun & the line, the reason is, because this day the sun was distant of the line, 21. degrees: which was his declination towards the part of the North: so that I having taken the sun in fourscore degrees, there was from me to the sun, ten degrees, and as I am between the sun and the line, I being ten degrees distant from the sun towards the line, there was from me to the line eleven degrees, which lacketh for the twenty one, which is the declination of the sun.  
   

The third rule, when the sun is towards the North, and the shadows towards the South, and the declination, and altitude, are nienety degrees just.  
THE sun towards the North and the shadows towards the South, if joining the altitude and declination, they be nienety degrees, you are under the Equinoctial line.  
He that taketh the altitude in the time that the sun goeth towards the North in one of three parts, he may stand that the shadows may be from him towards the South, The first is when he is between the sun and the line, and this hath been already declared in the rule, before this. The second is, the sun being towards the North and he that taketh the altitude in the self same line. The third is, the sun being towards the North, and he that taketh the altitude towards the part of the South, therefore of the second, which is, the man being in the line, the rule saith,  
The sun at the North part if the shadows go towards the South, join the declination with the altitude.  
It is to be noted, that always when the sun goeth to one part, and the shadows to an other, the declination is to be joined with the altitude, And if they be ninety degrees just. Even like if there were seventy degrees of altitude and 20. of declination, or eighty of altitude and ten of declination, or any other number, wherein the altitude and declination be ninety degrees just, when it is so: you are under the Equinoctial live.  

An Example.  
The 11. day of july I took the sun in my Astrolabio, in 68 degrees, there was this day of declination, 22. degrees, join the altitude & declination, and they amounted to ninety degrees, than was I under the Equinoctial line.  
The reason is, because the sun was towards the part of the North, and the shadows going from me towards the South, I was more towards the South, than the sun, there, fore taking sixty eight degrees of altitude, I was distant from the sun twenty two degrees, and this day had the sun twenty two degrees of declination, so that the sun was distant from the line twenty two degrees, and I distant from the sun towards the line, the said twenty two degrees, by the which I knew that I was under the said line. For by how much the sun was distant from the line, so much was I distant of the sun from the said line.    

The fourth rule when the sun is towards the North, & the shadows towards the south, and the altitude and declination do not amount to nienetie degrees.  
THe sun at North and the shadows at south, if joining the altitude and declination, they come not to ninety degrees, those that do lack for ninety, you are distant of the line towards the part of the south, and the line willbe between you and the sun.  
It hath been declared that when the sun goeth towards the part of the North, if the shadows go from him that taketh the altitude towards the South, he may be in one of these three places, that is to say, towards the North, between the sun and the line, and in the said line, and at the part of the South, the line being between him and the Sun, for in any part of these that a man is, the sun going towards the North part, always at the midst of the day, the shadows will go towards the South, of these three, two have been declared, of the third this rule speaketh.  
The sun towards the North, if the shadows be towards the South, and joining the altitude and declination, if they come not to ninety degrees.  
If the altitude which you have taken in the Astrolabio, were fifty or sixty degrees, and the declination fifteen or twenty, so that all being put together, come not to nienetie.  
Those which do lack for nienetie, you are distant from the line towards the South.  
So that those Degrees and Minutes few or many, that be less than nienetye, You are distant of the line, towards the part of the South, & then The line willbe between you and the Sun.  

An Example.  
The tenth of August, taking the altitude, the shadow was from me towards the South: I took the sun in the Astrolabio, in seventy degrees. This day he had of declination twelve degrees: I joined the altitude and declination, and they amounted to eighty and two degrees, there lacked eight degrees for ninety, these eight degrees was I distant from the line towards the part of the South. The reason is, that taking the Sun in seventy degrees, there was from me to the Sun, twenty degrees, and this day the Sun was distant from the line, twelve degrees: which was his declination towards the part of the North: so that the eight which lacketh for twenty, was I distant of the line towards the part of the South, so that from me to the line was eight degrees, and from the line to the Sun twelve, these be the twenty which were from me to the Sun.  
   

The fifth rule, when the sun is in the Equinoctial, and you take his altitude in less than ninety degrees.  
WHen the sun is in the Equinoctial, if you take his altitude in less than ninety degrees, those which are less than ninety, you are distant from the line towards that part which the shadows are from you.  
There hath been declared the rules of the altitude of the sun, when he goeth towards the part of the North: now this rule serveth for the days of the year, that the sun is in the Equinoctial line, and sayeth, when the sun is in the Equinoctial line.  
The sun is in the Equinoctial, the eleventh of March, & thirteenth of September, so that in any of these days, If you take his altitude in less than ninety degrees, so that if you take it in 75. which are less by fifteen then ninety, or in eighty or more or less:  
Those which you take less than ninety, These fifteen, or ten, or five, or as many as are less than ninety, you are distant from the line unto the part which the shadows doc fall from you.  
So that if the shadows go from you towards the North, those degrees which you find less than ninety, you are distant from the line towards the part of the North, and if the shadows go from you towards the South, the same degrees you shall find yourself towards the South.  

An Example.  
The 11. of March I took the sun in eighty degrees, the shadows were from me towards the North, this day the sun hath no degree of declination, therefore the 10. degrees, which I took less than ninety, I was distant from the sun. The reason is, because the sun was in the line, the same degrees that I was distant from the sun, the self-same am I from the line, & because the shadows went from me towards the North, was I towards the part of the North, the which if they had gone from me towards the South, the self-same degrees should I have been towards the part of the South.  
   

The sixth rule, when the altitude is taken in ninety degrees, whether in the sun be a declination o● no.  
WHen you shall take the altitude of the sun in nienety degrees, the sun is over your head, look upon the declination of this day, & if there be no declination, you and the sun be in the line, & if there be any declination, that which is, you are distant from the line, towards that part which the sun goeth.  
This rule declareth how the altitude of the sun should be known, when he that taketh him, hath him in the zenith, or point that is right over his head, the which rule hath two parts, that is to say, one, when the sun is in the Equinoctial line, & the other when it is forth of it, of the first it speaketh.  
When you do take the altitude of the sun in ninety degrees. It is to be understood, that the measurer of the world, showeth in your Astrolabio, the ninety degrees just, when it is so. Know ye that the sun is right over your head:  
In such sort, that your shadow shall not go to any part, therefore then Look on the declination of this day:  
Is to be understood the degrees and minutes, which the sun is distant from the Equinoctial.  
And if there be no declination, Which will be the eleventh of March, and the thirteenth of September, them the declination is of few minutes.  
You and the sun be in the line, the sun beingin the ●●ne than he hath no degrete nor half a degree of declination, and you are in the line, seeing that you are under the sun.  
And if there be any declination: This is the second part of this rule, wherein is declared, when the sun, and he that taketh the altitude be out of the Equinectiall, the which will be known in the degrees, that the sun hath of declination, because it saith, that which is, is to be understood few degrees, or many. So much you are distant from the line so that seesing you are under the sun, and the sun is distant from the line, that the same degrees & minutes, that the sun hath of declination, the same you are distant from the line, towards the part where the sun goeth.  
If it be that the sun goeth to the North part, you are toward the North part, & if he go towards the South, you are toward the same part of the South, and because with this that is declared, this rule may be well understood, there is put in it no more declaration.   

The seventh rule, when the sun is towards the part of the South, and the shadows go likewise towards the South.  
THe sun towards the part of the south, and the shadows towards the South, the sun is between you and the line, look how many degrees of altitude, you took, and how many do lack for ninety, and with those that lack, join the declination of this day, and being altogether the degrees that be, you are distant from the line, towards the South.  
This rule is, when the sun is towards the part of the South, and the shadows go towards the South, is agreeable with the first rule, which was declared when the sun goeth towards the part of the North, and because it is declared according to his proper meaning, & this is agreeable to that, there shall not be put here any other declaration, but the same that is there declared, is to be understood in this. Only making difference of the names, that is to say, from the North to the South, but because this rule is for the time when the sun goeth towards the South, I will put an example of the part of the South, in the manner following.  

An Example.  
The fourth of October, taking the altitude, the shadows went from me towards the South, and I took the sun in 85. degrees in my Astrolabio, this day the sun had 8. degrees of declination towards the south, therefore taking the altitude in 85. degrees, there lacketh siue, for nienetie, these five was I distant from the sun, and with these five, I joined the eight of declination, they amounted to thirteen degrees, these thirteen degrees was I distant from the line, because from me to the sun was five, and from the Sun to the line eight, which are thirteen, so that I was distant thirteen degrees from the line towards the part of the South.  
   

The eight rule, when the sun is towards the nouth, and the shadows towards the ●orth, and the declination and altitude are more than ninety degrees.  
THe Sun towards the south, if the shadows be towards the north, join the declination with the altitude, and altogether if they pass of ninety degrees, those which are more, you are distant of the line towards the south, and you are between the sun and the line.  
This rule is declared in the second rule before written when the sun goeth towards the north part, for the same account or reckoning that is made the sun being towards the north and he that taketh the altitude at the same part of the north, between the sun and the line, the self same is to be done, the sun being towards the part of the south, and he which taketh the altitude in the same part between the sun and the line.  
Therefore the declaration which is written for the one, by the self same form serveth for the other, and to know that he which taketh the altitude is between the sun and the line, the rule declareth in what altitude and declination, they should pass of nienty degrees, as it is showed in this example.  

An Example.  
The xiii. of january I took the sun in seventy eight degrees, this day he had of declination nienteene degrees, I joined the declination and altitude as the rule showeth and did amount to ninety and seven degrees, these seven, degrees that passed of nienty, was I distant from the line towards the south. The reason is, that taking the sun in seventy & eight degrees, I was distant from the sun xii. degrees, & seeing that the sun was distant from the line ri●. degrees, & I being between the sun & the line, therefore there are from me to the sun xii degrees, & from me to the line seven which are nienteene, so many are the degrees which the sun is distant of the line.  
   

The ninth rule, when the Sun is at the south, and the shadows at north, and the altitude and declination are ninety degrees just.  
THE Sun at south and the shadows at north if joining the altitude and declination they be ninety degrees, you are in the equinoctial line.  
It hath been declared that the sun being at north, he which taketh the altitude, may be in one of 3 parts whereby his shadows, may go towards the south one of them is towards the part of the north, between the sun and the l●n●e, another in the said line, the other towards the part of the south▪ the line between him and the sun▪ the same is understood the sun going towards the part of the south, that he which toketh the altitude in one of three parts, he may be that the shadows go from him towards the north, the one being toward the part of the south between the sun and that line, the other being in the said line. The third being towards the part of the north the line between him and the sun.  
Seeing of the first it hath been written of, and in the rule going before, of the second, which is the sun being towards the part of the south, & for him which taketh the altitude in the line is put this present rule, the which because in the third rule when the sun goeth toward the part of the north, it is declared. Only here is to be noted, the example following.  

An example.  
The second of December I took the sun in sixty seven degrees, this day he had of declination twenty three degrees, join the declination, and the altitude they amounted to ninety degrees, and being so I was in the equinoctial, for because the sun at south, the shadows going from me towards the north, I was more towards the north than the sun, the sun this day was distant of the line twenty three degrees which was his declination, so that taking the altitude in sixty seven degrees, there was from me to the sun twenty three degrees, in such sort that the same twenty three degrees which the sun was distant of the line, the same was I distant of the sun towards the line, so thereby I knew that I was in the said line.  
   

The tenth rule, when the Sun is towards the South, and the shadows towards the North, if the Altitude and declination being joined, they come not to ninety degrees.  
THe Sun at South, and the shadows at North, if the altitude and declination do not come to ninety degrees, those which do lack for 〈◊〉 you are distant of the line towards the part of the north, and the line should be between you and the Sun.  
The third difference which hath been spoken of, wherein he which taketh the altitude, may be the sun being towards the South, and the shadows going towards the North, is, being towards the part of the North, the line between him and the Sun, as this rule showeth, whose declaration is written in the fourth rule, when the Sun goeth towards the part of the North. And it is to lie noted, that at all times when the sun goeth towards one part, & the shadows towards another, the declination is to be joined with the altitude, and if they pass ninety degrees, those which are more, you are distant of the line, towards the part which the sun goeth and if they be ninety just, you should be in the line, and if they come not to ninety, those which are less you are distant at the contrary part where the sun goeth, as in this rule is declared, and therefore in this example following is to be noted.  

An Example.  
The thirty of September I took the sun in sixty degrees, and the shadows were from me towards the north, and the sun this day had six degrees and a half of declination, I joined the declination and the altitude, and they amounted to sixty and six degrees and a half, there lacked twenty three degrees and a half for ninety. These twenty three degrees and a half was I distant from the line towards the part of the north. The reason is, for that taking the sun in sixty degrees there was from me to the sun thirty. I was towards the part of the north, and the sun towards the part of the south distant from the line, six degrees & a half, so that of the thirty degrees, which were from me to the sun, taking out the six and a half which the sun is distant from the line, there will be from me to the line twenty three degrees and a half.  
    

The sixth chapter, wherefore the rules of the height of the sun do show the degrees that a man is distant of the equinoctial line more than by any other part.  
IN the rules before written hath been declared how that every day that you will take the altitude of the sun, you shall know at what part of the line you are, and how many degrees distant as well of the one part as of the other.  
Of this may be 〈◊〉 what the cause is, wherefore all the rules of the ●●●tude of the sun, are made and ordained that a man should understand how many degrees he is distant of the equinoctial line, more than from the pole, or from the other tropics or from any other part.  
To this is to be answered, that the reason whereby only we would know the distance, that is from the said line, more than from any other part, is, because the said equinoctial line, as before hath been declared, is put and ●●tuated in the midst of the world, and all the cards of navigation whereby the pilots & sailors do rule themselves by. In the card of navigation a● ordained and put the ports, and bays, rivers, capes, Islands, and shooldes, & all other things, which are marked in them, according to the degrees that every thing is distant from the said equinoctial line, as well towards the part of the north, as of the south: and being known by the pilot or sailor, with the altitude which he taketh, how many degreees he is distant of the said line, to one part or to another, or if he be in the said line, likewise he knoweth if he be equal in altitude with the place which he goeth to seek according as in his card he hath pricked, or if he aught to rise up or go down, and how many degrees, until he put himself right of the place, and for this cause the line is more sought for, than any other part.   

The seventh chapter, by what reason all rules of the altitude of the sun are reduced to nienty degrees, more than to any other number.  
IT may be asked by what reason all the rules of the altitude of the sun, as before hath been declared go reduced to this number of ninety degrees, more than to any other, for that it is so written, that the degrees of altitude are to be seen, wherein the sun is taken in the Astrolabio, how many do lack, unto ninety and in other rules is said that the altitude and declination is to be joined and seen if they amount to ninety degrees, or if they pass ninety degrees, or if they come not to nienty degrees, in such sort, that all the rules are made and ordained to this number of nienty, therefore it aught to be known wherefore more to this number than to any other. For the understanding of this doubt is to be imagined that wheresoever a man standeth is the midst of the world, and he seethe half the heaven, in such sort, that as the roundness of the world hath three hundredth & sixty degrees, the horizon discovereth the half which are a hundredth and eighty, and they are understood in this manner▪ from any manner of part of the horizon unto the Cenith are nienty degrees, and from my zenith unto the other part of the horizon other ninety. Which is to be understood in this manner, imagine that in what place so ever a man is in, he is right in the midst of this circle, which circle is his horizon.  
Therefore I say that I am in the midst of the circle, and from the point A. which is the horizon unto my head are ninety degrees, and from my zenith to the point C. other ninety, which are a hundredth and eighty, and from the point B. unto my head ninety, and from my head unto the point D. other ninety, and so there is ninety degrees from my head to any part of my horizon. Therefore declaring the doubt, I say that the reason why the rules of the altitude of the Sun are reduced to this number of ninety, is because the Sun cannot rise up above the horizon, more than ninety degrees, which is until he come right over our heads, and so when we take him in ninety degrees of Astrolabio, we say that we have the sun right over our heads, & when we take him in less, that which is less than ninety is the sun distant from us: so that because the sun cannot rise up, upon the horizon more than ninety degrees, with the which as I have said, he cometh until he be upon our heads: therefore the rules of his altitude go reduced to this number, and not to any other.   

The eight Chapter, wherein is declared wherefore we say, that the man is distant of the sun, the degrees that he taketh in the Astrolabio less than ninety.  
OF the rules of the altitude of the Sun before written, hath been said, and declared, that at all times when the Altitude is taken, the degrees are to be looked for which do lack in the Astrolabio of ninety, and that those same, the man is distant of the Sun. And because it is convenient and expedient that this rule be well and thoroughly understood and known, I will most evidently declare it, in this manner following.  
It is to be noted, when the Sun doth begin to appear by our horizon which is, when he goeth forth in the morning, than he hath no Altitude but from thence he goeth rising up, and how much more he riseth, so much he goeth having more Altitude, upon the Horizon, in such sort that if one hour after he is come forth, he hath raised himself up five degrees, in two hours he shall have raised himself up ten or twelve, and in three hours 〈…〉 up vn●●● the myddist the day, and from of thence he t●●●eth to desc●●●● by the 〈◊〉 order that he went rising up, until he put or hide himself under the horizon. Of that which hath been said, two things are to be noted, the first is, that from the time the Sun 〈◊〉 forth, until it be the midst of the day, he goeth always rising up, and augmenting in his 〈◊〉, until he come to 〈◊〉, Meridian, and alwayee the Meridian is in the midst of the bow, which the Sun maketh, from the time that he cometh forth until he is set▪ This is because always the man is in the midst of the roundness, which roundness is his horizon.  
The second is, that this Bow which the Sun maketh upon our horizon, is not every day equal, but at some times is greater than at other some, even as the day is great or little, but although that the bow be great or little, always the Sun goeth rising up, until he come to the Meridian, and from thence he descendeth. And it is to be noted, that always the Sun cometh forth, and setteth in equal distance from us, but at the midst of the day, he is not always in equal distance of us, but at one time he is near, and at another time far off, this is from the right of our heads, which is to be understood in this manner. I put the case that I be distant from the equinoctial line ten degrees, and the Sun hath of declination the same day the same ten degrees, towards the part that I am, and being so, when the Sun came forth this day, and began to appear in the horizon, than he was from me ninety degrees, and from thence he went rising up until the midst of the day, and being come to my Meridian, he shall be precisely right over my head.  
Insomuch that if a line be imagined▪ that rightly doth descend from the Sun unto the earth, this line would come upon my head, and this would be so at all times, when I were as distant of the line, as the declination is, which the sun hath this day, because I am in that way where the Sun that day doth make his moving, by the which that day at the midst of the day, I shall have it upon my head: but if I be distant of the way of the sunue, although that when he came forth, he was from me ninety degrees, it is to be understood, that when it is the midst of the day, I shall not have it right over my head, but I shall have it as far of, as the distance is from the place, where I am, to the place of the way of the sun, in such sort that if the distance, which is of the place or way, where I am, to the place or way where the Sun came forth, were five degrees, or ten, or more, or less: Those same the Sun shallbe at the midst of the day distant from the right of my head, so that, if there were laid two strait lines or strekes, from the East into the West, the one by the place where the Sun cometh forth, and the other by the place where I am: the degrees of distance that should be from one line to the other, the self-same at the midst of the day, willbe of distance of the Sun to my zenith. And do you note, that in this distance, which the Sun maketh from me is not to be looked, how much there is from me to the Sun, but do you look how much the Sun is distant at the midst of the day, from the right of my head, for so much as this distance is, so much will I say, that I am distant of the Sun, to one part or other.   

The ninth Chapter, wherein is declared, how it is understood, that a man hath the Sun right over his head.  
IT hath been declared in the Chapter going before, that when a man findeth himself in the course where the sun maketh his way, that that day at the midst of the day, he shall have him right over his head, of this may be had a great doubt, (which is this.)  

A doubt.  
It hath been declared in the second Chapter of this fourth Book, according to the opinion of Ptholome, and Al●rag●no, that the Sun is an hundredth sixty and six times greater than the earth: and that the Sun is so great, it appeareth well, seeing that continually he giveth light to all the stars of the heaven, the heaven being so great, and the stars so many in number, as the royal prophet saith, that God only doth reckon and number them. Likewise the greatness of the Sun doth show, in the which, although that there be always put all the roundness of the water and earth between the Sun and the Heaven in such sort, that continually, he putteth himself before, according to the sight of man, whereby we see not any more than half the heaven: and although the earth and the water are so great bodies, yet they occupy not any thing, nor detain the light of the Sun, that it do not pass to give light to all the stars. This is because the earth and water are so little things in respect of the sun, that well near they may be compared to a grain of mustard seed, put before a great torch lighted, which doth let nothing of the light thereof, but that it doth extend to all parts. Therefore all the earth being so little in comparison of the Sun, and the man being well near of no quantity in respect of all the earth, it seemeth to be far out of reason, to say that a man should have the Sun right over his head in any time or place, even as there should be no reason to say, that a great ship going by the Sea, may be right upon the point of a little nail, which were in the depth of the water: or that a great cloud should be right upon a little worm of the earth, even as well it seemeth, that there is no reason to say, that the sun is right over the head of a man: seeing that the sun is always, and showeth itself upon the half of all the earth, by the which reason likewise it seemeth, that it aught not to be thought, that the sun in one time is in the Equinoctial, and another time at the North part, and another at the South part, seeing that these are parts of the earth, and the sun not only is greater than these parts, but in very great quantity, greater than all of them, as it is said, and so it is proved & seemeth that it is an improper thing, to say that the sun is right upon our head, or that he is in one part or other of the earth.   

A declaration.  
For the declaring of this doubt, is to be noted, that although the sun is of so great a quantity, as before hath been declared, this doth not let, that a man may have him right over his head, and in the discourse of the year he be in one part or other of the earth, the which is understood in this manner, that the greatness of the sun is not to be considered how great it is in itself, but how great it is to us, I will say according to our sight, and according to the effect which it maketh with us. (An example of this is) that many times it happeneth to men that go sailing, and they see very far of in the Sea a ship, and although she be very great, and goeth very swiftly, it seemeth to him that beholdeth her, that she is little, and that she moveth not: the same doth hap to us with a great cloud, which the wind doth carry with great lightness: this is caused for the great distance that is from the one to the other, in such sort, that we judge not as it is, but according as the sight doth represent it to us: even so the sun although he be very great, and moveth with great haste, we judge not of it, but according to our sense, for because in as much as toucheth the hastiness of his moving, as the earth is well near a point of the circle, which the sun maketh, it is certain, that it cannot be perceived or known according as his moving is, this is by reason of the great distance that is between him and us, and so by this great distance he cometh to diminish himself so much in our sight that he may be right over the head of of one man, and not right over the head of another, that is one league from him.  
This is showed, that in taking the altitude of the sun, one man will take him very precisely right over his own head, & another although he be near, will find him far of from him, this is because he was more right over the head of the one then of the other. Likewise this is showed by the shadows, the which do show infallibly the moving which the sun maketh from one part to another: in such sort, that in one place one man may have his shadow so right, that at the midst of the day, the sun doth make no shadow to any part, and to another that is not far from thence, although he be in the same Meridian, and at the same hour and minute, the shadow will decline to some part, whereby it manifestly appeareth▪ to have the sun right over our head, and how if moveth not only by the midst, but likewise by the sides of the earth. And for the better declaration of that aforesaid is to be noted, that naturally all things which we see, the sight doth comprehend it by A pyramid, so saith Alacen in the perspective in the 17. rule, that the comprehension of all things visible is by a rooted pyramid. The pyramid is to be imagined in this manner.    

The tenth Chapter, to know how the altitude of the Sun aught to be seen if it be leap year, or what year it is.  
IN the sixth Chapter of this fourth book, I said how it is necessary when the altitude of the sun is taken to know the year, if it be the leap year, or the first or second, or third after the leap year, because the days of one year, with those of the other have not the degrees and minutes equal, and the reason is, because as in the third chapter of this fourth book hath been declared, that the year called Solar, hath three hundredth sixty five days, & six hours, and that those six hours of every one year, from four to four years, do make a natural day, and that such a year is called a leap year, so that the first year after the leap year, hath three hundredth sixty five days and six hours. And the second year, three hundredth sixty five days and twelve hours, the six of the first year, and six his own, and the third year, three hundredth sixetie five days and eighteen hours, the twelve of the two years the first and second, and the vi. his own, and the fourth year three hundredth sixty six days, so that in this fourth year is shut up the hours of all four years, and the fourth year being past, The first beginneth, and so the other years successively as it is said, and for this cause they be not equal in degrees and minutes all days one with another: Therefore it is convenient, as it is before declared, when the altitude of the sun is to be taken, that it be seen what year it is, and seek what day and month you are in, and there you shall find the declination, or distance which the sun hath, from the line, as in the tables following is contained, therefore to know the year that you are in, if it be a leap year, or the first, second, or third after the leap year, look over the two rules of the discourses following, for in them plainly is showed, by reckoning the year of our L●●be, a thousand five hundredth forty five in the first house of the which is the first year, and so successively in every year one house, & the house being ended of the last rule, return to the beginning, and so this account is for ever.  

A rule to know the leap year.  
1545. ☜ 1. 2. 3. B 1. 2. 3. B 1. 2. 3. B 1. 2. 3. B 1. 2. 3. B 1. 2. 3. B 1. 2. 3. B.  
When you will know if the year be a leap year, or not without looking in the book, look in the year of the birth of our Lord, & leave the thousand five hundredth, the rest divide in the midst, and when every half were of even number in payers or cupples it is the leap year.   

The tables of the distance or declination which the Sun maketh from the equinoctial line every day of the four years, aswell towards the part of the north as towards the south.  


¶ The declination of the Sun.  
The first year.  januarie. February. March. days Degrees. Minutes. days Degrees. Minutes. days Degrees. Minutes. 1 xxi ●i 1 xiii iviii 1 iii xxxix 2 xxi xl● 2 xii● xxxviii. 2 ●i xv 3 xxi xxxi 3 xiii xviii. 3 two iii 4 xxi xx 4 x● lviii 4 two xxviii 5 xxi ix 5 xii xxxvii 5 two iiii 6 xx lviii 6 xii xuj 6 i xli 7 xx xiv 7 xi lv 7 i xvii 8 xx xxxiii 8 xi xxxiiii 8 0 liii 9 xx xxi 9 xi xii 9 0 xxx 10 xx viii 10 x ●i 10 0 vi 11 x●x lv 11 x xxix 11 0 xviii 12 x●x xli 12 x seven 12 0 xiii 13 x●x xxvii 13 ix x●vii 13 i v 14 x●x xiii 14 ix ●●iii 14 i xxix 15 xviii lviii 15 ix  15 i lii 16 xviii xlii 16 viii xxxviii 16 two xuj 17 xviii xxvii 17 viii xv 17 two xl 18 xviii xi 18 seven 〈◊〉 18 iii iii 19 xvii liv 19 seven xxx 19 iii xxvi 20 xv●i xxxviii 20 seven seven 20 iii xlix 21 xvii ●x●i 21 vi xliiii 21 iiii xii 22 xvii v 22 vi xxi 22 iiii xxxv 23 xuj xlv●i 23 v lviii 23 iiii lviii 24 xuj xxix 24 v xxxv 24 v xxi 25 xuj xi 25 v xi 25 v xliiii 26 xv liii 26 iiii xlviii 26 vi vi 27 xv xxxv 27 iiii xxiiii 27 vi xxix 28 xv xuj 28 iiii ● 28 vi liii 29 xiiii lvi    29 seven xv 30 xiiii xxxv●i    30 seven xxxvii 31 xiiii xvii●    31 seven lix  

¶ The declination of the Sun.  
The first year.  April. May. june. days Degrees. Minutes. days Degrees. Minutes. days Degrees. Minutes. 1 viii xxi 1 xvii 14 1 23 ● 2 viii xliii 2 xviii ● 2 23 13 3 ix v 3 xviii 24 3 23 17 4 ix xxvi 4 xviii 39 4 23 21 5 ix xlviii 5 xviii 54 5 23 24 6 x ix 6 nineteen 8 6 23 26 7 x xxx 7 x●x 21 7 23 28 8 x lii 8 nineteen 35 8 23 30 9 xi xii 9 nineteen 47 9 23 31 10 xi xxxiii 10 xx 0 10 23 32 11 xi liii 11 xx 13 11 23 33 12 xii xiiii 12 xx 24 12 23 33 13 xii xxxiii 13 xx 36 13 23 33 14 xii liii 14 xx 47 14 23 32 15 xiii xiii 15 xx 59 15 23 31 16 xiii xxxii 16 xxi 10 16 23 29 17 xiii li 17 xxi 20 17 23 27 18 xiiii x 18 xxi 30 18 23 25 19 xiiii xxix 19 xxi 40 19 23 22 20 xiiii xlvii 20 xxi 49 20 23 18 21 xv vi 21 xxi 57 21 23 15 22 xv xxiiii 22 xxii 6 22 23 11 23 xv xlii 23 xxii 14 23 23 6 24 xv lix 24 xxii 〈◊〉 24 23 2 25 xuj xuj 25 xxii 29 25 22 ●7 26 xuj xxxiii 26 xxii 36 26 22 51 27 xuj l 27 xxii 42 27 22 45 28 xvii seven 28 xxii 49 28 22 39 29 xvi● xxiii 29 xxii 58 29 22 32 30 xvi● xxxviii 30 xxii 0 30 22 25    31 xxiii 4     

¶ The declination of the Sun.  
The first year.  julie. August. September. days Degrees. Minutes. days Degrees. Minutes. days Degrees. Minutes 1 xxii xvii 1 xv xxxii 1 iiii xivi 2 xxii i● 2 xv xiiii 2 iiii xxiii 3 xxii i 3 xiiii ivi 3 iiii 0 4 xxi two 4 xiiii xxxvii 4 iii xxxvii 5 xxi xliiii 5 xiiii nineteen 5 iii xiiii 6 xxi xxxiiii 6 xiii 0 6 two li 7 xxi xxiiii 7 xiii xli 7 two xxviii 8 xxi xilii 8 xiii xxi 8 two iiii 9 xxi iii 9 xiii two 9 i xl 10 xx 〈◊〉 10 xii xliii 10 i xvii 11 xx xli 11 xii xxii 11 0 liv 12 xx xxix 12 xii iii 12 0 xxx 13 xx xviii 13 xi xliii 13 0 vi 14 xx vi 14 xi xxii 14 0 xviii 15 nineteen li●i 15 xi ● 15 0 xli 16 nineteen xl 16 x xl 16 i v 17 nineteen xxvii 17 x nineteen 17 i xxviii 18 nineteen xiii 18 ix lvii 18 i lii 19 xviii ●ix 19 ix xxxvi 19 two xuj 20 xviii xlv 20 ix xv 20 two xl 21 xxviii xxx 21 viii liii 21 iii iii 22 xviii xv 22 viii xxxii 22 iii xxvi 23 xviii 00 23 viii ix 23 iii l 24 xvii xliiii 24 seven xlvii 24 iiii xiii 25 xv●i xxix 25 seven xxv 25 iiii xxxvi 26 xvii xliii 26 seven iii 26 v 0 27 xuj ●vi 27 vi xli 27 v xxiii 28 xuj xl 28 vi xvii 28 v xlvii 29 xuj xxiii 29 v lv 29 vi ix 30 xuj vi 30 v xxxii 30 vi xxxiii 31 xv xlix 31 v ix     

¶ The declination of the Sun.  
The first year.  October. November. December. days Degrees. Minutes. days Degrees. Minutes. days Degrees. Minutes 1 vi i've 1 xvii 29 1 23 7 2 seven nineteen 2 xvii 45 2 23 11 3 seven xli 3 xviii 2 3 23 16 4 viii iiii 4 xviii 18 4 23 20 5 viii xxvii 5 xviii 33 5 23 23 6 viii xlix 6 xviii 49 6 23 26 7 ix xi 7 nineteen 5 7 23 28 8 ix xxxiii 8 nineteen 19 8 23 30 9 ix lv 9 nineteen 33 9 23 32 10 x xvii 10 nineteen 47 10 23 33 11 x xxxix 11 xx 1 11 23 33 12 xi ● 12 xx 14 12 23 33 13 xi xx●ii 13 xx 20 13 23 32 14 xi xliiii 14 xx 38 14 23 31 15 xii v 15 xx 51 15 23 30 16 xii xxvi 16 xxi 3 16 23 28 17 xii xlvi 17 xxi 14 17 23 26 18 xiii seven 18 xxi 25 18 23 23 19 xiii xxvii 19 xxi 36 19 23 19 20 xiii xlvii 20 xxi 46 20 23 15 21 xiiii seven 21 xxi 5● 21 23 11 22 xiiii xxvii 22 xxii 4 22 23 6 23 xiiii xivi 23 xxii 13 23 23 1 24 xv v 24 xxii 21 24 22 56 25 xv xxiiii 25 xxii 29 25 22 50 26 xv xliii 26 xx●i 36 26 22 4● 27 xuj i 27 xxii 44 27 22 35 28 xuj xi● 28 xxii 51 28 22 28 29 xuj xxxvii 29 xxii 56 29 22 20 30 xuj lv 30 xxiii 1 30 22 12 31 xvii xiii    31 22 3  

¶ The declination of the Sun.  
The second year.  januarie. February. March. days Degrees. Minutes. days Degrees. Minutes. days Degrees. Minutes. 1 xxi liv 1 xiiii iiii 1 iii xliiii 2 xxi xliiii 2 xiii xliii 2 iii xxi 3 xxi xxxiii 3 xiii xxiii 3 two lviii 4 xxi xxiiii 4 xiii iii 4 two xxxiiii 5 xxi xiii 5 xii xlii 5 two x 6 xxi i 6 xii xxii 6 i xlvi 7 xx xlix 7 xii i 7 i xxiii 8 xx xxxvii 8 xi xl 8 0 lix 9 xx xxiiii 9 xi xviii 9 0 xxxv 10 xx xii 10 x lvii 10 0 xii 11 nineteen lviii 11 x xxxv 11 0 xii 12 nineteen xliiii 12 x xiii 12 0 xxxvi 13 nineteen xxxi 13 ix li 13 0 lix 14 nineteen xvii 14 ix xxix 14 i xxiii 15 nineteen two 15 ix seven 15 i xlvi 16 xviii xlvii 16 viii xiv 16 two x 17 xviii xxxi 17 viii xxii 17 two xxxiiii 18 xxviii xv 18 seven lix 18 two lvii 19 xvii lix 19 seven xxxvii 19 iii xx 20 xvii xlii 20 seven xiiii 20 iii xliii 21 xvii xxvi 21 vi li 21 iiii seven 22 xvii ix 22 vi xxvii 22 iiii xxx 23 xuj lii 23 vi iiii 23 iiii liii 24 xuj xxxiiii 24 v xli 24 v xv 25 xuj xuj 25 v xviii 25 v xxxviii 26 xv lviii 26 iiii liv 26 vi i 27 xv xxxvii 27 iiii xxxi 27 vi xxiiii 28 xv xxi 28 iiii viii 28 vi xlvii 29 xv two    29 seven x 30 xiiii xliii    30 seven xxxii 31 xiiii xxiii    31 seven liii  

¶ The declination of the Sun.  
The second year.  April. May. june. days Degrees. Minute's Days Degrees. Minutes. Daye● Degrees. Minutes. 1 viii xuj 1 xvii x●x 1 23 8 2 viii xxxviii 2 xviii vi 2 23 12 3 viii lix 3 xviii xx 3 23 16 4 ix xxi 4 xviii xxxv 4 23 20 5 ix xlii 5 xviii l 5 23 23 6 x iiii 6 nineteen iiii 6 23 26 7 x xxv 7 nineteen xviii 7 23 28 8 x xlvi 8 nineteen xxxi 8 23 29 9 xi seven 9 nineteen xliiii 9 23 31 10 xi xxvii 10 nineteen lvii 10 23 32 11 xi xlviii 11 xx x 11 23 33 12 xii x 12 xx xxii 12 23 33 13 xii xxviii 13 xx xxxiii 13 23 33 14 xii xlviii 14 xx xliiii 14 23 32 15 xiii viii 15 xx lvi 15 23 31 16 xiii xxvii 16 xxi seven 16 23 29 17 xiii xlvi 17 xxi xviii 17 23 27 18 xiiii vi 18 xxi xxviii 18 23 25 19 xiiii xxv 19 xxi 37 19 23 23 20 xiiii xiiii 20 xxi 46 20 23 19 21 xv ● 21 xxi 55 21 23 16 22 xv nineteen 22 xxii 4 22 23 12 23 xv xxxvii 23 xxii 12 23 23 7 24 xv lv 24 xxii 20 24 23 3 25 xuj xii 25 xxii 27 25 23 58 26 xuj xxix 26 xxii 34 26 22 53 27 xuj xiv 27 xxii 41 27 22 47 28 xvii iii 28 xxii 48 28 22 40 29 xvii nineteen 29 xxii 52 29 22 33 30 xvii xxxiiii 30 xxii 58 30 22 27    31 xxiii 3     

¶ The declination of the Sun.  
The second year.  julie. August. September. days Degrees. Minutes. days Degrees. Minutes. days Degrees. Minutes. 1 xxii nineteen 1 xv xxxvi 1 iiii lii 2 xxii xi 2 xv xviii 2 iiii xxix 3 xxii iii 3 xv 0 3 iiii vi 4 xxi liv 4 xiiii xlii 4 iii xliii 5 xxi xlv 5 xiiii xxiiii 5 iii nineteen 6 xxi xxxvi 6 xiiii v 6 two lvi 7 xxi xxvii 7 xiii xiv 7 two xxxiii 8 xxi xvii 8 xiii xxvi 8 two x 9 xxi vi 9 xiii seven 9 i xlvi 10 xx lv 10 xii xlvii 10 i xxiii 11 xx xliiii 11 xii xxvii 11 0 lix 12 xx xxxii 12 xii viii 12 0 xxxv 13 xx xx 13 xi xlviii 13 0 xii 14 xx ix 14 xi xxvii 14 0 xii 15 nineteen lvi 15 xi vi 15 0 xxxv 16 nineteen xliii 16 x xlv 16 0 lix 17 nineteen xxx 17 x xxiiii 17 i xxiii 18 nineteen xvii 18 x iii 18 i xlvi 19 nineteen iii 19 ix xii 19 two x 20 xviii xlix 20 ix xx 20 two xxxiiii 21 xviii xxxiiii 21 viii iix 21 two lvii 22 xviii nineteen 22 viii xxxvii 22 iii xx 23 xviii liii 23 viii xv 23 iii xliiii 24 xvii xlviii 24 seven lii 24 iiii viii 25 xvii xxxiii 25 seven xxxi 25 iiii xxxi 26 xvii xvii 26 seven ix 26 iiii liv 27 xvii i 27 vi xlvi 27 v xvii 28 xuj xliiii 28 vi xxiii 28 v xli 29 xuj ●xviii 29 vi 0 29 vi iiii 30 xuj xi 30 v xxxviii 30 vi xxvii 31 xv liv 31 v xv     

¶ The declination of the Sun.  
The second year.  October. November. December. days Degrees. Minutes. days Degrees. Minutes. days Degrees. Minutes. 1 vi li 1 xvii 25 1 23 5 2 seven xiiii 2 xvii 41 2 23 10 3 seven xxxvi 3 xvii 58 3 23 15 4 seven lviii 4 xviii 14 4 23 19 5 viii xxi 5 xviii 29 5 23 22 6 viii xliiii 6 xviii 46 6 23 25 7 ix vi 7 nineteen 1 7 23 27 8 ix xxviii 8 nineteen 15 8 23 29 9 ix l 9 nineteen 29 9 23 31 10 x xii 10 nineteen 43 10 23 32 11 x xxxiiii 11 nineteen 57 11 23 33 12 x lvi 12 xx 21 12 23 33 13 xi xvii 13 xx 23 13 23 33 14 xi xxxix 14 xx 36 14 23 32 15 xii 0 15 xx 48 15 23 30 16 xii xxi 16 xxi 0 16 23 28 17 xii xli 17 xxi 12 17 23 26 18 xiii two 18 xxi 23 18 23 23 19 xiii xxii 19 xxi 33 19 23 20 20 xiii xlii 20 xxi 43 20 23 16 21 xiiii two 21 xxi 53 21 23 12 22 xiiii xxii 22 xxii 2 22 23 7 23 xiiii xlii 23 xxii 11 23 23 2 24 xv i 24 xxii 19 24 22 57 25 xv xx 25 xxii 28 25 22 51 26 xv xxxix 26 xxii 35 26 22 44 27 xv lvii 27 xxii 42 27 22 37 28 xuj xv 28 xxii 49 28 22 30 29 xuj xxxiii 29 xxii 55 29 22 22 30 xuj l 30 xxiii 0 30 22 14 31 xvii viii    31 22 5  

¶ The declination of the Sun.  
The third year.  januarie. February. March. days Degrees. Minutes. days Degrees. Minutes. days Degrees. Minutes. 1 xxi lvi 1 xiiii viii 1 iii l 2 xxi xlvi 2 xiii xlviii 2 iii xxvi 3 xxi xxxvi 3 xiii xxviii 3 iii iii 4 xxi xxvi 4 xiii viii 4 two xl 5 xxi xv 5 xii xlvii 5 two xuj 6 xxi iiii 6 xii xxvi 6 i ●●i 7 xx lii 7 xii vi 7 i xxviii 8 xx xxxix 8 xi xlv 8 i v 9 xx xxvii 9 xi xxiii 9 0 xli 10 xx xv 10 xi two 10 0 xvii 11 xx two 11 x xl 11 0 vi 12 nineteen xlviii 12 x xviii 12 0 xxx 13 nineteen xxxiiii 13 ix ivi 13 0 liv 14 nineteen xx 14 ix xxxiiii 14 i xvii 15 nineteen v 15 ix xii 15 i xli 16 xviii l 16 viii l 16 two iiii 17 xviii xxxv 17 viii xxvii 17 two xxviii 18 xviii nineteen 18 viii iiii 18 two lii 19 xviii iii 19 seven 42 19 iii xiiii 20 xvii xlvi 20 seven nineteen 20 iii xxxviii 21 xvii xxx 21 vi lvi 21 iiii i 22 xvii xiii 22 vi xxxiii 22 iiii xxiiii 23 xuj lvi 23 vi x 23 iiii xlvii 24 xuj xxxviii 24 v xlvii 24 v ix 25 xuj xx 25 v xxiii 25 v xxxiii 26 xuj two 26 v 0 26 v lvi 27 xv xliiii 27 iiii xxxvi 27 vi xviii 28 xv xxv 28 iiii xiii 28 vi xli 29 xv vi    29 seven iiii 30 xiiii xlvii    30 seven xxvi 31 xiiii xxviii    31 seven xlviii  

¶ The declination of the Sun.  
The third year.  April. May. june. days Degrees. Minutes. days Degrees. Minutes. days Degrees. Minutes. 1 viii ix 1 xvii 46 1 23 7 2 viii xxxi 2 xviii 2 2 23 11 3 viii liii 3 xviii 17 3 23 15 4 ix xuj 4 xviii 31 4 23 19 5 ix xxxvii 5 xviii 46 5 23 22 6 ix lviii 6 nineteen l 6 23 25 7 x xx 7 nineteen 14 7 23 27 8 x xii 8 nineteen 28 8 23 29 9 xi two 9 nineteen 41 9 23 31 10 xi xxii 10 nineteen 54 10 23 32 11 xi xliii 11 xx 7 11 23 33 12 xii iiii 12 xx 19 12 23 33 13 xii xxiii 13 xx 30 13 23 33 14 xii xliii 14 xx 42 14 23 32 15 xiii iii 15 xx 53 15 23 31 16 xiii xxii 16 xxi 4 16 23 30 17 xiii xlii 17 xxi 15 17 23 28 18 xiiii i 18 xxi 25 18 23 26 19 xiiii xx 19 xxi 35 19 23 23 20 xiiii xxxviii 20 xxi 44 20 23 20 21 xiiii lvii 21 xxi 53 21 23 17 22 xv xv 22 xxii 2 ●● 23 13 23 xv xxxiii 23 xxii 10 23 23 9 24 xv l 24 xxii 18 24 23 4 25 xuj viii 25 xxii 25 25 22 59 26 xuj xxv 26 xxii 32 26 22 54 27 xuj xli 27 xxii 39 27 22 48 28 xuj lviii 28 xxii 46 28 22 42 29 xvii xv 29 xxii 52 29 22 35 30 xvii xxx 30 xxii 57 30 22 28    31 xxiii 2     

¶ The declination of the Sun.  
The third year.  julie. August. September. days Degrees. Minutes. days Degrees. Minutes. days Degrees. Minutes. 1 xxii xxi 1 xv xl 1 iiii lvii 2 xxii xiii 2 xv xxiii 2 iiii xxxiiii 3 xxii v 3 xv iiii 3 iiii xii 4 xxi ivi 4 xiiii xlvi 4 iii xlix 5 xxi xlviii 5 xiiii xxviii 5 iii xxv 6 xxi xxxix 6 xiiii ix 6 iii two 7 xxi xxix 7 xiii l 7 two 39 8 xxi nineteen 8 xiii xxxi 8 two xuj 9 xxi ix 9 xiii xii 9 i lii 10 xx lviii 10 xii lii 10 i xxviii 11 xx xlvi 11 xii xxxii 11 i v 12 xx xxxv 12 xii 13 12 0 xli 13 xx xxiii 13 xi lii 13 0 xviii 14 xx ix 14 xi 32 14 0 vi 15 nineteen lix 15 xi xi 15 0 30 16 nineteen xlvi 16 x l 16 0 liii 17 nineteen xxxiii 17 x xxix 17 i xvii 18 nineteen xx 18 x viii 18 i xl 19 nineteen seven 19 ix xlvii 19 two iiil 20 xviii lii 20 ix xxv 20 two xxviii 21 xviii xxxviii 21 ix iiii 21 two lii 22 xviii xxiii 22 viii 42 22 iii xv 23 xviii viii 23 viii xx 23 iii xxxix 24 xvii lii 24 seven lviii 24 iiii two 25 xvii xxxvii 25 seven xxxvi 25 iiii xxv 26 xvii xxi 26 seven xiiii 26 iiii xlix 27 xvii v 27 vi lii 27 v xi 28 xuj xlviii 28 vi xxix 28 v xxxv 29 xuj xxxii 29 vi vi 29 v lviii 30 xuj xv 30 v xliii 30 vi ●1 31 xv lviii 31 v xxi     

¶ The declination of the Sun.  
The third year.  October. November. December. days Degrees. Minutes. days Degrees. Minutes. days Degrees. Minutes 1 vi xlv 1 xvii 21 1 23 4 2 seven viii 2 xvii 37 2 23 9 3 seven xxxi 3 xvii 54 3 23 13 4 seven liii 4 xviii 10 4 23 17 5 viii xuj 5 xviii 26 5 23 22 6 viii xxxix 6 xviii 42 6 23 25 7 ix i 7 xviii 57 7 23 27 8 ix xxiii 8 nineteen 12 8 23 29 9 ix xlv 9 nineteen 26 9 23 31 10 x seven 10 nineteen 40 10 23 32 11 x xxix 11 nineteen 54 11 23 33 12 x li 12 xx 7 12 23 33 13 xi xii 13 xx 20 13 23 33 14 xi xxxiiii 14 xx 33 14 23 32 15 xi lv 15 xx 45 15 23 31 16 xii xuj 16 xx 57 16 23 29 17 xii xxxvi 17 xxi 9 17 23 27 18 xii lvii 18 xxi 20 18 23 24 19 xiii xvii 19 xxi 31 19 23 21 20 xiii xxxvii 20 xxi 41 20 23 17 21 xiii lvii 21 xxi 50 21 23 13 22 xiiii xvii 22 xxii 0 22 23 8 23 xiiii xxxvii 23 xxii 9 23 23 3 24 xiiii lvi 24 xxii 17 24 22 58 25 xv xv 25 xxii 26 25 22 52 26 xv xxxiiii 26 xxii 33 26 22 46 27 xv lii 27 xxii 40 27 22 39 28 xuj xi 28 xxii 47 28 22 32 29 xuj xxix 29 xxii 53 29 22 24 30 xuj xlvi 30 xxii 59 30 22 16 31 xvii iiii    31 22 7  

¶ The declination of the Sun.  
The leap year.  januarie. February. March. days Degrees. Minutes. days Degrees. Minutes. days Degrees. Minutes 1 xxi lviii 1 xiiii xiii 1 iii xxxii 2 xxi xlix 2 liii liii 2 iii ix 3 xxi xxxix 3 xiii xxxiii 3 two xlvi 4 xxi xxix 4 xiii xiii 4 two xxii 5 xxi xvii 5 xii liii 5 i lviii 6 xxi seven 6 xii 32 6 i xxxiiii 7 xx lv 7 xii xi 7 i x 8 xx xliii 8 xi l 8 0 xlvii 9 xx xxx 9 xi xxix 9 0 xxiii 10 xx xviii 10 xi seven 10 0 i 11 xx v 11 x xlv 11 0 xxiiii 12 nineteen li 12 x xxiii 12 0 xlviii 13 nineteen xxxviii 13 x i 13 i xi 14 nineteen xxiiii 14 ix xxxix 14 i xxxv 15 nineteen ix 15 ix xvii 15 i lix 16 xviii liv 16 viii lv 16 two xxii 17 xviii xxxix 17 viii xxxiii 17 two xlvi 18 xviii xxiii 18 viii x 18 iii ix 19 xviii seven 19 seven xlvii 19 iii xxxii 20 xvii l 20 seven xxv 20 iii lv 21 xvii xxxiiii 21 seven two 21 iiii xviii 22 xvii xviii 22 vi xxxix 22 iiii xlii 23 xvii i 23 vi xv 23 v iiii 24 xuj xlix 24 v lii 24 v xxvii 25 xuj xxv 25 v 29 25 v l 26 xuj seven 26 v v 26 vi xiii 27 xv xlix 27 iiii xliii 27 vi xxxvi 28 xv xxx 28 iiii nineteen 28 vi iviii 29 xv i 29 iii lvi 29 seven xxi 30 xiiii lii    30 seven xliii 31 xiiii xxxiii    31 viii v  

¶ The declination of the Sun.  
The leap year.  April. May. june. days Degrees. Minutes. days Degrees. Minutes. days Degrees. Minutes. 1 viii xxvii 1 xvii 58 1 23 10 2 viii xlix 2 xviii 13 2 23 14 3 ix x 3 xviii 28 3 23 18 4 ix xxxii 4 xviii 43 4 23 22 5 ix liii 5 xviii 58 5 23 25 6 x xv 6 nineteen 11 6 23 27 7 x xxxvii 7 nineteen 25 7 23 29 8 x lviii 8 nineteen 38 8 23 31 9 xi xviii 9 nineteen 51 9 23 32 10 xi xxxix 10 xx 4 10 23 33 11 xii 0 11 xx 16 11 23 33 12 xii xx 12 xx 28 12 23 33 13 xii xxxix 13 xx 39 13 23 33 14 xii lix 14 xx 50 14 23 32 15 xiii nineteen 15 xxi 2 15 23 30 16 xiii xxxviii 16 xxi 13 16 23 28 17 xiii lvii 17 xxi 22 17 23 26 18 xiiii xuj 18 xxi 33 18 23 24 19 xiiii xxxv 19 xxi 42 19 23 21 20 xiiii liii 20 xxi 51 20 23 17 21 xv xii 21 xxii 0 21 23 14 22 xv xxx 22 xxii 8 2● 23 10 23 xv xlvii 23 xxii 16 23 23 6 24 xuj iiii 2 xxii 24 24 23 0 25 xuj xxi 25 xxii 31 25 22 35 26 xuj xxxviii 26 xxii 37 26 22 49 27 xuj iv 27 xxii 44 27 22 43 28 xvii xii 28 xxii 50 28 22 37 29 xvii xxvii 29 xxii 56 29 22 30 30 xvii xliii 30 xxiii 1 30 22 23    31 xxiii 6     

¶ The declination of the Sun.  
The leap year.  julie. August. September. days Degrees. Minutes. days Degrees. Minutes. days Degrees. Minutes. 1 xxii xv 1 xv 27 1 iiii xl 2 xxii vil 2 xv ix 2 iiii xvii 3 xxi lviii 3 xiiii l 3 iii liv 4 xxi l 4 xiiii xxxii 4 iii xxxi 5 xxi xii 5 xiiii xiii 5 iii seven 6 xxi xxxi 6 xiii lv 6 two xlv 7 xxi xxi 7 xiii xxxv 7 two xxi 8 xxi xi 8 xiii xbi 8 i lviii 9 xxi 0 9 xii lvi 9 i xxxiiii 10 xx xlix 10 xii xxxvil 10 i x 11 xx xxxviii 11 xii xvii 11 0 xlvii 12 xx xxvi 12 xi lvii 12 0 xxiii 13 xx xiiii 13 xi xxxvii 13 0 0 14 xxi ill 14 xi xuj 14 0 xxiiii 15 nineteen xlix 15 x lv 15 0 xlviii 16 nineteen xxxvi 16 x xxxiiii 16 i xi 17 nineteen xxiii 17 x xiii 17 i xxxv 18 nineteen x 18 ix li 18 i lviii 19 xviii xuj 19 ix xxx 19 two xxii 20 xviii xli 20 ix ix 20 two xlvi 21 xviii xxuli 21 viii xlviii 21 iii ix 22 xviii xi 22 viii xxv 22 iii xxxiii 23 xvii ivi 23 viii iii 23 iii lvi 24 xvii xl 24 seven xli 24 iiii nineteen 25 xvii xxv 25 seven nineteen 25 iiii xliii 26 xvii ix 26 vi lvii 26 v vi 27 xuj lii 27 vi xxxiiii 27 v xxix 28 xuj xxxv 28 vi xi 28 v liii 29 xuj nineteen 29 v xlix 29 vi xuj 30 xuj two 30 v xxvi 30 vi 39 31 xv xliiii 31 v iii     

¶ The declination of the Sun.  
The leap year.  October. November. December. days Degrees. Minutes. days Degrees. Minutes. days Degrees. Minutes. 1 seven two 1 xvii 33 1 23 8 2 seven xxv 2 xvii 50 2 23 12 3 seven xlviiii 3 xviii 7 3 23 17 4 viii x 4 xviii 22 4 23 21 5 viii xxxiii 5 xviii 38 5 23 24 6 viii lv 6 xviii 53 6 23 26 7 ix xxii 7 nineteen 8 7 23 28 8 ix xxxix 8 nineteen 23 8 23 30 9 x i 9 nineteen 37 9 23 32 10 x xxiiii 10 nineteen 50 10 23 33 11 x xlvi 11 xx 4 11 23 33 12 xi seven 12 xx 17 12 23 33 13 xi xxix 13 xx 30 13 23 32 14 xi l 14 xx 42 14 23 31 15 xii xi 15 xx 54 15 23 29 16 xii xxxi 16 xxi 6 16 23 27 17 xii lii 17 xxi 17 17 23 25 18 xiii xii 18 xxi 28 18 23 22 19 xiii xxxii 19 xxi 38 19 23 18 20 xiii liii 20 xxi 48 20 23 14 21 xiiii xiii 21 xxi 57 21 23 10 22 xiiii xxxii 22 xxii 7 22 23 5 23 xiiii lii 23 xxii 15 23 22 59 24 xv xi 24 xxii 23 24 22 54 25 xv xxx 25 xxii 31 25 22 48 26 xv xlviii 26 xxii 38 26 22 41 27 xuj vi 27 xxii 46 27 22 33 28 xuj xxiiii 28 xxii 52 28 22 26 29 xuj xlii 29 xxii 58 29 22 18 30 xvii 0 30 xxiii 3 30 22 9 31 xvii xvii    31 22 0  

¶ The Calendar.  januarie. February. March. 1 a New years day. 1 d  1 d 2 b  2 e Prufication of Ma. 2 e 3 c  3 f  3 f 4 d  4 g  4 g 5 e  5 A Shrove Sunday. 5 A 6 f Twelve day. 6 b  6 b 7 g  7 c  7 c 8 a  8 d  8 ● 9 b  9 e  9 e 10 c  10 f  10 f 11 d  11 g  11 g 12 e  12 A  12 A S. Gregory. 13 f  13 b  13 b S. Leonard. 14 g  14 c  14 c 15 a  15 ●  15 d 16 b  16 e  16 e 17 c  17 f  17 f S. Gabriel archan. 18 d  18 g  18 g 19 e  19 a  19 A  20 f S. Fabian & Seba. 20 b  20 b  21 g  21 c  21 c  22 A S. Uincent martyr. 22 d  22 d  23 b  23 e  23 e  24 c  24 f S. Mathias apost. 24 f  25 d Conuer. of S. Paul. 25 g  25 g Anuntia. of Marie. 26 e  26 A  26 A Easter day. 27 f  27 b  27 b  28 g  28 c  28 c  29 A     29 d  30 b     30 e  31 c     31    

¶ The Calendar.  April. May. june. 1 g  1 b S. Phil. and Jacob. 1 e  2 A  2 c  2   3 b  3 d Innuenci. of the cross. 3 g  4 c  4 e ascension day. 4 A  5 d  5 f  5 b  6 e  6 g  6 c  7 f  7 A  7 d  8 g  8 b  8 e  9 A  9 c  9 f  10 b  10 d  10 g  11 c  11 e  11 A Barnaby apostle. 12 d  12 f  12 b  13 e  13 g  13 c  14 f  14 A Whitsunday. 14 d . 15 g  15 b S. Isidore archbish. of Seville. 15 e  16 A  16 c 16 f  17 b  17 d  17 g  18 c  18 e  18 A  19 d  19 f  19 b  20 e  20 g  20 c  21 f  21 A  21 d  22 g  22 b  22 e  23 A S. George matyre. 23 c  23 f  24 b  24 d  24 g S. John Baptist. 25 c S. Mark evang. 25 e  25 A  26 d  26 f  26 b  27 e  27 g  27 c  28 f  28 A  28 d  29 g  29 b  29 e  30 A  30 c  30 f S. Peter and Paul.    31 d      

¶ The Calendar.  julie. August. September. 1 g  1 c  1 f  2 A  2 d  2 g  3 b  3 e  3 A  4 c  4 f  4 b  5 d  5 g  5 c  6 e  6 A Transfigu. of our Lord 6 d  7 f  7 b  7 e  8 g  8 c  8 f The nativity of our 9 A  9 d  9 g Lady. 10 b  10 e Saint Laurence. 10 A  11 c  11 f  11 b  12 d  12 g S. Clare virgin. 12 c  13 e  13 A  13 d  14 f  14 b  14 e  15 g  15 c Assumption of Ma 15 f  16 A  16 d  16 g  17 b  17 e  17 A  18 c  18 f  18 b  19 d  19 g  19 c  20 e  20 A  20 d  21 f  21 b  21 e  22 g Marie Magdalen. 22 c  22 f S. Matthew apo. 23 A  23 d  23 g  24 b  24 e S. Bartholomewe apostle. 24 A  25 c Saint James. 25 f  25 b  26 d Saint Anne. 26 c  26 e  27 e Saint Christopher. 27 A  27 d  28 f  28 b S. Austin. 28 e  29 g  29 c The cutting off of saint John Baptist 29 f S. Michael archan 30 A  30 d  30 g S. Jerome. 31 b  31 e head.     

¶ The Calendar.  October. November. December. 1 A  1 d All Saintes day. 1 f  2 b  2 e The remembrance 2 g  3 c  3 f of them that are. 3 A  4 d  4 g dead. 4 b Saint Barbara. 5 e  5 A  5 c  6 f  6 b  6 d S. Nicholas bisho. 7 g  7 c  7 e  8 A  8 d  8 f Conception of Ma. 9 b  9 e  9 g  10 c  10 f  10 A  11 d  11 g Saint Martin. 11 b  12 e  12 A  12 c  13 f  13 b  13 d S. Luce virgin. 14 g  14 c  14 e  15 A  15 d  15 f  16 b  16 e  16 g  17 c  17 f  17 A  18 d S. Luke evangelist. 18 g  18 b  19 e  19 A  19 c  20 f  20 b  20 d  21 g The xi. M. virgins. 21 c  21 e S. Thomas apost. 22 A  22 d  22 f  23 b  23 e Saint Clement. 23 g  24 c  24 f  24 A  25 d  25 g Saint Katherine. 25 b  26 e  26 A  26 c Christmas day. 27 f  27 b  27 d S. Steven martyr. 28 g S. Simon & Jude. 28 c  28 e S. John evangelist. 29 A  29 d  29 f Holy Innocentes. 30 b  30 e S. Andrew apostle. 30 g  31 c     31 A     

¶ A Rule to know the Dominical letter every year.  
FOr to know in what day of the week is every feast of the year. It is necessary you know what letter it is that serveth for sunday. This is to be known by the rules of the letters under written, in the which, the first letter which is D. serveth for the Dominical letter, this year of 1545 and so successively in every year one letter serveth, and the two rules being ended, return again to the beginning, and this is for ever. And it is to be noted that in the leap years are two Dominical letters. The letter above being uppermost serveth from the first day of Januarie, unto the xxv of February, and the other unto the end of the year. 1545. D C B. A F E D. C A G F. E C B A. G B D G E D C B G F E. D B A G. F F A C E    

The eleventh Chapter, wherein is declared howeby the Calendar before written, a man may know the month, and the day wherein he is.  
THe Philosopher saith, that the art doth emitate nature as much as he may, Likewise the said art many times helpeth the defects of nature, this is proved, wherein we see that a man which by nature doth want his sight, the art doth help and remedy his want, that is, by looking on a pair of spectacles, whereby in such sort, the sight is gathered together, and is cause that he seethe, the which he doth not without them for that it is scattered abroad. The self same which is said of the sight, may be said of the memory, that many times it lacketh in men, but it is certain that in some it cometh by nature, but in others by their own uncarefulness that they forget themselves so much, that in things which standeth them much upon, they take no heed. And concerning this I do remember as we came sailing in a ship, nienteene men, which were seven passengers, and twelve mariners, and having been many days at the sea, because the weather was contrary, there happened a cause whereby it was convenient that the purser should writ it down in his book for to give reason thereof when time should serve, and he with the other that were there, knew not what day of the month it was, nor there was any that had it in his remembrance, nor knew what day was the first day of the month, until I told him, nor any book in the ship to look in whereby it might be known. And this being brought for my purpose, I say that here before hath been declared. that one of the things which aught to be seen and known, for to take the altitude of the sun, is the declination or distance which it hath that day from the equinoctial line, for not knowing the declination how much it is, the said altitude can not be known, whereby it is necessary that the Pilot or any other person which shall take the said altitude should know in what month he is in, and how many days of the month it is, without having any error or want therein. And because of that as I have spoken of before, which happened, it may happen the like in others, or likewise if he that taketh the altitude be alone, or with little company, and do not remember the reckoning aforesaid, for this it seemeth to me to be a convenient thing to help the memory by putting here the calendar before written, whereby may be kept a certain remembrance & a reckoning of the month and day wherein he is, by looking what day every month beginneth, without any need to ask it of any. And because such as do go by some ways which hath not much used it, are accustomed to set marks to know it the better. So in this Calendar, for the better knowledge thereof, I have put marks which are the saints days. Therefore I say to know what day in the week is every holy day of them aforesaid. The letters must be seen which standeth before those days of every month, & see what letter of these serveth in this year for sunday, and is called the the Dominical letter, which shall be known by the rule afore written, and being known, to stay in it which is sunday, & in another which is next monday, & in the other tewsday. And so all the seven days of the week named by the seven letters ABCDEFG. And by reckoning in this manner, see what day is the letter that is next to the holy day, and in that year that is the proper day of such a feast, the leap years as before hath been declared, have two dominical letters, the one serveth unto the xxv day of February, and the other unto the end of the year.   
The end of the fourth book.   

¶ The fifth book of the Altitude of the Poles.  

The first Chapter, what thing a pole is, and how between the two poles the roundness of the world is divided.  
These Zonas the first is called Septentrional, the second solstitial, the third Equinoctial, the fourth female, the fifth austral. And it is to be noted, that these two poles▪ the one is superior, and the other is inferior. And according to Albertus the great in the second book of the heaven, & the world, the first treaty, the six chapter, they are to be considered in this manner, in as much as toucheth the moving of the circle of the fired stars.  
The pole Antarctic is the superior, and the pole Arctic is the inferior, and according to the circle of the Planets, the pole Arctic is the Superior, and the Antarctic the inferior, and it is to be understood that such as devil in the Equinoctial line, only the place of the one pole they see, and so we do only see in the heaven, the place where we imagine the one pole to be: & this is called Arctics, likewise Septeritrional, or Boreal: It is called Arctic, because it is near to the image called Artery. It is called Septentrional, by the seven stars of the Vrsa minor, which doth move round about the said pole. It is called boreal by the wind Boreas, which we call North. The other pole is called Antartico, which is against, as though it were put contrary or opposite to the Arctic, and austral, because from that part cometh the wind called Austro: it is also called Meridional, because it is towards the part of the midst of the day, it is to be understood, that it standeth towards the part of the midst of the day to such as do devil towards the North, out of the tropic of Cancer, because in all times of the year at the midst of the day, we have the Sun towards that part▪   

The second chapter, how the altitude of o● the pole Arctic is to be taken, and of the effect wherefore he is taken.  
THe P●●ot or an● other person that will take the Altitude of the pole arctic, which commonly we call the Altitude of the North, let him take his Ballestila or quadrant, or the instrument that he hath most used, let him take the altitude of the said star, as precisely as he can, and for the better taking thereof, let him put himself near to the mast of the 〈◊〉, luthere shall 〈◊〉 feel lead●● all the moving a● the 〈◊〉. And it in to 〈◊〉, that the altitude of the pole to token, to know the distance of the degrees, that are 〈◊〉 hori●d unto the p●le, 〈◊〉 there degrees being known, is known how many degrees are from him which taketh the altitude unto the Equinoctial line, and it is known in this manner. The pole arctic, or the antarctic either of them, is distant from the Equinoctial line, ninety degrees, therefore let him look that taketh the altitude how many degrees he hath raised the pole upon the Horizon, & he shall understand, that the self-same degrees are from the place where he is unto the Equinoctial line, so that if he be under the Equinoctial, he shall not take altitude of any of the poles, because he shall have them in the Horizon. But being come forth of the Equinoctial, how much he is distant from her, so much he shall have the one pole raised up, and the other put down, so that how many degrees he is distant from the line, in so many he shall take the altitude of that pole, towards ●he part where he is. For so many, he hath raised upon him his Herizon, In such sort, that if he took the altitude of the pole in ten degrees, the said ten degrees he is distant of the Equinoctial, & if in twenty, twenty, and so the rest. In such sort, that whensoever the altitude of the pole is taken, looking by her the degrees that are raised upon the Horizon, the self same he which taketh the altitude is distant from the Equinoctial line.   

The third Chapter, how the reckoning which is taken of the height of the pole arctic or North is, to be understood.  
IT hath been declared in the chapter before this, that how many degrees are taken of the altitude of the pole, so many is he which taketh her distant of the Equinoctial line, because for this effect to know the distance of the said line, the said altitude is taken, therefore in this present, I will speak how this altitude which is taken of the pole is to be understood. Of the which it is to be understood, that when a man is in the Equinoctial line, he hath both poles in the Horizon, as before hath been declared, and by how much he is going from the said line, and coming towards the pole arctic or North pole, which is this that we speak of, by so much the said pole goeth rising upon his Horizon, so that if the man be distant of the line twenty degrees, the same twenty he hath the pole, above his Horizon. Of this is to be noted, that the degrees which are taken of the altitude of the pole, are not to be understood of those which are from him, that taketh the altitude unto to the pole itself: But it is to be understood, that those have gone raising up the said pole above his Horizon. For because like as in the altitude of the sun, is not noted how much the sun is raised above him that taketh his altitude, but it is to be seen, how much he is raised above the Horizon, which is seen by these degrees, which are taken in the Astrolabio, so that in the altitude of the North, it is not to be looked, how much the pole is risen upon him, which taketh his altitude, but that which he is risen above his Horizon, in such sort, that to know the height of the pole, there is no account or reckoning, to be taken between him that taketh it and the pole, but the reckoning is between the pole and the Horizon. For if the man should keep reckoning with the pole, it would be said in this manner, from the Equinoctial line, to the pole, are nienty degrees, therefore if he which taketh the altitude is twenty degrees, distant from the Equinoctial line: than it should be threescore and ten degrees from the pole, and would say, seeing I am in seventy degrees of altitude, I am so many from the pole.  
This aught not to be understood so, for it would be a very great error, so much that being in twenty degrees of altitude, he that should so make his reckoning, should make that he were in seventy. But let the reckoning be kept, as aforesaid, which is, that how many degrees I do take of altitude with my Ballestisa, or other instrument: these have I raised the pole, not above me, but above my Horizon, & the self same degrees am I distant of the Equinoctial line.   

The fourth Chapter, of the North star, and of the guards of his moving.  
THE North star being very well seen and known of all the sailors, is the first of the 7. stars, which that Vrsa minor doth set in order, and commonly he is called Bozina. These 7. stars do seem clear & bright, & three of them are like to a half circle, & the other 4. like to a quadrangle in this manner. The seven stars do always move round about the pole, describing their circle's from the East into the West, and always in one self distance one with the other, and in every four and twenty hours they give a turn about the pole. But as the North star is more near the pole, than any of the others, his turn is lesser and done with more ●eysute, than any of the other stars: because how much more every star goeth farther of from the pole, so much the greater circumserence he maketh, and so much the hastier he moveth. Therefore I say, that by this statre of the North is known, how much the altitude is, which the pole hath upon the Horizon: In such sort, that although the pole is seen, yet by this star is known the place where the pole is, the which is known by an other star of the same seven, the most shining. Of the two called guards, which are in the month of the Bozina, which star is called the formest guard, and also he is called the horologial star, because he goeth always like to a wheel of a clock, giving to understand in all times of the year, what hour of the night it is, by that reckoning, that is called the midst of April, midnight in the head. And note ye, that between the north star, and the guards, is always the pole, in such sort, that when the guards are above the pole, the north star is under, and so contrary, seeing by the course or place where the guards are, is known to what part of the pole, and in what distance of him, the said star is.   

The fifth Chapter, how that according to the course wherein the guards are, is known how many degrees the north star is under or above the pole.  
IT hath been declared in the chapter going before, that the north star moveth himself round about the pole, and that likewise the two stars called the guards, do make their moving round about the said star, and of the pole. By the which it is necessary to know, in what course the guards are in, with the said star, because with this, will be known by the rules here under written, in what course the said star is in with the pole, as also how many degrees he is under or above him: for the which knowledge, the rules following are so be looked on, in the which is to be noted that besides the rules of the principal winds, you shall find rules for the halfa parts, because the said altitude more easily at any hour of the night may be taken.  
The which rules go set with their figures in such sort, that in every course that the guards are in, may be known likewise in what course the said north star is in, it is ordained in the manner following.  

The guards in the east, the most fore guard is with the north star, east and west, and the said star a degree and a half under the pole.  
The guards in the east North-east, the north star is three degrees under the pole.  
The guards in the North-east, the one guard is with the other east and west, and the north star is three degrees and a half under the pole.  
The guards in the north North-east, the north star is three degrees and a half under the pole.  
The guards in the north, the foremost guard is with the north star north and south, and the said star 〈◊〉 three degrees under the pole.  
The guards in the north north-west ●est, the north star is two degrees 〈◊〉 ●●r the pole.  
The guards in the northwest, the one guard is with the other north & south, the said star is half a degree under the pole.  
The guards in the west northwest, the north star is one degree above the pole.  
The guards in the west, and foremost guard is with the north star east and west, and the said star is a degree and a half above the pole.  
The guards in the West south-west, the North star is three degrees above the pole.  
The guards in the south-west, the one guard is by the other East and West, and the North star is three degrees and a half above the pole.  
The guards in the South south-west, the North star is three degrees above the pole.  
The guards in the South, the North star is with the foremost guard, North and South, and the said star is three degrees above the pole.  
The guards in the South, Southeast, the North star is two degrees above the pole.  
The guards in the Southeast, the one guard is by the other North, and South, and the North star is half a degree above the pole.  
The guards in the East Southeast, the north star is half a degree under the pole.    

The sixth Chapter, how the rules of the altitude of the North star aught to be applied, and how they aught to be put to, or taken away, according to the place where the guards are.  
THerefore when you take the altitude of the pole, look in what place the guards are, & by them you shall understand if the north star be under or above the pole, as it is said. And mark, if the star be under, you shall join with the altitude that you take, those degrees that are under and altogether so much is your altitude: and if the star be above the pole, you shall take away from the altitude that you took, the degrees that the star is above, & that which remaineth, is the altitude wherein you are.  

Example.  
I say the guards being in the North-east, you took xl. degrees of altitude; join with these xl. three degrees and a half, that the star is under the pole▪ which doth amount to forty three degrees and a half, this is your altitude▪ and if the guards be in the south-west, take a way of the forty degrees, three and a half that the star is over the pole, there doth rest thirty six & a half and this is the altitude wherein you 〈◊〉 to that when the star is under the poles you shall join with the altitude those degrees that he is under, and when he is above, you shall take away the degrees that he is above, & so you shall make your account just, and you shall know the place where you are.    

The seventh Chapter, wherein be declared certain doubts that in this moving of the north star may be had.  
IN the third chapter of this fifth book hath been said, that the stars which are near to the pole, do move themselves more slowly than they that are far off, & it seemeth that of this may be a doubt, because that every thing which moveth their parts in rule, do move so equally, that one moveth not more siow, nor the other more hasty. And as all the heaven doth move equally, as the sight both manifest it, and so is the beginning of Astronomy, that the moving of every day is in rule, whereby it aught to be said, that the parts of heaven do move equally, & not the one part more slowly than the other Likewise this is proved because that one self intelligence, moveth all the circle and all his parts seeing that the parts nearest to the pole, are less than those which are far off, therefore the said intelligence hath a greater proportion upon them, and of the great proportion cometh greater swiftness, whereby may be said, that the parts which are most near to the pole, do move more speedily or with m●● hast then the others.  
Item, in the fifth chapter of the first book hath been declared how the heaven is round, and seeing that it is so, it may be said, that in the heaven is no part from above the pole, nor part under the pole, because that all round bodies, naturally have no part high nor low: for if one part were more high or low than the other, than the body should not be round, whereby it seemeth, that it cannot be said, that the star of the North, nor the guards are in no time under nor above the pole.  
The third doubt is, that likewise we say, that the North star doth give an equal turn round about the pole, and seeing it is so, that it is equal: wherefore at sometimes is he distant of the pole under or above half a degree, and at other times three degrees and a half.  
To that which is said in the first doubt, all the Philosophers and Astronomers are against, for that all of them hold that the pole moveth not, but is fixed, and upon him all the parts of heaven do move in circle manner and in such sort, that that which is near, moveth slowly, and that which is far of, moveth with more haste, whereby that which moveth itself by the Equinoctial, because that there it is farthest of, there the moving is more hasty, then in any other part, and this showeth itself by experience. We see in the moving of a wheel, that the Ex standeth still, and always remaineth in one place, and all the parts of the wheel do compass it about, of the which, those parts that are near to the Ex, go more slowly, and those that are farther of they move with more hasty moving, so the uppermost part of the wheel his moving is more hasty than any of the other parts: as Aristotle showeth it in the Mechanica.  
To that which is said, that the heaven moveth itself equally, it is to be understood in equality of time, but not in equality of place, in such sort, that in equal time they make their parts in equal moving, because these parts cannot of continuance 〈…〉 by themselves. A continuance is that whose moving is one, and is to be understood wholly together: so that it cannot be, that at one time one part is moved, & at another time another, but at the moving of one part, all the other parts, and all together are moved: so that when the Heaven moveth, because his moving is a pure moving, of his place to his moving all the parts do move place.  
Item although that one self intelligence do move the parts of the poles & likewise the others, which are more distant, because all be continual, they are moved together. And it is so, because these parts are not put asunder, nor divided the one from the other. And if they were it is certain that the lesser parts should move more hastily than the greater parts, the which is not because the said intelligence doth move them together, & the mover hath his proportion to all, and not to part.  
And this is manifest, because in the continual movable, there are parts of an infinite smallness, for that to any part that is marked may be given a lesser.  
To the second doubt which is in the round body, that there is no part high nor low: truth it is, that naturally there is not, respectively there is. And to say that the North star is sometime above the pole, and at other times under, it is to be understood, not naturally, but to our respect, and so he that were in such a place, that had the pole for zenith: the North star should not be from him more high nor more low, at one time then at another. But to him whose zenith is not under the pole in the moving which the star maketh at some time, he willbe under the pole, & at other t●●es above and to know how the North star is under or above the pole, do you imagine the f●●ure of a ●an in the pole arctic, which having his face towards the midst of the day, and being so put, the left arm shallbe towards the East, and the right towards the West, therefore when the North star doth go from the left to the right, which is from the East towards the West by the head which maketh the half of his circle, we say that he is above the pole, because then the pole is between the star and the Horizon, so there are more degrees, from the Horizon to the star, then to the pole: and when he goeth from the right arm to the left, which is from the West to the East, in the other half turn that he maketh by the foot, we say, that he is under the pole, because then the star willbe between the pole and the Horizon, and then there are more degrees from the Horizon to the pole, then to the star, as appeareth by this figure.  
The Horizon,  
And so it is to be understood, that the North star to be under or above the pole.  
To the third is to be noted, that the north star doth go round about the pole, but although the turn, which he giveth, be in equal roundness, he goeth distant from the pole, more in one place then in another, this is to be understood not as much as toucheth the roundness, but as much as toucheth the straightness of the pole, in this manner.  
When the star is in any of the arms of the east or of the west, than he is neither more high nor more low than the pole but in one equality with him.  
And for as much as toucheth his turn, he goeth from the said arms, by the part of the head, or by the part of the foot, so much he goeth aside of, from the straightness of the pole. In such sort, that when he is in the head, is, when he is farthest of the pole, by the uppermost part: and when he is in the foot, is, when he is farthest of by the lower part, the which is not to be understood, that the circumference is greater in the head or the foot, then in the other parts.  
But unto our respect is that which he goeth distant above or under the pole as here it is showed.   

The eight Chapter, how the altitude of the North, is to be taken, although the guards be not seen.  
IT happeneth many times to such as be sailors, when they go near the Equinoctial by reason the pole is near to their Horizon, they see not wholly the turn which the guards do make, round about the pole, so that when the guards do descend from the West; and go towards the East, in all those courses of the west south-west, South West South south-west, South, South Southeast, Southeast, East Southeast, they cannot take the altitude, because he is not seen when the guards do come to every one of these said courses. And for this in this chapter shallbe declared, how it shallbe known, when the guards do come to every one of these courses aforesaid, & taking the altitude how much it is that justly shallbe taken away from the altitude, according to the place where the star is, is to be understood, that which is above the pole: for the which it is to be noted, that besides the two stars which we call guards, which before have been spoken of, there are other three stars, which go well near in the same distance, that the guards go in, that go round about the North star: and although the guards be not seen, yet by these three stars, or by any of them, the altitude of the pole is to be known, as well as by the guards, which is to be known in this manner. These three stars which before are spoken of, are called the third, the sixth, and the ninth, and although they have other names, these names we name them by, because it maketh for our purpose, and the reason is, because the star, which we call Tercera, or third star, goeth three hours, which is one course or wind before the foremost guard: and the Sesta or six, two courses or winds which are six hours: and the Novena or ninth, three courses or winds which are nine hours. And to know these stars, do you note that the third star hath near to him other two stars, and all three do make well near one triangle, in this manner.  
This star whensoever that the foremost guard is in the head, then is she in the North-east, and if the guard be in the West, then is she in the Northwest, and if the guard be the South, then is she in the south-west, & so it is to be understood of the other courses, that always he goeth one wind behind the guard.  
The sixth is one star alone, the which goeth well near as distant of the North star as the guards.  
This star goeth two winds behind the guard, so that if the guard be in the head, she is in the East, and if the guard be in the West, she is in the North, and so it is to be understood in the other courses.  
The ninth is one star alone which is nearer to the North star, than the guards, this star goeth three winds behind the guard, so that if the guard be in the West, she is in the North-east, and so contrary.  
And these three stars being known, although the guards be not seen, by these or by any of them is to be known, in what course the guards are in reckoning the courses in the manner, as it hath been declared: the which rule I have had experience of, and have found it certain.   

The ninth Chapter, how the altitude of the North, is to be taken, although the Horizon be not seen.  
IT happeneth many times to such as sail, that they cannot take the altitude of the North, because they cannot see the Horizon. This is because either the earth doth cover it, or some cloud or vapour which riseth of the water, or it maketh so much darkness, that it cannot be discerned, or for some other cause. And how to know the Horizon is a thing so necessary, that lacking it the altitude of the North cannot any manner of way be taken with the Ballestilla of this cause the sailors receive very great hurt, for that many times it happeneth to them, to pass many days without taking the altitude and most of all in the winter.  
Therefore to take away this hurt & inconvenience, I will declare in this present Chapter, in what manner the said altitude may be taken although the Horizon be not seen, the which is this. The pilot or other person, that should take this altitude, let him take a staff or rod of the greathes of a finger little more or less, and so high, that being put upright in the ground, it come justly to his sight, and being made of this greatness, no more nor lose: let him make at the top of it a Cross, and when he will take the altitude, let him join his feet together, and lay down the rod strait and equal from the point of his feet, as far as the rod will reach, and let him make two points, the one where he hath his feet, and the other as far as the rod doth reach, and in that point where the rod doth reach, there do you take him up, and let some body hold him upright, and the Ballestilla being taken his feet being put in the point that he first had them put, let him take his altitude, making the Horizon in the highest part of the rod or staff where he marked the Crosse. And ye shall understand that this is his Horizon, wheresoever he findeth himself. And it is to be noted, that if the night were as dark, that the highest part of the rod cannot be seen. That which I have said is his Horizon, then put upon the top of the rod, a sign or show of fire, by the sight of the which he may hit to put his Ballestilla right with the said rod, and so he shall take his altitude precisely doing in the rest, to take away or put to the degrees, according to the place wherein the guards are, as before hath been declared.   

The tenth chapter, of a clock by the north star whereby may be known what hour of the night it is, in any manner of time and place that a man is in.  
IN the third Chapter of this fifth book, I said, that the foremost guard is called horologial, because he goeth always round about the North star, like to the wheel of a clock giving knowledge what hour of the night it is. And because this knowledge bringeth much profit, and it is convenient that every one should know it, therefore in this present Chapter, I will speak how it should be known in any manner of place, wheresoever a man is, & in any time of the year, what hour of the night it is, and for to know it, is to be noted that which followeth.  
First of all, look upon the North star and imagine upon him a Cross in this manner.  
Of this cross the uppermost part, we call head, and the lower most part foot, and the other two the right arm, and the left, in this manner.  
This being had, is to be understood, that between these four courses or strekes, we put other four which do divide or part these in the midst which we call lines, in this manner.  
So that there is a line between the right arm and the head, and a line between the head and the left arm, and a line between the left arm and the foot, & a line between the foot and the right arm: this imagination being made, it is to be understood, that the greater star of the two guards, which is the foremost, which before hath been named the star of the clock, this star in twenty four hours doth pass these eight parts, tarrying three hours from the one to the other. So that it at xii. of the clock in the night, he be in the head at three, he shallbe in the line between the head and the left arm, and at six in the said arm, & in that sort, the rest is to be reckoned.  
Of this doth remain, that being known in what part this star should be when it is midnight, forthwith will be seen, that if he be there it is midnight, and if he be not come thither it is not, & if he be past, it is more than midnight. For this, it is necessary to know two things: the one is, to know in every month of the year, in what part the guard star aught to be in, to know when it is midnight: & the other, how it is to be known, what hour it is, more or less than midnight. Of the first this is to be noted, that the account or reckoning, that is to be used in this, is, that at the midst of the month of April, when it is midnight, than the said guard star will be in the head, with the North star, and from thence forward every fifteen days, the middle of the night, is one hour forward: for in every day he goeth forward four points or minutes, and giving to every hour threescore points, so that it cometh to pass in every fifteen days one hour forward. But in this I say that I have made experience sometimes with clocks of precise hours, and setting them punctually, at the point that the Sun setteth, and I find that unto the twenty day of April, the guard and the star, do come precisely at midnight in opposite, but because the difference is little: I do follow the order of the figure following. To the second is to be noted, as before hath been declared, that in every three hours the star called the guard, doth pass from one course to another, by the which there is to be divided with the imaginative, that space in three parts, and every part of space will be one hour. In such sort, that the place of the guard star being known where he should be at midnight, is to be known, if he be there, or if he be one hour, two, or three, behind or before, and so it willbe known what hour it is: and to know in what part the guard is in at midnight, every half month of the year, it must be seen in this figure of following.   

The eleventh Chapter, how the altitude of the pole, antarctic is to be taken.  
SEeing there hath been declared the altitude of the pole arctic, or North with his demonstrations, it is convenient to speak of the altitude of the pole antarctic, how he should be known, because the sailors or any other person finding himself towards the South part▪ they may know how to take him, and to govern themselves thereby. Of 〈◊〉 is to be known, that the tokens or knowledge, that we have of the pole antarctic, are four stars, put Cross wise in this manner.  
These stars be not of any of the signs of the Zodiac, nor of the other thirty six images of the heaven, therefore they are called Cruzero, and these four stars we name, head, foot, & arms, and to know which star is the head, and which are those of the other parts, is to be understood, that the star of the foot is greater than any of the others, & by this, the other are known.  
Therefore it is to be noted, that when these four stars are a cross, the head being right with the foot, that then the greater star which is the foot, is more near the Horizon, and then he is distant of the pole antarctic thirty degrees above the said pole, and the altitude of this star is taken, and of no other: And he is to be taken when he is in right of the head, for there is his own place. Therefore when you will know the altitude of the said pole, do you stay until the star of the foot, be in his place, because with the moving of the heaven, he moveth with the others, and being in his place, then take his altitude, even as you take that of the North, and look that the altitude which you take of him, either they must be thirty degrees or more or less, if they be thirty ●ust, you are in the Equinoctial: If they be more than thirty, those which are more, you are distant of the line towards the part of the South, & if they be less than thirty, that which is less you are distant of the line towards the part of the North.  

An Example.  
I say that the said star being in his place, I took his altitude in forty degrees, than I say that I am in ten degrees, distant of the line towards the part of the south, the reason is, because this said star hath thirty degrees of declination or distance of the pole, therefore if I had taken him in the said thirty degrees, than should I have had the pole in the Horizon, and having the pole in the Horizon, I am in the Equinoctial, and so the degrees, which are more than thirty, in the which I took the altitude those am I distant of the line towards the part of the South: for thirty from the star to the pole, and ten from the pole to the Horizon, are forty, in so many took I the altitude, so that these ten degrees, is the pole raised above my horizon, so that by how much, I shallbe distant of the line, so much the pole shall rise up above my horizon, and in so many more degrees, I shall take the altitude of the said star and the thirty being taken out, which the star is above the pole, those which are more, I am distant of the line towards the said pole, and so many shall the said pole be raised above my horizon, and if I should take the altitude in twenty, I am distant of the line ten degrees towards the part of the North, and if I should take him in ten, I am distant twenty, and if I should take him in five, I am distant twenty five, & if I had the said star in the horizon, I am distant thirty degrees of the said line, towards the part of the North, so that when I shall take him in thirty degrees, I am in the Equinoctial, and when in less, towards the part of the North, and when in more, towards the part of the South.    
The end of the fifth book.   

❧ The sixth book, of the Compasses to sail by.  

The first Chapter, of the Compasses to sail by, and of the defects which they may have, and how they may be amended.  
The first is, by the styles not being well touched with the loadstone, that he lacketh the virtue. And this ceasing which is the cause, the effect ceaseth, which is to show the North.  
The second, because the capital is wrested, and not upright, that he doth not suffer the rose to go right in his step.  
The third, because the step is broad, so that the rose cannot move with quickness.  
The fourth, because the rose lieth down, and hangeth more to one side then to another.  
The fifth, because the chest of the rose is open, in such sort that the air entereth into it.  
The sixth, if the sphere or the hinges, whereby the said box or chest is sustained, are not so light that the chest and the rose may go equal.  
To the first, the pilot aught to carry in his chest a loadstone, & that he have experience that it be good, and with the face thereof to rubbbe or touch the points of the compass subtly until there cleave to it, a little of the said stone, & see that it be with the face of the said stone, the which he aught to have marked, to which part it is, for if it be with another part it maketh not the true effect.  
To the second, which is the capital to be laid down, for to know when it is so, take a compass & put the one point in the head of the capital, and the other in one of the circles of the rose, & thereby you shall know to which part he is wrested, & how much it is needful to dress him, & it is to be understood, that if the capital be not very upright, the rose will put him clean out of his place, although he be very well touched.  
To the third, if the step be broad or flat, he aught to be finely filled, so that it be seen, that the rose run not hasty nor to slowly, and if by ●yling of him, it be seen that the rose doth run over much, touch him subtly with some iron in the point, that he may be somewhat broad, so that the rose may run ordinately.  
To the fourth, if the rose go somewhat laid down, & do not go very equal, you may put to him some wax, or pitch▪ or a thing that may cleave fast to him in the under part, until that he go upright, without leaning to one part more than to the other.  
To the fifth, he aught to look that the box or chest where the rose goeth be so near, that there go not in any air as well by the part of the glass, as by the part which is shut, and if it be open in any part, with the said wax or pitch, it aught to be shut.  
To the sixth, I say that he aught so look to the Sphera or hinges, wherein the said chest or box goeth put, upon the which it is sustained or held up that it be so good and light that the said box or chest go always equal, in such sort, that although the ship do held or do lie down to one side or to the other, the said box and rose be always right, for if the irons, wherein they move, be hurt they 'cause that when the ship doth held to one side or other, the box and the rose cannot judge the North in his proper place.  
So that it is convenient that the said Compass or needle be precisely made without having defect or lack, or if there be any inconvenience, although it be very little, it causeth much error.   

The second Chapter, how the winds of the Compass aught to be understood, and how the sun passeth every day by them.  
IT is necessary, that the pilot understand two things in his compass, the one is, how the East & West, which are marked in the Compass aught to be understood.  
The second, how that in every four and twenty hours, the Sun doth pass all the courses of the Compass.  
To the first is to be noted, that this name East and West is taken two ways, (that is to say) natural and respective: the East and West is natural, and is understood by the Equinoctial line, & not by any other part, because it is the midst between the two extreme parts, (that is to say) the two poles, as his definition declareth.  
The respective is by any other manner of part where a man is, now near the line, now far off, so that if a man be five degrees from the line, or ten, or more or less, all that he is in the same degrees, he shall be towards the east and respective towards the west, in such sort, that all that he is from the place, where the Sun riseth to the Meridian where the man is, he shall be towards the east, and that which he is from the man unto the place where the sun setteth, he shall be towards the west, and this likewise, is to be understood being in the equinoctial, as also forth of the equinoctial.  

An example.  
Of this may be asked, if the city Seville be towards the east or west, that is, towards Levant or Poniente, it is answered, that it is not in the east & west natural, and as much as toucheth the respective, it is towards the east, and it is towards the west, I will say, that likewise it is towards the Levant, & it is towards the Poniente, in this manner. Of that which it is most occidental is towards Levant, and of that which is most oriental, is towards the Poniente, so that if Seville be in thirty seven degrees of the equinoctial, towards the part of the north, all that it is in the right course of the thirty seven degrees it is with Seville east and west, in such sort that all that it is from the Meridian of Seville unto the part of Poniente, Seville hath towards the Levant, and that which is from Seville towards the part of the Levant, Seville hath it towards Poniente. We have an author of this, who is Saint Luke in the first chapter, where he saith, that the three kings came from the oriental parts to Jerusalem, it is to be understood, that as Jerusalem was more occidental, then from whence they came, so they came from the orient, to occident, which is from the east to the west.  
Therefore I say to our purpose it is not to be understood that the course which is marked in the compass, is the east & west, respective, or accidental, but the natural which is by that strait course which the Sun doth describe in that moving which he maketh the eleventh of march, and thirteenth of September, for that is east & west, that is marked in the compass, (that is to say) by the equinoctial, so that from the east unto the north are ninety degrees, and seven courses, besides the east and the north, and the like unto the south, And if the east of the compass were respective the ninety degrees, nor the seven winds or courses, should not be reckoned the which would be a very great error.  
To the second, I say that how much a man is farthest of the equinoctial, so much the days will be greater to him when the Sun goeth of this part where he is, and by reason that the days are greater to him, the rising of the Sun may be different to him, in this manner, those which inhabit under the equinoctial, or in any other part, when the Sun doth describe the said line, always he cometh forth to them in the east, and setteth to them in the west, and they have twelve hours of day, and twelve of night, so that in the four and twenty hours wherein the Sun maketh his daily wooving he passeth all the eight winds or principal courses of the navigation, In such sort, that from three to three hours, he goeth from one wind to another, and so he riseth and cometh forth to us at si●e of the clock, at the east, and at nine at the southeast, and at twelve at the south, and at three at the south-west, and at six at the west, and there he setteth. So that in xii. hours he goeth four courses, but out of the equinoctial, how much the day is greater so many more courses the sun goeth in the day, and less in the night, so that if the day be of fifteen hours, the sun goeth in the day five courses and by night three: and if the day be of eighteen hours the sun goeth in the day six courses and by night two: and if the day be of one and twenty hours, the sun goeth in the day seven courses, and by night one: and if the day be of four and twenty hours the sun goeth twenty four hours in the day, which are eight courses, and that day there is no night: as it happeneth to those which inhabit in the circles, when the sun cometh to the tropics. And that which is understood of the days when they go increasing, and the nights diminishing, the same is to be understood by the courses which the sun goeth by night when the day goeth diminishing, and the night increasing: as shall be declared in the sixth chapter of the eight book, so that the quantity of hours being known which the day hath, the pilot may know to what course of the compass the sun riseth and setteth from him every day, this reckoning will serve for many things of the navigation.    

The third chapter, wherein is declared, the opinion that is had in the north-easting, and northwesting of the compasses.  
THere is an opinion among such as sail that the compasses do north steer, and northwestear, and it is said that in the Meridian of the Islands of the Acores, that there the Compass doth show the pole in his place. And from thence passing towards the west, it doth Northwestear, this is that he showeth not the pole in the place where he was first, but that he goeth aside towards the Northwest. And if they come from the said Meridian, towards the East, that the Compass doth Northeastear, that is, to make the said difference towards the part of the North-east, so that they say, that only in that Meridian the Compass doth show the pole, and not in any other place: but to one part or other: and how much more they depart from him, so much the Compasses have more the said defect, but those which understand this, give no cause nor any reason, nor how much this difference is, which the Compass maketh, nor how far it goeth, so that they know not what to say more, but marking their Compasses, it seemeth that which is said to be so.  
Hereupon I have procured to seek some Author or reason, or some thing wherein this should have a foundation, and I say that of this variation which is spoken of the compass. I find not any thing written, nor reason, nor experience, that is certain: therefore here I will speak my opinion, touching this, persuading myself to that which is most natural and true of the navigation.  
Therefore coming to the cause, I say putting an example, if I make two compasses of one self style, and of one temperance, and touched with one self stone, and two ships go sailing with them, departing from the said Meridian one towards the east, and the other towards the west, that these compasses shall make, different effects in such sort, that in the one, the stone and the style, should have virtue to cause north-easting, and in the other to cause northwesting which are contrary effects, it seemeth not to me, that there is any foundation, or reason to have the like. But let us see if this be in any thing of the navigation, let us seek it in three parts, which is in the pole or the compass, or in the way where sailing now is used.  
To the first, to say that the pole doth make any variation or distance from his place or point, this aught not to be thought, because it should be to put out of order all the order of the Sphera, in such sort that all the ●ixed circles; should be movable▪ besides this, if the pole should move with him that saileth towards the east, it would move itself in the same tune with him which saileth towards the west. This is unpossible how much more, that the pole cannot move to one part or to another because it is a point imagined always fixed in one place.  
To the second, I say that it aught not to be thought or understood, that the compass by himself maketh the said difference, for it is certain, that the said natural virtue or property which the stone and steel have in the place where the compass was made, the self same they have in the said Meridian, and in the new Spain, and in Calicut, and in all parts. And there is no reason to say, that this property is of such quality, that in the said Meridian it hath one virtue, and in all others, which are well near infinite, it hath it in every one, different, for if it were so, it would be to give a great inconvenience, the which is that 〈◊〉 no part forth of the said Meridian, there could be made a true compass, seeing that in no part the compass doth show the pole but there, and to say so it were a very great error, because an instrument, so important to the navigation, should not be said, that in no part it could be made certain, for if it were so, it were to give to the navigation an instrument with a known error.  
To the third, that is by the way where you sail, this is known, that in any manner of place where a man is, there he hath his Meridian, the which goeth precisely to remain at the point, which is the pole, without making any distant or difference in any thing.  
And if it should be said, that by reason of the way which the Ship saileth, the compass maketh the said difference as well towards the one part, as to the other, this would be to make many Meridian's different, the one from the other, and so they should go to remain at different poles in such sort that how many differences the compass went making, by reason of the way: so many different Meridian's, the way should have: and too every Meridian of necessity, there should a pole 〈◊〉 given, where he should make an end, for otherwise it would be an infinite process, so that there should be given an infinite number of poles. And to think this should be a very great error▪ so that it appeareth well, that neither by the part of the pole, neither of the compass, nor of the way where you sail, the said compass do make any variation or difference from his proper place, but making more inquiry of this variation, which of the compass is spoken: I say that commonly is understood that the compass doth show the pole, but of this there is no writing which doth say so: that which I find written of the loadstone, and of iron is, that Pliny in his thirty six book of the natural history saith, and also Saint Isidore in the sixteenth of the Etimologi●s, that the loadstone by one hidden virtue or property, that it hath doth specify that it draweth to it iron of this Avicen speaketh in the Book of Viribus Cordis, the tenth Chapter, he asketh what the cause is, wherefore the loadstone doth draw unto it iron, to the which he answereth, that there is no other thing can be said, but because it hath a natural virtue to draw it to him, and he saith that some understood that he draweth it to him by reason of heat or coldness, or because of similitude, that both of them have in nature, or for other reasons, all the which he saith is false, for that he draweth it not, but only with his property, and declaring what thing property is, he saith, property is found in nature in the compounded bodies, proceeding in them, a most high and full influence, so that we see the load stone doth draw to him the iron: likewise we see that the iron being rubbed with the said stone, I say in one only part of it the virtue renia●●●th with the iron to show always one point, which is answerable to the place where we do show in the horizon the wind at north: so that ●eeing the pole is imagined in the heaven, and is not seen, & the compass doth show him in the horizon without any rising, one only degree above the horizon: it is clear that neither the compass doth show the pole nor by the said compass the pole can be seen when it is equal with him, nor when it is at one part nor at another, even as I should not know, when I am right with that which I see not, nor when to one part nor to another. This being understood, I mind to declare here whereupon they ground themselves, which are of opinion that the compass hath a north-easting & a Northwesting, and the manner whereby they say, that they know it, which is this. The pilots which do ma●●e their compasses do behold the North star to mark them by her, but because this star doth always move, as before it hath been declared, therefore they tarry until the guards be in the North-east, or in the Southeast, for than they think, that the said star is in opposite of the pole, under or above him, and then they imagine a streke which descendeth from the said star unto the Horizon, & they imagine another streke which goeth from the point of the flower of the compass, unto that point of the Horizon, so that in these two strekes, which they put in that point, they look if that point be strait under the North star, and so they speak what their opinion is without having in this any other account or reason.  
To this is to be noted two things. The first that the guards being in any of these said courses are not in opposite of the North star, and the pole rather is a point different, for because to stand in opposite, the guards aught to be in the North-east, and by North, or in the south-west and by South.  
The second, that this making just of the compass is always done by night, because by day there is no star seen. And from the star unto the Horizon the distance is very great, by which the true point that is corespondent to the said star, cannot be known in the Horizon: But that at one time is ●●dged one, and at another time another. Likewise for the great distance, that is from the said compass unto the point which is imagined in the horizon: And as that point is imagined, and invisible, always the sight goeth wavering without establishing itself, which hath happened sometimes to me, making experience in this. And therefore I say, that according to the perspective rule, the precise point of the Horizon cannot be taken with the only sight which is imagined under the said star, nor it can make justly equal, the point of the flower of the compass, by reason there is no certain point, and the distance very great, which is to that as is imagined. For the sight faileth when the object is very distant. Whereby I conclude, that it cannot be precisely known in the compass, by the manner as it is said, if he make the said distance of the pole, nor how much it is, nor I by this way could ever attain to it.   

The fourth Chapter, of the inconveniences, which may follow by the north-easting, and Norwesting of the Compasses.  
AMong other inconveniences, that will follow in the navigation, if the Compasses should make the said variation or difference, I find four very principals, which are these following.  
The first if it be true, that the compasses have a north-easting, & a Norwesting, likewise it may be said, that they have a southeasting and southwesting, and the reason is this, it is certain that the variation or difference which the compass doth make to the part of the north, the same aught to be made, towards the part of the south, I will say that how much the north point of the compass departeth from his own point, so much the south point of the said compass goeth distant to the other part, and so the north point of the compass doth North-east a quarter or more, and the south point doth south-west the like, for the north point cannot go aside, but the south point doth the like. And so when you shall sail towards the part of the south, seeing that there the north star is not seen to mark by her, either it must be said, that of that part the compass doth not make variation, or if it do, that in the south, it is to be known: and so when you shall sail to the river of plate, otherwise called Rio de Plata, or to the strait of Magalanes, or by the south sea, or to the cape of Buena Esperanca which is in english, good hope, and from thence to Calicut or the Maluco, then will be said, that the south point of the compass doth southeast or south-west, and to say so should be a great error.  
The second if the north point of the compass do make the said distance of his proper place and point, it is certain that the self same difference and distance all the other winds of the navigation should make from their proper places, because how much any wind doth depart from his proper place, the self same all the others should do by the agreeable order, and equal distance, that they have in the compass, the one with the other, and so none would answer to the certain point, that is showed in the Horizon, so that likewise, there would move from their place, the east, and the west, and all the other winds, this would be a great inconvenience, for the compasses, would never agreed with the cards, this is because always the winds of the cards are fixed in one point, without moving from thence, therefore if the winds of the compass do make many differences, it is certain, that they cannot be agreeable, and not agreeing: The place which you go to seek cannot in any manner of wise, be precisely hit, but with great compass, this will 'cause it by reason the card saith one thing and the compass another, and so there cannot be had a certain account, in the degrees and leagues which are sailed, rather all the accounts or reckonings of the leagues which is given for a degree in every course, should be false seeing the pilot doth not sail by the course, which he thinketh he doth, and so the reckoning which is made by such a course, should not be certain, and if he would give allowance it would be nothing worth, for he knoweth not of what part nor how much, and so it would be to add one error to another.  
The third, if the variation or difference which is spoken of the compass, were certain it would follow, that the compasses which were very distant of the said Meridian at the east or at the west, they should have great difference, if it be true, that how much more they are distant, so much more they have the said defect, and so all the earth, that should be discovered, with these compasses, and should be set down in the card, should not be in his true point, the reason is, because the principal winds of the card (that is to say) the north and the south, the east and the west, are marked in four fixed points equally distant, which are the two poles and the equinoctial line: and according to these all the other winds of the card are marked and parted, for if there were put into the cards any other thing it would be to make an error at the beginning, which is not convenient in a thing so certain, as the navigation is, so that all these winds are always steadfast and fixed, in their own points, without making variation or any difference, so that all which is placed with the compass by reason of his difference, will not be aunswearable with the certain point; according to the winds which are in the card.  
The fourth, if the variation of the Compass be true, immediately would follow great difference between the course and the altitude, because if I, by my way or course do seek a land, which I know is in thirty degrees, or more or l●sse, and I sail by one point the which I have chosen agreeable to the Altitude. It is certain, that by reason of the variation of the said Compass. I shall not go by this course to that Land which I go to seek, but rather when I have gone, the said way, I shall find myself forth of that place, whether I go very different, of the which, the error of the Compass was cause thereof.  
And so in long ways will always happen great hurts & inconveniences. Therefore I say, seeing that the said opinion hath no more reason nor foundation, then that which is before said, that such as do follow it, let them look to the hurts and dangers which may follow them.   

The fifth Chapter, of the allowance, which the Compasses have, and how it aught not to be given them.  
SOme which make compasses have a custom, that at such time as they do set the styles in the rose of the winds, they do not precisely put the flower of the rose upon the points of the styles, which are touched with the loadstone, but they put them aside of the flower half a point for the North-east, and this they say they do to give allowance to that which the Compasses do North-east, so that the Compass doth remain, made in such manner that the styles, and the slower are not uniform in showing the North point, because the flower doth show him to one part, and the styles do show him to another: this is a known error, and it aught not to be done in no manner of wise, for the reasons following.  
The first, if it be true, that the Compasses do North-east and northwest: it is also said that they do as well North-east as northwest, so that the difference which is given to the one part, the self-same is given to the other, and if it be so, by what reason should be given to it the allowance, always to the one part, and not to the other, therefore it is certain, that it to the navigation that is made towards the West, the allowance doth profit that which is made towards the East, it would hurt, seeing they are different the one with the other, so that what it doth benefit the one, it will hurt the other. Likewise, with the self same compasses, which they go one any voyage, with the self-same they return, without taking away, or putting to any thing in them, thereby it is clear, that the said error is to be perceived, seeing that the allowance cannot serve to both parts.  
The second, if it be true that in the Meridian of the Acores the Compass doth not make any difference from the pole, I say that this cannot be known, by the said compasses. (The reason is) because the virtue of the Compass is in the styles, and not in the flower, and the pilot looketh not unto the styles, but to the flower, because he cannot see the styles, and the flower showeth one, and the styles another, whereby as he ruleth himself by the flower he cannot know the truth.  
Likewise what reason is there, that there is given there to the Compass, as much allowance, as in other parts which are far of. Of this doth follow, that for the allowance or difference put in the said compass cannot be known, when the pilot is in the said Meridian. Therefore it is so as it hath been said, when the styles do show, the flower doth not show. And so the said Meridian cannot be known, if it be not in seeing the said Islands, by reason of the difference that is between the styles & the flower.  
The third I say, that there is no reason, wherefore so much allowance should be given to the Compass in the sailing of a hundredth leagues, as in the sailing of two thousand by the which reasons, it is not convenient, that to any compass the said allowance or difference be given between the flower and the styles, but that they be made even very precisely, so that they may be uniform in their showing.   

The sixth Chapter, of an instrument, with the which the Compasses may be marked, and known if they be certain and true.  
IT hath been said, that by the point of the Horizon, which is corespondent to the North star the compasses cannot be marked, because it is an uncertain point, so that because the compass is an instrument so little & so subtle, it is necessary to bring him in order with another instrument, such a one as the sight and the reason may rectify.  
Therefore when the pilot will mark his compass, and know if he be true or not, let him make the instrument following: with the which I have many times marked compasses, and have found it certain, set down your compass upright, and put upon him a little thin table & plain, a little longer than the compass, and narrower than the rose, so that the North and the South be seen of the rose: And in this table make a circle with the compass, well near of the greatness of the rose, & make in the said circle a streke very equal & strait, that may go from the North to the South of the rose, so that the rose standing still, the streke of the circle of the table, be such, that he come precisely with the North & south of the rose, this being done, put in the point with the compass made in the midst of the circle of the table, a little small mast upright, and that he be so great that the shadow which he maketh go forth of the circle, & being put so, then set your compass in the sun before the midst of the day, & there make equal the streke of the circle with the rose, as before is declared, & the compass standing quiet & the table fixed above, do you stay until the shadow which the little mast doth make, do come shortening until he come to the said circle, and when he is come, make a point there. And after that stay until the said shadow do turn to go forth of the circle, & when he cometh to it, make there another point, this being done, take your compass, and part justly that which is from one point to the other.  
And to this point of the partition, the Meridian of that place is corespondent, it is to be seen if the streke which was made in the circle of the North & South, of the compass do come by the said point of the partition, than the compass is good, and if not, there it is to be seen, to which part he maketh difference, and how much it is.   
The end of the sixth book.   

¶ The seventh book of the Moon, and how her ebbings and flowings do serve in the Navigation.  

The first Chapter, what thing the moon is, and wherefore her light is not equal, but always increaseth or diminisheth.  
THE Moon is one of the seven planets, constituted in the first Heaven more near unto us then any of the others, of this some had opinion, that she had light of herself, and when she was in one sign with the Sun, by means of the great light of the Sun, she gave no light, and how much the more she went from the Sun, so much her light began to appear, and the nearer she was, the less it did appear. This is not so, because the Moon hath no clearness nor brightness of her own, as in the first book the seventh Chapter, hath been declared, the which is seen by experience, because the Moon doth suffer Eclipses, when she is deprived of the light of the Sun, as there is a let, that she cannot receive it, she remaineth dark. This light is let by means of the Earth, as the Philosophers and Astronomers do show, because in the moving which the sun and the Moon make, as they come into the point, that the earth is directly between the Sun and the Moon, the light of the Sun giveth in the earth, and so the Moon remaineth in her own likeness, which is dark, so that of herself, she hath no light nor clearness, but the sun which is over her, doth light her, although not every day alike towards us, because as the Moon is a body dark, when she is right under the sun, she is lightened of the uppermost part, & remaineth dark towards the earth, & therefore in her conjunction with the sun, we see her not. And it is to be noted, that in the conjunction of the moon, she & the Sun rise not in one self place, but they rise at one self time, & so by means of the light of the sun, the moon doth not appear, because coming forth at one self time and in one place the sun would be eclipsed, and so the eclipse of the sun happeneth in the conjunction of the moon, when she is in the head or tail of the Dragon. And as by her moving, she goeth away from the sun, she beginneth to appear unto us, and appeareth in the manner of a thin horn, and the farther she goeth from the sun, the more she shineth to us. And at the eight day she shineth parted in the midst, and at the fifteenth day she is full, for than she is farthest of the sun, the which is proved because it happeneth, when the sun doth set to us in the west, she beginneth to come forth in the east, and then all the brightness, which the moon receiveth of the sun descendeth towards us, and after she beginneth to go nearer to the Sun, by the same manner that she went departing, and when the light goeth upward the shadow descendeth, and so she turneth decreasing, in the like sort as she went increasing. And it is to be noted, that the moon doth pass the circle of the zodiac, in twenty seven days & eight hours, and although that in this time, she maketh an end of her circle, there is given to every moon twenty niene days & a half. The reason is, because in those said twenty seven days & eight hours, she doth not overtake the sun, and therefore passeth forward other two days, and four hours, a little thing more or less, and so twenty nine days decying past, and twelve hours, and a few minutes, in some more, and in others less, the conjunction of the Moon and the Sun is made. This is according to the half moving of the Moon, wherewith is made equal, the moving of all the days, because according to the true moving which she maketh, at sometime it is said to be slow, and at other times swift, the which moving is also made equal by the middle moving, this is largely declared by the king Don Alonso in his tables.   

The second Chapter, of the Golden number, & how it is to be reckoned from one to nienteene, and wherefore no more nor less.  
IT is a necessary thing to take out the reckoning of the Moon by the Golden number, for that the Golden number is a thing whereby many reckonings are made, and therefore it is called the number of Gold, whereof I mind to declare in this Chapter, that of the Golden number which maketh to our purpose, where I say that this reckoning of the Golden number is, from one to nieneteene, so that the Golden number is accomplished in the time of nieneteene years, and the nineteen years being past, returneth again to one and so for ever. The reason why it hath this number, & no more nor less is because the nineteen years being past, the Moon turneth to one only day, of the year, of the Sun, and in this time she finisheth and endeth all those diversities of conjunctions and fullness, and other aspects, which she hath with the Sun in one only day, degree, and minute, in this manner following.  
I put the case that the Moon made conjunction the first day to januarie of this year. The year following she will not make the same conjunction in the same point, but before or after, and so we will speak the like of the fullness, and other aspects. And as these be not in an infinite number, it is certain that they are comprehended under some number, or space of time.  
These are those said nieneteene years, in the which are to be noted, as it is said, all the diversities of aspects, aswell of conjunctions, and fullness, as of any other cause, which the moon maketh with the Sun, in such sort, that the nieneteene years being ended. The Moon doth not turn to make a new conjunction or opposition in any degree or point of the Zodiac, that in the said time, she hath not already done, and by this reason this reckoning of the golden number is ended and finished in the time of nieneteene years, and not in more nor less.  

❧ A Rule to know the Golden number of every year.  
TO know every year how many are of the Golden number, look on the numbers following and counting in the first house, the year of our Lord 1545. which are seven of the Golden number, and one house is to be reckoned every year, and the last house being ended, return to the first and so for ever.  
1545. 7. 8. 9 10. 11. 12. 13. 14. 15.  
16. 17. 18. 19 1. 2. 3. 4. 5. 6.  
WHen you will know in any year that you are in, how many are of the Golden number, without looking on the book, see in what year you run, and leaving out the thousand five hundredth, of the rest take out the nieneteenes, and that which remaineth, so much is of the Golden number that year, and if the number of the years come just in nieneteenes, that year is nieneteene of the Golden number.    

The third Chapter, wherein is declared the day and hour, wherein the Moon maketh conjunction in every month of the year for ever.  
THere hath been declared in the Chapter before, how it should be known every year how many are of the golden number, according as the account in it is declared, and because it is necessary for the navigation to know in every month the day and hour of the conjunction, therefore in this Chapter, shallbe declared, how a man may know every day what day and hour the conjunction of the Moon was, or shallbe. And for this are to be noted, two things, the first, that this account goeth taken out by the Golden number, and by him you must rule yourself, even according as the number is, which that year, wherein you are, do run of the Golden number. In that said year, look the month where you are, or the month that you would know, and in him you shall found the day, and hour that the Moon was or shallbe in conjunction. The second is, that in this account a day is understood from this day the midst of the day, until to morrow, the midst of the day, so that if we say, this day is the fifteenth day of the month it is understood, from this day the midst of the day, until to morrow the midst of the day, and from the midst of the day to morrow, doth sixteen begin, because this is the manner, that the Astronomers do reckon the days, so that those hours which are over and above, the days are from the half day forward.  

If they be one of the Golden number. If they be two of the Golden number. If they be three of the Golden number. Months Days Hours Months Days Hours Months Days Hours januarie. 19 16 januarie. 8 20 januarie. 27 14 February. 18 6 February. 7 13 February. 25 9 march. 19 7 march. 8 4 march. 27 1 April. 18 1 April. 6 16 April. 25 4 may. 17 9 may. 6 2 may. 25 0 june. 15 15 june. 4 9 june. 23 8 july. 14 23 july. 3 15 july. 22 16 August. 13 8 August. 1 7 August. 21 0 September. 11 21 September. 29 19 September. 19 8 October. 11 12 October. 29 9 October. 18 19 November 10 6 November. 28 1 November. 17 7 December. 10 1 December. 27 20 December. 16 22  
If they be four of the Golden number. If they be six of the Golden number. If they be eight of the Golden number. Months Days Hours months Days Hours months Days Hours januarie. 15 0 januarie. 23 20 januarie. 2 3 February 14 19 February. 22 9 February. 31 22 March. 16 3 march. 22 22 march. 31 22 April. 14 19 April. 21 8 April. 29 17 May. 14 9 may. 21 4 may. 29 3 june. 12 11 june. 19 19 june. 27 14 july. 12 7 july. 19 9 july. 27 3 August. 10 16 August. 18 0 August. 25 29 September. 9 1 September. 16 13 September. 24 12 October. 8 10 October. 16 2 October. 23 6 November. 6 20 November. 14 14 November. 22 23 December. 6 7 December. 14 1 December. 22 15  
If they be five of the Golden number. If they be seven of the Golden number. If they be niene of the Golden number. Months Days Hours Months Days Hours Months Days Hours januarie. 4 20 januarie. 12 11 januarie. 21 4 February. 3 11 February. 10 21 February. 19 15 March. 5 3 March 12 8 March. 21 0 April. 3 20 April. 10 19 April. 19 8 May. 3 13 May. 10 7 May. 18 16 june. 2 2 june. 8 20 june. 17 0 july. 1 4 july. 8 10 julie. 16 9 August. 29 16 August. 7 2 August. 14 21 September. 28 2 September. 5 17 September. 13 12 October. 27 12 October. 5 10 October. 13  November. 25 22 November. 4 1 November. 12 1 December. 25 8 December. 3 15 December. 11 19  
If they be ten of the Golden number. If they be twelve of the Golden number. If they be fourteen of the Golden number. months Days Hours months Days Hours Months Days Hours januarie. 10 12 januarie. 17 9 januarie. 25 7 February. 9 3 February. 18 15 February 23 23 march. 9 16 march. 17 21 March. 24 15 April. 8 ● April. 16 11 April. 23 7 may. 7 9 may. 15 23 May. 22 22 june. 5 16 june. 14 8 june. 21 13 july. 4 23 july. 13 16 july. 21 1 August. 3 7 August. 12 00 August. 19 13 September. 1 18 September. 10 8 September. 18 1 October. 31 8 October. 9 17 October. 17 11 November. 29 19 November. 8 5 November. 15 22 December. 29 14 December. 7 18 December. 15 8  
If they be eleven of the Golden number. If they be thirteen of the Golden number. If they be fifteen of the Golden number. Months Days Hours Months Days Hours Months Days Hours januarie. 28 8 januarie. 6 10 januarie. 13 18 February. 27 1 February. 5 3 February. 12 6 March 28 15 March. 6 21 March. 13 19 April. 27 1 April. 5 15 April. 12 9 May. 26 9 May. 5 6 May. 12 0 june. 24 16 june. 3 19 june. 10 20 july. 23 23 julie. 3 6 july. 10 5 August. 22 7 August. 1 15 August. 8 20 September. 20 17 September. 29 10 September. 7 10 October. 20 5 October. 28 19 October. 7 0 November. 18 21 November. 27 6 November. 5 13 December. 18 14 December. 26 18 December. 5 0  
If they be sixteen of the Golden number. If they be eighteen of the Golden number. months Days Hours months Days Hours januarie. 3 10 januarie. 12 2 February. 2 20 February. 10 14 march. 3 6 march. 11 0 April. 1 17 April. 0 7 may. 1 4 may. 8 8 june. 29 15 june. 6 23 july. 28 21 july. 6 8 August. 27 13 August. 5 19 September. 26 6 September. 3 8 October. 25 22 October. 3 1 November. 23 13 November. 1 19 December. 24 1 December. 1 14  
If they be seventeen of the Golden number. If they be nineteen of the Golden number. Months Days Hours Months Days Hours januarie. 22 12 januarie. 30 5 February. 20 22 February. 28 14 March 22 7 March. 30 1 April. 20 16 April. 28 9 May. 20 1 May. 27 16 june. 18 11 june. 25 13 july. 17 23 julie. 25 6 August. 16 14 August. 23 16 September. 15 7 September. 22 4 October. 15 1 October. 21 20 November. 13 19 November. 20 14 December. 13 11 December. 20 19  
It is to be noted, that for the conjunctions of the moon before written, shallbe taken out, the opposition or the fullness of the moon that is, by reckoning fourteen days, and sixteen hours, after the conjunction, a little thing more or less.    

The fourth Chapter, of a short account or reckoning to know without the book briefly the days which the moon hath in any month of the year.  
OF the account of the Moon which before hath been declared, you may at all times when you will, know how many days old the moon is, & what day & hour the conjunction was, but because without the book it cannot be known. I thought good to put here a short account; that by memory it may be known, how many days old the Moon is, at all times when you will know it: the which is to be reckoned i● this manner.  
In what day soever you are in, look how many be of concurrent in that year which you run, according as you shall find in the account before 〈◊〉 and join with them the number of the Months which are passed from March unto that month, & likewise join the days of the month which you have unto the day wherein you are: these three numbers together if they pass of thirty, those which are more, the Moon is old, and if they be thirty just, the Moon is in coviunction, and if they come not to thirty, those which are, so many days old the Moon is.  

An Example.  
In the year of 1545. we have seventeen of concurrent, therefore the twenty of August, I will know how many days old the Moon is: I say that of concurrent is seventeen, join six of the months which are from March to August, it amounteth to twenty three, and twenty of the month are forty three, take away thirty, there remaineth thirteen, so many days the Moon is old, the twenty day of August. And by this manner you shall take out the days that the Moon is old, every time that you william.  
1545 17 ●8 9 20 1 12 23 4 15 26 7 18 29 11 22 314 25 6   

In the year of 1545. we have seventeen of concurrent, the next year following, we have twenty eight, and so reckoning in every year one house of these and it serveth for ever.  
OF this account of the concurrent, know ye, that it increaseth every year eleven, and it cannot pass above thirty, and if they do pass thirty, you must leave the thirty, and take that which remaineth. And so know this reckoning of the concurrent quickly by the head, do you in this manner set down in the root of the thumb, ten, and in the joint of the midst twenty, and the uppermost thirty, and this being done put the Golden number in the three joints, reckoning one in the root of the thumb, and in the middle joint, two, and above three, & turning again beneath four, and in the midst five, and so discoursing until you come to the Golden number of that year, and if it stay in the root of the thumb you shall join that which it is of Golden number, with the ten that was put there, & joining one number with as many more: you shall have of concurrent as much as both numbers doth amount too, and if the Golden number d●e rest in the middle joint you shall join with the Golden number, the twenty that was put there, and all being joined together, it willbe so many of concurrent, and if the Golden number, do rest in the uppermost part of the thumb, join with the Golden number, the thirty which was put there, having always remembrance, when all the number doth pass thirty, you shall leave the thirty, and that which remaineth, is the concurrent.    

The fifth Chapter, how by the days of the Moon, and the course where the Sun will be, shallbe known at what hour the tide will come every day.  
ALL persons which do do sail, it is necessary that they know how the tides do fall every day, & at what hour it is full Sea, or low water, for this is convenient, aswell for to enter in by any bard haven, as for other things, which may serve in the navigation.  
Therefore in this Chapter, I will declare, how the reckoning of the said tides aught to be kept, & at what hour they come, for to profit thereby, of the which is to be understood, that the Moon goeth the thirty two winds of the navigation in 24. hours, in the which she maketh her daily moving, with more that she hath gone of her own moving, & in this time she bringeth two tides, that is to say, two floods & two ebbs, so that the sea floweth six hours, & ebbeth other six, which are twelve, and the like is done in other twelve, but it is to be noted, that these flowings and ebbings are not equal, nor alike in all times & places, as much as toucheth the time they be not equal, because seven days the waters go rising, and we call them spring rides, & other seven they go decreasing or ●ayling, & we call them nepe tides: so that from the first day of the Moon unto the eight day, which is the quarter, the waters go decreasing, and from the quarter unto the fifteenth which is the full Moon, they go increasing, and from the full Moon to the third quarter, they go decreasing, and from that to the conjunction they go increasing: & declaring this more at large, I say that the first day of the Moon, is the head of the water, and the second day, the increasing is as great, and the third day well near the like, and the fourth day it decreaseth, and so it goeth every day decreasing, until the Moon be eight days old, and then it is altogether neap tides: and the ninth is the like, and the tenth well near alike. The eleventh it beginneth to increase something, and so it goeth increasing every day unto the fifteenth which is full Moon, which doth turn to be the head of the water. And the sixteenth it increaseth the like, and the seventeen well near the like. The eighteenth it decreaseth, and so it goeth decreasing every day unto the two and twenty, which is altogether nepe tides, and the three and twenty it is the point of the water, and goeth increasing every day unto the thirty day which is the conjunction. And the first day it turneth to be the head of the water, and so successuiely, it goeth increasing and decreasing as it hath becue●●eclare●. Likewise it is to be understood, that these increasings, are not at all tunes equal or alike, but in some 〈◊〉 they are greater and in other 〈…〉 as by experience we see.  
Likewise it is to be noted that these increasings and decreasinge● in all plates are not alike, for th●rauses that I will speak of.  
And for to know the how, when the tides do come, it is to be understood, that always the Moon being in the North-east it is full Sea, and in the Southeast low water, and in the south-west full Sea, and in the Northwest low water.  
And to know when the Moon is in every one of these courses, it must be taken out by the course where the Sun is in this manner.  
The first day, of the Moon, the Sun being in the North-east and by East, the Moon is in the North-east, and that hour full Sea.  
The second day, of the Moon, the Sun being in the North-east is full Sea.  
The third day, when the Sun is in the East and by north it willbe full Sea.  
The fourth day, the Sun in the East full Sea.  
The fifth day, the Sun in the East, and by South, the Moon in the North-east.  
The sixth day, the Sun in the Southeast, the Moon in the North-east.  
The seventh day, the Sun in the Southeast, and by east, the Moon in the North-east.  
The eight day, the Sun in the Southeast, the Moon in the North-east.  
The ninth day, the Sun in the Southeast and by south, the Moon in the North-east.  
The tenth day, the Sun in the South Southeast, the Moon in the North-east.  
The eleventh day, the Sun in the South, and by east, the Moon in the North-east.  
The twelfth day, the sun in the South, the Moon in the North-east.  
The thirteenth day, the sun in the South, and by west, the Moon in the Northwest.  
The fourteenth day, the sun in the South, south-west, the Moon in the North-east.  
The fifteenth day, this day we reckon two quarters together, by reason that the points are thirty two, and the days thirty, we give in the midst one quarter, and in the end another, so that at the fifteenth day the Sun being in the south-west, the Moon willbe in the North-east, & this hour it willbe full Sea.  
The sixteenth day, the sun being in the south-west & by west, the Moon willbe, in the south-west, & that hour willbe full Sea.  
The seventeenth day, the sun in the West, south-west, the Moon in the south-west is full Sea.  
The eighteenth day, the sun in the West, and by south, the Moon in the south-west full Sea.  
The nineteenth day, the sun in the West, the Moon in the South West, full Sea.  
The twentieth day, the sun in the West, and by north, the Moon in the south-west.  
The twenty one day, the sun in the West, Northwest, the Moon in the south-west.  
The twenty two day, the sun in the Northwest, and by west the moon in the south-west.  
The twenty three day, the sun in the Northwest, the moon in the south-west.  
The twenty sour day, the sun in the Northwest, and by north, the moon in the south-west.  
The twenty five day, the sun in the nor northwest, the moon in the south-west.  
The twenty six day, the sun in the North and by west, the moon in the south-west.  
The twenty seven day, the sun in the North, the moon in the south-west.  
The twenty eight day, the sun in the North, and by east, the moon in the south-west.  
The twenty niene day, the sun at North north-east, the moon at south-west, and at that hour full Sea.  
The thirty day, which is the conjunction is to be reckoned two points, which are the North-east and by north, and the North-east.   

The sixth Chapter, wherein is declared more at large, the aforesaid Chapter, with a demonstration.  
OF the account which before hath been declared, you shall take out every day at what hour the tide cometh, the sun being in the point or course as before is mentioned. But for the better understanding thereof, it is to be noted, that always at 12. of the clock in the day you have the sun at south, if you be more towards the North than the sun, so that at six of the clock in the morning you had it at East, and at nine at Southeast, and at three after the midst of the day, you shall have it at south-west, and at six, at West, and at nine, at Northwest, and at twelve of the night, at North.  
And at three after midnight at North-east, and if the sun be more towards the North, then at the midst of the day, you shall have him at North, and at twelve of the night at South. And by these courses you shall take out the rest, according to the place and time, wherein you shall find yourself. Likewise it is to be noted, as before hath been declared.  
The Moon being in the North-east or south-west, it is full Sea, and in the Southeast and Northwest, it is low water. And to know when he is in these courses, the course must be sought where the Sun should stand according as the days of the moon are,  
And of this is understood that although here goeth written, the courses where the Sun aught to be, because the Moon should be in the North-east, and that hour full Sea. Likewise it is to be understood, that the Sun being in the contrary course of that, the Moon 〈◊〉 in the south-west, and it willbe likewise full Sea, and the 〈◊〉 willbe at the low water. And in this sort the account serveth, as well 〈◊〉 the first tide, as for the second, the which may be, taken out by the figure 〈◊〉 lowing.  
Of this figure is to be noted, that being known how many days the moon is old, and seeking it in this account, and the Sun being come to that course, where the like number is, or to his contrary, that hour will be full Sea, keeping reckoning that at twelve of the clock of the day the Sun is at South, and at twelve of the night at North: And that in three quarters of an hour the Sun passeth from one point to another.   

The seventh Chapter, how by the hour wherein the conjunction was, the tide may be known, and the allowance that aught to be given to the rivers.  
IT hath been declared, how it shallbe known, at what hour the tides come every day, by counting the number of days of the moon, & by that means looking in the course where the sun should be, as in the Chapters before written hath been declared. And besides this, it seemed good to me, to put here a rule, and account, because not only by the days of the moon, & courses of the sun, but by the hours, the hour being known wherein the conjunction was, shallbe known every day, at what hour of the day or the night, the tide will come: and for this you must know the account following.  
Look in what day and what hour the moon was in conjunction, and being known, you shall find that every day the tide doth come four quintos or four five parts of an hour forward, so that if the tide come this day at one of the clock, to morrow he will come at one and four five parts of an hour, and the next day at two, and three five parts, and so the rest of the days as by this account appeareth.  
Days. Hours. Fifthes. 1  4 2 1 3 3 2 2 4 3 1 5 4  6 4 4 7 5 3 8 6 2 6 7 1 10 8  12 8 4 12 9 3 13 10 2 14 11 1 15 12 2● 16 12 4 17 13 3 18 14 2 19 15 1 20 16  21 16 4 22 17 3 23 18 2 24 19 1 25 20  26 20 4 27 21 3 28 22 2 29 23 1 30 24   
IT is to be noted that the hours here 〈◊〉, being joined with the hours of the moon which she hath in the conjunction, besides those days that be more than four and twenty, there shallbe taken out once twelve, or twice if it he needful, and t●ose which remain shall be the hour in the which the tide 〈◊〉 come. Item it is to be noted that the accounts which before hath been declared, whereby may be known, at what hour the tide will come, is as much as to the natural course of the moon, more it is so that accidentally, it is not in all parts, or in all coasts that the tides are equal, although they be in one Meridian, they come not so at one time, by reason of the great currents, or the straights of the Sea, great gulfs, or entrance of Land into the Sea, or winds, or for other cause, by the which always the practice of the Land aught to be looked unto.  
Likewise, it is to be understood, that there aught to be given allowance to the rivers, because they make not the tides according to the bar, and there should be given them allowance, a quarter later because in the coasts, the tides beginneth to ebb more speedily, and in the rivers it cannot be done, by reason of the holding back or stay of the waters that cometh from above, and the like is to be given at the flowing, this is common, but the allowance is not always equal to all rivers, because some do flow and ebb more than other some.  
This is by reason that some rivers have more current than other some, and likewise when the flowing is helped with wind, therefore the disposition of the place is to be looked on.   
The end of the seventh Book.   

❧ The eight book of the days of the year.  

The first Chapter, what thing a day is, and how it is reckoned, and in how many parts it is divided.  
In such sort, that how much the variation of the Horizon is, so much is the variation of the days in length or shortness, and if this should he made even for all Horizontes, it were convenient, to have for every one a Table of equality of the days, where should be well near an infinite number, so that the Astronomers to fly so great adiversitie, began the day, in the midst of the day, because one is sufficient for all parts, and seeing that we have spoken of the natural day, let us speak also of the artificial day.  
The artificial day is the time which the sun doth show light unto us, going above our Hemispherio, and is called the artificial day, because he is different in diverse parts, & because the Artificers do make their works in him, the which is divided into four parts accoring to 4 differences, which the Sun maketh. In the first he shineth, in the second he heateth, in the third he burneth, in the fourth he warneth, the night consequently hath four parts. The first is the first sleep, the second is midnight, when all things hold their peace, because it is no apt time to work any thing, the third when the Cock croweth, the fourth when the day doth begin to appear. There is another time called Cropusculo, and is, when it is neither day nor night: so between day and night, as between night and day.  
This Cropusculo is that bright time, which we have in the Morning, before the Sun riseth, as likewise that which we have in the Evening, after that the Sun is set: until the darkness of the night do come.  
This Cropusculo is greater or lesser, according as the day is great or little, and so in the Summer we have a greater Cropusculo than in the Winter, and in that part it should be greater, where the days are greater, and so we see, that in Flaunders in the Summer, at ten of the clock in the night, although it be two hours after Sun let, there is so much light, that any letter may be read.   

The second Chapter, how in the artificial day the Sun riseth and setteth, differently to such as inhabit in the world.  
IT hath been declared, what thing a day is, and how the natural day, and artificial day, are understood. In this I will speak how the sun coming forth in the Horizon, & rising up by our Hemispherio, cometh to the Meridian, and from thence descending, and cometh to the orrident, where he setteth to us, and as this is done indifferently to such as inhabit in the world, of the which it is to be understood, that the going forth which the sun maketh, every day by our horizon, is not equal one day with another, and that this is true, experience doth show it. And to be likewise so, the quantity or greatness is not equal one day with another, but of this is to be noted, that in the degrees or distance of the equinoctial, wherein the sun cometh forth every day, in the same he setteth, likewise it is to be noted, that although the day be great or little, always a man being in one place, the sun cometh every day at the midst of the day, into one self Meridian, without any manner of variation.  
Likewise it is to be understood, that because the sun cometh not forth equally at one time to all such as inhabit in the world, nor all of them do see him at one time, so the midst of the day is not made at one time to all. In such sort, that how much the more any place is more easterly, than other, by so much, such is inhabit there, do see the sun rather, & doth begin to appear rather to them then to such as are more westerly. And in this manner successively, even as the sun goeth rising above the Horizon of some, so he goeth showing & appearing indifferent parts to others: so that when to us it is the midst of the day, such as are more westerly, to some it willbe xi. a clock, to other x, & to others it. And so how much more distant he is of us towards the west, so much the later the sun cometh forth to them, and so by the said reason, he cometh later to their Meridian, I say more late to our respect, and such which are from us more easterly, because the sun came forth to them first, then to us, they had the day first. And in this manner, is to be understood that at the xxiiii. hours, that the sun goeth about the world, when to some it is day, to othersome it is night, & when to some it is the morning, to others it is the Evening, and when he riseth to some, he setteth to othersome, and when to some it is midday, to others it is midnight. This is because as the sun moveth himself round about the world, & always goeth lightning the half of the roundness, doth cause the said differences. And it is to be noted, that in the moving which the sun maketh, he moveth every house by the roundness of water and earth, 262 leagues, because the vi. thousand three hundred leagues being parted, which the roundness hath in the xxiiii. hours of the natural day, it cometh to every hour 262 leagues. And so by this reckoning, looking what hour it is of the day in the place where a man as, he shall know what hour it is in any other part, knowing the distance of the leagues which are to that said place.   

The third Chapter, how that under the Equinoctial, the days and nights are always equal.  
IT was an opinion of some ancient writers, that under the Equinoctial, and likewise all the Torrida Zona was inhabitable, the which they believed, because that there the sun doth sand his perpendicular beams, there should be such excessive heat, that it was not habitable: of this opinion was Virgil, and Ovid, & other singular men. Others there were, which healed that some part was habitable, following Ptholome, which in the book that was compared to the art of the Sphera, saith, it is not convenient, that we should think the Torrida Zona to be altogether inhabitable. Other there were, which healed that there it was not only temperate, & without too much beat, but also most temperate. And this is affirmed by S. Isidore, in the first of the Etimologias, where he saith that the earthly Paradise is in the East part under the Equinoctial, a most temperate place, and Ptholome likewise saith in the third of the Quadri partiti, that all the temperate complexions do proceed of the Equinoctial. The experience doth now show us, that not only under the Equinoctial, but all the Tortida which is from one tropic to the other, is habitable, rich, and plentiful, because well near all the year, the days and nights are almost equal: so that the freshness of the night, doth temper the heat of the day, and so continually the earth hath season to bring forth and increase her fruits.  
But it is to be noted, that touching the equality of the days & the nights, there may be had a doubt, and say that the sun in no time doth make equality of the day with the night, but always the artificial day is greater than the night by these reasons following.  
It is certain that a shining body being greater, lighteth the darkness more than half, and as the sun is greater than all the earth, so that as it hath been said, that it is the opinion of Alfragano in the difference twenty two, that the Sun is 166. times greater than the earth, so that the Sun doth light the earth more than the half.  
The lesser part remaining dark, in such sort, that the Sun is seen in a greater part of the earth, then in that part where he is hid, and as the presence of the Sun is cause of the day, and his absence causeth the night, it followeth, that the sun never maketh equality of the day, and of the night. Likewise the aforesaid is proved, wherein a case is given, that the half of the Equinoctial, is above the Horizon, and the other half beneath, for the greatness of the Sun is the greater part where he lighteth, then in that which he hideth himself: it seemeth evident, that the part is greater that the sun lighteth, then that which he leaveth dark. By the which reason is proved that the Sun maketh not equality of the day with the night.  

A declaration.  
Contrary to that which is said are many reasons, I will speak of three in short time. The first is, that our sight doth manifest, how all days are not equal, but some days greater, and some lesser, by the which wheresoever is given greater and lesser, is like wise necessary that there be given an equality, so that as there is a day greater than the night, & a night greater than the day, of necessity must be given day and night equal, because it cannot pass from one extremity to another, but by the mean: To the second, the Philosopher saith in the sirt of the natural philosophy, that the sun being come to the Equinoctial, the moving which he maketh above the earth, is equal with that which he maketh under. And in like sort, the time of the day is equal with the time of the night.  
The third, answering to the reasons aforesaid, I say that it is true, that the Sunite lighteth more than half the earth, as the perspective reason showeth it, but it is to be denied, that the day in the Equinoctial is greater than the night, not because when soever any part of the light of the Sun is seen, the day beginneth, but it beginneth when the Ce●●er of the sun cometh forth, and not the parts circumferentials. And so likewise when he setteth, the night beginneth. The reason is because the Planets, and the stars do occupy a great quantity, and their place, and moving is not to be taken, by any manner of part, but it aught to be taken by the Centre, and so it is said that the Sun is in the Equinoctial, when his Centre is there.    

The fourth Chapter, how the days and the nights go always increasing or diminishing unto such as inhabit forth of the Equinoctial.  
IN the first Chapter of the fourth book hath been declared, that from the Eqnivoctiall, to the pole arctic is called the North part, & from the Equinoctial to the pole antarctic, is called the South part. Therefore it is to be understood, that such as inhabit from the Equinoctial, towards the North part, or the pole arctic, as the sun cometh to the tropic of Capricorn, the thirteenth of December, & so beginneth to return to the line, how much he cometh from the said tropic, so much the days go increasing, and to such as inhabit towards the South part, they go decreasing. And the sun being come to Aries the eleventh of Match, he describeth the Equinoctial line, and maketh in all parts the days and nights equal, and being past the first point of Aries, the days begin to wax greater than the nights & to those of the other part, the days lesser, & the night's greater, & the sun being come to Cancer the eleventh of June, the day is greater, and the night lesser, & to the other part the contrary: for then the sun is more near to some and more distant to other some, & from thence the sun turneth to descend, & as he goeth away from that part, the days go decreasing, & the nights increasing, & being come to Libra, the 13. of September, he returneth to describe the Equinoctial, and the days & the nights are to all equal, & from thence he goeth descending to Capricorn, & the nights begin to be greater than the days, & towards the South part, the days greater, and the nights lesser, & as he cometh to the said tropic, it maketh a greater night, and a lesser day, & to those of the other part, the day greater, and the night lesser, for there the Sun goeth more distant from some, and cometh nearer to other some.  
Whereby it is to be noted, that if there be taken two days of the year, equally distant of the Equinoctial line, of contrary parts, that how great the artificial day is of the one, so great the artificial night is of the other. Likewise it is to be understood, that how much in every habitation, the pole is more raised above the Horizon, so much the days & the nights are greater, so that those whose zenith is in the circle arctic. To whom the pole riseth above the Horizon, sixty six degrees and a half, when the sun cometh to the first point of Cancer, the eleventh of June is to them one day 24. hours, and the night very short, because in one moment the sun toucheth that day his Horizon and immediately cometh forth, and that touching they have for night. And the thirteenth of December, when the sun cometh to the first degree of Capricorn, than he is to then a night of 24. hours, and a little moment for the day, for in one instant, the sun toucheth his horizon, & forthwith he hideth himself, and that touching they have for a day, by the contrary, such as inhabit under the circle antarctic, have the like. And those whose zenith is between the circle and the pole of the world, whiles the Sun goeth towards the North part, it willbe to him one day, that which his Horizon doth discover of the Equinoctial, continually without night, and if that were of the quantity of one sign that day would be of one month. And if of two sign, it would be of two Months, and so the rest: and he that were under any of the poles, all the year would be to him one day and one night: In such sort, that if he were under the pole arctic, the six months which the Sun goeth to the part of the North, would be to him one day without any night, and the other six which he goeth towards the part of the South, would be one night, without day, and so contrary it would be, if he were under the pole antarctic, so that half the year, it would be to him one day, and the other half, one night. The cause is, by reason the roundness of the world, how much it goeth towards the poles, so much it goeth to be lesser, and so the Horizon of such as are nearest to the poles, do discover more part of the turn which the Sun giveth in the heaven, when he goeth from that part: In such sort, that the earth, nor the water, doth not occupy the sight of the Sun, all the time that he goeth, rising up, and turneth descending, until he cometh where his Horizon doth not discover any thing of the circle or turn, that the Sun maketh to the world, and so how much more, the part is which is seen of this turn, so much the day willbe greater.   

The fifth Chapter, how the increasing and diminishing of the day is not in all parts alike.  
MAny things are put in the common opinion of the people that reason, & truth doth show it to be in another manner. And among others, one is that many do think that the increasing, & decreasing of the days through all the year are made equal, I will say that the time, which those days goeth increasing, so much increaseth one day as another, and so when they decrease even by the like sort.  
And according to the quantity of hours which the day increaseth, from the lesser day to the greater, those being parted by the time of the 6. months, which the day doth increase, they consider how much it is that it increaseth every day, giving equal number or quantity of time to one day, & so much to another. And likewise when the day goeth decreasing how much it is that it decreaseth: in such sort, that the lesser day, having nine hours, and the greater 15. these 6. hours which he increaseth, divided into 6. Months, the days should increase one hour every month. And so by the contrary in the other 6. Months, it would decrease an hour every month: (This is not so) for in truth only in the month of March, the days do increase as much as they did increase in the 2. Months of Januarie and February, and by the contrary, they do decrease so much in the only month of September, as they do decrease in July and August: also in the Calendars, in the head of all the Months is written, that the days have in every month, so many hours, and the night so many. Of this is to be understood, that neither the days are equal in all the month, nor the number of the hours are one in all places. For in the city of Cevill, the days are of one quantity, and in Toledo, of another, & in Burgus another, and so proceeding to the place where the day is of 24. hours: so that the days of every month be not equal in hours, nor the days be not equal in all parts, the cause is, as the sun maketh difference from one month to another in coming near, or going from the Equinoctial line, so the days go increasing or diminishing this coming near, or going away of the sun, he doth it not always alike, but he doth it in this manner.  
From the 12. of March, that he goeth forth of the Equinoctial, he beginneth to rise up, by the part of the north, from thence until the 12. of April, he hath gone from the said line, 12. degrees, and from the 12. of April, to the 12. of May, he hath gone distant other 8. degrees, & from the 12. of May, to the 11. of June, which he cometh to the tropic, he goeth distant other three degrees and a half, which are in all 23. degrees and a half, which the sun hath of declination or distance, from the said line, in such sort, that the first month he goeth distant, the half of the said declination, and the second month the third part, and the third, the sixth part, and so in the increasing of the days. The 11. of March, the days & nights are equal, and from thence to the 11. of April, the day increaseth half of all the time that he will increase, & from the 12. of April, to the 12. of May, he increaseth the third part, and from the 12 of May to the 11. of June, he increaseth the sixth part, whereby that in the strait course, where the greatest day hath 15: hours, the 12. of March, it hath 12. and the 12. of April, 13. & a half, and the 12. of May 14. and a half, and to the 11. of June 15. And by this reason in the strait course, where the greatest day hath 16. hours, and in him where he hath 14. or more, or less: the 12. of May, or in any other day, except in the Equinoctials, the days will not be equal, but one willbe greater than another, in such sort, that the day hath more increased to them which have 16. hours then to them which have fourteen, so that such as have sixteen, the twelfth of May, the day hath increased two hours, and to such as have fourteen, it hath not increased more than one, And as the day went increasing at the rising up of the sun, so he returneth diminishing or decreasing, when he descendeth. And so the reckoning aught to be kept in all parts, according to the quantity of the time and hours, which the greatest day hath.  
And it is to be noted, that how much the day increaseth of twelve hours upward: so much he decreaseth of twelve hours downward, therefore to know the quantity of hours, and points, that the greatest day of the year hath in every degree of distance of the Equinoctial line: In the table hereafter written, shallbe declared, the which is likewise to be understood for the part of the South, as for the part of the North.  
And it is to be known what day it is called in this reckoning from the time that half the body of the sun riseth, until the other half be set, & all the other is night, also the hours or parts of the day are not understood by the twelfth part of the day, or of the night, but by these vulgar things of the clock, for by another name they are called Equinoctials: for in every one of them riseth fifteen degrees of the Equinoctial, & other fifteen setteth. And likewise it is to be understood, that in this account threescore points or minutes do make an hour, & thirty, half an hour. And so of the rest.  

A Table of the hours, and minutes which the greatest day of the year hath, to such as inhabit in any manner of distance of the Equinoctial.  
Deg. Hour. Minut. Deg. Hour. Minut. Degrees Hours minutes. 1 12 1 23 13 27 45 15 27 2 12 3 24 13 30 46 15 33 3 12 5 25 13 34 47 15 40 4 12 8 26 13 39 48 15 50 5 12 12 27 13 43 49 16 2 6 12 17 28 13 48 50 16 11 7 12 21 29 13 52 51 16 22 8 12 25 30 13 57 52 16 34 9 12 29 31 14 2 53 16 45 10 12 34 32 14 7 54 17 0 11 12 40 33 14 12 55 17 15 12 12 45 34 14 17 56 17 30 13 12 49 35 14 22 57 17 45 14 12 54 36 14 27 58 18 0 15 12 57 37 14 32 59 18 20 16 13 0 38 14 38 60 18 40 17 13 4 39 14 45 61 19 0 18 13 7 40 14 52 62 19 30 19 13 11 41 14 59 63 20 0 20 13 15 42 15 6 64 21 0 21 13 19 43 15 12 65 22 0 22 13 23 44 15 19 66 23 0 66m 24 0    

The sixth Chapter, of the hours, points or minutes, that every day of the year hath in the altitude of forty degrees.  
IN the table before written, hath been declared the number of the hours and minutes, or points that the greatest day of the year hath in any manner of distance, of the Equinoctial line, and because it is likewise profitable, to know the hours & points, that successively, every day in the year, hath in every part. But for to make this apparent, to all persons, it were needful to have many tables. Therefore this is only taken out for the altitude of forty degrees, where the greatest day hath fourteen hours &, and fifty two minutes, which are well near fifteen hours. For in this altitude, is the midst of Spain, so that with little difference or more or less, it may serve in all Spain.  
In the other parts may be taken out the reckoning, according to the greatness of the greatest day, agreeable to the Table before written.  
januarie. February. March. Days Hours Points Days Hours Points Days Hours Points 1 9 22 1 10 22 1 11 34 2 9 23 2 10 24 2 11 36 3 9 24 3 10 26 3 11 39 4 9 25 4 10 29 4 11 43 5 9 26 5 10 3 5 11 44 6 9 28 6 10 34 6 11 47 7 9 30 7 10 37 7 11 50 8 9 32 8 10 40 8 11 53 9 9 34 9 10 42 9 11 56 10 9 36 10 10 44 10 11 59 11 9 38 11 10 46 11 12 2 12 9 40 12 10 48 12 12 4 13 9 42 13 10 50 13 12 8 14 9 44 14 10 53 14 12 11 15 9 46 15 10 56 15 12 14 16 9 48 16 10 59 16 12 16 17 9 50 17 11 4 17 12 18 18 9 52 18 11 7 18 12 21 19 9 54 19 11 10 19 12 24 20 9 57 20 11 12 20 12 26 21 9 0 21 11 15 21 12 29 22 10 2 22 11 18 22 12 32 23 10 4 23 11 20 23 12 35 24 10 6 24 11 23 24 12 37 25 10 8 25 11 26 25 12 39 26 10 10 26 11 28 26 12 41 27 10 12 27 11 30 27 12 43 28 10 15 28 11 32 28 12 45 29 10 46    29 12 48 30 10 18    30 12 50 31 10 20    31 12 53  
April. May. june. Days Hours Points Days Hours Points Days Hours Points 1 12 56 1 14 4 1 14 47 2 12 59 2 14 6 2 14 47 3 13 2 3 14 8 3 14 48 4 13 4 4 14 10 4 14 48 5 13 6 5 14 12 5 14 49 6 13 9 6 14 14 6 14 49 7 13 12 7 14 16 7 14 49 8 13 14 8 14 18 8 14 50 9 13 16 9 14 20 9 14 50 10 13 18 10 14 22 10 14 51 11 13 20 11 14 24 11 14 52 12 13 22 12 24 26 12 14 52 13 13 24 13 14 27 13 14 52 14 13 26 14 14 28 14 14 51 15 13 28 15 14 29 15 14 50 16 13 31 16 14 30 16 14 50 17 13 34 17 14 32 17 14 49 18 13 36 18 14 33 18 14 49 19 13 39 19 14 34 19 14 48 20 13 42 20 14 36 20 14 48 21 13 44 21 14 38 21 14 47 22 13 46 22 14 39 22 14 47 23 13 48 23 14 40 23 14 46 24 13 50 24 14 41 24 14 46 25 13 52 25 14 42 25 14 45 26 13 54 26 14 43 26 14 45 27 13 56 27 14 44 27 14 44 28 13 58 28 14 45 28 14 43 29 14  29 14 45 29 14 42 30 14 2 30 14 46 30 14 41    31 14 46     
julie. August. September. Days Hours Points Days Hours Points Days Hours Points 1 14 40 1 13 50 1 12 38 2 14 39 2 13 48 2 12 33 3 14 38 3 13 46 3 12 29 4 14 37 4 13 44 4 12 26 5 14 36 5 13 42 5 12 23 6 14 35 6 13 39 6 12 19 7 14 34 7 13 36 7 12 17 8 14 33 8 13 34 8 12 15 9 14 31 9 13 32 9 12 11 10 14 30 10 13 30 10 12 7 11 14 28 11 13 28 11 12 4 12 14 26 12 23 26 12 12 2 13 14 25 13 13 24 13 12 0 14 14 24 14 13 22 14 11 59 15 14 22 15 13 20 15 11 57 16 14 20 16 13 18 16 11 55 17 14 18 17 13 16 17 11 52 18 14 16 18 13 14 18 11 49 19 14 14 19 13 12 19 11 46 20 14 12 20 13 9 20 11 44 21 14 10 21 13 6 21 11 41 22 14 8 22 13 4 22 11 38 23 14 6 23 13 1 23 11 36 24 14 4 24 12 59 24 11 33 25 14 2 25 12 56 25 11 30 26 14 1 26 12 53 26 11 28 27 14 0 27 12 50 27 11 25 28 13 59 28 12 48 28 11 22 29 13 58 29 12 46 29 11 20 30 13 56 30 12 43 30 11 17 31 13 54 31 12 40     
October. November. December. Days Hours Points Days Hours Points Days Hours Points 1 11 15 1 10  1 9 15 2 11 12 2 9 58 2 9 15 3 11 9 3 9 56 3 9 14 4 11 6 4 9 54 4 9 14 5 11 4 5 9 52 5 9 13 6 11 1 6 9 50 6 9 12 7 10 58 7 9 34 7 9 11 8 10 56 8 9 46 8 9 11 9 10 53 9 9 44 9 9 10 10 10 50 10 9 4● 10 9 9 11 10 48 11 9 40 11 9 9 12 10 46 12 9 38 12 9 8 13 10 44 13 9 36 13 9 8 14 10 42 14 9 34 14 9 8 15 10 39 15 9 33 15 9 9 16 10 36 16 9 32 16 9 9 17 10 34 17 9 30 17 9 10 18 10 31 18 9 28 18 9 10 19 10 29 19 9 26 19 9 11 20 10 26 20 9 24 20 9 12 21 10 23 21 9 23 21 9 13 22 10 20 22 9 22 22 9 13 23 10 18 23 9 21 23 9 14 24 10 16 24 9 20 24 9 14 25 10 14 25 9 19 25 9 15 26 10 12 26 9 18 26 9 16 27 10 10 27 9 17 27 9 17 28 10 8 28 9 17 28 9 18 29 10 6 29 9 16 29 9 19 30 10 4 30 9 16 30 9 20 31 10 2    31 9 21   

The seventh Chapter, of the hour, and point which the sun riseth, and setteth in every one day of the year.  
ANd seeing there hath been declared in the Chapter going before, the hours, and minutes which every day hath, it is convenient to speak in this at what hour and minute the sun riseth and setteth, in every day of the year: for the which first of all, it is to be noted, that for to take out the hour when the sun shall rise, is to be reckoned from xii. of the clock in the night. And the hour when it shall set, is to be reckoned from xii. of the clock in the day. Therefore look over the hours and points which the sun hath, and divide them in the midst, & that which one half doth amount to, take it out of twelve, and that which remaineth shallbe the hour, wherein the sun riseth, and the same half shall be the hour wherein the sun setteth, so that for when he riseth take out of xii. half of the number which the day hath: And to that which remaineth, is the point, where the sun riseth and setteth himself after the midst of the day, at the point which is half of the number that the day hath.  

An example.  
The first day of Januarie, he hath niene hours, and xxii. points, half this is iiii. hours, and forty one points, therefore these four hours, and forty one points, taken out of xii. hours, remaineth seven. hours & nienteene points, and so the first day of Januarie, the sun cometh forth at seven. of the clock, and nienteene points after midnight, and setteth at four of the clock, and forty one points, after the midst of the day, which was half the number that the day hath.    

The eight Chapter, how the sun giveth his light at equal time of the year to such as inhabit in the world.  
IN the rules and accounts before declared, there might be a doubt saying, seeing that in some parts of the world, The days be great, and in other parts little, let us see if in any one part of the world the sun shineth in all the year more time then in other. To this is to be noted, that although it be true, that in some part of the world, & times of the year, the days & nights be greater than in other some, it is to be taken, that the sun by his own moving, that he maketh in the year, at equal time of the year is seen and giveth light in all parts, so that as long time of the year he is seen in the part where the days be little, as in the part where they be great, the which is known in this manner, consider that which every part hath in it, of the day, and that which it hath of the night in this manner, such as inhabit under the equinoctial, as they have continually, the days equal with the nights, every one of them xii. hours, it is certain that half the time of the year they have day, and they see the sun, and he showeth light to them, and the other half they have night, that they see him not, and such as devil in forty and two degrees which have the greatest day of xv hours, they have also day of niene hours, and so as the day goeth increasing from xii. to xv. hours, so they come decreasing unto nine, in such sort that the said time, which they have of day, the same they have of night, so consequently those which inhabit in sixty degrees which have the greatest day of xx. hours, they have likewise day of four hours, and as the sun goeth lighting of them, & the days increasing unto twenty hours, likewise they go decreasing until the day be no more but iiii. hours, and the night goeth increasing and diminishing the like. And of those which inhabit in sixty six degrees and a half, have the greatest day of twenty four hours, likewise they have night of the said xxiiii. hours, and such as have day of one month without night, have likewise a month of night without day, and such as should have six months of day without night, should have other six months of night without day, and so the time being considered which every part hath of day, and being seen, that as much justly it hath of night: So shallbe found that not only in the torrida zona, by the which the sun continually moveth, but likewise in the other parts very distant and far off, and also under the poles themselves, so long time of the year it is that the sun is seen, as the time that he is not seen, in such sort, that the sun giveth his light in equal time in all parts, and not in one more than in another. So the omanipotent God, maker of the heavens, of the earth, & of all that is in them, did dispose and ordain, whose name be blessed, in the worlden worlds. Amen.   
The end of this book of Navigation.  
God save the Queen.   

❧ Imprinted in London at the three Cranes in the vinetree, by Thomas Dawson, and are there to be sold. 1581.