THE Art of Navigation.  
Containing a compendious description of the Sphere, with the making of certain Instruments and Rules for Navigations, and exemplified by many Demonstrations.  
Written by MARTIN CORTES spaniard.  
Englished out of Spanish by RICHARD EDEN, and now newly corrected and amended in divers places.  
¶ At London printed, at the charges of Richard Watkins. 1589.   

¶ To the right worshipful Sir William Garerd Knight, and Master Thomas Lodge, Aldermen of the City of London, and governors of the honourable Fellowship or Society, as well of certain of the Nobility, as of Merchant's Adventurers, for the discovery of Lands, Territories, islands, & Signories unknown, and not before their first adventure or enterprise by Sea or Navigation commonly frequented.  
And to the right Worshipful the consuls, Assistants, and Commonalty of the same Society, RICHARD EDEN wisheth health and prosperity.  
WHat so ever he was (right Honourable and Worshipful) that first believed that the frame and coaptation of the body of man, with the functions, offices, and duties of the parts and members of the same, knit together in a certain unity to a common ministration, did represent a lively image & similitude of a perfect Common wealth: I think that he was a man of no vulgar judgement, or object mind, but rather of singular wisdom and prudence, in the contemplation of divine & human things. For he saw, that as in the small native seed of all growing or living things, is contained the form that bringeth them to their perfection: so in certain small and obscure members of the Common wealth, consisteth no small increase to the perfection of the whole. He saw likewise, that herein, as in the body of man, representing the parts and members of the world (as I have said) are divers parts of divers and sundry actions & motions, greatly differing in form, number, and quantity, yet all the same to be so knit together, and so to consent in one uniformity, to the common profit of the whole, that a greater concord & harmony can not be imagined, then is proportioned by the friendly unity of divers and contrary. He saw likewise in the same, such a mutual compassion of part to part, and member to member, by one common sense existent in them all, that no one part or member can feel either joy or pain, but that in manner all the other are partakers thereof more or less, if they be lively members, and not withered, or otherwise unsensate by reason of dead flesh, which only by cutting and burning aught to be divided from the sound and whole. But as in man (whom Plato calleth the less world) the vigour and agility of the immortal soul and mind never ceaseth from continual moving, but is ever exercised in excogitations & inventions of great things (herein resembling God, whose carat it beareth) by providence foreseeing, and by intelligence understanding, and devising what is to be done, and what to be eschewed, doth immediately move and raise up the faculties, powers, and members of the body to execute the same: Even so, in the greater world, the providence of God, and universal counsel and consent of men, hath elected & appointed certain principal men, to bear like rule & authority in the body of the Common wealth, as hath the intellective soul in the members of our body to move and command the same. To Princes therefore, counsellors, Rulers, Governors, and Magistrates, as to the most intellective and sensitive parts of the society of men, hath God and Nature given pre-eminence and governance of the Common wealth, that by their providence, wisdom, and aid, it may universally flourish, not only by just administration of good laws, with due correction of malefactors, but also by liberal rewarding of such as have well deserved, and especially by maynteinance of such Arts and Sciences, as the Common wealth can not well be without. And to draw nearer to the applying of my similitude, I say, that what so ever Virtue, what so ever Arte. or the ingenious industry of men, hath to this day invented, all the same is to be imputed to the benevolence and liberality of such as have honourably maintained, and freely rewarded the travails, pains, and charges of them that have spent their lives, goods, and wits (as many have done) in the inventions of necessary and profitable Arts and Sciences. For even as wholesome and temperate air, with seasonable weather, and favourable influence of the heavens and planets, causeth fruitfulness on the earth, and contrariwise, barrenness by the contrary: Even so the favour of Princes and Magistrates, nourisheth, augmenteth, and amplifieth, all Arts and Sciences by liberality, and extinguisheth the same by miserable covetousness and parsimony. And although in some men of rare and noble nature, the desire of honour and fame, only for virtues sake, and study toward their Country and Common wealth, have moved them (in manner to their own undoing, through their great loss and hindrance) to set forth and invent divers things for the commodity of the common wealth, and other, rather than for their owne● yet undoubtedly, who so well considereth, and indifferently weigheth that I have said, shall find and see by daily experience, that in manner only munificence, liberality, and reward, or the hope thereof, giveth spurs to them that attempt great and virtuous enterprises, as I could more largely prove by so many testimonies of histories, both holy & profane, that the rehearsal thereof should be but tedious, and not greatly necessary for my purpose, especially writing unto your Honours and Worships, of whose munificence, and liberality, I have had great experience, both in myself, and others, who by your aid and maintenance, have attempted, & performed many goodly inventions, voyages, navigations, and discoveries of lands and seas, heretofore unknown. Wherein, what great charges you have sustained, and how liberal and constant you have bee● in furthering the same, doth well declare, th●t hitherto you are rather losers than gainers thereby. The which thing doubtless, is more to your commendation, in that it may hereby appear that you have attempted the same, rather for knowledge and virtues sake, then for covetousness of gains: as is furthermore well known by your first voyages of discovery attempted to Cathay, by the North-east seas, upon certain loss and detriment, for uncertain hope either of gains, or of any such way to be found, otherwise then by certain likely conjectures: not much unlike to the shining flowers of Marchasytes, which outwardly appearing in mineral mountains, are signs and tokens whereby is conjectured what metal is contained therein, and whether the same be to be followed or not. And although it sometime so chance, that such signs are failable, showing more in appearance, than they contain in substance: yet are not such signs, tokens, or shows to be contemned, but rather earnestly to be followed, for as much as it hath been often proved, and found by experience, that by following the same, have been found great and rich mines of metals, as Georgius Agricola in his books De rebus metallices, doth largely declare and prove by many examples. But to write at large what great things have proceeded of small and obscure beginnings, and in manner mere conjectures, it would so far exceed the measure of an Epistle or Preface, that it would rather increase to the just quantity of a book. For in manner all the late discoveries both of the Spaniards and Portugals, had their beginnings of such small conjectures, with uncertain hope (as it were praeter spem sub spe) until God and good hap, by the constant travail and valiant mind ●f such as first attempted the same, gave them to enjoy that they hoped for. But what so ever they have obtained, and do enjoy, this may I boldly say in your behalf (right Honourable and Worshipful) that there hath not lacked in you, either the like or greater promptness of mind, forwardness in attempting, magnificence in expenses, or liberality in rewardes● For beside the great charges, and losses that you have been at otherwise, what should I speak of the great gifts that you have sent to the Emperor of Russia? What of your last chargeable viage of discovery among the innumerable Rocks, Islands, and movable mountains of ice in the frozen sea, by innumerable lands and islands unknown to the Antiques, even under and far within and beyond the circle Arctic, where they thought that no living creature could draw breath or life for extreme cold? whereas nevertheless the same hath been by you discovered, even unto the mighty river of Ob, that falleth into the Scythian Ocean, or Oceanus Hyperborei, not far from the mountains called Hyperboreus, so named, because they are situate almost under the North Pole, and thought therefore to be inaccessible. A voyage doubtless of such difficulty, and in manner impossibility, that considering the infinite dangers thereof (as I have learned by the information of Steven a Burrough, that was then the chief Pilot of the same voyage) it may seem impossible that they should ever have escaped, except the mighty hand of God, by the expert skylfulnesse of so excellent a Pilot, had delivered them from those dangers. And although in deed (as religion bindeth us) it is convenient in all things to give all honour, glory, and thanks to God: yet are we not thereby restrained to be thankful to such men, as by their art, ingeniousness, travail, and diligence, have deserved both just commendation, and large reward. And therefore referring the reward to you (right Honourable & Worshipful, to whom it appertaineth) if I should not here give him at the least such commendation as in my judgement he hath well deserved, I might seem both to defraud him of his worthy deserts, and also to forget the friendship and good will I bear him, only for his virtues and excellency in his profession. For certainly when I consider how indigent and destitute this Realm is of excellent and expert pilots, I can do no less of conscience, then, in respect of your own commodity, yea rather for the commodity of the Queen's Majesty, and the whole Realm, to exhort you, and put you in remembrance (although I may herein seem to put the Spurss to a running Horse, as saith the Proverb) so to regard him, and esteem him, and his faithful, true, and painful service toward you, that he may thereby be further encouraged, and not discouraged, either for lack of maintenance, or otherwise by the injurious assaults of such his enemies, as only his virtues and excellency have moved to bear him displeasure: as envy doth ever follow virtue, as saith the Latin Proverb, Virtuti comes invidia. And how true a sentence this is, is well verified by the saying of a certain Philosopher (whose name I do not remember) who hearing one vainly rejoice that he had no enemies, answered, that that was a token he had done little good: meaning thereby (as daily experience proveth) that if he had excelled in any virtue, he could not have lacked some enemies. And having here touched ●o speak of envy, I remember that when I was a young Scholar, I have read in the Poet Hesiodus of two kinds of envy, whereof the one is called invidia, and the other Aemulatio, which is more tolerable than the first, for that it is joined with some virtue, and envieth that any should excel him in any excellent quality that he professeth. But for as much as this envy of emulation proceedeth of some singular virtue of them that are so maliced, they may herein rejoice, that they shall ever have a hundred friends for one enemy: yea, and although they had none, yet is virtue a reward to itself, and to be embraced for itself only, as the Philosophers affirm. What then shall we say to such, as forgetting this reward of virtue, do not only favour, but rather hinder the preferment and maintenance of such expert men, more esteeming certain fishermen that go a trawling for fish in Catches, or Mongers, and Dradgies for Oysters about the sands, between the South furland and Wyntertonnesse, and the sands about Thames mouth, than they do such excellent Pilots as are able without any Rutter or Card of Navigation, not only to attempt long and far voyages, but also to discover unknown lands and Islands, as have done of late years many excellent men, to the great honour and enriching of their Prince and Country. But as touching Ste●en a Borough, the chief Pilot of your voyages of discovery, it may hereby well appear, that he is neither malicious nor envious of his Art and Science, in that he desireth the same, for the common profit, to be common to all men: and for the same inte●t was the first that moved certain Worshipful of your company, as Sir William Garrerd, Master William Mericke, Master Blaze Sanders, and Master Edward Castlen, to have this work translated into the English tongue: Who of their own good nature, favouring all virtuous studies, and the professors of the same, did soon incline to his ho●●st request herein, and therewith not only desired me, but also with liberal reward entertained me, to take in hand the translation. Which being now finished as well as my poor learning may perform, I desire your Honours, and Worships, to accept in good part, as I have meant herein to grat●●●e you, and do such service as my ability may suffice. Now therefore this work of the Art of Navigation, being published in our v●lger tongue, you may be assured to have more store of skilful Pilots. Pilots, (I say) not Pirates, Rulers, nor Rovers, but such as by their honest behaviour and conditions, joined with art and experience, may do you honest and true service: Which is not to be looked for of such as being destitute aswell of the fear of God, as of all moral virtues, superabound in all notorious vices, accounting desperateness for boldness, rashness for hardiness, impudency for stoutness, and cruelty for manhood. What other thing (I say) is to be looked for of such, then of such trees, such fruits, Et mali corui, malum o●um. But forasmuch as these have no place appointed them in the body of our common wealth, which we have here before compared to the members of the body of man: therefore are they no otherwise to be esteemed, then as excrements of the body, to whom Nature hath appointed no place in the same, but laboureth continually to cast th●● forth divers ways, lest by their filthiness they should infect the other members, even as the pomp of the Ship, if it be not avoided, is noyous to the Ship, and all that are therein. But the wise and honest Pilotte, first having before his eyes the fear of God, and putting his chief trust in him, shall secondarily trust in his Art and Science, without any such vain observations, as the superstitious Horoscopers (Astrologiers I mean, and not Astronomers) are accustomed to use in the elections of hours, times, and days, by constellati●ns and aspects of the Stars and Planets, as many fond men have done, thinking thereby to have escaped such dangers, as they have thereby the rather fallen into, through contempt of Art and Science, by foolish confidence in superstitious Astrology: which for the vanity and uncertainty thereof, the right Worshipful, and of singular learning in all Sciences, Sir Thomas Smyth, in my time the flower of the University of Cambridge, and sometime my Tutor, was accustomed to call Ingeniosissimam artem mentiendi, (that is) The most ingenious art of lying. Omitting therefore the superstitious and fantastical observations of the judicials of Astrology, it shallbe better and more necessary for all pilots that desire to excel in their profession, to learn and observe the principles of this Book, whereby they may have such knowledge of the Sphere, as may instruct them the making and use of divers goodly Astronomical instruments pertaining to the art of Navigation, by knowledge of the movings of the Sun and Moon in their Spheres, and the other planets and fixed Stars: thereby to attain to the true knowledge of hours, times, and tides, with the variation of the Compass, and many other goodly natural observations of weather, tempests, and calms, by certain infallible signs and tokens of the same, very necessary to be observed, and this by the true principles of Astronomy, and not of Astrology. And this is the true Astronomy, whereof the divine Philosopher Plato hath written so divine a sentence, that I have thought the same here worthy to be alleged, that by the authority of so famous an author, we may know what is true Astronomy, with the use and commodity thereof. Therefore in his book entitled Timeus vel de Natura, these are his words.  
Rerum autem optimarum cognitionem, nobis oculi attulerunt. Nam haec que de mundo disputantur, nunquam inventa fuissent, si neque Sydera, neque Sol, neque Coelum, suscipe potuissent. Cognitio vero diei ac noctis, ab oculis orta, fecit ut dimensione quadam mensium, annorumque ambitus metiremur, tempus cognosceremus, a● universae naturae ordinem scrutaremur. Quibus ex rebus, Philosophiam adepti sumus.  
That is to say, Our eyes have brought unto us the knowledge of most excellent things. For whatsoever is disputed of the world, had never been invented, if neither the Stars, neither the Sun, neither Heaven, could have been seen. For the knowledge of the day and night, taking beginning at the eyes, cau●ed us, as it were by certain limits and bounds, to measure the circuits of months and years, whereby we came to the knowledge of times, and the order of universal nature. And hereby also we obtain the knowledge of Philosophy. etc. And thus by the authority of divine Plato, (whom for his excellency Cicero called Deum Philosophorum, that is, the God of Philosophers) we may understand, that the true Astronomy, is the perfect knowledge of the miraculous movings of the Planets, Stars, and heavens (and especially of the Sun and Moon) whereby is caused the variety of times, and diversity of all natural things, by natural causes: as by the qualities of Elements, as hot, cold, moist, and dry, which are augmented or diminished by the more or less influence of these two Luminaries, as they come near unto us at sometimes, or depart farther from us at other times, with divers motions in divers climates, which causeth not only variety of times in sundry climates, but also the variety of divers complexions, forms, and dispositions of all creatures under the face of heaven, none other accidental, contingent, voluntary, or violent cause, to the contrary notwithstanding. And this is it that Plato meaneth by these words, Vt tempus cognosceremus ac universae naturae ordinem, etc. That is, to know the times and universal order of nature. And doubtless, who so well considereth the marvelous effects that are caused, especially by the variable moving of the Sun in the Zodiac, must needs acknowledge it to be the chief instrument and mean that God useth in the generation, preservation, and alteration of all creatures that are contained in the world of generation and corruption. And for this consideration, certain of the ancient Philosophers called it the soul of the world: Other, the eye: and other also the heart of the world. Plato also affirmeth, that the soul of the world is the Sun, and that all other living things receive life from thence. And hereof cometh the saying of the Philosopher, Sol & homo, generant hominem: (that is) the Sun and man, beget man. And therefore (as writeth Marcilius Ficinus) of all Idolaters they are most tolerable that honour the Sun for God. The which, although it be not, yet undoubtedly are his effects so great and wonderful in this inferior world, that it may seem in manner to be God's Vicegerent, Lieutenant, and Viceroy, in all the works of nature, except where and when it pleaseth him in any thing miraculously, otherwise then by the common order and course of nature, to command the contrary.  
And if it may not be tedious unto you (right Honourable and Worshipful) it shallbe a pleasure unto me, for the better declaration hereof, to make a brief discourse of the marvelous and strange effects that are caused by the Sun: which perhaps few have done, otherwise then dispearsedly here and there, as occasion hath served. first therefore let us consider what it hath done over the Equinoctial line, and under both the Poles at one instant, diversly and contrarily the one to the other. For so hath the infinite wisdom of the great God of nature, the supreme Architecture of the universal world, disposed all things in such perfect order, that to them that are under the Equinoctial, and have their Horizon passing by the two Poles, the day is of twelve hours, and the night as much, and their year also is divided into twelve months: But they that dwell just and perpendicularly under our Pole, and that have their Horizon passing over the said line, have the day of the six months: That is to say, beginning from the tenth day of March, when the Sun cometh over the said Horizon, until it return to pass under the same at the tenth of September. And contrariwise, one night of six months have the inhabitants under the Pole An●articke: whose year (that is to say, all the course that the Sun maketh by the twelve signs of the Zodiac) is accomplished in one day and one night: a thing doubtless most wonderful and marvelous. Likewise, when we have summer, they that are under our Pole, have the day of six months, and they of the opposite or contrary Pole, have their night of the same length. Again, when it is winter with us, then under our Pole is the night of the said six months, and under the opposite Pole, is the day of the same length. So that, as it were, course by course, when we have the night, they have the day: and contrariwise, when we have the day, they have the night. The which, although it be so long, & of so great space of time, yet is it not continually obscured with darkness. For the Sun maketh his course in such order, that the inhabitants of that part, live not during that time altogether in darknesses, as Moles live under the ground, but as other creatures that live upon the globe and face of the Earth, they have such light as may suffice to sustain and maintain their life. For the body of the Sun declineth no more either beneath the Equinoctial line, either above the same line (which is the Horizon to both the Poles) then 23. degrees, that is to say, no lower or higher than the Tropikes, which are no more than 23. degrees, or there about, from the said Equinoctial, that is their Horizon, as is aforesaid. And yet in these 23. degrees, he maketh not his course by the opposite Diameter, but goeth continually round about in circuit: so that his beams reverberating heaven, represent such a manner of light, as we have in Summer two hours before the Sun rise. And this example which we have taken of the diversity of the Orisons of the Equinoctial, and under the two Poles, is to demonstrate the marvelous effect that the Sun maketh, departing from the xii. hours of the Equinoctial (that is to say, from Aries to Libra) and coming by little and little, illuminating the Globe of the earth, and so reducing the year of xii. months, into one only day, a●d one night, as is said before. Under the infinite variety of the which course, sometime with long days, and sometime with short, all the Inhabitants of the world are formed and disposed, of such strength and complexion of body, that every of them are proportionate of the Climate assigned unto them, be it hot or cold, and may dwell and abide there, as in their natural place and temperament, not lamenting, or desiring to dwell elsewhere, so great a love resteth in them to their native situation. But not to departed from the viage which the Sun maketh in one whole year, as sometime approaching near unto us, and sometime departing from us, I say, that at one self same time, in divers parts upon the round Globe of the earth, it causeth the Spring, summer, Autumn, and Winter. And nevertheless, at the same instant and punct of time, it maketh day and high noon in one place, and night and midnight on the opposite part. The which variety, although it appear incomprehensible to the slenderness of our wits, yet beholding the same with the eyes of understanding, and therewith considering the unestimable moving that the Sun maketh continually, we shall find it to be true, having respect to the divers situations of the earth, as it is continually illuminate more or less by the Sun. And this variety is made with such a harmony and consonancy, and such a law perpetual and immutable, that if any point or prick thereof should fail, it is to be doubted lest the Elements should be confounded together, and return to their first Chaos.  
And to have said thus much of the wonderful effects of the course of the Sun, it may suffice for an example to prove how necessary a thing it is, not only for all Pilots and Sea men to have the knowledge hereof, but also for all other such as shall attempt great and far voyages in unknown lands, and strange countries, as did of late Master jenkinson, a worthy Gentleman, set forth by you, and maintained at your charges, more like an Ambassador sent from any Prince or Emperor, then from a company of Merchant men. Wherein, what commendation you have deserved, to the increase of your perpetual fame and honour, I refer it to that I have said before. And as touching Master jenkinson, what travails, pains, and dangers he hath sustained, and hardly escaped, and what diligence and art he hath used in the searching of strange countries, and in the description of those his voyages, it were but in vain for me to write much unto you, unto whom the same is better known then to me. And therefore to conclude, with rendering just commendations both unto you and him, I can say no more, but as Plato writeth in his Book De Legibus, Decens est eos cives laudibus ornare, qui corporis vel animi viribus, res arduas praecláras que gesserunt, & legibus libenter paruerunt. That is to say, It is decent to commend those Citizens, that by their industry of body and mind, have done great affairs, and have willingly obeyed good laws. And thus eftsoons desiring your Honours and Worships to accept in good part whatsoever I have said of good will and affection toward you and your proceed, and with your shield of justice and authority, to defend me against the assaults of such as are enemies to virtue, and captious of other men's doings, I rest at your commandment to the uttermost of my power, to do you what service I may.   

The Epistle dedicatory of Martin Cortes, to the most mighty and victorious Monarch CHARLES the Emperor, the fifth of that name, King of Spain.  
SO greatly were esteemed the inventors of certain Arts and Sciences in ancient time (as writeth Saint Augustine in his 
The first inventors of Artes.  books De Civitate Dei) that they took them not for mortal men, but honoured them as immortal gods. 
Isis.  Isis' arriving in Egypt, ordained common weals with just governance, gave them laws, and knowledge of letters, and taught them also the use of Flax. In consideration whereof, she was honoured of such as then knew her, and reverenced of them that came after her: In so much, that they established a capital penalty or punishment of death, against all such as either in sport or in earnest affirmed her to be an earthly woman, and not rather a d●uine Goddess. 
Ceres.  Ceres' being of lively wit and clear understanding, 
The Sicilians.  beholding in the Sicilians human similitude and shape to the outward appearance, and inwardly the fierceness of bruit beasts: bridled their customs, and reformed them with new Statutes, teaching them to tame Oxen to bear the yoke, to sow Wheat for their great commodity, to grind in the Mill, to knead in the ho●se, and to bake in the Oven. In recompense whereof, they made sacrifice unto her, and builded many sumptuous Temples in honour of her. Saturnus coming from Creta, 
Saturn gave Laws to the Latins.  gave laws v●to the Latins, whereby they might govern themselves, and ●r●scr●bed them manners of living, teaching them to Till and Manure the ground, 
Tillage of the ground.  and sow Corn, and to gather ripe fruits in due season. And if Saturn were profitable to those nation's, and they not unthankful unto him, in that they builded him altars, celebrated unto him festival days, and accounted him in the number of the heavenly Gods, naming him also the father of the Gods. And (if I say) he was to them so profitable, and that world judged so happy and prosperous for having so valiant a King, and so just a Law giver, that it was therefore by the mouths of all men called, The Golden World, 
The g●lden worlie, and ●aigne of Sa●urn●. The worthy facts of Charles the fy●th. Sicilia.  and Reign of Saturn: Certes, except I greatly deceive myself, this our time is nothing inferior to that. For we know certainly, that your Majesty hath been more profitable to Spayre, then ever was Saturn to the Latins: and also a more excellent Law giver, in manner to all Europe, and further, to the new World, lately discovered, than he that gave laws but only to a l●ttle corner of Italy. Whereby I consider, that th● felicity of your majesties time, ha●h been ●o l●ttle commendation to your doings, in that you have banished unce, honoured virtue, punished offenders, a●d favoured innocente●: so that the quiet have thereby lived more peaceably, the unquiet restrained, the good exalted, and the evil chastised: In so much that now, by reason of just ministration of good order in your majesties d●minions, they that walk in the night, go in safet●e, whereas we know, that in other Provinces, such as walk in the day go in danger and peril. And therefore in th● most happy time of your Majesty, it appeareth that Spain is renewed, 
Spayn● reform.  not only in the excellency of Mechanical or handy crafts, but also in the knowledge of letters, and discipline of war: In so much, that she that sometime lacked herself, may now abundantly minister to her neighbours that have need. And whereas to your imperial Majesty, it should not suffice to ordain laws, if power and arms should fail to defend and punish: who, comparable to your Majesty, 
The triumphs and victories of Charles the fy●th.  enjoyeth the one, and wanteth not the other, having triumphed over Kings and Kingdoms, enlarging also the name of Spain in many unknown and barbarous Lands and Nations? Greater duty therefore own your Subjects unto you, than ever did the Egyptians to Isis, or the Sicilians to Ceres, or the Latins to Saturn, for as much as they have received of your majesty more common and profitable benefits.  
It is not long since your Majesty hath forbidden and abolished the use of Mules, 
Mules.  and restored again the exercise of Arms, so lo●g out of use, that the one w●th the other, hath been no small profit and commodity to your Subjects and Domini●ns. For by taking away the use of Mules, is so increased the ●umber of Horses and Horsemen, 
horses and horsemen.  that such as before never durst or could in manner light up upon a Horse, can now easily and aptly manedge them. So that you sleme to have revived the d●yes of Belle●ophon the son of King Glaucus, 
Belleropho●.  and likewise the time of Saturn, when men had first the knowledge how to make Horses to abide the bridle, and to bring them up to serve for divers uses and necessit●e● of men. And right sure I am, that by reason of such laudable Statutes and Ordinances in your Dominions, shall fail neither Horses nor Horsemen, as well for the Court, as for the Campe.  
Who knew in manner how to g●rde a Sword, 
Wearing of weapons and armour.  b●fore that your majesty permitted Weapons and Armour to be worn, even in your Court, and that elsewhere all men might do the like? before which time dexterity failed, where courage abounded. Over and beside the profit and commodity that hath risen hereof, what honour you have obtained by the same, is manifest by Francis the French King, 
Francis the French king taken prisoner.  who by your Majesty being taken prisoner in the Park of Pavia, was brought to Madrid, in the year a tho●sand five hundred twenty and five, where seeing many young men in manner without beards, and yet laden with Armour and Weapons, said, O happy Spain, that bry●gest forth and nourishest men of War. In your most happy days also, the Christian Faith is amplified, 
The Christian faith ●nlarged.  and in manner whole Spain flourisheth daily more and more in sumptuous buildings, 
The sumptuous buildings and riches of Spain.  and is abundantly enriched in treasure brought from your Indieses, far surmounting the riches of Solomon brought from Ophir. Yea, and to say the truth, consyderi●g the Navies of Gold and Silver, 
The Indies navies of gold and silver.  which have been ordinarily brought from thence to your Majesty, this time may rather be called the golden age, then that of Saturn. Not omitting also, that by your prosperous attempts, have been discovered so many Lands and Islands, 
New lands and Islands discovered.  heretofore so unknown to the Cosmographers, Geographers, and Historiographers, that they never heard of their names. Which nevertheless, a●e now so well known to your Subjects, that they have trodden them with their feet, and measured them by paces. Who before this time ever heard any mention of the rich and large Prou●nce of Peru, 
Pe●u.  or of the straits of Magalianes, 
The straits of Maga●●anes.  or of the river of Silver, called Rio de la Plata. They in times past seemed to have done no small thing, when they had knowledge of the fortunate Islands, 
Rio de la Plata.  the wh●ch, since they were conquered by your majesties Grandfather, have been called the Islands of Canaria. 
The fortunate Island, or Canaries.  And ●f it be, and hath been much to discover and subdue this new world: it is doubtless no less glory to your Majesty, not only to possess a●d enjoy it, but also that you daily procure to send thither judges to govern with Laws, 
Religion in the Indies.  and Preachers to instruct in Doctrine, to bring those Indians to the knowledge and honouring of the true God. And therefore considering your majesties godly desire a●d purpose, as touching these Navigations, and the dangers of such as go to discover this new world (although it be not new to the Spaniards to travail into far Countries, 
The Spaniards have ever travailed into f●r countries.  for as much as in the days of Caius Caesar, the son of Augustus, were found broken pieces of Spanish ships, lost in the Gulf of Arabia, as also Celius Antipater affirmeth, that certain ships of Spain were accustomed to sail for merchandise to the East parts of Ethiope) in consideration hereof, have I the more willingly published these my travails, for the furtherance of all such as shall hereafter attempt the like Navigation.  

The antiquity of Navigation.  And here do I not say that Navigation is not a thing of antiquity. For we read that in old time, the Argonanti sailed to Colchos, 

Argonanti.  
Colchos.   and Danaus brought the first Ship from Egypt to Greece. But I say, that I am the first that have brought the Art of Navigation into a brief compendiousness, giving infayleable principles, 
The Art of Navigation.  and evident demonstrations, describing the practice and speculation of the same, giving also true rules to Mariners, 
Things pertaining to navigation.  and showing ways to pilots, by teaching them the making and use of Instruments, to know and take the altitude of the Sun, to know the Tides or ebbing and flowing of the Sea, how to order their Cards and Compasses for Navigations, giving them instructions of the course of the Sun, and motions of the Moon: teaching them furthermore the making of Dyalles, both for the day and for the night, so certain, that in all places they shall show the true hours without default: and have likewise declared the secret property of the Lode stone, 
The lodestone falsely called in English Adamant, is in Latin called Magnes.  with the manner and cause of the north-easting and Northwesting (commonly called the variation of the compass) with also instruments thereunto belonging. And that, that which I shall say or do, be not accounted to be presumptuously done or spoken, I acknowledge that whatsoever I have well done or written, it is from above by the help of the divine grace, and by the favour and prosperous fortune of your Majesty. And thus shall they that now live, and likewise they that shall succeed us, see and perceive, how much more the world oweth and is beholding to your Majesty, than were the ancient Egyptians to their Isis. 

Charles the 5. greater than the hero's of old ●yme. Universal benefits.  
Comparison with the antiques.   She gave them letters to read, but your Majesty hath given rules and orders to sail on the Seas. The profit of Isis was only for one Province. But the commodity that ensueth of your doings, is universal for all Provinces and Nations, and for all Seas, aswell to go to places discovered, as also to discover Lands and Regions yet unknown. 
Pliny.  If they of ancient time had reached that we have obtained, 
Navigations of old● tim●.  the Indies had not now been to discover: neither should it be esteemed a miracle unto us, as at the time when Carthage flourished, that one Agnus went forth from the Bay of Cadiz, and sailed to the end of Arabia. Neither would Cornelius Nepos have written it for so famous a thing, that a certain man flying from King Latinus, came from the gulf of Arabia: Whereby it is manifest, that aswell Navigation, as other Arts, doth from day to day increase, and by little and little is come to perfection. For in those days they had neither compass nor card of sailing whereby to govern themselves. 
The perfections of arts at this day.  They lacked the consideration of the Stars, until the Phenitians found the knowledge thereof, and were the first tha● understood (that to such as should travail by sea) i● should be necessary to lift up their eyes to heaven, 
The rudeness of the antiquie●.  and consider the motions thereof. They that sailed to the Island of Tabrobana, (which in old time was called Antitono) carried for their voyages living birds. 
Aug●rium.  And when they thought good, let certain of them flee: ●nd by the flight of their wings● directed the h●lme and sails of their Ships. They sailed only three months in the yeer●. To them therefore it was necessary to observe 〈…〉 the time, until they found it to s●rue with a for● wind. They knewtson how 〈◊〉 h●lp● themselves with the bow ly●e, or side wind: neither saw they the North Star, 
The North Star.  or sought it, or had a●y knowledge thereof. A●d I believe verily that this was the cause of so long a voyage which the ships of Solomon made, 
The voyage of Solomon to Tharsis and Ophir.  sailing to Tharsis a●d Ophir, wherein they spent three years: although in deed that was no short voyage which they mad●● compassing about ●●d●a, and ma●y other Provinces. And whereas before I said, that Navigation by little and little came to perfection, I find by ancient histories, that Tipho first found the Governale or Rudder, 
The first inventors of ●●●igation.  Dedalus the Mast and Shrouds, and Icarus the Sails, the Thirreni found the use of the A●ker of one grasp or stooke, and Palaminus brought it to perfection, adding the other. And thus may it manifestly appear, that in these prosperous and fortunate days of your Majesty, it hath pleased God to bring the knowledge of Navigation to perfection, with this my brief discourse as touching the same, aswell profitable and necessary for them that travail by land, 
Commodities & difficulties of nauiga●i●●.  as by Sea. What can be a better or more charitable deed, then to bring them into the way that wander? What can be more difficult, then to guide a ship engoulfed, where only water and heaven maybe seen? One of the four most difficult things, whereof Solomon maketh mention in his proverbs, is the voyage of a Ship by the Sea. The which Galfrede expounding, saith, that in human things, none is more fearful or more dangerous, then to adventure life in a thin and weak piece of wood, or for a man to comm●t himself to the rage of furious winds, among the tempests of the Sea, and there to hazard that be loveth so well. O how much more should the same seem difficult to Solomon, if at these days he should see that few or none of the pilots can scarcely read, 
The ignorance of Pilots.  and are scarcely of capacity to learn? And whereas in the first Chapter of this Book, 
The goue●●●●●.  I have made mention, that the governal or steerage ought to be committed to expert men, and of good understanding, he should see, that now adays, the ignorant presume to govern other, which were never able to rule or govern themselves. I most humbly desire your Majesty; to receive in good part this my poor service, which, although it be little, yet being dedicated unto th● greatness of your regal person, it shall be much more the● great. The profit a●d commodity thereof 〈◊〉 notorious, and the benefit that thereby may be received, is universal. If therefore, when your Majesty shall find yourself released from greater affairs, it may please you to feed your eyes with these my travails, you shall find therein many new, delectable, and witty things, with also many profitable and certain rules, both to read and understand. To conclude, I eftsoons make humble petitions to your Imperial Majesty, not so much to consider what I write, as to respect the intent of my writing: and not the gift, but the affection and good will that remaineth in me to serve your Majesty.   

The first part of this work, which entreateth of the composition of the world, and of the universal principles for the Art of Navigation.  

¶ The first Chapter, of the general distinction of Creatures.  
THE infinite GOD, the beginning, and cause of the whole universal world, created three orders of creatures, differing in kind: 
Three differences of creatures.  that is to say, Corporal, as the Elements, Spiritual, as Angels, and compounded of these two, as man.. The corporal nature is divided into bright and shining bodies, 
Corporal ●●●●tures.  as the Stars: or into dark and thick bodies, as Earth and Metals: either into Diaphane or transparent bodies, as Air and Water. Of these creatures (as saith Saint Gregory) some have 〈◊〉 being, as S●ones, some live, as Trees, and other have sense, as Beasts, other understanding, as Man, who in holy Scripture is called all Creatures, 
Man is called all creatures● and the less world.  according to the saying of Christ to his Disciples, where he saith, Go and preach the Gospel to all Creatures. And therefore not without good cause was Man called of the Greek Philosophers, Microcosmos, (that is) the less World. 
Man compared to the wo●ld.  In the which we contemplate things of no less admiration, then in the great World. The similitude between them both, is, that even as the great world, and the whole Globe or Sphere thereof, is moved by the voluntary motion of an intellective substance, or an Angel: even so is this. For (as Aristotle writeth) What so ever is moved, 
All that moo●eth, is moved by an ot●er immoveable.  is moved by virtue of an other: As, Man is moved by the internal or inward form that is within him (that is to say) by the intellective soul that is proper unto him. In like manner, in the great world are found divers movable things: All which, are reduced to one immovable mover. So in man are found many things moved by divers motions, 
The intellective soul.  which are all referred to his intellective soul. The great world containeth the creatures within itself, and consequently is all really, as having nothing without it. Even so, man by knowledge is all, and knoweth all things, 
Man knoweth part of all things.  and nothing naturally is ●id from him, or unknown to him. Again, in this less human world, are two motions, Intellective, and Sensu●●●. 
Two motions in man.  〈…〉 the great world hath two local mot●ons: the one, wherewith the first movable is moved, and draweth with it all the other Spheres from the East to the West, 
Primum mobile.  and is called Rational moving. 
Rational motion.  The second, is the moving of the other Spheres, from the West into the East: and is called Irrational moving. 
Irrational motion.  But now leaving to speak of the less world, we will proceed to speak further of the great.   

¶ The second Chapter, of the definition of the world.  
THE world (as saith Isodorus) is Heaven and Earth, 
What is the world.  and the other works of God that are contained therein. It is compounded of things visible, and yet unsearchable. Moses and Saint john the Evangelist witness, that it was made by God. The Philosophers called it M●ndus a movendo, 
Or Mundus a Munditi●.  because it is in continual moving, and never in rest. The Greeks called it Cosmos, 
That is, clearness or fair●●nesse.  which signifieth, Fair, or Beautiful, and so named it, because of the marvelous ornament thereof, and diversity of Elements, with the resplendence or shining of the Sun, Moon, and Stars. And doubtless, nothing may be seen with the corporal eyes of man, more beaut●full than it is. In so much that the divine Philosopher Plato affirmed, 
Eyes were given to men to behold the fa●renesse and beauty of th● world.  that eyes were given to men to behold the beauty thereof, and to take pleasure in the contemplation of the heavenly bodies, and roundness of the world, which also for the roundness thereof, is called Spherical, 
The roundness of the world.  because that Sphera in the Greek tongue signifieth a round body.   

The third Chapter, of the definition of the Sphere.  

Definition of the Sphere.  THeodosius saith, that the Sphere is a whole and corporal figure, under one superficial: in the midst whereof, is a point or prick, from the which all right lines drawn directly to the circumference, 
The centre of ●●e Sphere.  are equal.  
This poyut or prick, is called the centre of the Sphere: according to Euclid, it is the passage of the circumference of half a circle, which is turned round about his Diameter that is fixed, until it return to his own proper place again, as where it was at the first. By the centre of the Sphere, passeth a right line, and thextremities or ends thereof, touch in the circumference. And this line (imagined) is called the Axis, 
The axis and Poles of the world.  or Exeltree of the Sphere, and the ends thereof are called the Pales. Upon this Axis is the Sphere of the world moved.   

The fourth Chapter, of the division of the world.  
IT is to be presupposed, that there is ● difference between Element, 

Quinta Essentia. Aristotle calleth it the fift ●lement.  
The fift essence is incorruptible.  
What is element.  
The inferior ●lements are not pure nor ●●mple.   and Elementate, and the fift, being called Quinta Essentia. The Quint essence, or fift substance, is a body of itself, differing from all Elements, and things Elemental, aswell in matter as in form, and no less in nature and virtue: and having in itself no contrariety, is certainly without corruption. And hereof cometh it, that the Philosophers called the heavens and heavenly bodies, the fifth substance, or fifth essence, by reason of the inco●ruptibilitie thereof. Element is that, whereof any thing is co●●ounded. It is the first of compositions, and of itself is not compounded. Whereby it followeth, that neither the earth, the air, the water, nor the fire, that are near unto us, or about ●s, are pure and simple Elements. For these Elements do sometimes mingle themselves one with another, and especially where they are near together, and touch one another. Of these elements every part is named by the name of the whole: As every part of fire, is called fire, and every part of earth, is called earth, and so of the other. They are called simple bodies in respect of other compound and mixed bodies. 
The elements are divisible into parts. The commi●●tion of elements.  They are divisible into parts of divers forms: and of the commixtion of them, are made and engendered divers things of sundry kinds. These four (that is to mean, Earth, Air, Water, and Fire) although they are named simple, but in respect as aforesaid, yet are they the Elements (that is to say) beginnings and principles of all other compounds and mixtes. A pure Element can not be seen, 
Pure & simpl● elements ca● not be seen. The division of elements. What is ●l●●mentate.  forasmuch as that that is pure, lacketh colour: and that that hath no colour, is not visible. The Elements (as saith Isodorus) were divided by the hand of God. The imperial Heaven was replenished with Angels, the air with birds, the sea with fishes, and the land with men, and other beasts. Elementate, is every body compounded of the four Elements. Not that they are Elements formally, but virtually in mixed bodies. This known, we will show how the world is divided into two regions: Celestial, and Elemental. 
Division of the world into Celestial and elemental.  The region Elemental, which is continually subject to alterations, is divided into four Elements: which are, Earth, Water, Air, and Fire. These Elements, the Greeks call Yctogia, for the communion and concord that they have between themselves. The heavenly or aetherial region (called Quinta Essentia 
Quintae Essentia. ) compasseth and containeth the Elemental world within it.   

The fifth Chapter, of the number, order, and property of the Elements and Heavens.  

Th● orders of Elements.  THE Earth (after the Philosopher) is a prick or point in the midst, called the centre, to the which they assign the lowest place. Next unto the earth, 
Earth.  and about it, the Water occupieth the second place, 
Wa●●●.  and the Air the third. 
Air.  The Fire is higher than any of the other elements. 
Fire.  And it is to understand, that the water hath two superficials. 
The four●● of the water.  One, which is called concave, or halow●: the other, convex or embowing. You may compare the inward part of the concave to a dish or a bowl, whose outward part is called convex. As touching the concave, the water compasseth about the earth, leaving discovered that part that serveth for the respiration and life of men, and other beasts. As concerning which, 
Th● Ocean S●●.  sam● think that the Ocean Sea is higher than the earth: and ask the question why the S●a covereth not the whole earth, and why the earth is not sunk in the water: To this it may be a sufficient answer, that it hath so pleased the will of G●d, according to the saying of the prophet D●uid: 
Psal. 107.  Terminum posuisti quem non transgredietur, neque conuertet●r operir● terram. 
job. 38.  That is, Thou hast appointed limits, which it shall not pass, neither shall it return to cover the earth. Beside the will of God, 
The will of God, is the cause of 〈◊〉.  which is the chief and sufficient cause thereof, we say that nature faileth not in her necessaries. For she sometime admitteth a little inconvenience, to avoid a greater evil: as when heavy things, which naturally should descend, do not only not descend, but rise up: And a● also sometime it chanceth that fire descendeth, and w●ter ariseth to fill the void or empty places, lest any where should be fou●d void or empty, which nature so greatly abho●reth. 
Nature abhorreth emp●●●●s.  T● this purpose, nature foreseeing the kinds of many things that could not elsewhere live then on the earth, neither be conserved within the water (as men, and other earthly beasts) determined before to m●ke the earth not perfectly round, 
The earth is not p●●fec●ly round.  contrary to the nature thereof: whereof it followeth, that it is not altogether covered of the water. And as (saith Origen) the earth remaineth discovered of water, that it might bring forth fruits, trees, 
Division of the ayr● into thre● Region●  and plants. As touching the convex aforesaid, the water and earth discovered, are contained under the concavity of the air, which is divided into three Regions, as the lowest, highest, and middlemost. The lowest is hot, by reason of the reflection or rebounding of the beams of the Sun, stricken back by the earth. The highest also is hot, by participation of the fire, and dearness thereunto. The middle region is cold, as is manifest by the snow and hail, 
The highest air is incombustible.  engendered in the same. The air near unto the region of the fire, which is pure heat, doth neither burn nor lighten, because it hath no combustible matter, and so hath it power, and not act. It is near unto, and reacheth the circle of the Moon, which compasseth it about. The heaven, 
The order of the heaven.  or circle of the Moon, is next unto the heaven of Mercuri: and Mercuri unto Venus: Venus, unto the Sun: the Sun, to Mars: Mars, to jupiter: jupiter, to Saturn, which is next, and reacheth unto the heaven of the Stars, called the Firmament, 
The Firmament.  because that in it are all the Stars (except the Planets) firm and fixed as a knot in a table. The knowledge of the Planets was had by seven sundry motions they have among themselves, 
The Planet's.  and by their course, not uniform to that of the Stars of the eight heaven, because that sometimes the Planets appear unto us joined together, and sometimes divided. The Crystalline heaven, 
The Crystalline heaven.  compasseth about, or containeth within it the heaven of Stars. This Crystalline heaven, is transparent, and perspicuous, as clear water or glass that may be seen through, by reason of the clearness and pure substance thereof. It is by an other name called, the heaven of water, 
The heaven of water.  whereof holy Scripture speaketh, saying, Aquae quae supra caelos sunt, laudent nomen Domini. 
Psal. 148.  That is to say, 
Daniel. 3.  Let the waters that are above the heavens, praise the name of the lord 
The moving of the first movable.  It was created for the conservation of corporal things, and to temper the heat engendered of the moving of the first movable, which being so great of body, that it not only compasseth all the Elements, but also all the inferior heavens is moved so swiftly, that it daily perfectly moveth all the aforesaid Spheres. And least by reason of the great heat thereof, caused by his swift motion, it should consume inferior things, God ordained this Crystalline heaven, 
Th● coldness of the Christalin●●●a●●n. The heau●n of the first movable.  that the coldness thereof might temper the extreme hea●e of the other. This Crystalline heaven, reacheth unto the fi●st movable heaven, called Primum mobile. A●d this reacheth to the Imperial heaven, which is the twelfth, called Emperium, 
The hea●e● called Emperiu●, is not moved, & is the habitation of Angels.  by reason of his clearness and resple●●●●●●. T●●● is 〈…〉, a●● is mo●t p●●fect. The Philosophers had no knowledge hereof. B●● we believe by holy Scripture, that such a heau●n there is, and the same to be the habitation of Angels, and Spiritual creatures. It is also called Coelum Coelorum, that is, The heaven of heavens: because it containeth and includeth within it all the other heavens. It is of greater clearness than all the other heavens, and was created immediately with the Angels. In this also remaineth the humanity of jesus Christ our GOD, 
The ●●●ani●ie of Christ in ●he Imperial heaven.  and in dignity above it. It containeth three holy orders or principalities, called, Hierarchias. Whereof the first is called Supercelestial, 
Three orders of angels.  and hath in it also three orders, Seraphims, C●eru●ims, an● Thrones. The second is called Celestial, and containeth Dominations, Principates, and Potestates. The third, called Subcelestial, containeth Uirtutes, archangels, and Angels. And to conclude, it hath abundance of all goodness and perfect felicity, with privation or want of all evil. 
The ●●periall ●eauen pr●seru●th ●ll the 〈◊〉 he●ue●●.  The heaven also giveth influence of constancy, steadfastness, and durability to things, against the fluxabilitie and inconstancy of the other heavens: the order whereof, doth appear in the demonstration following.  
  

The vi. Chapter, of the immutability or immobility of the Earth.  
THE Pythagorians, and other ancient natural Philosophers (as saith Aristotle) were of opinion that the earth did move, 
Opinion that the earth moveth.  yet not by a right forth motion, 
Molus in loco.  but circulerly about the midst of one place. The which error, both Aristotle himself, and the Astronomers do● confute and reprove by evident causes, and manifest demonstrations: For circular motion, is proper to the heavens. And as the earth differeth from them in nature, 
The ●arth is immoveable.  so likewise in moving. And although it be so that the earth may naturally move by certain of his parts, yet to move in the whole, and without the circuit of his Sphere, it is impossible, being founded and established upon his own centre, the which of itself is naturally immovable: for as much as in it the reason of all heaviness consisteth. 
All heavy things incline to the centre of the earth.  Whereas otherwise, every part that is moved should ascend, contrary to the nature of all heavy things. B●t there is found nothing heavy that doth not naturally incline directly to the centre of the earth, and would actually descend thither, if it had no impediment of some other thing to resist it: and when it toucheth there, or is come thither, would still rest and remain there. And hereby it followeth, that the earth, 
The earth is founded upon his own centre.  being founded upon his own centre, is not moved. The w●ich thing the Prophet David also affirmeth, saying: Fundasti terram super stabilitatem suam, (that is) Thou foundedst the earth upon his stability. 
Psal. 130.    

The seven. Chapter, of the roundness of the Earth and Water.  

The roundness of the earth.  THAT the Earth is round, it appeareth by manifest evidence: For if it were plain or flat, the dawning of the day or day spring, should equally and at one time appear to them in the West, 
The rising of the Sun.  as to them in the East. But we see the contrary, that it appeareth first to them that dwell in the East, and afterward to them in the West. This is proved by the Eclipse of the Moon, 
The Eclipse of ●he Moon.  which beginning at one instant, they of Jerusalem see it begin at four a clock of the night, and we of Andalusie in Spain, at one a clock of the night. It followeth hereby, that to them it nighteneth three hours sooner than unto us in Spain: and this is caused by the roundness of the earth.  
But here some may move a doubt, saying, that on the earth we may see many Mountains, 
how the earth is round.  and consequently many great Uallyes and Plains, with many diversities of sundry other deep and unequal places, by reason whereof, the earth can not truly be called round. To this I say, that in two manners, the earth is called and understood to be round. As after one manner, speaking precisely, it is called round, as a Circled or a Sphere, which we call round, because that all right lines drawn from the centre thereof to the circumference, are equal. The other roundness, is considered without this preciseness: and is such, as not by all his parts is equally distant from his midst or centre, but hath some parts higher, and some lower, yet not in such quantity as may destroy the roundness of the whole. As if in a Bowl there we●e certain clyftes or holes, it should not thereby leave to be round, although not perfectly or precisely round. And for this cause saith Auerrois, that although both the heavenly bodies and the Elements are of round form, yet differ they in this, that the heavenly Spheres have perfect roundness, and the Elements not. As the earth, by reason of his Mountains and Uales, the Sea by his increasing, and decreasing, the Air also for his dearness to the fire, and by his contrariety doth sometime do, and sometime suffer (that is to say) is sometime active, and sometime passive. 
The air is actium and passive, and not perfectly round.  So that following the one, it fleeth the other, by reason whereof, it also lacketh perfect roundness. But the fire, for as much as it is near to the concave of the circle of the Moon, which is Spherical, may therefore be called Spherical or round. 
The fyr● is ●ound.    

The viii. Chapter, of the motion of the Heavens and Elements.  
IT is not to be forgotten, that all the Elements are wholly movable by local motion, except the earth. The water is moved by the motion of the Moon, or tossed by the Winds. The fire (as saith Aristotle) is moved circulerly by the motion of the day, 
how the fyr● is moved.  and is drawn of the circles● that embrace it, or compass it about: as is manifest by the Comets, or blazing Stars, and other fiery exhalations, contained and engendered in it: Which being carried with this motion, conclude, that the fire moveth in like manner. And with this motion is the superior part of the air violently carried about, 
how the air is moved.  as the other impressions therein do show. The inferior part is moved by divers motions, (that is to mean) laterally, as by experience we see when the winds blow. 
The Moon.  The Moon with her Heaven or Sphere, by her proper motion giveth her turn from the West to the East, in xxvii. days, and seven. hours, with xv. minutes. Venus, 
Venus.  Mercuri, 
Mercuri.  and the Sun, 
The Sun.  in a year, which is the space of three hundred threescore and five days, with five hours, and forty and nine minutes. 
Mars.  Mars in two years. jupiter in twelve years. Saturn in thirty. years. The eight heaven, which is the Firmament, or Starry Heaven, 
The Starry heaven o● firmament.  by his own proper motion is moved by the nienth Heaven, upon the beginning of Aries and Libra, and upon these two points accomplisheth his Revolution in seven thousand years.  
This motion is called Motus trepidationis (that is to say) 
The Crystalline heaven.  the trembling motion, or motion of access and recess. The ninth heaven endeth his motion from the West to the East, in forty and nine thousand years: And by this motion moveth the eight heaven. T●e tenth heaven, called Primum mobile, is moved from the East to the West: 
First movable.  and in twenty and four hours (which is a natural day) performeth one revolution, and with the mighty force and swiftness of his motion, carrieth with him all the other inferior heavens, and maketh them to give the same turn in twenty and four hours, where as nevertheless they cease not in the mean time to keep the course of their own proper motion. 
how the fi●st movable draweth the other hea●●●s.  As (for example) if an Ant or Pismire should go about the wheéle of a Mill, contrary to the moving of the wheel: before the Ant in going still forward, should come again to the point from whence she first departed (which is once about, or one turn) the wheéle should in that space make many turns.   

The ix. Chapter, of the division of the Sphere into formal parts.  
THE Sphere of the world, is divided in two manners, (that is to say) by substance, and by accident. By substance into ten Spheres, as we have said. By accident, 
The right and crooked or obliqne Spher●.  into a right Sphere, and obliqne or crooked Sphere. They have the right Sphere that dwell under the Equinoctial line, and is called right, because to them the P●les are equally in the Horizon, as appeareth by this Figure following.  

The x. circles of the Sphere.  The Sphere is compounded of ten circles imagined. And (as saith john de sacro bosco in his book of the Sphere) six of them are greater, and four less. The greater Circle, is that which divideth the Sphere into two equal parts, and hath his centre with the centre of it. These are the Equinoctial, the Zodiac, the two Coluri, the Horizon, and the Meridian. The less Circle, is that that divideth the Sphere into two unequal parts.  
These are the two Tropykes, and two Poler Circles.   

The x. Chapter, of the Equinoctial Circle.  
THE Equinoctial, is a Circle that divideth the Sphere into two equal parts, 
The Equinoctial.  and is by every part equally distant from both the Poles. It is one of the greate● Circles in the Sphere, and is the greatest Circle of those which are described in the Sphere, by the motion of Primum mobile, or first movable. This Circle, for his equality, and regularity, is more noble than the Zodiac, which we have described in the eight● sphere, and also then any of the other. It is imagined to gird the world round about by East and West. 
The equality of the day and night.  It is called Equinoctial, because this word Equinoctium, signifieth equality of nights and days, whereof the cause is, that the Sun coming to this Circle, the Ark of the day is equal with the Ark of the night, and then is the Equinoctial. It is also called the Zone, or girdle of the first movable. 
The first movable.  For even as a girdle doth gird a man by the midst, so doth this Circle gird in the midst between both the Poles, upon the which the first moveable is moved. One of these imagined on our pa●te of the Sphere, is called Polus Arcti●us, because it is near unto certain Stars, which the Astronomers call Arcturus, which is the great Bear. 
The Pole A●tyke.  It is called Septentrional, or Septentrion, because that round about it are moved the seven. Stars, which make the less Be●re, commonly called Bozina, (that is, the horn. 
The hor●e.  The Star which is in the tail of the lesser Bear, is called the North Star, 
North Star.  because it is nearest unto the North Pole: the which Pole is a certain point in the Firmament, which can not be seen, although the night be never so clear. This Star (as the Poet Homer saith) doth move little or nothing, 
Pole Antar●ike.  because of his little distance from the Pole. The other Pole is imagined on the other contrary part, and is called Polus Antarticus, of the word Ante, which signifieth against, contrary, or opposite, because it is on the contrary pa●te from the Pole Artyke. It is also called the South Pole, because that from that part of heaven cometh the Wi●de, commonly called the South: and is likewise called Meridional, because it is right South from us. 
The cross●●eer● unto the Pole Antarctic.  This is never seen to us. They that dwell under the Equinoctial, or come near unto this Pole Antarctic, have for a sign or mark to know it, four Stars, in form of a Crosse. And when the greatest of these is lowest in the foot of the Cross, they say it is thirty. degrees above the Pole. And as we can not see their Pole from hence, so they can not see our Pole from thence.   

The xi. Chapter, of the Zodiac Circle.  

Zodiac.  THE Zodiac is defined to decline or bend itself from the Equinoctial. It is a great Circle, which divideth the Sphere in two equal parts, cutting the Equinoctial by obliqne or crooked angles: So that being thus cut or divided by it into two equal parts, one part thereof declineth toward the South, and the other toward the North. This Circle is called the Zodiac, of this word Zon, 
Th● twelve signs of th● zodiac.  which in the Greek tongue signifieth life, because that according to the moving of the Planets under it, is the life of inferior creatures: Or is so named of Zodion, which signifieth a living beast. And is therefore divided into twelve equal parts, whereof every part is called a sign, and every sign hath an especial name of some beast, in respect of some property agreeable to the same: or for the order and disposition of the ●ixt Stars in those parts, somewhat representing the similitudes of such beasts, it is called Zodiac.  
The Latins called this Circle, 
how the Sun is cause of generation and corruption.  Signifer, (that is) the sign bearer, because it carrieth these signs or images in it also, because the twelve parts, 

Division of the twelve Signs.  
Division of the signs into degrees.  
Division of the zodiac by latitude.   into the which this Circle is divided, are called the xii. Signs. That part which declineth to the North, containeth vi. Signs septentrional, and the other that declineth to the South, containeth other vi. called Meridional. Furthermore, it is to consider, that the zodiac may be divided in two manners. One, by longitude or length into the xii. signs aforesaid, and every sign is divided into thirty. degrees, which make Ccclx degrees, likewise, every degree is divided into lx. minutes, and every minute into lx. secondes, and every second into lx. terces, and so to ten. The other division of the zodiac is, by latitude or breadth. By latitude it is divided into xii. degrees, and in it we imagine a line that divideth his latitude by the midst, having vi. degrees on every part or side. And this line, 
The Ecliptic line.  which divideth into two equal parts the breadth or latitude of the zodiac, is called the Eclyptike line, because that when the Sun and Moon are directly divided under this line, either joined together by conjunction, or divided by opposition, then is the Eclipse of the Sun or of the Moon. Under this zodiac the seven planets are moved. The Sun also moveth in the midst of the said zodiac, alongst the Ecliptic line, not inclining more to the one part then to the other. But the other planets do sometime go toward the North, and otherwiles toward the South, and sometime also toward or traverse the ecliptic. It is likewise to be noted, that these signs whereof we have spoken, are not the constellations or stars that make those figures, 
The moving of the Sun and the other Planets in the zodiac.  which the ancient Astronomers did appropriate to certain Beasts, and other things: For these figures are moved according to the motion of the eight Sphere, and pass from one sign of the zodiac to another. As we see that the Star, called Oculus Tauri, (that is) the Bulls eye, is in two degrees of Gemini. And the two Stars that are the head of Gemini, 
The figures o● beasts and other things imagined in heaven besides the xii. ●ignes.  are in xiii. and xvi. degrees of Cancer. And Spica verginis (that is) the spike of the Virgin, is in xvi. degrees of Libra, and the heart of Scorpion ● in two degrees of Sagittarius. And by this order do they pass from one sign to another: so that we may not understand the signs by these stars, but the xii. parts of the Ark of the Zodiac, taking the beginning of the Equinoctial of Aries. The names of these signs, with their Caractes and qualities, are described in this table here following.  
Numb. Names. Charact. Qualities. 1 Aries. ♈ Hot and dry. 2 Taurus● ♉ Cold and dry. 3 Gemini. ♊ Hot and moist. 4 Cancer. ♋ Cold and moist. 5 Leo. ♌ Hot and dry. 6 Virgo. ♍ Cold and dry. 7 Libra. ♎ Hot and moist. 8 Scorp. ♏ Cold and moist. 9 Sagitt. ♐ Hot and dry. 10 Capri. ♑ Cold and dry. 11 Aqua. ♒ Hot and moist. 12 Pisces. ♓ Cold and moist.   

The xii. Chapter, of the Circles● called Coluri.  
THere are two circles in the Sphere, called Coluri, so named of the Greek word Colon, which signifieth, a member: And of Vros, which signifieth a wild Ox. The tail of this beast, maketh a semicircle, or half Circle, not perfect. And as this beast moveth his tail laterally or side ways, and not by longitude: even so do the Coluri move to us, and are cut in right spherical Angles, upon the Poles of the world. The one passeth by the Poles of the world, and by the points of the Equinoctials, and is called the Equinoctial Colour: 
The Equinoctial Colour.  the other likewise passeth by the Poles of the world, and also by the Poles of the Zodiac, and by the points of the Solstitialles, and is called the Colour Solstitial, 
The Solstitial Colour.  called Solstitium, as Solis statio (that is) the standing or staying of the Sun: because that when the Sun cometh to this point, it declineth no more, but turneth toward the Equinoctial. These circles divide aswell the Equinoctial, as the zodiac into four equal parts, by the points of the Equinoctialles, and Solsti●ialles. In the Colour Solstitial, 
Th● greatest declination of th● Zodiac,  are the greatest declinations of the zodiac, which are two arks of this Colour, contained between the Equinoctial and the zodiac. And these arks are equal to the other two of the same Colour, included between the Poles of the world, and the Poles of the zodiac.   

The xiii. Chapter, of the Meridian Circle.  
THE Meridian, 
Definition of the Meridian Circled.  is one of the great Circles, imagined to traverse the sphere by the Poles of the world, cutting the same in two equal parts by the zenith or vertical point. It is called Meridian for this effect, that wheresoever a man becometh, and at what soever time of the year, when the Sun (by the moving of the first movable) shall come to his Meridian, 
The midday or noon.  to him shall it be high noon at midday, and is therefore als● called the circle of the midday. It is also to be noted, that there are as many Meridian's, 
divers Meridian's.  or Meridian lines, as are differences or habitations by longitude: so that they that dwell in the East, have other Meridian's then they that dwell in the West: So that the interposition of the ark of the Equinoctial, between the Meridian of one City, and the Meridian of the other, is called the difference of longitude from one Region to another, and from one City to another, as we will further declare hereafter.   

The xiv. Chapter, of the horizontal Circle.  
THE Horizon (after the Astronomers) is a Circle which divideth that part of the heaven which we do see, from the other part which we see not, so that the said Horizon divideth the Sphere of the world into two equal halves, 
Definition of the horizon.  called Hemispheres. The half which we do see, is called the Hemisphere superior, and it which we see not, is called the Hemisphere inferior. 
hemisphere or horizon.  This Horizon, changeth to them that move: for as one doth move, his Horizon doth change. And hereof it cometh, that how many places are upon the earth, 
divers orisons.  and the circumference thereof, it is possible there should be so many Orisons. The Astronomers suppose the Horizon, after two manner of sorts, that is to say, a right Horizon, and an obliqne, or crooked Horizon. The right Horizon, is to them whose zenith or vertical point is directly in the Equinoctial: and this right Horizon, passeth by the Poles of the world, and divideth the Equinoctial in right spherical angles. 
The right and obliqne horizon.  The other obliqne or declined Horizon have they, unto whom the Pole of the world doth rise above their Horizon. This Horizon is also called obliqne, because it divideth the Equinoctial in unequal and obliqne or crooked angles.  
Also it is to be understood, that the Pole of the Horizon is called Zenith, or the vertical point of heaven, perpendiculerlye, or directly over our head. Whereby is inferred, that as much as is the elevation of the Pole of the world above the Horizon, so much is the distance of the Zenith from the Equinoctial. 
Distance of the zenith from the Equinoctial.  For the Zenith by all his parts, is distant from the Horizon by ni●ntie deg●eés. And all other impediments excluded, we may ever see half the heaven: And in as much as any shall pass from the Equinoctial, toward the one Pole or the other, so much falleth the Horizon under or beneath the Pole, toward the course he intendeth, and likewise as much shall it be raised above the contrary Pole, as shall appear by a demonstration in the end of this Chapter. 
how the horizon is divided by th● Meridian.  This Horizon is divided by the Meridian into two equal parts, that is to say, the East and West parts of the said Horizon. The E●st part is, where the Sun and Stars begin to arise to us, and appear in our sight. The West part is, where the Sun and Stars doth set and begin to be hid out of our sight, under the said Horizon. Moreover, it is to be understanded, that there be two manners of the East and West, that is to say, the true East and West, 
The true and untrue East and W●st.  or the untrue. The true East, is the point in the East part of the Horizon, where it doth cut with the Equinoctial: for when the Sun is in the points of the Equinoctial, than he riseth in the point of the true East. And likewise is to be understand of the point of the true West, to be in the West part of the Horizon, where the Equinoctial doth cut with the said Horizon. The untrue East and West is variable, according as the Sun riseth and setteth daily in divers points of the Horizon, which is distant from the points of the true East and W●st, sometimes more to the Northward, and sometimes more to the South.   

The xv. Chapter, of the four less Circles.  
Having entreated of the vi. biggest Circles, it remaineth to speak of the four less Circles.  

The less Circles.  A less Circle (as we have said before) is that, whose superficial divideth the Sphere into unequal parts, not passing by the Centre thereof. And of these, two are named Tropikes: 
Tropykes.  so named of Tropo the Greek word, which signifieth Conversion, because the Sun coming to any of these Tropikes, is converted, and turneth toward the Equino●tiall. These Tropikes are described by the motion of the first movable, with the points of the Solstitials. The one with the beginning of Cancer, and this is called the tropic of Cancer, or E●tiuall, or Summer Tropike: The other is described with the beginning of Capricorn, and is called the tropic of Capricorn, or Hiemall, or Winter Tropike. These two Tropikes and the Pola● Circles (whereof I will say more hereafter) are called Paralelles: 
Paralelles.  so named, for that they are equally distant by their circumferences one from an other, as well as from the Equinoctial. The Polar Circles are described in this manner: 
The Polar Circles.  so that as the Zodiac declineth from the Equinoctial, so do the Poles of the Zodiac decline from the Poles of the world. 
The Poles of the zodiac, and Poles of the world.  And as the eight Sphere is moved at the motion of the first movable, so sha●l the Zodiac move, which is part of the Sphere. And the Zodiac being moved, his Poles shall likewise move above the Poles of the world. 
The great●●● declination of the Sun.  And as the Poles of the Zodiac are distant from the Poles of the world xxiii. degrees and a half (which is as much as the greatest declination) they shall describe certain circles distant from the Poles of the world, in the self same xxiii. degrees and a half. These Polar Circles, take their name or dominion of that Pole of the world that is most near unto them, and therefore is the one called Artyke, 
The Artyk●, and Antarctic.  and the other Antartyke.   

The xuj. Chapter, of the five Zones.  
THE ancient Astronomers divided the Sphere into v. Zones. 
The Sphere divided into five zones.  The fi●st, from the Pole Artyke, to the Circle Artyke. The second, from the Circle Artyke, to the tropic of Cancer. The third, from the tropic of Cancer, to the tropic of Capricorn. The fourth, from the tropic of Capricorn, to the Circle Antarctic. The fifth, from the Circle Antartyke, to the Pole Antartyke. Of these five Zones, 
Zones habitable and unhabitable.  they have certain knowledge, that two of the Poles were unhabitable for extreme cold: and also that the burnt Zone (called Torrida Zona) whereby the Sun passeth by the midst of them, should be unhabitable for extreme heat. That from the tropic of Capricorn, unto the Circle Antartyke, they called desert, because they knew not that it was inhabited. And this our Zone, 
The division of the earth according to the five zones of heaven.  that is, from the tropic of Cancer, to the Circle Artyke, they called inhabited, or habitable. And to have more perfect knowledge hereof, it is to imagine, that the earth is divided proportionally into five Regions or Portions, which answer directly to the said five Zones, as saith the Poet Ovid in this Verse.  
Totidemque plague, tellure praemuntur. (That is)  
And so many Regions, are on the earth beneath.  
Every of these Regions or portions of the earth, is situate under one of the five Zones aforesaid. But whereas certain men of authority have moved the question, whether the earth under the Zone, from the tropic of Cancer, to the Circle Antartyke, is desert or no: Ptolemy, 
An error of Ptolemy and the Astronom●●.  and the Astronomers affirm, that it is unpeopled. But Aristotle, Ovid in the second of his Metamorphoses, Pliny also, and john de Sacro bosco, affirm the contrary: as for the more certainty thereof we know the experience of such as go and come daily from those parts. Moreover than this, we know that that land is not only well replenished with people of good corporature, and of white colour, but the same to be also very rich in Gold. For they that sail to the East Indies, touch in the cape of Buena speranza, or Caput bone Spei, which is in this Zone. Likewise the land of Brasile, 
The land of Brasile.  and the confines of Rio de la Plata, with all the coast, unto the straits of Magalianes, even unto the 54. degrees of the south part. 
The straits of Magalianes  This land was discovered by Magalianes, in the year 1520● or 1521. whereby that is now we●l known by sight, whereof Ptolemy had no knowledge by hear say. The ●●rnt Zone (called Torrida Zona) they also described to be unhabitable, by reason of the great heat thereof, as Aristotle, P●inie, and in manner all other ancient authors affirm: whereof the Poet Virgil writeth thus. 
Quinque tenent coelum Zonae, quarum una corrusco.  
Semper sole rubens, & torrida semper ab igne.  Which in the English tongue is thus much to say in effect. 
In Zones five, the heavens contained be,  
Whereof the one with burning Sun is red:  
Scorching the Earth subject to his degree,  
That for the heat thereof it is unhabited.  Likewise ovid in his Metamorphoses, toucheth the same, saying. 
Quarum quae media est, & torrida semper ab igne. etc.  Yet that the burnt zone is inhabited, and well replenished with people that live there, we know so certainly by the number of them that daily pass too and fro the Indies of your Majesty discovered, 
The West Indies.  in your most happy days, that to say any thing to the contrary, it should be a manifest error, and therefore is it greatly to be marveled, that certain wise men have affirmed these parts to be unhabitable: whereas nevertheless they had knowledge of Arabia, Foelix, Aethiopia, Tabrobana, and divers other Regions situate under the burnt Zone. Pliny writeth, that a Ship came from the sea of Percia by the Ocean, round about Ethiope, and came to the pillars of Hercules, which is now the City of Cadiz, where at this present I writ this brief treatise. They of Guinca, Calicut, Gatigara, and Malaca, live all under the burnt Zone, 
People of long life under the zone.  and many of them live very long. And doubtless, many things ought to persuade us, that under the burnt zone, the earth is furnished with all things pertaining to the life of man: for that in that region, or portion of the earth, is in manner continual Equivoctiall, and the coldness of the night doth sufficiently temper the heat of the day. Again, they that inhabit under that Zone, have two summers, and two Winters in the year: 
Cold Regions habitable.  whereby is concluded that the ancient authors erred, not only in affirming this Zone to be unhabitable by reason of the great heat thereof, but in like manner erred, in affirming the Zone that is between the circle Arctic, and the pole Arctic, to be also unhabited by reason of great cold. The contrary whereof, we may well affirm, knowing as we know, that Island, 
Island.  with part of Gothland, 
Gothland●  Norway, 
Norway.  Russia, 
Russia.  and divers other Lands, are inhabited and well peopled.  
This is the figure and demonstration which followeth.   

The xvij. Chapter, of longitude and latitude, and of the proportion which the less circles have to the great circle.  
THE Sphere or globe of the earth, is also divided in breadth, 
The division of the Sphere by longitude and latitude.  and in length. The breadth (which is called latitude) is by degrees: for from the Equinoctial, to either of the two poles, is 90. degrees. The length (which is called longitude) is by the degrees of the Equinoctial, which is divided in ●60. degrees. The first degree of longitude, doth begin at a certain Meridian, which passeth by the islands of the Canares, called the fixed Meridian: and the order of the numbering of the said longitude, is always toward the East. By every degree of the said longitude in the Equinoctial, may be understanded a great circle (called Meridian) to pass, each one of them passing and meeting the poles of the world, so that the said great circles, or meridians, doth divide every parallel or less circle, proportionally into 360. degrees: 
The degre●● of the Equinoctial circled.  but we must not understand these degrees to be equal (that is to say) as great in one circle, as in another: for the greater the circle is, the greater is the degree in it: and the greater the parallel is, the nearer it is unto the Equinoctial line. Every degree of the Equinoctial, containeth in longitude 60. minutes, so likewise it is to be understanded of the degrees of latitude, which be divided each one into 60. minutes of latitude, because the degrees and minutes in the great circles, do not differ in their bigness the one from the other: but the degrees in the parallels, as they are distant from the Equinoctial, and come near to either of the two Poles, they diminish consequently, so that one degree in the parallel, of 7. degrees of latitude, doth make in quantity but 59 minutes, and 33. seconds of the Equinoctial circle: and to one degree in the parallel of 12. degrees of latitude, goeth but 58. minutes, and 41. seconds of the Equinoctial, and to one degree in the parallel of 16. degrees of latitude, there goeth 57 minutes, and 41. seconds.  

The Table of minutes, which every degree containeth in every of the parallels.  G M S G M S G M S G M S G M S G M S 1 59 59 16 57 41 31 51 26 46 41 41 61 29 5 76 14 31 2 59 58 17 57 23 32 50 53 47 40 55 62 28 10 77 13 30 3 59 55 18 57 4 33 50 19 48 40 9 63 27 14 7● ●2 2● 4 59 51 19 56 44 34 49 45 49 39 22 64 26 18 79 11 27 5 59 46 20 56 23 35 49 9 50 38 34 65 25 21 80 10 25 6 59 40 21 56 1 36 48 32 51 37 46 66 24 24 81 9 23 7 59 33 22 55 38 37 47 55 52 36 56 67 23 27 82 8 21 8 59 25 23 55 14 38 47 17 53 36 7 68 22 29 83 7 19 9 59 16 24 54 49 39 46 38 54 35 16 69 21 30 84 6 16 10 59 5 25 54 23 40 45 58 55 34 25 70 20 31 85 5 14 11 58 54 26 53 56 41 45 17 56 33 33 71 1● 32 86 4 11 12 58 41 27 53 28 42 44 35 57 32 41 72 18 32 87 3 8 13 58 28 28 52 59 43 43 53 58 31 48 73 17 33 88 2 5 14 58 13 29 52 29 44 43 10 59 30 54 74 16 32 89 1 3 15 57 57 30 51 58 45 42 26 60 30 0 75 15 32 90 0 0   

The xviii. Chapter, of the circuit or compass of the Earth and Water, according to the opinion of the ancient and latter authors.  
IT may here appear to be necessary for our purpose, to declare what space of the superficie of the earth or water, the ancient writers di● suppose to answer to one degree of a greater circle in the heaven: for in divers countries, they used to count by divers sorts of measures: as, the Latins counted by miles, 
Myle●.  the Greeks by furlongs, 
Furlongs.  the Spaniards & Frenchmen by leagues, 
Leagues.  the Egyptians by signs or marks, and the Persians by saguas. But they all agree, that four grains of Barley make a finger breadth, 
grain.  four fingers, 
finger.  a hand breadth, four hands a ●oote, five foot, 
Foot.  a Geometrical pace (for two simple paces, 
Pase.  make five feet.) Also 125. Geometrical paces, make a furlong, eight furlongs, one mile, which is a thousand paces: and three miles, one l●ague. In Germany they make leagues of more feet, and in some places more than in other. In France, they count thyr●ie leagues, to one degree. The Spaniards, count sixteen leagues and two terces, and seventeen and a half for a degree of the great circled: this difference that one league is bigger than another, may come hereof, that one Barley corn is bigger than another. But to our purpose, let us give to every league three thousand paces, and to every pace five foot, and so shall every league have xv. thousand foot. In the Cards of the sea, that have their degrees of xvi. leagues and two terces, 
The degre●● of the sea Cards.  we say, that of these, the roundness of the land and the water containeth six thousand leagues. And in the Cards that have seventeen leagues and a half for a degree, of these we say that it containeth six thousand and three hundred leagues. And who so desireth to know how much is the Diameter of the earth and water, 
The diameter of the earth and water.  may know it by multiplying the circumference by seven, so that dividing the sum that riseth thereof by twenty and two, the part that riseth of that calculation, shall be the Diameter: and the half thereof● shall be the semidiameter.   

The nineteen. Chapter, of the seven Climates.  
THE ancient authors did also divide that part of the superficie of the earth, 
Division of the earth and water by Climates.  on the North side of the Equinoctial, which they supposed to be most habitable, into seven Climates, wherein they did find to be divers conditions and customs of men, 
Diversities of things in divers Climates.  and diversities of beasts, and of other natural things: the which things they perceived to have a diversity in the countries, as where the day of the one did increase or differ above the day of the other by half an hour, so that the space of the superficial of the earth between two paralelle lines, wherein the longest day doth increase or differ by half an hour, is called a Climate. The place where they suppose the first climate to begin, 
What is ● climate.  is distant in Latitude from the Equinoctial by 12. degrees, and 45. minutes, where the longest day is 12. hours, 
Differenc● of days.  and 45. minutes, & the place where the last climate doth finish, is in the Latitude of 50. degrees, and 30. minutes, where the longest day is 16. hours, and 15. minutes, 
The space of s●●●n climates  so that the increase of the longest day in the end of the seventh climate, doth exceed it in the beginning of the first climate by three hours and an half: and the whole compass of the earth, with all the seven climates, doth contain in breadth 37. degrees, and 45. minutes, but their length is supposed to extend to 180. degrees of longitude. In that manner, a climate, the near it is unto the Equinoctial, the more it containeth of the superficial of the earth, because the paralelle circles, the nearer they be unto the Equinoctial, 
The quantiti●●f the l●ss● circl●●.  the greater is the compass of the earth which they make in length, and the lesser the compass is, the nearer they be unto the poles, as doth appear evidently by the Meridian's, where they do all concur, and meet in the poles, ●heir distances waxeth continually lesser and lesser, the nearer they be unto the said poles, so that the nearer the climate is unto the pole, the lesser it containeth of miles in the length. In like manner shall you understand, that greater is the breadth of the first clime, then of the second, and the second than the third, and likewise of the other. For in how much the more the Equinoctial you come near to the pole, so much the more is the Sphere obliqne or crooked, and consequently the day increaseth more: by reason whereof, 
The Latitude of Climates.  in less space is found the increaseth of half an hour, in which the climate maketh difference and doth vary. Which thing shall be more manifest to him that beholdeth the Latitude of them all, as may appear by the Table here following: In which you may see the hours which the greatest day containeth of every climate in his beginning, midst, and end, with also the elevation of the Pole, or distance from the Equinoctial, and also the degrees of Latitude, which every Climate containeth.  
The longest day.   The elevation of the Pole.  Differences of the latitude. Climates. Beginning. Midst. End. beginning. Midst. End.     Ho. M Ho. M Ho. M G M G M G M G M 1 12 45 13 0 13 15 12 45 16 40 20 30 7 45 2 13 15 13 30 13 45 20 30 24 15 27 30 7 0 3 13 45 14 0 14 15 27 30 30 45 33 40 6 10 4 14 15 14 30 14 45 33 40 36 24 39 0 5 20 5 14 45 15 0 15 15 39 0 41 20 43 30 4 30 6 15 15 15 30 15 45 43 30 45 24 47 15 3 45 7 15 45 16 0 16 15 47 15 48 40 50 30 3 15  
The first Climate, is called Dia Meroes. 
Dia M●r●●.  Meroe is a City of afric, under the burnt Zone, on this side the Equinoctial, 16. degrees.  
The second, is called Dia Sienna. 
Dia Sien●  Sienna is a City in the confines of Ethiope, where there is a well that showeth the Summer solstitial, because that place is under the circle of the tropic of Cancer, and the Sun seemeth to stand directly over that place at midday of the solsticiall, whereby the well is then very clear, and hath in it no shadow at all: as the Poet Lucan maketh mention in Farsalia, where he saith.  
Vmbras nusquam flectentes.  
That is to say, Shadows no where reflecting.  
The third is. Dia Alexandro's. 
Dia Alexandro's.  Alexandria is a famous City in afric, builded by great Alexander, and is the chief City or Metropolis of Egypt.  
The fourth is, Dia Rhodos. 
Dia Rhodos.  Rhodes is an Island of Asia the less, where were sometime the Knights of the Rhodes, called the Knights of the order of Saint john, 
knights of the Rhodes.  or Knights of Jerusalem, who were driven from thence, when the Island and City was taken by Solton Suliman the great Turk, 
The Rhod●● taken by th● Turk.  in the year 1522. Philippe Vrlerio Frencheman, being then grand Master of the Rhodes. Within this fourth Climate, is the City of Jerusalem, within the holy land called Palestina, and also a great part of Spain, with many other Provinces.  

Dia Rome's.  The fifth, is Dia Rome's. Rome is the most famous City of Italy, and most notorious of all Europe, sometime the head of the world, dommatrix of Nations, and now the See of the Bishop of Rome.  

Dia Boristhenes.  The sixth, is Dia Boristhenes. Boristhenes is a great River of Scythia, the fourth arm of the river Istro. It falleth into the sea Euxinum: and where as all other rivers of Scythia are troubled, this is clear and fair, also dolesome to be drunk, and full of fishes.  

Dia Rifeos.  The seventh, and last Climate, is called Dia Rifeos. The Mountains called Rifei, are famous in the part of Europe called Parmatia, and are cont●●●lly covered with Snow. Out of these, springeth the river Tanais, 
The river Tanais.  well known in the world by fame. When it is written with ph, it is the name of certain Mountains of Arcadia. And here ought we not to be ignorant, that whereas the authors assigned only seven Climates, they might have made many more. And for that they judged the part of the Pole Antarctic not to be inhabited, they assigned no Climates thereto. Stoflerine added the eight Climate, 
Stoflerine.  counting from the end of the seventh Climate, unto 57 degrees: and other added more. In like manner describing Meridional or South Climates, 
The Meridian or South Climate.  we call them by the self same names, as we did the aforesaid Septentrional, or North Climates: saving that it is necessary to put before every of them this Greek proposition Anti, which in the Latin tongue signifieth Contra, or Contrarium, (that is) contrary, or against. So that as we named the first North Climate, Dia Meroes, we must to the first of the South, add this word Anti, and so shall the first South Climate be named Anti Dia Meroes: The second, Anti Dia Sienes, and so forth of the other, as is seen in the Figure here following.   

The xx. Chapter, of certain principles, that aught to be known for this science.  
Entreating of the Sphere, we have spoken of Circles, Circumferences, Centres, Diameters, lines, with such other words, appropriate to this science: The which, what they are, it is convenient further to declare.  
A right line, 
A right line.  is a short extension from point to point.  
An angle, 
An angle.  is the touching of lines in one superficial, whose touch shall not be direct: for if it be, it sha●l be a line, and not an angle. 
〈◊〉.  Solide is a body, which by divisions hath length, breadth, and depth.  

A circled.  A circle is a plain figure, contained under a line drawn in compass, in whose midst is a point or prick, from the which all right lines coming forth to the circular line that compasseth it about, are equal.  
The circumference of a circle, is a line that containeth the circle, 
The circumference of a circle.  (that is to mea●e) that line to the which all right lines that proceed from the centre of the circle unto it, are equal: and this is called the roundness of the circle.  

The centre of a circle.  The centre of a circle, is that point or prick from the which all right lines proceeding unto the circumference, are equal.  

Diameter  The Diameter of a circle, is a right line, which passing by the centre of the circle, and extending his ends to the circumference, divideth it in two halves.  

Semicircle  The half circle, is a plain figure, contained between the Diameter of the circle, and the half circumference.  

Zenith.  Zenith, is a point or prick imagined in the heaven, directly over the ●oppe of any thing, as if we should imagine a right line to pass by the centre of the earth, extended from thence directly to heaven, and passing through the feet and head of a man standing upright, so that the extremities or ends of this line, should reach unto and touch the circumference of heaven: then the imagined point or prick of heaven, where the end of the line toucheth, is called Zenith, o● point of the head, or vertical point. The same is to be understood of a City, or any other thing, when we speak of the Zenith thereof.  

Ecc●ntricke.  Eccentricke, is a circle, which hath his centre distant, or divided from the centre of the world, and is described in the heaven of the Su●ne, imagining a line from the centre of the Eccentricke, to the centre of the Sun, making a complete revolution at the proper motion of the Sun, in the other heavens, imagining a line from the centre of his Eccentricke, to the centre of his epicyle, and being moved a whole revolution at the proper motion of the epicyle.  
The epicyle, 
epicyle.  is a circle, or little roundel fixed in the depth of the Eccentricke: in which the Planet fixed, and near to his centre, is moved circularly.  
The Auge, 
Auge.  is a point in the circumference of the Eccentricke, nearest unto the firmament: or it may be said, that the Auge is a point farthest distant from the earth. Aux in the Greek tongue, is as much to say, 
Oppos●●● of Auge.  as the greatest longitude, or greatest elevation from the earth. The Opposite of Auge, is an other point in the circumference of the Eccentricke, nearest unto the earth, and farthest distant from the firmament.   
¶ Here endeth the first part.   

¶ The second part, entreating of the motions of the Sun, and the Moon, and of the effects caused thereby.  

¶ The first Chapter, of the course of the Sun in the Zodiac, and the effects caused by the same.  
WE have briefly spoken of the Sun, 
The Sun●e is the guide in Navigation.  and of the other heavens. But for as much as the Sun must be our mark, guide, and governor in Navigation, whereof we intent to give perfect instructions, it shallbe necessary especially, and precisely, to declare the course and motions thereof.  
Therefore (as we have said) the Sun is moved under the Zodiac, 
The moving of the Sunn● under the zodiack●.  and upon his poles in the line Ecliptic, passing by the xii. signs, beginning in the first degree of Aries, where he maketh Equinox, that is to say, he maketh the day equal unto the night in all places. Then from Aries, he entereth and moveth into Taurus, approaching nearer and nearer unto us on the North part, whereby the length of the days are increased with us, and the nights are shortened. Then entereth he into Gemini, and from Gemini into Cancer, where in the beginning of the first degree he maketh Solstice, and toucheth the Summer or estival Tropike, 

The Summer Tropic.  
Declination of the Sun.   and then are the days longest with us, and the nights shortest. Then declineth he no farther from the Equinoctial: but returning toward it, passeth by this sign, shortening the days to us, and lengthening the nights. From this sign of Cancer, it entereth into Leo, and passeth by it into Uirgo, and by it entereth into the first degree of Libra, where he is in the Equinoctial, and then he maketh the other Equinox, so that the night is then equal unto the day over all the world. And passing by this sign, goeth declining from the Equinoctial toward the pole Antarctic, increasing the nights to us, and shortening the days: and so entereth into Scorpio, and from thence into Sagittarius. And passing by it, entereth into the first degree of Capricorn, to the hyemal or Winter Tropike: 
The Winter Tropike.  and then are the longest nights unto us, and the shortest days. From hence he returneth toward the Equinoctial, shortening unto us the nights, and lengthening the days. He passeth by this sign of Capricorn, and entereth into Aquarius: and passing by it, entereth into Pisces: and passing from thence, 
The cause of increasing and decreasing of the day and nights.  returneth to his first point of the Equinoctial of Aries, wh●●e he beg●n. Hereby it followeth, that as the Sun goeth the half of the Zodiac on this part of the Equinoctial, and the other half on the other part of it, and in these halves hath divers declinations, is caused the increasing or decreasing of the days and nights, to one more, and to another less, according as every one with his Horizon discovereth of the course of the Sun, by the little or much that he is departed or distant from the Equinoctial, or as the pole is raised above his Horizon. So that when as to them that are on this part of the Equinoctial, is the longest day and the shortest night: even so to them on the other part, is the longest night, and shortest day. And contrariwise, when unto us is the shortest day, unto them is the longest, which shall further appear by evident demonstration in the last Chapter of the third part.  
The discreet Reader shall here note, 
The moving of the Sun in the centre of his Sphere.  that the Sun is not moved regularly in the Zodiac, making so much by his proper motion in one day, as in the other, because his regular motion is in respect of the centre of his own proper sphere or orb wherein he is moved, whose centre is distant without the centre of the world, toward that part of Cancer, so that the greater part of his orb eccentricke, is toward the septentrional part, where the Sun passing by the septentrional signs, is more distant from the earth, and hath more to go of his orb eccentricke, then being in the South signs: for passing by the North signs, he ●aryeth nine days more, to describe that half of the Zodiac, than the other half toward the South part, and for that cause the Sun is more swifter in his motion in the Zodiac one time then another, for his motion in one day in the South signs, shall be greater than it is in one day in the North signs, as shall appear in the table that followeth: whose use is, for the finding of the motion and true place of the Sun in the Zodiac for every day of the year. And hereby it followeth of the said unequal moving of the Sun, and by the obliquite of the Zodiac, certain days of Wi●ter, with their ●yghtes, are longer than certain other of Summer, with their nights: that is to say, that the day natural in the Winter, doth surmount that in the Summer, because the right ascension, which answereth to one days motion of the Sun, being in the South signs, is greater than the ascension for one days moving, being in the North signs.   

The ij. Chapter, of the true place of the Sun in the Zodiac.  
THE true place of the Sun is a point or prick in the Zodiac, 
To find the true place of the 〈◊〉.  which is thus found: that drawing a right line from the centre of the world, to the centre of the sun, and carrying the same continually right forth unto the Zodiac, where this line showeth or toucheth, that is the true place of the Sun. This place is found in three manners. One way, by a table: an●ther way, by an instrument: and the third way, by a certain rule, to be borne in memory. To find the true place of the Sun by a table, 
The equ●●ion of the year.  seek in the table following, the month that you are in, in the front or head of the table, and the days of the month, on the left side of the table. Then directly against the days, under the little of the months, you shall find two numbers, which are the degrees and minutes of the sign which you shall first find, named over the head, or above the said numbers. T●en to the degrees and minutes which you shall find, you shall add the equation, that is directly of the year in the which you are, or seek to know. And this shall you seek in the table of equations, which is after this: and that which doth amount or rise thereof, shall be the true place of the Sun. And here is to be noted, that in the common years (which are they that have not the bisextile or leap years) from the end of February, until the end of the year (I say of December) shall ever one degree be diminished or taken away: and the degrees and minutes that shall remain, is the true place of the Sun. How to know this by an instrument and by memory, shall be said in the seventh Chapter.  

The Table of the true place of the Sun.  Months january. February. March. april. May. june. Signs. Caprico. Aquarius. Pisces. Aries. Taurus. Gemini. Days. G M G M G M G M G M G M 1 20 22 21 53 20 55 21 24 20 21 19 55 2 21 24 22 54 21 55 22 22 21 18 20 52 3 22 25 23 54 22 54 23 21 22 16 21 49 4 23 26 24 55 23 54 24 19 23 11 22 46 5 24 27 25 55 24 53 25 17 24 13 23 43 6 25 28 26 56 25 53 26 16 25 8 24 40 7 26 30 27 56 26 52 27 14 26 6 25 37 8 27 31 28 56 27 52 28 12 27 3 26 34 9 28 32 29 57 28 51 29 10 28 0 27 31 10 29 33 ☉ ♓ 57 29 50 ☉ ♉ 8 28 58 28 28 11 ☉ ♒ 35 1 57 ☉ ♈ 49 1 6 29 55 29 25 12 1 36 2 58 1 48 2 4 ☉ ♊ 52 ☉ ♋ 22 13 2 37 3 58 2 47 3 2 1 50 1 19 14 3 38 4 58 3 46 4 0 2 47 2 16 15 4 39 5 58 4 45 4 58 3 44 3 13 16 5 40 6 58 5 44 5 56 4 41 4 10 17 6 41 7 58 6 43 6 54 5 38 5 7 18 7 42 8 58 7 42 7 52 6 36 6 4 19 8 43 9 58 8 41 8 49 7 33 7 1 20 9 44 10 58 9 39 9 47 8 30 7 58 21 10 45 11 58 10 38 10 45 9 27 8 55 22 11 46 12 58 11 37 11 43 10 24 9 52 23 12 47 13 57 12 36 12 40 11 21 10 49 24 13 48 14 57 13 34 13 38 12 18 11 46 25 14 48 15 57 14 33 14 36 13 15 12 43 26 15 49 16 56 15 32 15 33 14 12 13 40 27 16 50 17 56 16 30 16 31 15 10 14 37 28 17 51 18 56 17 29 17 28 16 7 15 34 29 18 51 19 56 18 28 18 26 17 4 16 31 30 19 52   19 27 19 23 18 1 17 29 31 20 52   20 25   18 58    

The Table of the true place of the Sun.  Months. july. August. September. October. November. December. Signs. Cancer. Leo. Virgo. Libra. Scorpio. Sagittari● Days. G M G M G M G M G M G M 1 18 26 18 ● 18 4 17 39 18 49 19 24 2 19 23 1● ● 19 2 18 39 19 50 20 26 3 20 20 19 58 20 1 19 38 20 51 21 27 4 21 17 20 55 21 0 20 38 21 52 22 29 5 22 14 2● 53 21 58 21 38 22 53 23 30 6 23 11 22 51 2● 57 22 38 23 54 24 31 7 24 8 23 48 23 56 23 38 24 55 25 33 8 25 5 24 46 24 55 24 38 25 56 26 34 9 26 2 25 44 25 54 25 39 26 57 27 36 10 27 0 26 42 26 53 26 39 27 58 28 37 11 27 57 27 40 27 52 27 39 28 59 29 39 12 28 54 28 38 28 51 28 39 ☉ ♐ 0 ☉ ♑ 40 13 29 51 29 36 29 50 29 39 1 1 1 42 14 ☉ ♌ 48 ● ♍ 34 ☉ ♎ 49 ☉ ♏ 39 2 3 2 43 15 1 46 1 32 1 48 1 40 3 4 3 45 16 2 43 2 30 2 47 2 40 4 5 4 46 17 3 40 3 28 3 46 3 40 5 6 5 48 18 4 38 4 26 4 45 4 41 6 8 6 49 19 5 35 5 24 5 45 5 41 7 9 7 51 20 6 32 6 22 6 44 6 42 8 1● 8 52 21 7 30 7 21 7 44 7 42 9 11 9 54 22 8 27 8 19 8 43 8 43 10 12 10 55 23 9 25 9 17 9 42 9 43 11 13 11 57 24 10 22 10 16 10 42 10 44 12 14 12 58 25 11 20 11 14 11 41 11 45 13 15 13 59 26 12 17 12 13 12 41 12 45 14 16 15 1 27 13 15 13 11 13 41 13 46 15 18 16 2 28 14 12 14 10 14 40 14 47 16 19 17 3 29 15 10 15 8 15 40 15 47 17 20 18 5 30 16 7 16 7 16 39 16 48 18 22 19 6 31 17 5 17 5   17 49  22 20 7  

The Table of the Equation of the Sun.  The years of our lord The equation to be added. The years of our lord The equation to be added. The years of our lord The equation to be added. The years of our lord The equation to be added.  G M  G M  G M  G M 1545 R1 0 1581. 1 16 1617. 1 32 1653 1 48 1546  45 1582 1 1 ●618 1 17 1654. 1 33 1547  30 1583  46 1619 1 2 1655 1 18 1548  15 1584.  32 1620  47 1656 1 3 1549 1 2 1585. 1 18 1621. 1 33 1657 1 49 1550  47 1586 1 3 1622 1 18 1658 1 34 1551  32 1587.  48 1623. 1 3 1659. 1 19 1552  18 1588.  33 1624.  49 1660 1 4 1553 1 4 1589 1 ●9 1625 1 35 1661. 1 51 1554  49 1590. 1 4 1626. 1 20 1662. 1 36 1555  34 1591.  49 1627. 1 25 1663. 1 21 1556  19 1592.  35 1628.  51 1664 1 7 1557 1 05 1593. 1 21 1629 1 37 1665 1 53 1558  50 1594 1 ●6 1630 1 22 1666 1 38 1559  35 1595  51 1631 1 7 1667 1 23 1560  21 1596  37 1632  53 1668 1 9 1561 1 7 1597 1 23 1633 1 38 1669 1 55 1562  52 1598. 1 8 1634 1 23 1670 1 40 1563  37 1599  53 1635 1 8 1671 1 25 1564  23 1600  39 1636  54 1672 1 10 1565 1 9 1601 1 25 1637 1 40 1673 1 56 1566  54 1602 1 10 1638 1 5 1674 1 41 1567.  39 1603  55 1639 1 10 1675 1 26 1568  25 1604  40 1640  56 1676 1 12 1569 1 11 1605 1 26 1641 1 42 1677 1 58 1570  56 1606 1 11 1642 1 27 1678 1 33 1571  41 1607  56 1643 1 12 1679 1 28 1572  26 1608  32 1644  8 1680 1 13 1573 1 12 1609 1 28 1645 1 44 1681 R2 ☉ 1574  57 1610 1 13 1646 1 29 1682 1 45 1575.  42 1611  58 1647 1 14 1683 1 30 1576  28 1612  44 1648 1 0 1684 1 15 1577 1 14 1613 1 30 1649 1 46 1685 2 2 1578  59 1614 1 15 1650 1 31 1686 1 4 1579  44 1615 1 10 1651 1 16 1687 2 32 1580  29 1616  46 1652 1 2 1688 1 8  
This Table of the Equation of the Sun, serveth from the year of 1545. where it hath his root or beginning, until 1680. and in the year of 1681. it shall return to the root, adding thereunto one degree more. As for example. In the year of 1681. add one degree upon the other degree that the root hath, and so shall the year of 1681. have two degrees of Equation, and the year of 1682. shall have one degree, and 45. minutes, which is to add one degree upon 45. minutes, that had the year of 1546. etc. And having passed other 136. years, you shall return to the root, adding two degrees.   

The iij. Chapter, of the declination of the Sun.  
THE declination of the Sun, is the ark of the greater Circle, 
What is the declination of the Su●●e.  which passeth by the Poles of the world, included between the Equinoctial and the Zodiac. And here is to be noted, that whatsoever four points or pricks which are equally distant from the points of equinoxes (which are the beginnings of Aries and Libra) shall have equal declinations.  
Whereof if followeth, that the four quarters of the Zodiac have equal declinations. And to avoid prolixity, I will add hereunto a Table of the declinations of only one quarter of the Zodiac, so that all having one self same manner of declinations, it may serve for all, and the order of it is this. The signs whose declination increaseth, are in the head or front of the Table, and the degrees of these signs descend by the left side thereof. And the signs whose declination decreaseth, are in the foot of the Table, and the degrees of these signs, rise by the right side of the same. The disposition of the Table being understood: then to know what declination the Sun hath in every degree of the Zodiac, you ought Signs ♈ ♎ ♉ ♏ ♊ ♐ Signs G G M G M G M G 0 0  11 30 20 12 30 1 0 24 11 51 20 25 29 2 0 48 12 12 20 37 28 3 1 12 12 33 20 49 27 4 1 36 12 53 21 0 26 5 2 0 13 13 21 11 25 6 2 23 13 33 21 22 24 7 2 47 13 53 21 32 23 8 3 11 14 13 21 42 22 9 3 35 14 32 21 51 21 0 3 58 14 51 22 0 20 11 4 22 15 10 22 9 19 12 4 45 15 28 22 17 18 13 5 9 15 47 22 25 17 14 5 32 16 5 22 32 16 15 5 55 16 23 22 39 15 16 6 19 16 40 22 46 14 17 6 42 16 57 22 52 13 18 7 5 17 14 23 57 12 19 7 28 17 31 23 3 11 20 7 50 17 47 23 8 10 21 8 13 18 3 23 12 9 ●2 8 35 18 19 23 15 8 ●3 8 58 18 34 23 19 7 24 9 20 18 49 23 22 6 ●5 9 42 ●9 4 23 24 5 26 10 4 19 18 23 ●6 4 27 10 26 ●9 32 23 28 3 8 10 47 19 46 23 29  29 11 9 19 59 23 30 1 30 11 30 20 12 23 30 0 Signs ♓  ♏ ♒ ♌ ♑ ♋ Signs to know the true place of the Sun (as in the Chapter past is declared) for the day of the declination which you desire to know, and the sign which the Sun shallbe found in that day, shall you seek in the front or foot of the Table. And if it be in the front, you shall seek the number of the degrees on the left side. And if it shallbe at the foot of the Table, you shall seek it on the right side. Then above or under the sign, in the front of that degree of the said sign, you shall find two numbers, whereof the first is of degrees, and the second of minutes: and those degrees and minutes of declination the Sun hath that day. And this is understood without having respect to the odd minutes above the degree, which the true place of the Sun hath.  
And if you desire to verify this more precisely, note the declination of that degree, and of the degree following: and take the less from the more, and that wh●ch remaineth, shallbe the difference of the declination from the one degree to the other, of which difference ye shall take a part proportionally, as are the minutes of the place of the S●nne unto 60. And this part of minutes must be added to the first declination of it, and be less than the second, or must be taken from it if it shall be greater, and then that riseth thereof, shallbe the precise declination for that sign, degree, and minute. As for example. In the year 1546. the tenth day of September, the Sun shallbe in 26. G. 38. M. of Virgo, & to the 26. G. precise, shall correspond 1. G. 36. M. of declination. And to verif●e the declination that cometh to 38. minutes, which is more of the 26. G. you must mark the difference that is from the declination of 26. G. (which is one G. 36. M.) to the declination of the 27. G. which is 1. G. 12. M. The difference is 24. M. Of these you must take such part proportionally, as the 38. minutes beareth unto 60. which are almost two terces of a degree. Then the two terces of 24. are 16. which must be taken from one degree 36. M. which correspond to the 26. G. of Virgo, because the declinatio●s go decreasing, and remaineth 1. G. 20. M. and if the declinations increase, you must add thereto, as you take away when they decrease.  

another example for this year of 1561.  
Example for the year 1561. the 20. of Apryll, I find the true place of the Sun at noon, in 9 degrees 54. minutes of Taurus: then in the Table of the signs present, I seek for 9 degrees of Taurus, to which doth answer for the declination 14. degrees. 32. minutes, & to the next degree following, doth answer 14. degrees 51. minutes: then take the lesser out of the more, so resteth 19 minutes. Then from a rul● of 3. & say, if 60. minutes give 54. minute's (which 54. minutes doth rest before of the 9 degrees of Taurus) how many doth 19 minutes give? which 19 minutes are the diversity of the 9 & 10. degrees of Taurus. S● I find, that 19 minutes giveth 17. minutes, and 6. seco●des, which 17. m●nutes, and 6. seconds, I add to the 14. degrees 23. minutes, which answereth to the 9 degrees of Taurus. And it cometh to fourteen degrees. 49. minutes, and two seconds, which is the true declination for the twenty day of Apry●l. Anno. 1561.  
It is also to be noted, that I add these seventeen minutes and six seconds, because the declination doth increase: for if it decreased, it were to be taken out so much, and the rest is the declination. So is the declination for the twenty of Apryll in the year 1561. fourteen degrees. 49. minutes, and two seconds.    

The iiij. Chapter, of the increase of the Sun into the twelve Signs. And of the Equinoctials and Solstitials which divide the four times of the year.  
OF that is said in the Chapter before, 
The entrance of the Sun into the fou●● principal signs.  it followeth that the sun entering into the four principal signs, causeth the four times of the year. For entering into Aries, it changeth the time to us from winter to the spring time. And entering into Cancer, it changeth the time from spring to summer. And entering into Libra, from summer to Autumn. Likewise entering into Capricorn, it changeth from Autumn to Winter. So that when to us that be on the part of the North, is summer, then is it winter to them that are on the South part. Or contrariwise, being summer to them on the South, it is winter to them on the North. The entrance of the sun into these signs, and all other of the Zodiac, hath not been ever at one self same time of the year. The cause of this is, that the Latin y●ere is not equal with the moving of the s●nne in the Zodiac, 
The Latin● year.  as shallbe said in the x. Chapter, 
The E●uinoctialles in the y●ere of Christ●s birth.  where we will entreat of the year. In the time that Christ our redeemer was borne, were the Equinoctialles. The one at the eight of the ●ale●des of april, and the other at five of the kalends of October: So that they had the Equinoctial of the Spring, at the xxv. of March, and the Equinoctial of Autumn, at the xxvii. of September, as writeth john Baptist Capuano, upon the second Chapter of the Sphere of johan. De sacro bosco. They judged then the Solsticialles, 
The Solsti●●●ls.  as that of the Somme●, at the eight day of the kalends of july, which is the xxiiii. of june: the other of the Winter, they judged at the eight day of the kalends of I●nuarie, which is the xxv. of December. And here will I not omit to say how in those times, at these four days (that is to mean, in the two Solstitialles and two Equinoctialles) were celebrated, or did chance four marvelous things in the world.  
For in the spring Equinoctial, which was at the xxv. of March, the Son of GOD was incarnate, and afterward borne of the Virgin Marie in the Solstitial of Winter, 
●our notable things.  which was at the xxv. of December.  
In the Equinoctial of Autumn, which was the xxvii. of September, was conceived blessed john Baptist, the crier and precursour of Christ: and was borne in the summer Solsticiall, that was the xxiiii. of june. And this is the sixth month whereof Saint Luke speaketh in the Gospel. Which thing also john chrysostom doth verify, saying that S. john was borne when the days began to decrease, and our Lord when they began to increase. And it may certainly seem worthy to be had in memory, that in the said Equinoctial of the spring, Christ suffered, Adam was created and lost the estate of innocency, Abel was slain, Melchisedech offered bread and wine, Isaac by Abraham was brought to be sacrificed, john Baptist was beheaded at Macherunta, Peter delivered out of prison, Saint james beheaded by Herode, the good Thief enjoyed Paradise, and the bodies of many Saints rose with christ. And who so further desireth more precisely to know the entrance of the Sun into Aries, 
To know more precisely the entrance of the Sun into the four principal ●ign●●.  and into the other principal signs, shall in the third part of this work, in the eight Chapter, find rules which shall bring him to the knowledge thereof. B●t ●o return to our time, I say that this present year of 1545. the Sun entereth into the first degree of Aries, at the tenth of March, at four of the clock at after noon, and into the first degree of Taurus the ninth of Apryll 2. hours, and 7. minutes, and into Gemini the 11. of May 2. hours and six minutes, into Cancer the 11. of june. 14. hours. 44. minutes, into Leo the 13. of july. 3. hours. 50. minutes, into Virgo the 13. of August 9 hours 56. minutes, into Libra the 13. of September 4. hours 4. miwtes, into Scorpio the 13. of October. 7. hours 13. minutes into sagittary the 12. of November just at noon, into Capricorn the 11. of December 8. hours 16. minutes, into Aquarius the 9 of januarie. 2. hours, one minute, into Pisces the 8. of February 1. hour 30. minutes after midday (that is to say) from noon 1. hour 30. minutes. 
To know when the Sun entereth into every of the xii. Sign●●  And that we may in the years to come, know the day, hour, and minute, in the which the Sun entereth into every sign, we will follow this order.  
Upon the days, hours, and minutes, that the Sun entereth into every sign this said year. 1545. we must add for every year five hours and 49. minutes, which with the 365. days, which every year containeth, shallbe the time in the which the Sun accomplisheth his Revolution. 
Leap ye●r●.  And because that in the year of the Bisextile or Leap year, is added to February one day more to his 28. which he hath once in four years, from 6. to 6. hours, if we shall take from the computation that which we have given him, turning one day backward (as shallbe in the year 1548.) and upon that that remaineth shall return in the year following of 1549. to add five ho●res 49. minutes, and as much more every other year following, shallbe a certain rule for ever.  
And it is to note, that the degrees and minutes which we have touched before, are properly for the City of Cadiz. And if we desire to apply them for other Cities or places more Eastward: then for every xv. degrees that they are distant from Cadiz in longitude, we must add one hour. And if for Cities, or places more Westwards 
Variation of hours by the rapt moving of the Sun from the East to the West.  in like manner for every xv. degrees we must take away one hour, by reason of the course of the Sun by his rapt moving from the East to the West. For it is certain, that when with us in Cadiz it is xii. hours of the clock, t● them that are xv. degrees Eastward from us, it is one of the clock, and to them that are from us xv. degrees toward the West, it is xi. of the clock.  
Now that we have Rules to know the entrance of the Sun into the xii. signs, thereby may we also know his entrance into the four Cardinal or principal signs, which are they that determine and end the Equinoctialles and Solstitialles, whereby are caused the four times of the year. And forasmuch as the general change of times, is by reason of the Sun, 
The entrance of the Sun into the iiii. principal signs, causeth the change of tyme.  who by his coming near, warmeth, by his remaining drieth, with his departure, cooleth, and by his long tarrying away, causeth maystnesse, we will show the qualities of the principal winds, elements, regions, humours, and ages, in one brief Table: and then consequently in an other will we describe the beginning, midst, and end of the four times of the year, aswell in the months, as in the heavenly signs.  

The Table of the qualities of the Elements.  
Qualities. Hot & dry Hot & moist Cold & moist Cold & dry Parts of the year Summer Spring. Winter. Autumn. Principal winds East. South. West. North. Elements. Fire. Air. Water. Earth. Regions. East. South. West. North. 4. Humours. Choler. Blood. Phlegm. Melancholy 4. Ages. Youth. Man's state. Aged. Age.   

The Table of the four times of the year.  
times. Beginning. Midst. End. Spring. March. Aries. Apryl. Taurus. May. Gemini. Som●er. june. Cancer. july. Leo. August. Virgo. Autumn. Septem●. Libra. Octob. Scorpio. novemb. Sagit. Winter. Decemb. Capricor. janua. Aquar. Februa. Pisces.    

The v. Chapter, of the Moon, and of her motions and properties.  
IN the Chapters passed of this second part, 
The Sun and Moon are the principal luminaries  we have entreated of the Sun, and of his motions and effects, as the most noble and principal luminary. In this present Chapter we will entreat of the Moon, which is the second luminary, although in the order of the heavens she is the first, and nearest unto us of all other Planets or Stars.  
The M●one therefore is a round body, of heavenly substance, solid and dark in respect of the Sun, having no proper light of his own, but is apt to receive light. She is moved from the West into the East, according to the order of the signs, every day 13. degrees little more or less, and somewhat more than 10. minutes, 
The Eclipse of the Moon  by the proper motion of the heaven or sphere upon the Ares and Poles of the Zodiac. I said more or less, because that over and beside the moving of her deferent or circle, which is moved every day the aforesaid 13. degrees and 10. minutes, almost 11. she hath an Eclipse where the Moon is fixed: at the motion whereof, sometimes she is moved more swiftly, and sometimes more slowly: Nevertheless, according to herself motion, she maketh her course in 27. days and almost 8. hours: 
The conjunction of the Moon with the Sun. The Moon receiveth her light of the Sun.  and having no light of her own, she is lightened of the Sun, as manifestly appeareth hereby, that being in conjunction with the Sun, or near unto him, we see her not lightened: because the light which she then receiveth, is only her uppermost or highest part, whereby she directly beholdeth the Sun, forasmuch as he is in the fourth heaven, and she in the first. And departing from the Sun by her prop●r moving, 
The aspect of the Moon to th● Sun.  the Sun remaineth on the West part. Then toward that part we begin to see a little of the part of the Moon lightened, and so more and more by little and little, as she departeth farther from the Sun. And at this time she hath her horns or corners toward the East, because the Sun is in the West. During this time also, she is said to increase, or that she goeth increasing unto the opposition which we see, 
The increasing and opposition of th● Moon.  by the part of her, which the Sun directly beholdeth. And so do we see her altogether lightened, and call it the full Moon. Then passing from the opposition, she cometh nearer the Sun by little and little, being darkened and hid f●om us, and lightened only by her highest part: and this time is called the decreasing or wane of the Moon. Then also hath she her horns toward the West, because the Sun is in the East: and this until she turn again in conjunction with the Sun, and that we see her not lightened at all.  
The Moon is less than the Stars or other Planets, except Mercury, 
The bigness of the Moon.  and less than the earth. And if any shall affirm the contrary, saying, that it is written in the first of Genesis, that God made two great lights: the greatest to give light to the day, and the less to lighten the night, (as David also affirmeth.) To this I answer, that the Moon being nearest unto the earth, appeareth unto us greater than she should do, if she were further distant from us. And although she be great of light (received as we have said) and big of body, yet is she not great in respect of the other Stars. And therefore the words of Genesis aforesaid, 
The Moon is ●earest unto the e●●th.  may be understood to be spoken in such manner and phrase as holy Scripture often useth, to humble and apply itself to the weakness of our understanding, and grossness of our senses.   

The vi. Chapter, of the conjunctions and oppositions of the Sun and the Moon.  
THE Sun and the Moon are moved under the Zodiac with divers motions. The Moon with a swifter motion than the Sun followeth him, 
The motion of the moon●.  overtaketh him, and goeth before him, until she place herself in Diameter with him. And when she hath thus overtaken him, so that they are both in one self-same degree of the Zodiac, then is the conjunction. 
The conjunction.  Then departing from him, and being in equal degrees of the signs opposite according to the Diameter, is the opposition. To know the times of these conjunctions and oppositions, 
Th● opposite.  is very profitable and necessary for Mariners. These times may be known in two manners. 
To know th● times of oppositions and conjunctions.  One way, by the Ephimerides or Almanac, or other tables, or Luna●ie instruments. And by these means is known precisely the day, hour, and minute of the conjunction and opposition. It may likewise be known by the rules of computation, which are the rules that are known by memory, although not precisely, as by the books aforesaid. And here is to be understood, that from one conjunction to another, according to the half movings of the Sun and the Moon, there passeth 29. days, twelve hours, and 44. minutes. And consequently from conjunction to opposition, and from opposition to conjunction, the half thereof, which is fourteen days 18. hours, and 22. minutes. To know the●e conjunctions by rules of computation, is presupposed to know the golden number, and by it, the concurrent or Epacte.  
The golden number, 
To know the golden number.  is the number of nienteene years. In which time, the conjunctions of the Sun and the Moon make all their varieties in the times of every year: so that if the conjunction were the twelfth day of March in this year of 1545. from this year in the nienteene years following, which shallbe in the year of 1564. the conjunction shall return to be at the twelfth day of M●●che. It was first called the golden number by the Egyptians, who first found the use thereof, and sent it to Rome written in golden Letters. To find this number, it is needful to know his roots, which is this. In the year that Christ our Lord and redeemer was borne (whereby we make this account) the golden number was the number of one, 
The roots of the golden number.  which was the year of the root or begi●●●ng: and the first year of the birth of Christ, was two of the golden number. So that joining to the years of our Lord one of the root or beginning, and from all take away the nienteene, than the rest shall be the golden number. And if you desire to make computation by a nearer root, take for the root the year of 1500. when nienteene was the golden number, and in the year of 1501. did begin one of the golden number, and so consequently ever taking away the nienteene.  
This present year of 1545. we have seven of the golden number. And in the year of 1546. we shall have eight. etc.  

The concurrent.  The golden number being known, it is necessary for this computation of the Moon to know the concurrent. The concurrent of every year, is the number of the days passed of the conjunction of the Moon at the beginning of March. And the●e grow of the difference of the Solar year to the Lunar: 
The Solar and Lunar years.  As the Lunar year hath 354. days, and the Solar year 365. so having every year eleven days of difference, which are added every year until they come to the number of thirty, and passing thirty, those that do pass are of the concurrent.  

To find the number of the concurrent.  The number of the concurrent of every year, is found in this manner.  
And the better to bear it in memory, you must imagine three places: and these commonly are assigned on the thumb. As the first place at the root of the thumb, the second in the middle joint thereof, and the third and last, in the top of the thumb. Then ●n the first place put ten, in the second twenty, and in the third thirty. Then by the order of these places shallbe counted the golden number: As one in the first place, two in the second, and three in the third, returning four to the first place. etc. vnti●● the golden number of that year for the which the concurrent is sought. And the number of that place where the golden number endeth, must be joined with the number of the golden number: and that doth amount thereof, shall be the concurrent, so that it pass not 30. But if it pass 30. then that that is more than 10. is the concurrent of that year.  
And here is to be noted, that the years of this computation of the Moon, begin at the first day of March, and last until the last day of February, so that this present year of 1545. by computation of the golden number, we have seven: which accounted by the said places, endeth in the first, which is 10. which also joined with the golden number of seven, make 7. and so much is the concurrent of this present year.  
Likewise, this number of Epacte, 
Epact.  or concurrent, is found in multiplying the golden number by 11. & dividing the sum by 30. then that remaineth, is the Epact or concurrent.  
The concurrent being thus known, 
To know th● days o● ag● of the Moon●.  then to know the days of the Moon, it is necessary to know three numbers. The fyrst● is the concurrent. The second, the number of the month in which you are, beginning at March. The third, the days passed of the same month. And joining th●se three numbers, if they come not to 30. so many days old is the Moon●. And if they be 30. it is the conjunction. And if they pass 30. they also that pass, are the age of the Moon.  
This is understood in the months that have 3●● days, for in them that have only 30. days, the conjunction is at the 29. day, and they that pass of 29. are the age of the Moon. As for example.  
The first day of August, of the concurrent 17. of months from March 6. and of days of the month 〈◊〉 make 24. and so much is the age of the Moon.  
another example. The tenth of September, of concurrent 17. of months seven, of days ten, which are in all 34. And because that September hath only 34. days, we must take away 29. of the 34. and so rest five days, which are the age of the Moon. And in like ma●ner shall w● give to February 29. days of the Moon.  
It followeth, 
To know t●● day of the conjunction.  that the days of the Moon being known, then vnreckon●●g or disreck●ning backward, we find for example. The 20. of july, the Moon hath 12. days taken from the 20. remaineth 8. Then the eight day was the conjunction.  
The day of the conjunction is likewise known by joining the months (beginning in March) with the concurrent, and if they come not to 30. then at so many days of that month as lacketh of 30. shallbe the conjunction.  

Example.  
In August 6. of the months, and 17. of the concurrent, are 23. which of 30. lacketh 7. Then at the seventh day was the conjunction, and if they pass 30. then taking them that pass from the number of the days which the month had next before, and then that which remaineth, doth show the day of the conjunction. Like as the Moon of September of the year 1546. we shall count the concurrent 28. of months 7. which are 35. Then taking away the 5. from 30. and one which August hath, remaineth 26. and so the 26. of August, of the year to come of 1546. the Moon shall make conjunction.    

The seven. Chapter, of the declaration and use of an Instrument, by the which is found the place and declination of the Sun, with the days and place of the Moon.  

To know the place of the Moon in the Zodiac, and what aspects she hath with the Sun.  IN the second and third Chapter, I have given rules to know the true place of the Sun, and his declination. In this Chapter I will describe an instrument, whereby may be knowe● the declination and place of the Sun, and knowing by the Chapter past, the days of the Moon, shall also be known her place in the Zodiac, and how much of her is lightened, and what aspect she hath with the Sun.  
This Instrument is in square form, and hath by the sides 23. degrees and a half, of the which the 23. and a half that descend from the midst downward, 
The description of the Instrument.  is the declination of the South signs: and the other from the midst upward, are the declinat●ons of the North signs. Within this quadrature is described a circle, by the circumference whereof, are the twelve signs and their degrees, joined to the circumference: and further within, is the number of them, and then their names. Yet further within this, is another circle, where are the twelve months, with their numbers and days.  
Then to the centre of this circle, are annexed two rundles, whereof the greatest and lowest is called the rundel of the Sun.  
This hath an Index or shower, in which is painted the Sun, and in the circumference of it are the days of the age of the Moon. In the other circle, in the circumference thereof, is a round hole, representing the Moon: directly from the which, is another Index coming forth of the circumference of this roundel, in which roundel are all the aspects which the Moon maketh with the Sun.  
Having described the Instrument, let us declare the use thereof, which is this.  
first to find the true place of the Sun, 
The use of the Instrument to find the tru● place of th● Sun.  we must put the Index of the roundel of the Sun, upon the day of the month in which we are, or desire to know the place of the Sun. Then in the circle of the signs, it shall show the sign and degree in the which it is: and in like manner, resting still upon the degree, looking in the parallels that touch in the circumference, and proceeding by that line that toucheth the Sun which the Index doth note, ye shall see in the side of the Instrument, the number of the degrees of the declination which the Sun hath at that day.  
To find the place of the Moon, 
To find the place of the Moon.  we must hold the Index of the roundel of the Sun, fast upon the day of the moveth in the which we desire to know the place of the Moon. And accounting in the roundel of the Sun, the days that have passed from the day of the Conjunction (as I have said in the Chapter before) and where endeth that number of the days, if there we apply the index of the Moon, it shall show in the circle of the signs, the place where she is. And so shall she appear in the instrument lightened, or darkened, more or less as in heaven. In like manner, considering the place of the Sun and the Moon, shall be seen what aspect they have, by the lines that traverse the superficial of the Lunar circle of the Moon.  
The aspects which the Planets have one to another, or whereby they behold one another, are five. 
Five aspected of the Planets.   
Conjunction is, when two Planets be under one self same degree and minute in the Zodiac, 
Conjunction.  whos● charact is this. ♂  
Opposition is, 
Opposition.  when between the place of the Planets is half a circle, which are 180. degrees, and is thus figured. ☍  
Trinall aspect is, 
Trinall.  when between the planets shallbe four signs, which are 120. degrees, and is figured thus. ⊦  
Quadrine aspect is, 
quadrine.  when one Planet is distant from another by three signs, which are 90. degrees, whose charact is this. □  
Sextile aspect is, 
Sexti●e.  when two signs are between them which are threéscore degrees, and is marked thus. ⚹  
And if by memory you desire to know the true space of the sun, 

To know th● place of the Sun by th● rule of memory.  
To know in what degree the Sun is.   without respect of minutes (which may sufficiently be done with the astrolabe) bea●e in memory these numbers, 10.9.10.11.12.13.14.13.14.13.12. Of the which the first serveth for januarie, the second for February, with their signs: and so of the rest. Then to know in what degree the sun is, you shall take away the days that are applied to every month, according to the said numbers of the days for the which you desire to know the true place of the sun, and in them that remain, in so many degrees is the sun of the sign into the which it entereth the month. And if the days passed of the month, shallbe less then the days applied to the same month: you shall join thirty with those days passed of the month, and of the sum that amounteth, you shall take away the days applied to the said month, and the rest shallbe the degrees in which the sun shallbe of the sign of the month past, as for example.  

Example.  
januarie. 10 ♒ February. 9 ♓ March. 10 ♈ Apryll. 10 ♉ May. 11 ♊ june. 12 ♋ july. 13 ♌ August. 14 ♍ September. 13 ♎ October. 14 ♏ November. 14 ♐ December. 13 ♑  
The 22. of October, taking away four●teéne that were applied, remain eight degrees of Scorpio, where the Sun is.   

Another Example.  
The six of December, which are lesser than twelve which is applied unto it, if we join two to thyr●ie, which are the days of the month next afore, they make 36. and from them we take away the 12. rest 24. So in 24. degrees, is the sun, of the sign of the month before, which is sagittary.    

The viii. Chapter, of the Eclipse of the Moon and the Sun.  
THe Eclipses of the sun and of the Moo●e, is a thing that causeth great fear and admiration among the common and ignorant people, and ●o them that understand the cause thereof, nothing at all. And therefore have I thought g●od to declare the effects thereof.  
It is to understand, that the sun is much bigger than the earth, and by perspective, the shadow of the earth in how much the farther it parteth from it, becometh sharper and sharper, until it come to a point: so that the shado●● of the whole earth, is piramidally sharp. And as the Moon is less than the earth, yet (although his shadow goeth sharpening) it sufficeth to eclipse the Moon, if she pass by the midst thereof.  

The Eclipse of ●h● Sun.  The Eclipse of the Sun, is the interposition of the Moon between us and the Sun, as if the Sun be in the fourth heaven, and the Moon in the first, she being a dark body, and by her proper motion overtake the Sun, then putting herself between him and us, she covereth him in part, or in the whole, and this is the Eclipse of the Sun. As the Sun also goeth ever under the Ecliptykes, at that time that he cometh to the head or tail of the Dragon, if then the Moon make conjunction with him, shallbe the Eclipse of the Sun, for as much as they are both under the Ecliptyke.  

The Eclipse of the Sun is not universal.  The Eclipse of the Sun can not be universal in the whole earth, I say, unto all them that may see the Sun at the time of the Eclipse, as is the Eclipse of the Moon universal. For if the Moon have one part Eclipsed, all that may see her, shall see her Eclipsed: But the Sun some may see all wholly Eclipsed, and other in part, or other also not at all Eclipsed: and this all at one self same time. The cause whereof, is the diversity of the aspect, which is, to see the Moon in the Zodiac out of her place: as if the Sun and Moon should make conjunction in the beginning of Aries, and in the head of the Dragon, they that then should be in the Equinoctial, under the Sun and the Moon, or that the Sun and the Moon should be in their Zenith, they should see the Moon hide all the Sun.  
And they that should be in the North Climates, should see, that the Moon hideth or darkeneth only the South part of the Sun, 
●ow ●h● Sun is eclipsed in the whole, or i● par●.  and not al. Again, they on the South part, should see the Moon hide the North part of the Sun, and not all. And if at the time of the conjunction, she have a little passed the head of the Dragon, or lack a little to come to the tail, so that she be in the North latitude: they that then should be in the North Climates, should see the Moon Eclipse all the Sun: and they of the Equinoctial should see only the North part of the Sun Eclipsed, and they of the South should see him nothing at all Eclipsed. So that although the Eclipse of the Sun shallbe total or particular, it can not be universal in the whole earth.  
It is also to be noted, 
why the Moon seemeth sometime bigger, and sometime less than the Sun.  that although the Sun be bigger than the Moon, yet at sometime the Moon seemeth greater than the Sun. And this shall be, when the Sun is in the Auge of the Eccentric, and the Moon in the opposite of the Auge of the epicyle.  
And when it so appeareth, he may be all Eclipsed. Sometimes also the Moon seemeth less. This is when the Sun is in the opposite of the Auge of the Eccentricke, and the Moon in the Auge of the epicyle. Then although we should see the centre of the Moon in the centre of the Sun, she can not hide him all wholly, because the Sun shall appear greater.  
Of this that we have said, 
The Sun is Eclipsed in conjunction, & the Moon in opposition.  it followeth that all the Eclipses of the Sun●e, must of necessity be in the coniuncttion, and the Eclipses of the Moon, in the opposition: whereby is inferred, that the Eclipse of the Sun in  ●● 
By the description of other, the great year is when the eight sphere jointly with all the A●ges, 
The revolution on o● the ●ight Sphere.  make one perfect revolution at the moving of the ninth Sphere. And this shall be in the space of xlix. thousand years.  
The solar year, 
The Sol●r year.  is a revolution of the Sun, carried by the proper moving of his heaven upon the Axis and Poles of the Zodiac, ending where it began, and returning an other year by the self same course, as the Poet Vi●gil affirmeth, saying.  
Atque in se sua per vestigia voluitur annus.  
That is to say, The year turneth again to himself by his own proper steps.  

how the Egyptians painted the year.  The Egyptians lacking the use of Letters, and having the same consideration, painted the year like unto an Adder, biting her own tail: and heéreof was a ring called Annulus, as it were Annus (that is, a year) because a ring turneth round in itself, 
The quantity of the year.  as doth the year. Of the quantity of this year were divers opinions and computations among them of ancient tyme. The Arabians and Persians accounted it regularly by xii. Moors, which are 354. days. Romulus gave to his year x. months, because that time sufficeth to a woman to bring forth her birth, and also for that during so much time, it was not lawful for a Widow to marry after the death of her husband. Numa Pompilius added two months, to make it up twelve months in 350. days, 
The year of the hebrews.  which was the m●st ancient year of the hebrews, according to the which, they account at this day. The Greékes and Egyptians, 
The Greeks.  considering the course of the Sun, made the year of 365. days. Then by the commandment of julius Caesar 
julius Caesar.  (whose order we now observe) were added six hours, to the end to make equal this number of days with the course of the Sun: and hereof the Bisextile or Leap year had his beginning, 
L●●pe year.  from four to four years. But to say the truth, they erred: The one, by somewhat too much, and the other by somewhat too little.  

Days of the ye●r●.  This y●ere containeth 365. days. 5. hours, & 49. minutes.  
Likewise at the first, the year had divers beginnings. Numa Pompilius began it from the Winter solsticiall, 
Beginning of the year.  because th●t then the Sun beginneth to rise toward us, 
ovid.  as Ovid affirmeth in these verses: 
Brum● novi prima est, 
bruma is the stay of the sun in winter, the winter solstitial, and shortest day of the year.  veterisque novissima Solis.  
Principum capiunt Phoebus & Annus idem.   
Which may thus be englished.  
Brume is the first of the new year,  
And last day of the old:  
The Sun and year begin at once,  
As Ovid hath us told.  
Romulus began it at March, at the Equinox of the spring, because that then all things revive and flourish: and by the opinion of the D●ui●es, 
The Creation of the world.  it seemeth good reason to begin the year at March, because the world was created the 25. of the kalends of Apryl, which is the 18. of the month aforesaid. Likewise, God speaking of this month to the people of Israel, 
Exod. xii.  said unto them, This shallbe the first of the months of the year. The Arabians begin from the Summer solstitial, whose opinion is, that the Sun●e was made in the sign of Leo. Other begin the year in September, about the Equinoctial of Autumn, as do the jews, resting in the authority of Genesis, where it is written thus: Let the earth bring forth green herbs, to have fruit agreeable to their kind. etc. And because Autumn is a fruitful time, they began from thence to account their year. The Greékes, Persians, and Egyptians, account it from October. The Christians, 
Where the Christians begin the year.  some from the Incarnation of Christ, other from his birth, and other from the first day of januarie.  
In like man●er, 
Diversity in the number of the years or the date.  is great diversity in beginning the number of years, which we call Era, that is, the date. The Greékes began their date, from the death of great Alexander. The Egyptians, from the death of Nabuchodonosor. The Persians, from Gesdargit. The Arabians or moors, from the preaching of M●chomet, 
Machomet.  who was after the birth of Christ 626. years. Other also from the Roman Emperors. The Christians began the account of our Saviour jesus Christ 500 years after his birth, 
The date of the Christians  as writeth Cardinal Cusanus. And here it shall not be from my purpose, to show how justly and rightfully was commanded by Don john King of Spain, the first of that name, that i● the Courts and parliaments which he held in Sego●ia, in the year of 1383. leaving the dates that they had begun from the Emperor Octavian, for tributes and other payments specified in writings and Privileges, they should no more put the date of the Emperor, for as much as the day in the which the Son of God became man, and was borne by the blessed Virgin, was so excellent a thing, and most worthy to be had in memory. So that in Spain, since that time, in all common writings, the date is made from the Nativity of our Lord, beginning there the first day of the year, and commonly the first day of january. Some Astronomers begin it the first of March.  
We have in this Chapter entreated of the great year, and of the Solar year, with his quantity, beginning, and date. In the Chapter following, we will entreat of the Lunar year, which we call a month.   

¶ The xi. Chapter, of the month, and of his differences.  


The Lunar year, or mo●eth.  
Revolution of the moon.   considering the month ●bsolutelye● without having respect to the Solar year, it may be called a year, according to the division we have made in the Chapter of the year. For it is a revolution of the heaven of the Moon whic● moveth slowly in compar●son of the first heaven. And if we consider the month as part of the year, then is the name of a month more proper unto it. For this word Mens mensis, in Latin, is derived of Mensur●, which signifieth measure. And so the month and year referred to time, all may be called month: forasmuch as all is the measure of time, as we have touched in the said Chapter of the year.  
The month is to be considered in two manners: either (as it is) part of the Solar year, or is caused by the course of the Moon. The month that is part of the Solar year, is that which at this day we use. And into xii. o● these months, 
The division of the yeer● into twelve months.  is the year divided: as Ianuar●e, February, March, april, May, june, july, August, September, October, November, December.  
They are not all of equal days, Apryl, june, September, and November, have 30. days: all the other have 31. except February, which hath 28. and when the Bisextile or Leap is, it hath 29. The names and numbers of these months were assigned at the will and pleasure of men, and the cause why they have remained so long time, is the authority of the Emperors, that ordained them for the common people, who accepted them by the Roman Church, which admitted the use of them.  
The Lunar month hath two considerations. 
The Luna● month.  The one is the time which the Moon tarrieth from that she cometh forth from one point of the Zodiac, until she return thither by her proper moving, and this is called the month of the peragration, 
The mone●● of peragration  in which revolution she spendeth 27. days, and almost 8. hours. The other consideration is, having respect to the time which the Moon tarrieth, from that she is in conjunction with the Sun, until another conjunction. And this is called the month of Consecution, 
The month of consecution  and is more than the month of Peragration, by two days 4. hours. 44. minutes. For the Sun and the Moon being in conjunction under one punct of the Zodiac, 
The moving of the Su●ne and moon in conjunction.  and moving both by their proper movings, toward the East, as the moving of the Moon is swifter than the moving of the Sun, she leaveth him behind.  
And when she had ended her month of peregrination, she returneth to the point from whence she departed, and not finding the Sun there (because in the mean time the Sun of his proper motion hath gone almost 27. degrees) the Moon passeth from this point, and in the said 2. days. 4. hours 44. minutes, overtaketh the Sun: and so commonly hath this month of consecution 26. days. 12. hours, and 44. minutes. So that whatsoever is said of the Lunar month, is to be understood of this month of consecution, which all they use that account by Moons: as do the hebrews, Arabians, and Persians.  
The Mariners ought not to neclect this computation, because it is convenient for them to know the tides, 
To know the tides by the aspects of the Moon.  and other effects caused by the aspects of the Sun and the Moon, for their aspects do correspond to the parts of this month, as the conjunction to the beginning, the opposition to the midst, and the quartile aspect to the quarter, and so of the other. Likewise in this month, is considered the illumination of the Moon, 
The illumination or change of the Moon.  and the days that the light faileth her: so that neither by day nor by night weé may see her, for beéing burnt under the beams of the Sun. The time that she is so, is called Interlunium (that is) the change or hiding, 
Interlunium, is the space of time in the which neither the old Moon doth appear, nor the new Moon is seen.  which is sometime more, and sometime less. When the conjunction shallbe from the beginning of Capricorn until the end of Gemini, and the Moon hath North latitude, and her moving swift: then shall the new Moon soon be seen, and so ●hall the Interlunium be but little. And when the conjunction shallbe from the beginning of Cancer, until the end of Sagittarius, and the Moon hath South latitude, and her moving slow, the longer will it be or the new Moon show herself to us: and certain of the causes concurring, and not all, so shall the Interlunium be in a mean between both.   

The xii. Chapter. Of the week.  
THe weéke is a time of seven days, 
The week of the Iew●s.  the beginning whereof is Sunday, and so did the jews count their first day, saying, Prima Sabati, secunda Sabati, (that is) the first of the Sabbath, the second of the Sabbath. etc. to the sixth of the Sabbath, and then the Sabbath. The Romans that called the Planets Gods, 
The Roman●●.  forasmuch as the sun was principal among them, called their first day, the day of the sun, the second, of the Moon, the third, of Mars, the four●h, of Mercury, the fifth, of jupiter, the sixth, of Venus, the seventh, of Saturn. 
The Christians.  The Christian's solemnizing the sunday, began their account from it: as, on such a day our Lord was borne: 
Ferine, signifieth vacant days, or sometime holy or festival 〈◊〉.  on such a day he rose: and on such a day he sent the holy Ghost upon his Apostles. etc. They also account the days of the weéke for Ferias.   

The xiii. Chapter, of the day, and of the night.  
THE day is of two sorts, as, the natural day, and the artificial day. The natural day, 
The na●●●all day.  is the space of time, wherein, the sun is carried by the first movable about the earth, from the Meridian, to the West, and from the West under the earth, coming to the East, and from thence returning again to the said Meridian: and this time hath the Equinoctial given one whole turn, and more, such part of it as correspondeth to the proper moving of the sun: or otherwise, the natural day is a circle described with the centre of the sun, at the moving of the first movable. The Romans began this natural day, from midnight, and ended it in the midnight following, 
The beginning of the natural day.  and so do we account it for fasting days: and from evening to evening, in celebrating of festival days. The Athenienses began it at the Sun set, or going down of the Sun. The Babylonians, at the rising of the Sun. The Umbria●s, and Ethuscos, from the midday, or noon, and ended it the noon day following. In ●his manner do the Astronomers begin it, and find that the day sh●ll ever begin at one self same hour for the quality of the Meridian's. And if they had begun it from the rising or fall of the Sun, it should not be ever at one self same hour, because the Sun riseth and falleth at sometimes sooner, and at other times later: 
The end of the natural day.  and so should the beginning of the day beé variable. And it is to understand, that when we commonly say● at the tenth day of such a month: the same ●enth day doth end the same day at noon, and the hours that run from that noontide forward, are of the eleventh day: and so do the Astronom●rs account them.  

The artificial day.  The day artificial, is part of the day natural, and is the time that the Sun tarrieth from that it riseth in the East, until it fall in the West, And the night is that part that lacketh or faileth for the natural day, 
The night.  which is the time that the Sun tarrieth from that he hideth himself in the West, until he return to appear in the East: and so the day artificial and the night, make one natural day. And according heéreunto, it is written in Genesis, that of evening and morning was made one day. Isodorus defining this artificial day, saith, that the day is the presence of the Sun, or the being of the Sun above the earth: as it is night unto us when he is under it. Or otherwise, the night is the shadow of the earth, extended diametrally opposite to the Sun. The quantity and differences of these days artificial, and their nights, and how they increase and diminish, we have largely declared in the first Chapter.   

The xiiii. Chapter of hours.  
AS there is two differences of the day, as the natural day, and artificial: so is there two differences of hours, as hours natural, which correspond to the natural day, 
hours natural and artificial.  and hours artificial which correspond to the artificial day. Hora or Ora is a Greéke name, and signifieth end. And so say we Ora maris, for the end or brim of the sea, or the list or edge of apparel, as saith Isodore in his Etimolagies. The hour natural or equal, 
The hour natural or equal.  is a 24. part of the day natural, a●d is the time of passing fyfteéne degrees of the Equinoctial. These 24. hours that make one natural day, the Astronomers doth begin the day at the Meridian, counting the hours after the order of the first movable, which is from the said Meridian, in the angle of midnight, where they account twelve hours, and from thence toward the East, and come to end the 24. hours in the same Meridian where they began: and this they use for the computation of the tables of the movings of the heavens. The Astronomers use the same in their instruments, as in the astrolabe, and Dial's horizontal, and vertical, and in all other instruments for hours. In Spain also we use to account these 24. in two times twelve, beginning at noon, and ending twelve at midnight: and again, beginning at midnight, and ending other twelve at noon. And to distinct the one from the other, they call the one afternoon hours, and the other forenoon hours: and commonly we say two hours of the morning, and two of the evening. In Italy they account them from the falling of the Sun, until the next fall the day following.  
The artificial or temporal hour, 
The hour artificial or temporal.  is a twelve part of the day ark, or the night ark.  
They are called temporal hours, because they ●a●●e in the times that the day varieth: For in the time that the days shall be great, so shallbe the hours: and when the days shallbe short, so likewise shall the hours be, and in like manner of the nights. So that, as the artificial day, great or little, is divided into twelve hours: even so the night great or little, is divided into other twelve. The ancients divide the day into four parts, 
The day and night divided into four parts.  and the night into other four, giving unto every quarter part three hours. At the rising of the Sun, which was the first hour of the first quarter, they called the first hour: and three hours passed, they called the third hour, and two hours passed of the day, they called the sixth hour, which was the midday or noon tide. Also the ninth hour, they named at niene hours passed of the day. And the Sun set, or going down of the Sun, they called the Evening: as saith the Poet Virgil in this verse.  
Ante diem clausam componet vesper olimpo.  

Interpretation of certain places of the Gospel.  And according to this computation, is to be understood that writeth Saint Matthew: That the labourers came to the vineyard at the eleventh hour, whereby is meant the fifth hour, one hour before the Sun was set. And when we read in S. john: The ague left him the seventh hour. etc. By this account it was one hour after noon, when Christ healed the son of the Ruler that was diseased in Capernaum. In like manner by these hours, the ancients divided the night into four quarters, 
The night divided into ii●●. quarters. Four watches of the night.  giving three hours to every quarter. And in these four parts of the night were Soldiers appointed to watch. In the first quarter, which they call Canticinium, (and we the first sleep) they watched all. In the second, which they called Intempestiwm, being the turn of midnight, the young men watched. In the third, which they called Gallicinium, of the crowing of Cocks, watched the Soldiers of middle age. In the fourth and last quarter, called Matutinum, or Antilucanum (that is, the spring of the day) the old Soldiers watched. And thus is understood the first, the second, and third watch of the night, in like manner ought the Mariners to keep watch and ward, 
how Mariners ought to watch.  to avoid aswell the peril of the sea, as also the dangers of Rovers: and to divide the night by quarters, after the manner of Soldiers, as did also the Mariners in old tyme.   

The xv. Chapter, of the making and use of an universal dial for the day.  
WHereas in the Chapter before, we have entreated of hours, and their differences, we intend here to describe the making of an Instrument general, 
To know the hours of the day by the Sun.  to know the hours of the day by the beams of the Sun, which is done in this manner. Take a round plate of Laton, and let it be called the Equinoctial circle, the circumference whereof, you shall divide into 24. equal parts by both the sides, and from the centre to every of these parts, you shall draw a right line: one of the which shallbe a Meridian. And in the one part of that, writ twelve, which shall be the hour of the midday or Noon. And in the other part write other twelve, which shall be for midnight. In the highest part, turning upon the centre, toward the right hand, writ one, two, three, fourer etc. In the lower, or neither part, you shall count toward the left hand, turning it upon the centre: so that the one hour of the one part, come upon the line of the one hour of the other part, in like manner two upon two, three upon three, and so forth of the other. And note that in the line of six at after Noon, and at the line of six in the Morning, there remain certain round pieces, corners, or ends, after the manner of Axis, of the thickness of the self same plate. Then make a half circle of the same metal, as big as the half circumference of the plate, and of the thickness of a piece of four rials of Plate, or somewhat more, even as the plate itself, and of the breadth of half a finger, if the instrument shallbe great: or less, if the instrument shallbe less. This half circle, shall you graduate or divide into 180. degrees, beginning at the one end, one, two, three, and so forth, unto 90. in the midst, and the like shall you do from the other end unto the same 90. Also, you must number them in the breadth of the same half circle: and this half circle, shall you make fast on the neither part of the instrument, so that the ends thereof may be fixed in the ends of the Meridian line. Then through the centre of the plate or Equinoctial circle, shall pass a round steéle or wire of the same metal, made fast or soldered in it, so that it rise and come forth equally from every side of the pla●e the fourth part of the Diameter of the same, and this shallbe called the Axis or exiltrée of the world. The instrument being thus made, you shall place it, or set it in a frame, having two arms, standards, or arches, so that it change between the said arches, borne up by the ronnde pieces or ends of the plate, left thereof at the ends of the line of the six hours aforesaid, in such sort, that being thus stayed, it may be directly turned. And in the midst between these two arms, beneath in the foot of them, or where they are placed, you shall raise a prick, or point: so that the plate which signifieth the Equinoctial, being perpendicular, the brim or edge thereof may fall upon the point or prick, and consequently the plate standing plain or flat, the ninety degrees of the half circle, must show or touch the said prick, as shall also the end or extremity of the Axis of the world, and the other end shall show the Zenith or vertical point.  
This instrument must be so placed, that the Meridian line be North and South: 
The placing of the instrument.  which you shall find in this manner. In an open and plain place, where the Sun shineth for the most part of the day, you shall make a circle with a pair of compasses, in the mids whereof, you shall set a steéle or wire, so upright, that it decline not, or bend not, either one way or other, and the same no longer than the fourth part of the Diameter of the circle. 
The finding of the Meridian line.  Then in the morning when the Sun riseth, the shadow shall be very long, and as it riseth higher and higher, so the shadow waxeth shorter and shorter. Then must you observe the time, when the extremity or end of the shadow toucheth in the circumference of the Circle, and where it toucheth you shall make a prick. Then goeth the shadow shortening unto the midday or noon tide, and as from thence the Sun declineth, so doth the shadow increase, and when it shall come again to the circumference of the Circle, you shall make another prick. Then shall you part in the midst, the ark that is between the one prick and the other, and from the middle pricke● draw a right line to the centre of the Circle: And that shall be the Meridian line, whereupon you shall set the instrument. Furthermore, in the foot of the frame of the instrument, you shall set a compass or dial, which shall show the Meridian line, This done, upon the arches of the frame, and corners of the six hours, you shall turn the Equinoctial so far, that it pass so much of the half circle by the middle prick, how many degrees the Pole is raised above the Horizon of that region or place where you are, 
The elevation of the Pole.  and then the shadow of the wire or steel, shall justly show in the Plate, the hour, and what a clock it is.  
Hear followeth the Figure of the Instrument.   

The xv. Chapter, of certain particular dials, Mural, and horizontal.  
AMong sundry manner and fashions of particular dials, there are two principal. Whereof the one is horizontal, 
dials horizontal and vertical.  which is placed in the superficial of the Horizon: the other is verticiall, and must be made or set on a wall perpendicular, and directly against the South or midday, from the true levant or East, to the true ponent or West, 
East & ●est.  the which the Mariners call East & West. To make any of these two Dial's, you must draw a right line, and call it the Axis of the poles of the world, upon the which you shall draw an half circle, and divide it in 90. equal parts. And where the half circle is cut with the line of the Axis, must be accounted by the circumference, the altitude of the pole for the city or place for the which you intend to make the Dial. And in the point of the circumference where endeth the altitude of the pole, you shall make a mark, and write there, The altitude of the pole. And from that point draw a right line unto the point where you began to account the altitude of the pole, which line shallbe called the Semidiameter, or half Diameter of the vertical circle. And from the same point of the altitude of the pole, draw another right line to the other extremity or end of the Axis, and this shall be called the Semidiameter of the Horizon: and likewise from the same point of the altitude of the pole, draw a right line perpendicular until it touch in the Axis, and this shallbe called the Semidiameter of the Equinoctial. Hereby is considered a Triangle, 
The Triangle.  which hath by the sides thereof the Semidiameter of the vertical, the Semidiameter of the Horizon, and the Axis of the world, which Triangle shall serve afterward. These three Semidiameters, of the vertical, the Equinoctial, and the Horizon, being found, you shall make the Dial in this manner.  
Draw a right line somewhat long, and call it the line of contingence. 
The making of the Dial.  This sh●ll you cut with an other ly●e i● right angles● after the manner of a cross, which sh●lbe the Meridian line. Then with your compass, ●ake from the Triangle the Semidiameter of the Equinoctial, and of this bigness draw a circle upon the Meridian line: so th●t the edge or brim of the circle, touch in the line of contingence. Then with a compass, take the Diameter of the vertical circle, if you will make a mural Dial, or the Semidiameter of the Horizon, if you will make a horizontal Dial, on a play●e or flat form. Therefore with such Semidiameter as you desire, you shall draw a circle upon the other part of the Meridian line, so that the circumference thereof touch in the line of contingence. Then shall you divide the Equinoctial circle into four equal parts, and the quarter that is toward the line of contingence, shall you divide into six equal parts. And setting the end of the ruler in the centre of the Equinoctial, and upon every point of them that divide ●he two equal parts, from thence shall you draw certain right lines, until they touch in the line of contingence. And from these points of the line of contingence, you shall draw other right lines, to the centre of the Horizontal circle, which lines shallbe the determiners of the hours. And near unto the Meridian line, where it toucheth in the line of contingence, you shall write twelve, and consequently toward the East, you shall write one, two, three, four, five, six: and from the sixth hour, you shall draw a right line, which shall pass by the centre of the H●rizontal circled equally distant from the line of contingence. The one quarter of the Horizontal being drawn by the self same, and of the same measure and bigness shall you draw the other, in such sort, that the same bigness that is from twelve to one, the self same shall you give from the twelfth, to the eleventh: and the same bigness and measure that is from one to two, shall you give from eleven to twelve, and so forth of the other.  
And note that the Horizontal Dial, after the sixth hour of t●e evening, shall have the hours of seven and eight, and in climates far North xi. also, and more if need shall require, and consequently must have the hours of five and four of the morning, 
hours of the horizontal Dial.  and in climates far North, three also: and these also must be so marked, that from six to seven, may be the same that is from five to six, and from seven to eight, the same that is from four to five: also, four and five of the morning, as seven and eight. The dial being thus drawn in paper, or on a table, 
Placing of t●● Dial.  or any other thing, must be painted (on a table, or in stone, or in what so ever you desire to make the Dial) a circle, of the same bigness as is the circle horizontal, and in that must be translated the lines and numbers of the said circle horizontal: Then must you make a triangle of metal, of the self same bigness and form that is made in the middle circle: and the side of this triangle (which is called the half diameter of ●he horizon) must be fixed upon the Meridian line of the horizon Dial, so that the side of the triangle (which is the Axis of the world) and extremity or end thereof, may fall in the centre of the horizontal Dial, and must stand so perpendicular, that it decline neither to the one part, nor to the other. The Dial being thus made, you shall set it upon a Meridian line, 
The Meridian line of th● Dial.  so that the Meridian line of the Dial may stand or rest upon it, and so shall the shadow of the triangle show the hour: and if for this place we desire to know it, we must fix it there. And if for any other place, so setting it, we shall have a certain hour. So may we in any instant remove it to another place, and likewise set it there, to make certain & true demonstration of the hour.  
¶ Hear followeth the Figure of this Demonstration.  

The making of the vertical Dial.  In like manner as is made the Horizontal dial, must be made the vertical, taking from the Triangle the Semidiameter of the Circle vertical.  
And note, that for the Circle vertical, it shall not be needful of more than six hours before noon, and other six after noon. And the triangle must be fixed in the meridian line upon the side that is called the Semidiameter of the Circle vertical. And if you will not make a triangle of metal, but that a wire of Iron may give the shadow, then must you make the said triangle of paste or paper. And according to the form or pattern thereof make the wire of Iron, and cause the same to be set in all sorts of Dial's, as is before.   

The xvii. Chapter, of the composition and use of an instrument general for the hours of the night.  
WHere as in the Chapters past, I have described the manner and form to make two Dial's for the hours of the day, me seemeth that for the more perfection of this work, it would be convenient here to teach the making of a dial to know the hours of the night, 
The Guard● stars.  by the Circle which the two Stars, called the Guardians, or the mouth of the horn, do describe by the moving of the first movable. But for as much as it is a common opinion, that in the midst of Apryll it is midnight when the Guards be in the head, whereof they take the beginning of the year, I will declare how it ought to be understood. 
what is midnight.  Certain it is, that to be midnight, is none other thing but the Sun to be by the moving of the first movable, to every one in that part of his meridian that is to him under the earth, even as is to him midday, 
Noon, or midday.  or noon, when to him it is in that part of the meridian that is above the earth. And in this present year of 1545. (to be out of doubt heéreof) I made experience with a precise astrolabe, so that the first or foremost Guard Star, being perpendicularly over or above the North Star, I found in the meridian, where the Sun maketh midnight, the ix. degreé of Taurus, whereby it followeth, that the Sun being in this degree, which is at the nineteen. of Apryl, the same Guard Star shall be perpendicularly over the North star, which is the line of the head, and consequently the Sun beéing in the nienth degreé of Scorpio, which is at the xxii. of October, the guard star shallbe in the line of the feet: and by this calculation may be known when it shallbe in the right or in the lea●t, 
An error.  and in all the other lines: so that they manifestly err, that account the midnight at the xv. of april, when the first guard star is in the line of the head, accounting a terce or third part of an hour sooner and more than they should do.  

The making of the instrument.  Having thus given principles for the instrument, you shall proc●éde in the making thereof, as followeth. In paste, or on a plate of ●aton, make a circle of the quantity of a span, or of the bigness that you desire the instrument or dial to be: then make an other circle somewhat less, so far distant from the greater, that between the one and the other may be a space, in the which may be signed or marked the days and months. Likewise shall you make another less circle, leaving space to set the numbers of the days of every month. And under this circle, shall you make an other, leaving space to write the names of the months: then shall you divide the first and greatest circle into eight equal parts, so that the nineteen. of Apryl may be in the highest or uppermost part of the instrument, which is where they say the line of the head to be, and the xxii. of October must be in the neither part. Also, the xiii. of januarie, in the right arm: and in the left arm, the xvii. of july: and so the other days that do fall to the other lines, according as they answer to the right ascension of the Sun, as you may see in this figure.  
This being done, upon the outward part of the great circle, you shall cut down the paper, paste, or plate of laton, leaving of the same for a sign or mark a flower Deluce upon the 19 of Apryl, for that it must be the head: and likewise at the 22. of October, may be left a handle to hold it by. Then must you make a rundel to the same paste or laton, of the bigness of the less circle, without the circumference whereof, shallbe left a tooth or index, in the which you shall write, Time. And from the one side of this index towards the left hand, you shall draw a right line, that may pass through the centre to the circumference, and this shallbe the Meridian line. Also to this rundel you shall give a circle, so much lower from the circumference, that there may be left a space where the number of the days may be written. And this rundel you shall divide into 24. equal parts, beginning at the Meridian line of the index at the twelfth hour of the night. Then in the next space toward the left hand, you shall make the number of one. Likewise in the second space the number of two, in the third, the number of three, and so forth of the residue, unto the other twelve of the day, in the opposite or contrary part of the index. So consequently proceeding i two. three etc. unto the twelve of the index, which shall be the xxiiii. hours of the natural day.  
Furthermore also you must make another piece, of the same substance of past or metal, in manner of a horn, 
The horn of the seven stars, which make the less bear.  in form and order as are in heaven the seven stars, which make the less bear: And this of such quantity, that the first or foremost guard star, may reach without the great roundel close to the circumference thereof, having the North star his centre, with the centre of the instrument. And from this star or centre unto the first and foremost guard star, must be a right line, by the which the horn must be cut near from the centre, unto the discovering or showing of the hours. Also, from the first guard to the second, must be two parts of nine, of that that is from the Star, which signifieth the North, to the first guard. Again, the second & last guard, must be toward the left hand, over or above the first, three quarter parts of one half Circle, which hath for the Semidiameter the two parts of nine, (whereof we have spoken before) given upon the right line that goeth from the North to the first guard. These two guard Stars, must be bored through with holes, of the bigness of an Aglet of a point, and likewise the North Star, with also the two rundles through the centre, and by that, all three pieces annexed, so that there remain a hole in the midst, like the holes of the guardes● so that by it, and by the other of the guards, may be seen the Stars in heaven, in such sort, that the less roundel and the horn may be turned round about the Axis, as doth appear in the demonstration following.  

To find the hour with the instrument.  The instrument thus ended, and brought to perfection, when you desire to know the hour, you shall turn the index of the less roundel in the which is written, Time, to that part of the great roundel where is marked the day in the which you desire to know the hour: and directing your face toward the North, you shall make the head toward the height of heaven, at the 19 of April. And seeing in heaven by the hole in the midst the star of the North, holding the instrument in such compass of the face, that by the circumference of the greater roundel, may be seen the guard star in heaven, you shall turn the horn round about, until in fall upon the Guards: so that by the two holes of the mouth of the horn, the two Guard stars may be seen, and by the hole in the midst, the North star, and all three with one eye: then the right ly●e that goeth from the North to the first Guard, shall show in the less roundel, the hour that shallbe.   

The xviii. Chapter, of the time of Tides, or rising and falling of the Sea.  
GReat account ought pilots and Mariner's to have of the Tides, to take Port, enter upon Bars, pass by flats, and finally, for all manner of Navigations. For being ignorant heéreof, great hurt and inconvenience might chance unto them, as did of late to the valiant Captain, Don john Gusman the Earl of Niebla, in the year of 1436. who was drowned before the City of Gibraltar, for that the Mariners kept no●e account, neither had consideration of the Tides. By reason whereof, not only he was drowned, but also with him died many worthy Gentlemen, and valiant Captains of Spain.  
The Mariners hold for a certain rule, 

The Mariner's opinion of ebbing and flowing of the sea, or tyd●s.  
Observation of the Moon● to know the tides.   that the Moon being in the North-east, or in the south-west, is full Sea: and being in the south-west, or Northwest, to be low Water. They affirm also, that at the first day of the new Moon, the Sun being at North-east, and a quarter to the East (that is North-east, and by East) the Moon shall be North-east, and then shall be full Sea, and three hours, and three quarters.  
And at the second day of the Moon, when the Sun shallbe at East north-east, the Moon shallbe at North-east, and then shall be full sea, and four hours, and two quarters. etc. Their account is, that the Sun beéing in the North, is midnight: and being in the North-east, they account, three: 
Eight principal winds.  and in the East, six. So that they account, three hours from wind to wind, by the eight principal winds, or lines, which the spaniards call Rumbos. These winds must be imagined upon the North, placed in the Angle, under, or beneath the Earth: and the Sun and the Moon at the moving of the first movable, and they ought not to be imagined in the Horizon, as the compass showeth. For speaking by the terms of Astronomy, you must understand, that the Moon touching in the circle of hours at the number of three, is ever full Sea: and touching in the same circle at the number of nine, is ever low water. No less ought they to observe just account of the hours, by quarters of hours. For to give 30. days to the Moon, it shallbe necessary to account by the fyftes of hours, as shallbe said heéreafter.  
Here is to be noted, that the spaniards think (be like) that a North-east and south-west Moon, maketh a full Sea in all other places, as it doth in Spain. But in that they be greatly deceived, and therefore the rule that they have set forth for the Tides, serveth only for such places where it floweth North-east and south-west Moon a full Sea.  
And the better to understand the increasing and decreasing of the Ocean Sea, 
The Moon causeth the ebbing and flowing of the Ocean Sea  it shall be convenient to know the cause thereof, whereunto we say, that the Moon is the cause of ebbing and flowing, or rising and falling, increase or decrease of the Sea: not only by her light, but also by her secret or hid property. The Moon compasseth about the earth, 
The moving of the Moon.  from the East into the West, until she return to the place or point from whence she departed: and in this course wasteth or spendeth so much more than one natural day, in how much her proper moving is more than the Sun against the first movable, so that she maketh her turn or course about the four quarters of heaven in xxiiii. hours, and four fyfthes of one hour, which are the twelve degrees that she goeth more than the Sun. And in this time the Ocean increaseth and decreaseth twice, so that this increasing and decreasing, answereth directly to the course of the Moon: whereby it followeth, that the sea increaseth two hours and one fifth part, and decreaseth other six hours, and one fifth. And if this day at the twelfth hour, was full sea, the low water shallbe at the sixth hour and one fifth part: and at the twelfth hour and two fifth parts it shall return to be full sea: and at the sixth hour and three fyfthes, shallbe low water again: and at the twelfth and four fyfthes of the other day, shallbe full sea. So that from one day to another, the tide doth shorten four fyfthes of an hour, 
The shortening of the tides.  which is the time that the Moon slacketh or carrieth more than one natural day, to return to the point from whence she departed by the twelve degrees, whereof we have spoken. Whereby it manifestly appeareth, how they beguile themselves that say, 
An error.  that the sea increaseth two hours, and decreaseth other six. For if it were so, the tides should ever be at one self same time and hour. But for as much as there is more than xxiiii. hours, 
The variation of the tides.  by the said four fifth parts, thereby is caused the variation of the tides: so that if this day, the tide be at one of the clock, to morrow it shallbe at one and four fifth parts, and the day following, at two of the clock and three fyftes. etc.  
For this account, I will describe a Table in circular figure, 
A Table to know th● variation of the tides.  although not precise, for the causes which we have touched before in the fifth Chapter, speaking of the Moon: who sometimes in her moving is swift, and sometime s●acketh as much, because the conjunction is not ever in one self same point of the Zodiac, as the Mariners presuppose for their rule. This figure shall have two circles, in the less (which shallbe the first, and next unto the centre) shallbe the days of the Moon, from one to thirty, which we count the conjunction. And in the second and greatest circle, shallbe found the hours of the tides. So that, who so desireth to know when the tide shallbe, where it floweth south-west and north-east, let him at that hour take heed to the days of the Moon, how many they are: as if thee be in the conjunction, or if it be the first or second of the Moon. etc. And the day being known, then in the second circle which answereth directly to the day, shall he find when shallbe high water, or full sea: and consequently, the ebb, or low water, which shallbe two hours and one fifth, after the full sea, and so likewise may he judge when shallbe the half tide: an● this aswell at the time when it increaseth (which shallbe three hours and half a fifth part of an hour, before the full sea) as also when it decreaseth, which shallbe the half ebb, three hours, and half the fifth of one hour, after the full sea.  
¶ The Table followeth.  
This increasing and decreasing of the Tides, is not ever in equal quantity. In the conjunctions and oppositions, they increase and decrease much, which the Mariners call high spring tides, and the greatest increase of all, they call the high springs. In the quarters of the Moon (which are at the 7. and 22. of the Moon, or near there about) they increase and decrease but little: which the Mariners call neap tides, low water, dead waters, or low floods.   

The nineteen. Chapter, of certain signs, which prognosticate tempests, or fair weather.  
A Good Pilot or Mariner, ought not to be ignorant of certain signs or tokens which the natural Philosophers describe of tempests. For as they signify unto him, so shall he leave his port, or enter into it: which if he can not, then ought he with patience and hope, to tarry the time that God hath appointed for him, who moveth and troubleth the Seas, when it pleaseth him, and appeaseth them again at his pleasure. Less hurteth and damageth the stroke which we see coming, or foreseé, then that which hath stricked us, and taken us careless. When the Sun riseth fair and clear, it signifieth a fair day: but if it show yellow, or deadly, tempest is like to follow. Again, if at the rising of the Sun his beams show themselves contract, 
Signs of fa●●● and soul weather.  or gathered together, and short, you shall have rain: if the mists or clouds make a circle about the Sun or Moon, how much the greater that circle shallbe, so much greater shallbe the tempest to come: and if ●here shallbe two circles, the tempest shall increase the more. And if it chance, that at the rising of the Sun the clouds be turned ●edde, it is a sign of no small tempest. When the Sun or the Moon shall have a circle, look toward the part where it breaketh, and from thence shall wind come: if it depart, or disperse equally, fair weather shall follow. When the Moon riseth bright and by the which they pass. We see that in some o●e region it raineth with one wind, and the self same wind in other places disperseth the clouds. The North-west wind is dry in Spain, yet in Lybia it is very moist and rainy. The South wind in Europe, causeth rain in most places, and therefore the Poets named it the wind of waters, and this wind in Palestina or jury is dry. The cause of this diversity, is, that when the wind bloweth in Palestina, it passeth by hot and dry regions, as by the deserts of Africa, and passeth not by any sea at al. But when it bloweth in these parts of Europe, it must of necess●tie pass by, and over the waters of the sea Mediterraneum, or the Levant sea, where it gathereth moisture and causeth rain. The Levant or East wind, in Malaga, and Gibraltar, is moist, and in shears De la Frontera, is hot as Hell.   

The xx. Chapter, of the bright and shining exhalations that appear in the tempests, which the Mariners call Santelmo, or Corpus sancti.  
IGnorance is the mother of errors, and therefore will I not omit to show the natural cause hereof, although among certain simple and ignorant people, it is accounted for a miracle, that in certain tempests on the Sea, the Mariners see certain shining and bright fires, which with great superstition they kneéle down unto, and pray unto, affirming that it is Santelmo that appeareth unto them, 
Some call these the fires of S. Elin and S. Nicolas.  and not contented herewith, some swear that they have seén● drops of green w●xe fall down. Other affirm that this wax is of such heat, that if it fall from the top of the Ship, it doth melt the rosin and pitch of the hatches of the Ship, with such other foolish imaginations, and therefore it shall be good briefly to speak hereof, to stop the mouths of such fond and ignorant persons. The exhalations or vapours of the gross ●umes or smokes that rise from the earth, 
wandering fierce engendered of exhalations and vapours.  are constrained or gathered together by the coldness of the night, and the air, and are thickened in the first region of the air, next unto the earth. This may, and is wont to be inflamed or kindled, and if it find a body whereunto it may cleave, it abideth in that until it be consumed. This fire is clear, and shineth, and yet burneth not. The Greékes call it Polyduces, 
Castor and Pollux.  and the Latins call it Castor and Pollux. It is accustomed to appear upon the shrouds, and oftentimes is seen upon the pikes of soldiers, in the armies of men of war, as Pliny writeth, and this, aswell by reason of continual smoke, as also by the heat of much people. Certain it is, 
what is smoke and flame.  that smoke is none other thing than fire dispersed: as flame is an exhalation or evaporation that riseth in manner of smoke, from a gross or fat body, and at the time that it riseth, being gathered together, is constrained into flame, investured with fire. This resplendence or shining, is also often times seen, 
Exhalations of the land and water.  not only in journeying by land, but also in sailing by rivers: and when it appeareth on the land, it riseth of the smoke that is gathered together with the cold air of the night, and on the banks of rivers: this smoke is gathered of the exhalations of the water, and consequently being kindled, appeareth bright and shining. But now let us come to the Ships that sail by the Sea, and to the Mariner's ●hat are accustomed to tempests. To them therefore I say, that that light, 
Exhalations and vapours engendered in Ships.  or such other lights as they see, is engendered of the fumes and smokes of their Ship, with the heat of men couched close and near together in a narrow place, and when a tempest riseth, the said smoke is thickened, priest together, and beaten down by the winds, in such sort, that being tossed from one side to another, it is set on fire by moving, and taketh hold sometime on the shrouds, and sometimes on the top, and sometime also in the poop, or in the foreshyppe: So that to see this light, or the same to appear, is a natural thing, and not supernatural.  
When Captain B●zerra was at Corron, in the emperors Navy, with his company of Soldiers, he chanced to be in a tempest, and saw the said fire of Santelmo, which shortly after descended so low, that the Captain might easily come to it: and taking it in his cloak, he found it to be a little drop of water. Some have thought it to be a certain shining Fly, 
A shining fly  called Taros, which the sea men some time see in a calm in the Summer season: and thus Santelmo appeared no more. The Captain remained astonished at the mockery, and the other perceived it to be no miracle. The opinion of the Mariners that affirmed it to be Santelmo, 
A superstitious opinion of the Mariners.  may rise of Saint Erasmo, Bishop of Naples, who (as they say) not only in his life time, but also after his death, was a patron and helper of Mariners that called upon him in tempests. This name of Erasmo, they of Naples call Ereemo: and process of time taking away one e. by the figure of Sincope, remained the name of Santermo. And the Spaniards, who never can long keep any strange vocable, call it Santelmo, turning r. into l. Yet of this Santelmo, whereof the Mariners speak, there is neither scripture that maketh mention, nor authority that confirmeth it. I hear say that the Friar preachers had a religious man, 
A lie of the friar preachers.  of commendable life, and good conversation, named Friar Pero Gonzales, borne in Galizia, and that in his life time our Lord did certain miracles by him, and that this is he that shineth and giveth light in tempests. No doubt, but GOD worketh miracles in his Saints, and by his Saints, as saith David. But if this servant of GOD was Pero Gonzales, 
Psalm. 67. Testimony of ancient authors.  how then shall he be Santelmo? Another difficulty there is, as touching this light: for there are wittings of more antiquity than the law of grace and coming of Christ in flesh, which give testimony heéreof. For the Poet Uirgyll, in the second of his Aeneidos, writeth, that this fire appeared upon the head of julius Ascanius. And Titus Livius in his first book, affirmeth, that it appeared upon the head of Servius Tullius, the sixth King of the Romans.  
Pomponius Articus saith, that Rome began to be builded in the third year of the third Olympiad's, 
The building of Rome.  that is, in the tenth year of jonathan king of the jews, and from the creation of the world 3201. years, and 729. years before Christ our Saviour was borne. The Kings of Rome were seven, and reigned 244. years. 
The Roman● kings.  Eusebius saith, they reigned 246. Servius Tullius reigned 44. years. Tarquinus Superbus 25. years after him. So that discounting these years, it shall appear clearly as I say. Although the years were not discounted, let them read Diadorus Siculus, an ancient writer, let them read Plutarch, Aristotle, and other old auctors that have written hereof, and they shall find, that if tempests be near unto the Sea, these fires and lights appear in them: and appeared not only to the Gentiles, but at this day also appear to the Turks and moors in tempests. When only one light appeareth, it is taken for an evil sign: And hereof said Propertius thus.  
Candida foelici soluite vela toro.  
And why it is an evil sign, 

One light or fire is an evil sign.  
Two lights.   this is the cause: that if the tempest that riseth be great, it choketh the exhalation, although yet by the part least troubled, it appeareth. When there are two lights, it signifieth that it is sufficient to consume the matter of the tempest, or that the tempest beginneth to cease, and the gross humour hath the mastery. But sometime it chanceth, that two lights appearing, there may be a tempest, and one appearing shall not be so great, and often times there is a tempest without any light at all seen. The blind Gentility called these Castor and Pollux, 
Castor and Pollux.  and placed them in heaven in the sign of Gemini.  
Now remaineth to answer to one objection of the Marrines, 
an error of the Mariners.  who say, that never man that hath seen these Fires, hath perished. To this I say, that many may see, and have seen these lights, of whom, some have been in peril, and some drowned: notwithstanding, no man can affirm, that if the drowned might speak, they would say that they have seen them. Therefore the wise Christian mariner ought to have a clear conscience, and to call for the help of almighty God, lifting up his eyes and hands unto heaven, 
Psalm. 68  and say with the Prophet, Saluum me fac Deus, quoniam intraverunt aquae usque ad animam meam. Save me, oh my God, for waters have entered even unto my soul.   
Hear endeth the second part.   

The third part, entreateth of the composition and use of Instruments, and Rules for the Art of Navigation.  

¶ The first Chapter, of the number, order, and names of the winds.  
SO greatly esteemed was Aeolus, 
why Aeolus was feigned god of winds.  King of the Eolas Islands, or Islands of Vulcan, for having reason and knowledge of the winds, that they of ancient time called him the god and lord of them. With no less consideration, the prudent mariner ought not to be ignorant of them, for as much as the universal benefit, and commodity of Navigation consisteth therein. And to have the better knowledge thereof, you shall understand, that wind is fruit of the air, 
what is wind.  and vapour of the earth: the which by reason of his subtlety, pierceth the air, striketh it, and enforceth it. Other say, that wind, is air, moved or tossed by the vehement influence of vapours of contrary quality. It is in Latin called Ventus, because it is vehement, and violent, whose force is so great, that it overthroweth not only heaps of stones, or rocks, and casteth down treés: but also disturbeth the air and the earth, and moveth the seas. There are four principal winds, 
The four principal or Cardinal winds.  which come from the four cardinal or principal points of the Horizon. We have said that the Meridian circle, cutteth the Horizon in two points (that is) in the North a●d in the South, and the Equinoctial cutteth i● in other two, that is, in the East and West, and from these four points come these four winds, 
Luke. xvii.  whereof all the wh●le Scripture maketh men●ion. These four winds they in ancient time, named in this manner. That that cometh from the East they called Sub●olanus, 
East.  which we call the Levant, or East wind. That cometh from the South, 
Sou●h.  they named Auster, which we call the Meridian, or South wind. That cometh from the West, 
west.  they call Faucinus, which we call the Ponent or West. That from the North they named Septentrio, or Aquile, or Boreas, 
North.  which we call North. To every of these four winds, they adjoined two collateral winds, in manner as followeth. That that is from the East toward the part of the North, where the tropic of Cancer ariseth, or cometh forth, they called Vulturnus: and that that is from thence toward the part of the South, 
Collateral winds.  where riseth the tropic of Capricorn, they called Eurus: also that is from the West toward the part of the South, where the tropic of Capricorn goeth down, they call Aphricus: & that that declineth to the North, where the tropic of Cancer goeth down, they call Caurus. The Collaterals of the North and he South, answereth to the circumferences of the Polar circles: that that is from the North toward the Levant, or East, they call Aquilo: and that declineth toward the West part, they call Circius: that is from the South toward the East, Euro Auster, and toward the West, Euro Aphricus: thus many hath Aristotle in his Metheora. 
Twelve winds.  With these xii. winds, they sailed in old time, & made their compass by them.  
The Hydrographers of late days, & such as are travailed & exercised in sailing, agree with the ancients in the four principal winds, 

Eight whole winds.  
Division of the horizon by the four principal winds.   although they have chaung●d the names, calling the Levant, or Orient, East: the Ponent or Occident, West: the Septentrional, North: and the Meridional, South. Between these four winds, they divide every quarter of the Horizon into two halves, made of the two nearest, in this manner. Between the North and the East, taking name of them both, they name the North-east. Between the East and the South, they name the Southeast: and between the South and the West, south-west: between West and North, Northwest. These eight winds in navigation, they call whole winds.  
Between these eight winds, they place other eight, that are called half winds, which also are named of the two that are nearest unto them. 
Eight half winds.  That that is between the North a●d North-east, they call Northnortheast, Between North East, and is East north-east: and so forth of the other. Beside these half winds, they have other which they call quarter winds. 
quarter winds.  These take the name of the winds to the which they decline: as if to the quarter from ●he North, toward the North-east, they call it North, and a quarter toward the North-east, that is, North and by East. And that that is toward the Northwest, they call North, and a quarter toward Northwest. And so of the other, as shallbe verified in the figure following: 
The division of the wind●.  whereof is gathered, that dividing the eight principal winds into half winds, they are 16. And every half wind divided into two quarters, 
xxxii. winde● in al●●  are in all 32. winds. Some have been so curious, or rather so vainly careful and too precise, that they have divided them into 64. And in the Cards that they have, the confusion of lines is greater, than the profit that may be taken thereby.  
The demonstration of the winds.  
These names do they use that sail by the Ocean Sea. And it seemeth they had their beginning of the Almain or Flemish tongue: For these nations chiefly sail in the Ocean. They that sail in the S●a Mediteraneum, 
The names of the winds in the Italian or Tuscan tongu●.  or Levant Sea, call them by other nam●s, taking original of the Tuscan or Italian tongue. Or else that they have denomination of the parts from whence they come, in respect of the Sea Mediteraneum, as the wind called Graeco, because it cometh from Grecia, and Libe●co, because it cometh from Lybia, and Syroccho, because it cometh fr●m Syria, and beginning at the North, these are th●ir names, Tramontana, Graeco, Levant, Ponente, Maestro, and that that is between Tramontana and Graeco, they call Graeco Tramontana, and that is between Graeco and Levant, they call Graeco Levant, and that is between Levant and Syroccho, they call Levant Syroccho, and that is between Syroccho and Mezzo jorno, they call Mezzo jorno Syroccho, and so of the other: and the like of the quarters. And because they that sail in the Ocean, are governed by altitudes, we will use the names that they use, where we intend to entreat of altitudes, and every man shall use them as he lyst●th, for as much as the difference is not in the winds, but only in their names.   

The second Chapter, of the composition of Cards for the Sea.  
Arriving to the end desired (which is Navigation, 
What is Navigation.  the principal intent why I began this work) I say, that Navigation or Sailing, is none other thing then to journey, or viage by water, from one place to another, and is one of the four difficult●st things, 
Proverb. thirty.  whereof the most wise King hath written. These viag●s do differ from voyages by land, in three things: for the land is firm and steadfast, but this is fluxible, 
The danger and difficulti of navigation  wavering, and ●ooueable. That of the land, is known and termined by marks, signs, and limits: but this of the Sea, is uncertain and unknown. And if in voyages by land, there are hills, mountains, rocks, and craggy places, the Sea payeth the same seven fold with torments and tempests: therefore these voyages being so difficult, it shallbe hard to make the same understood by words or writing. The best explication, or invention, that the wits of men have found for the manifesting of this, is to give the same painted in a Card.  

Making of Cards for the Sea.  For the draft, or making whereof, it shall be requisite to know two things: whereof the one is, the right position of places, or placing of countries and coasts. The other is the distances that is from one place to another, and so the Card shall have two descriptions. 
The winds or lines are called Rumbos, in the Spanish tongue  The one that answereth to the position, shallbe the winds, which the Mariners call lines or points of the compass: and the other that answereth to the distances, shallbe the drawing and pointing of the coasts of the land, and of the Islands compassed with the sea. To point the winds, or lines, you must take saynnes of Parchment, or large Paper, of such bigness as you will the Card to be, and in it draw two right lines with black ink, which in the midst shall cut or divide themselves in right angles, the one according to the length of the Card, which shallbe East and West, and the other North and South. Upon the point where they cut, make a centre, and upon it, give a privy or hid circle, which may occupy in manner the whole Card. This circle, some make with lead, that it may be easily put out: these two lines divide the circle into four equal parts, and every part of these shall you divide in the midst with a prick or puncte. Then from one puncte to another, draw a right diametral line with black ink: and so shall the circle remain divided with four lines, into eight equal parts, which correspond to the eight winds. In like manner shall you divide every of the eight into two equal parts, and every part of these is called a half wind. Then draw from every puncte, to his opposite diametral a right line, of green, or azure: likewise shall you divide every half wind in the circle, into two equal parts. And from these punctes, which divide the quarters, you shall draw a certain right line with red ink, which also shall pass by the centre, which they call the mother Compass, 
The mother compass of the Card 32. lines which signify so ma●y winds.  or chief compass of the Card, being in the midst thereof: and so shall come forth from the centre, to the circumference 32. lines, which signify the 32. winds. Beside these said lines, you shall make other equal distant to them, and of the self same colours, in this manner. From the points of the winds and half winds that pass by the centre, draw certain right lines, that pass not by the centre, but be equally distant to those that pass by the centre, and of the same colours and equidistance, as are they that pass by the centre. And as these lines concur together aswell in the centre as in the points of the winds, and half winds, that are in the circumference of the circle, they shall leave, or make there other syxtéene compasses, 
The placing of many compasses in the Card.  every one with his thirty and two winds. And if the Card be very great, because the lines may not go far in sunder, if you will make there other syxteéne compasses, you must make them between the one and the other of the first syxteéne points, where the quarters are made with their winds, as we have said. It is the custom for the most part, to paint upon the centre of these compasses, a flower, or a rose, 
The flower, or rose of the centre.  with divers colours, & gold, differencing the lines, and marking them with letters and other marks: especially signing the North with a flower Deluce, and ●he East with a Crosse. This beside the distinction of the winds, 
The North.  serveth also for the garnishing of the Card. And this for the most part is done after that the coast is drawn. And thus much sufficeth for the draft of the winds.  
The situation of the places, 
The situation of ●he place. etc.  Ports, and Islands in the Card, according to their proper differences, consisteth in the particular, and ●rue relation of such as have travailed them, and therefore for this purpose it shall be needful to have patterns of Coasts, Ports and Islands, which must be painted in the Card, and ●hese of the best & most approved to be true: and not only to have patterns well painted, but also it shall be necessary to know the true altitudes of the Pole, of certain principal Capes, Ports, and famous Cities. This done, they must be translated into certain thin papers, 
Translation of the Card, from one to another.  & transparent, that may be seen through, and those of the best and finest that may be had, anointing them with oil of Line seed, and then drying them at the Sun. Then take the pattern or Card that is to be translated, and reach or streiche it forth upon a table. Then put the transparent paper, upon the one side of the pattern where you will begin. And the paper ●eing made fast upon the pattern with plomettes of lead, or a little wax, that may easily be taken off, you shall in the transparent paper mark with a fine pen, one East and West, and one North and South, or two, upon those that are seen by the self same paper in the pattern. And this is called tracing, or translating. In like manner shall you trace all the Costs, Havens, Ports, islands, Cities, Capes, and rivers, as appeareth in the pattern, unto the rocks that come forth of the water, and the known banks. And because this paper doth not suffice, you shall put thereto another, and more, is need shall require. And begin the translation in one, where the other endeth, until you have translated all that you desire, not forgetting to make in every one, lines of North and South, East and West, to serve for marks afterward. So that the line of North and South, of the one paper, may join close and even, with the line of the North and South of the other paper that is joined to it by longitude.  
And the pattern thus translated into these papers, you must put the ruled or lined paper or papers upon a plain, smooth, and steadfast table, where you shall stretch them forth, and make them fast with plomets or weights, or nail them to the table by the sides or corners, with small nails. Then upon the said ruled paper, you shall put the paper that is translated from the pattern, in that side or part that is correspondent from the pattern, to the ruled Card, so that the lines of East and West, North and South of the translation, may be upon the lines that answer to them in the ruled Card.  
This paper thus made fast by the one side or part, you shall by the other side (that it may remain in his place) put under it an other fine paper, smoked or smyred on the nethermost part (which is that, that falleth upon the ruled Card) either with a link, 
Some do this only with oil.  or with matches of pitch. These thus ordered, and made fast one upon another, you shall take a steéle bodkin, or wire, with a smooth and blunt point, that it raze not, 
Tracing of ●h● Card.  or bore not the paper, and with it shall you draw, pressing upon all the translation, and tracing it with diligence and discretion, marking ever how much in it is translated from the pattern: saving the winds or lines which the Mariners call Rumbos, and so shall remain all the impression of the smoke in the ruled Card, upon the which, with a fine pen you shall trace with ink: which being dry, you shall with ●rummes of bread make it clean from all the smoke, and so shall the coast appear in the Card drawn with ink.  
This done, 
The painting of the Card.  then with a small pen shall you describe in the Card, all the places and names of the coast in that part where they are, and as they are seen in the pattern. And first you must describe in red, the Ports, principal Capes, famous Cities, with other notable things: and all the residue in black. Then shall you draw or paint Cities, Ships, Banners, and beasts, and also mark the Regions, and other notable things. Then with colours and gold shall you garnish and beautify the Cities, Compasses, Ships, & other parts of the Card. Then shall you set forth the coasts with green, by the shore or banks of the lands, and make them fair to sight with a little saffron, or otherwise, as shall seem best. Likewise shall you describe certain letters, with their significations, in this manner.  
B. for a Bay. C. for a Cape. A. for an Angle. I. or Y. for an Island. M. for a Mountain. P. for a port. R. for a river.  
Then in place where is more room, 
The making of the trunk or scale of the leagues.  or that is least occupied, you shall draw two right lines, equally distant: and the one no further from the other then half a singer, or little more, and so long, that between them may be marked at the lest three hundred leagues. And this the Mariners call the trunk or scale of leagues, and place it or use it in this manner. They take with the compass, a hundred leagues of the trunk of the Card or pattern that is translated, and they set them just between the two lines, and this space they part by the half, and rest the foot of the compass in 50. and these divided again equally in two parts, they rest the compass in 25. and the 25. being likewise divided, they rest in xii. leagues and a half, and ma●ke them as appeareth in the demonstration following.  

The graduation of the Card.  The Card being thus made, then to graduate it, or divide it into degrees, you must draw three lines, which make right angles with the line of Ea●●●nd West, equidistant to the line of North and South: and 〈◊〉 also shallbe North and South. These shall be drawn by the Islands ●f Asores, or Soria, or neérer to Spain, or where the Card shall be less● occupied. And for this purpose, the one line 〈…〉 so far distant from the other, that in the two spaces wh●●● 〈◊〉 make, may be marked, in the one, the degrees, & in the other, the number of them, conformable to the graduation of the pattern: as the vumbers of degrees show East and West, with the Ports, Capes, and coasts in their proper altitudes.  
And if the Card have no graduation, you shall take with the compass in the trunk of the leagues, seven spaces of 12. leagues and a half, which are 87. leagues and a half. And these must be divided into five parts, which come forth at 17. leagues and a half for a part: and the four parts taken with the compass, make four degrees, and divided into four parts, every part is a degree, and is marked thus. °.  
And if you will make the degrees at 16. leagues, and two terces or more: 
The mark of a degree.  you shall give to every degree so much space as the leagues comprehend. This graduation must be begun from some one cape, whose altitude of the Pole is well known. And the whole Card being thus graduate, you must begin the number of the degrees from the Equinoctial line, one, two, thr●e. etc. toward the one Pole, and the like toward the other: so that to the known Cape, may answer the number of his altitude. And so shall you do to the whole Card. Also, the Equinoctial line shall be marked in his proper place.  
And in like manner shall you mark the Tropikes according as they are in the sphere. But forasmuch as in Spain, 
Cape S. Vincent.  Cape saint Uincent is the principal, they begin there to make graduation, & number it in 37. degrees. And from thence toward the Pole Arctic, the degrees do increase. And from thence toward the Equinoctial line, 
Increasing and diminishing of the degrees.  they diminish: and from that line, to the pole Antarctic, they increase again (as we have said) as is contained in the Card, and as appeareth in this demonstration following.  
And if the pattern have neither leagues nor degrees, you must take or know the altitudes of two Capes, 
If the pattern have neither league nor degree.  that are North, and South, of the degrees, and the difference of the degrees of the elevation, that is from the one Cape to the other, ye shall divide all that space in so many parts, and so each one part shallbe seventeéne leagues and a half, as answereth to one degree. Or according to the opinion of the leagues of the roundness of the earth, as we have said, as touching this in the eyghteénth Chapter of the first part. In Spain they use with the compass to take the space that is from Cape saint Uincent, to the midst of the greatest Island of Berlinga, which they account three degrees: so that after seventeéne leagues and a half for a degree, they are 52. leagues and a half: and so much do they put in this space. Other put fifty leagues, accounting after syxteéne leagues, and two terces for a degree, and in this manner they make of leagues, degrees, and of degrees, leagues. The sailing Cards, have no certain bigness limited them, because they only represent the description of the water and earth, and not the quantity, and for this cause some are painted in great space, and other in little. They that are in great space, are more manifest, and more precise: and these the Mariners call Cards of the l●rgest prick or draft. 
The quantity of Cards.  Some desire rather to have them in less space, because they are brieffer, and contain much in little room: and these th●y call Cards of the less● prick. And if for any consideration aforesaid, you desire to reduce any C●rde from the greatest prick to the least, or contrariwise: 
The reducing of Card● from a big form● to a less, or the contrary.  y●u must paint only the coast and islands on a paper, in manner as you did in the ruled Card, of the lines or winds, I say, let it be drawn upon paper, for destroying or rasing the pattern. And when it is traced only with ink, then upon that draft shall you draw certain right li●es equidistaunt made all by one compass, according to the length of the Card, and other lines that may cut them in right angles. and likewise equidistaunt, and of the same compass that the first are. These two orders of lines, shall divide all the superficial part of the Card, into perfect squares or quadratures. And it is to be noted, that the nearer the lines are joined together, and the squares the le●se, so much the more perfectly may it be reduced, and more easily. Then shall you take another paper, greater or less than the Card, according to the point that you desire to reduce it unto, and in the length and breadth thereof, you shall divide so many spaces as are between the lines of the other paper, and if it be greater, the squares shallbe greater: and if less, less. To ke●pe order in the correspondence of the squares (which shallbe a great light to translate the one from the other) you shall number the orders of the squares, as those of the longitude, by the ●ronte or uppermost part: and those of the latitude, by the side, as well in the one paper, as in the other, conformable: also, those of the front, from the left hand to the right, and those of the side, from above, downward. Then behold the coast how it goeth by the squares of the first paper, and likewise the tracting or drawing in the squares of the second, in the self same order and proportion, as it is there, and so shall it remain reduced to the point which you desire. And this shall serve for a pattern, to set in the ruled Card.  
Hear followeth the manner of the translating of the Card from one form into another, greater or less.  
Here followeth a similitude of the Mariner's Card.   

¶ The three Chapter, of the virtue and property of the loadstone, called in Latin Magnes, and in Spanish, P●edraymon.  
THe Lode stone (as writeth Cardinal Cusanus) hath substance, 
The virtue, substance, and operation of the loadstone  virtue, and operation. His ver●ue is engendered of his substance, essence, or being, and of his essence & virtue proceedeth this operation and effect, in such sort, that this stone communicating his virtue to iron, by reason thereof, causeth the iron to move, although between the one and the other be a cup, or plate of silver, or a table, or any other like thing. 
Virtue attractive.   
The attractive, or drawing force of the Lode stone, causeth the nature of iron to be and rest in it, and that so firmly and quietly, 
Cusan applieth this to th● glorified body of Christ, according to these words, If I shallbe exalted, I will draw all unto me.  that being naturally heavy and ponderous, it descendeth not, because his nature resteth not in himself, but is unite with the nature of the stone, which seemeth to extend itself, and as it were to cast forth a lively spirit of enchanting virtue. Insomuch that (as we see by experience) by the said union, it not only distributeth his virtue to one iron, but that iron likewise to another, and that other again to another, and so forth: until of many rings or links of iron, be made a chain.  
Saint Augustine (as he writeth in his books, De civitate Dei) did marvel that he saw an iron move itself upon a v●ssell, by moo●ing the Lode stone under the vessel.  
It is called Magnes, 
Why the Lode stone was called Magn●s, and the finding thereof.  because the inventor, or finder thereof, was so named: who (as Plin●e writeth) keéping cattle in East I●dia, had his shoes soled with plates of iron, and iron nails, such as they use in G●sconie, and had in his hand a staff with a pike, or hook of iron: and resting himself upon a quantity of this stone, could ●ot remove his feet, neither life up his staff. Then staying a while asto●yshed, as ignorant of the cause, at the length began to perceive the property of the stone, and to understand the attractive virtue thereof (the colour of it differeth not from iron) and was therefore called quick iron, or living iron.  
The best kind of these stones, is of Auzurine or blue colour, as the sea sometimes appeareth. 
Sundry kinds of the load stone.   
Of these, are found five kinds or differences. The first is, of Ethiope. The second, of Ma●edonie. The third, of Lechio in Boetia. The fourth, of Tro●da, near to Alexandria, And the fifth of Asia: but at this day, it is found in divers other places. It is found also in many places in Spain: 
The lodestone of ●payne.  as in the hill Mor●na, near unto the village of Calera, beéing of the order of saint james, in the province of Leon. Likewise in a hill of Moron, in the territory of the Earl of Vrenia, is great quantity thereof, and in divers other places. The stone that we most commonly use, is of the Island of Elua, 

The Island of Elua.  
The loadstone of Denmark.   of the Lord of Pomblina, which I judge to be better than that of Denmark. This and the other, have virtue to draw iron unto ●●ē. And true it is that Teanxedes writeth, 

The loadstone of Ethiope.  
divers opinions of the load stone.   that in Ethiope is found an other kind of this stone, that putteth iron from it. Averroes the commentator of Aristotle, denieth ●hat Magnes draweth iron unto it, but saith, 
The qualities and properties of the load stone.  that iron by his natural inclination doth move to the stone, as to his natural place, by a c●rtayne quality, which the stone impresseth in iron. And beside this ver●ue and property that it hath to draw iron unto it, 
The parts of the loadstone.  it hath also another: and that is, that it giveth unto iron ver●ue and power, to show the two points of the Horizon, where it cutteth the Meridian, that is in the two winds, of Nor●h, and South. These virtues are found more intent, in o●ely two parts of the stone: and these are ever opposite, or contrary the one to the other, and so are they contrary in operation. For iron touched with the one part, and placed where it may move freely, will show the North: and an other iron touched with the other part, will show the South. Finding this experience, may be known, 
What part of the stone au●sweareth to the North and South.  what part of the stone answereth to the North, which the Mariners call the face of the stone, and likewise of the South. This stone is so necessary, that without it, Navigation should be imperfect and uncertain, because it giveth life to the Neédle and Compass, which leadeth and guideth the Pilot, that he may go certainly in the day, and not err or wander in the night. Also it showeth and directeth to compass the world, 
The use and making of the Mariners compass.  and to know the winds. And therefore, for as much as the compass is so necessary, we intend to show the order and manner how it ought to be made, for it may chance to fail, or be lost in the voyage.   

¶ The iiii. Chapter, of t●e making of the Mariners compass for Navigation.  
TAke such paste or paper, whereof Cards are made, and make in it a Circle, of the quantity of a span, or little more or less. In the which you shall paint the 31. winds, with their colours, in such order as we gave in the first and second Chapter of the winds, and of the Card, 
The Flower deluse, and the cross.  not forgetting to mark the North with a Floure deluce, a●d the East with a cross. And more than this, may every man garnish and beautify the same, as seemeth best to his fantasy. Then on the lower or neither part of this paste, you must draw a line, which shall be directly under that of the North and South, which shall be the mark for the setting of the Irons and Steéles. 
The fly, flower, or rose of the compass.  Then shall you take wire of iron or steéle, of the bigness of a great pin, or according to the bigness or the roundness of ●he paste, flower, rose or fly, as it may be called. This wire must be bowed double, so that every of the parts may be equally as long as the Diameter of the fly, and a quarter part more. The ends or points of these iro●s or stéeles, must be pinched together, and made close, and open in the midst, the one from the other, until the ends come to be equal with the extremities of the Diameter of the fly, and so shall the ●●eéles remain in manner in form of an edge. These wires or irons must be made fast in the neither part of the fly: so that their extremities, ●nds, or points, come precisely by the line of North and South. 
The line of the North and South.   
And to fix or fasten them so, they must be covered with a thin paper glued, leaving the points and ends uncovered: And these ends must be ●ouched with the Lode stone, in this manner. The part that is under the floure deluce, must be rubbed on that part of the stone that answereth to the North, as is said in the Chapter before. 
The touching of the needle with the load stone.  And this shall suffice for the perfection of the compass. Yet some there be, that for superaboundaunce, do● touch the other part of the Iron, with that part of the stone that answereth to the South, although it may suffice to touch it only with the other part. This touching of the Iron with the stone, that the demonstrative or working virtue may show itself forth, 
The breaking of the ●tone, to draw out his virtue.  must be done with giving certain strokes with a hammer, on that part of the stone wherewith the Iron must be touched, that is to say, in the North part, or the South: And from these will come forth of the stone certain beards, like small icicles, whereon you shall rub the point of the Iron, as you would whe● a knife: and so shall certain of those beards of the stone, cleave and stick fas● to the Iron. And the Irons thus touched, with the beards cleaving to them, you must take a prick or point of laton, of Peramidal, sharp, or steeple form, which is broad below, & shared above toward the point, this is made round, or eight square, as seemeth best: and in the neither part or breadth, it must be bored (but not through) with a borer, which must also be of Pyramidal form, and centre into the midst of the said P●ramidall prick, or point of laton, unto the midst, or somewhat more. This Pyramidal point (which the mariners call the capitle) must be of height half a finger breadth, or according as the compass shall be, and must be put through the centre of the fly, so that the point come forth on the higher part thereof, and must there be made fast, and well ●ixte. Then shall you take a round box of wood, within the which the needle may be, 
The box of the compass.  not touching the sides of the same: And this must be of the height of the half Diameter of the compass. And the ground or bottom thereof must be set to it, as to the covering of a box, that it may be easily taken off, and put on, to have often recourse, to touch the irons with the s●one (which they call feéding) when need shall be, 
Feeding the needle with the stone.  that the virtue of the compass fail not. Also in the midst of the ground, or floor of the box, you must set a sharp point or prick, made of a wire of laton, this must stand right up, and upon the prick or point thereof, you shall se● the bored hole of the Capitel, and that the wind enter not above, you shall cover the box with a glass. And thus being touched with the stone and set upon the point, it shall show the true part of the North, and consequently all the other winds.  
And here is to be noted, that after the irons or neédle of the compass hath been touched in any of these manners, 
A notable experience of the Lodestone  if you bring the North part of the stone, to the North of the neédle or compass: then will the North of the neédle come to it. And if you bring the North part of the stone, to the South part of the needle, it will flee from it.  
And contrariwise, if you bring the South part of the stone, to the South of the neédle, it will come to it, and if to the North, it will flee from it. This is understood, the neédle or compass standing as it should be. And this also is a good sign, to know which is the North part and South part of the stone.  
Moreover, this box must be put within another box, in the which it must hang upon two circles of laton, annexed the one within the other: which serve that the compass sway not, or hang not toward the one side or the other, although the Ship sway, and this box also must have his cover of wood, to keep the other. You shall likewise observe that the point of the capitle, and the hole thereof, and also the point or prick upon the which it resteth, by upright, and likewise the Rose, that it decline not to one part or other. And if it be quicker than it ought to be, then make the point that it goeth upon somewhat blunter.   

¶ The v. Chapter, of the effect or property, that the compass hath to the north-easting or Northwesting, whereby is known the variation of the Compass.  

The variation of the comp●●.  MAny and divers are the opinions that I have heard, and also read in certain writers of latter days, as touching the north-easting and Northwesting of the Compass, and yet mee seemeth, that none doth touch the prick, and few the white.  
They call it north-easting, when the neédle showeth or pointeth from the North (which is his true mark) toward the North-east: and Northwesting, when from the North, it declineth toward Northwest. For the better understanding of these differences, whereby the neédles differ or vary from the pole, you must (being in the Meridian where the compasses show the pole) imagine a point under the pole of the world, 
The point attractive imagined under th● pole of the world.  and this point to be without all the heavens, contained under the first movable. The which point or part of heaven, hath a virtue attractive, that draweth unto it Iron touched with the part of the load stone, correspondent to that certain part of heaven imagined without or under all the heavens, moved by the first movable. For if it were imagined to be moved within any of the moved heavens, than the attractive point, by the moving of the first movable, & consequently ●he compass, should make the self same moving in 24. hours, which is never seen. And therefore this point is not in the movable heavens, neither in the pole. For if it were in it, the compass should not vary, north-easting, and Northwesting. 
The cause of the variation of the compass  Therefore the cause of north-easting or Northwesting, or departing from the pole of the world, is, that being in the said Meridian, the attractive point and the pole, are in the self same, or in one Meridian: and the compass showing the attractive point, 
Departing of the pole from the point attractive.  showeth directly the pole. And departing from the same Meridian toward the East (the world being round) the pole of the world remaineth to us on the left hand: and the point of the attractive virtue, shallbe on the right hand, which is toward the North-east wind. And in how much more we shall sail toward the East, the distance shall appear greater unto us, until we come unto the 90. degrees: and there shallbe the most and greatest north-easting. And passing from thence further forward, 
The greatest north-easting.  it shall appear unto us, that the attractive point, cometh nearer & nearer unto the Meridian line: and so much shall the compass go bettering or amending the north-easting, until it return to the self same meridian in the opposite or contrary part from whence they came, or where they began, & then shall the attractive point be to them directly upon, or against the pole of the world, & the compass shall show or point directly toward it. And again, passing further forward, the pole of the wo●l● sh●l remain to the right hand, and the point attractive to the left hand, and so shall the compass begin Northwesting, 
The greatest ●o●thwesting.  increasing it until it come from thence to the 90 degrees, & there shallbe the most of his Northwesting. For turning toward the Meridian from the attractive point, it shall go amending or bettering, until it return to the self-same Meridian from whence it departed, & there shall the compass show the pole of the world directly, by, or over against the attractive point, which is perpendicularly under the pole. 
The attractive point is under the Pole.  And if from thence they should turn, to pass toward the West, the pole should rest to the right hand, & the attractive point to the left, & so shall the variation be to the Northwest: and this is the cause of the north-easting, & Northwesting, or variation of the compass. 
The north-easting & Northwesting is not uniform.  Also it is not to be understood that this north-easting, & Northwesting, is uniform, as is the departing (or according to the departure) from the Meridian, where the compass showeth perfectly: but rather before at the beginning of the departing from the said Meridian, it maketh difference, or variation in a certain quantity, & the increase that is afterward, is little, and so much the less, in how much the more the departing is from the said Meridian. For it is a passion of the circles, 
The declination of th● Sun.  dividing or cutting themselves in the sphere: so that these differences are, as are they of the declinations of the Sun: which near unto the Equinoctials, are great, & near to the solstitials, are little. All the which shall evidently appear in the figure following, which is a circle divided by two Diameters, into 4. equal parts, cutting themselves in the centre in right angles. And from the centre point (called the pole) cometh forth a movable Meridian: & in it goeth a compass likewise movable about the circle. The attractive point is somewhat distant from the pole of the world, & from it, cometh forth a threéde, which must ever pass by the North & South of the compass. And the compass being in the Meridian of the point attractive, that passeth by the pole, shall show the pole. And without that shall go north-easting, or northwesting, so varying & departing from the true Meridian that cometh forth of the pole of the world. 
T●e Meridian that showeth 〈◊〉 Pole.  It is the opinion of some Mariners, that the Meridian where the compass showeth directly the pole, passeth by the Island of Sancta Maria, & other say, by the Island of Cueruo in the Asores.  
Demonstration of north-easting.  
And where as the inconvenience is manifest and notorious, the same must be remedied with prudence and time, 
Experience, the ground of reason.  and not to be negligent in the voyage: but ever to use & observe experience, more profitable than the subtile and curious questions of the secret searchers of natural things without experience, whereof reason taketh his principal ground. And therefore the wise Pilot ought to know by experience (as many of them do not) how much a good compass doth vary, 
Advertisement to Pilots.  north-easting, or Northwesting from one Port to another. So that to know how much the compass doth vary, north-easting, or Northwesting, from one place to another, (as to say, half a quarter, or more or less in quantity as they are distant from the said Meridian, where the compasses show the Pole) shall in the Navigation take heed, and well consider, in any such usage, north-easting or Northwesting, in the points of the compass. And this shallbe to sail truly by the points or lines that the Card doth certainly show. As for example. 
Example of ●aylyng.  In sailing from any Island that is in the said Meridian, or from any other part, in seeking of any port that is to them true North-east, if by this way the compass should North-east half a quarter, than sailing by the points or lines of the compass north-east half a quarter to the North, their Navigation shallbe (excepting other impediments) to the North-east which the Card showeth: And by this point or line, must be made the account of such a viage. And so by the points of the Card, they sh●ll directly find the Port that they sought. And by this order shall they go●●rne themselves in all Navigations. For the which, it is convenient that wise and expert Pilots, should make notes of observations of Nor●heasting and Northwesting, that is, from Port, to Port, and to make compilations and geatherings of such notes, to carry with them in their ships for regiments: and not to be busy or c●rious to amend their compasses, or with the stone to rub the Irons or S●eéles, neither on the one side or the other, from whence the Floure deluce doth show: For this should cause many inconveniences. Neither ought they to admit in their Cards, two graduations: 
The variation of the comp●●.  especially for that to know how much in every place the compass doth go aside, or vary from the true Meridian, may easily be made an instrument to show the same by the Su●ne in the day, and by the Stars in the night.   

The vi. Chapter, of the introduction and principles of the Art of Navigation.  
FOr as much as now we have the guide, which is the compass, it is convenient to enter into the way, which is Navigation. The which (as we have said) is to go or pass by water from one place to another. And this presupposed, I say that he that desireth to attempt Navigations, must know two things, which the Card shall show him. The one is, by what point or line he ought to sail: 
In Navigation what is chief to be considered.  and this shall the lines of the sailing Card show him. The other is, ●he leagues of the distance: and this shall the scale or trunk of the leagues show, taking with a compass the distance of two places, and applying it to the s●al●. The knowledge of these two things, ought the Pilot to bear in memory: and to put them in effect, aught to direct his foreship to the self-same wind, which the compass doth show. For the distance, 
The distance.  he ought to know how much the Ship goeth daily, well considering and observing the winds, tides, currents, and all such things as may be with him, or against him. And according heéreunto, he shall know how much he hath gone, and what remaineth for him to go, and whether he be far off, or near unto the place whither he intends to sail: the which in Navigation, is the end desired. And because this estimation or computation can not be just & exact, especially in a long viage, or in long time, it shallbe convenient that we rectify or amend it, knowing the place where the Ship is, on the superficial part of the water, by the place that answereth to it in heaven. 
The altitude of the Pole & Equinoctial.  This place of heaven, is known by the altitude of the pole: and by the altitude of the pole, is known the altitude of the Equinoctial: & by the altitude of the Equinoctial and declination of the Sun, is known the Meridian altitude: and contrariwise, 
The Meridian altitude.  knowing the Meridian altitude and declination of the Sun, is known the altitude of the Equinoctial, and by the Equinoctial, the pole, and by the altitude of the pole, is known the latitude: and this is the place that is desired to be known. But for as much as the heaven is movable from the East to the West, this place is not known as a certain point, but is known as a line or parallel at a certain distance from the Equinoctial, and it is known in what point of this parallel the Ship is, 
To know the place of heaven.  by the altitudes that are taken from heaven: but it is known by the line that the Ship hath gone, as we will further declare in the xiii. Chapter, of making a point or prick in the Card. And in this manner you shall have rectified the way that the Ship hath gone, 
To know the way of the viage.  and consequently the way that it hath yet to go.  
And forasmuch as these altitudes are so profitable and necessary, it shallbe needful to give rules how we may use them to our most commodity. 
Rules to know the altitudes.  And for this, is presupposed to know, that all places situate on the superficial part of the earth, and water, either they are under one Meridian, so that they have, or where they have one self same longitude, 
Longitude and latitude.  and differ in latitude, or are in one parallel, where they have one self same latitude, and differ in longitude, or are in divers Meridian's and paraleles, where they differ in longitude, and latitude. And I say, that if they have one self same longitude, they sail from the one to the other, by the line of North, and South, and how many degrees doth vary the altitude of the pole and of the Equinoctial in heaven, so many degrees have they gone by sea, or by land, If two places have one self same latitude, they pass from the one to the other by the line of East and West. And in such manner of voyage, the altitudes do not profit us, because there is no variation. If they differ or vary in longitude, and latitude, they sail from the one to the other by some of the other lines. 
Variation of degrees.  But there are more degrees that correspond the way that the Ship maketh, than the degrees that vary the altitudes of the Equinoctial, and the pole. And this difference shallbe greater, in how much the line shall draw near to the East and West: And how much it shall draw near to North and South, it shallbe less. Of the degrees or leagues that answer to every degree of the variation of the altitude, we will entreat hereafter in the xii. Chapter.  

how the altitudes are known,  These altitudes are known many ways, but especially by two: as by the Meridian altitude & declination of the Sun (as we have said) is known the altitude of the Equinoctial, and by it, the altitude of the Pole. The second way, they are known by the altitude of some fixed Star, 
The fixed Stars.  of those that are not hid. And among many other, the North Star, 
The North Star.  is taken, because it is nearest to the Pole. To know the altitudes by the Sun, 

To know the altitudes by the Sun.  
The Meridian.   three things are necessary, that is to say, an instrument, the declination of the Sun, and rules. The instrument to know the Meridian altitude shallbe the astrolabe, because it is most commodious for this purpose, whereof we will entreat in the Chapter following. The declination of the Sun (which is to take it away, or to join it with the Meridian altitude) we have already described in the third Chapter of the second part. The rule to know when the declinations must be joined with the Meridian altitude, 

The declination of the Sun.  
The altitudes of the Pole.   or taken from it, we will give in the viii. Chapter. To know the altitudes of the Pole, by the altitudes of the North Star, two things are necessary: that is, an instrument, and rules. The instrument wherewith the Mariners are accustomed to take the altitudes of the North, they call Balestilia, which is a cross staff, whereof we will write heéreafter in the nien●h Chapter. 
La●obes staff.  And the rules of the Turn or compass, which the North Star maketh about the Pole, we will declare in the tenth Chapter.   

¶ The seven. Chapter, of the making and use of the Astrolabie● with the which the mariners take the altitude of the Sun.  
TAke a plate of copper, or latten (which for this purpose is better than any other metal) of the bigness ●hat you desire to make the Astrolabi●, and is commonly of the bigness of a span of the Diameter, and let it be of the thickness of half a finger at the least: for the weightier that it shallbe, so much shall it be more steady to make the altitude. This place must be made round by a circle, leaving coming forth of the circle or corner, in the which you shall put a ring or handle with a hole, whereby you may hang the astrolabe, by a threéd or li●e to take the altitude.  
After it is thus made, with the ring or handle annexed thereto, make it bright, and smooth, publlyshed on both the sides, and all of one equal thickness, that one side be not heavier than another, which y●u shall try in this manner: 
The rectifying of the A●●rolabie  hang the plate by the ring or hole that you have made, and from the same hole hang a plomet of lead, fasted to a here, or fine threéde of silk. The astrolabe thus hanging, free, and at liberty with the plomet, if then the threéd fall upon the centre of the astrolabe, 
The threed● and plomet.  it is well: but if the thread do lean or swar●e to the one side, or to the other, from the centre, then is that side thicker and heavier than the other, and must therefore be made th'inner, until the thread fall justly upon the centre. This done, make a circle upon the said centres a little within the circumference of the astrolabe. Then draw a Diameter from the centre of the hole, in the which the ring or handle is, unto the centre of the astrolabe, traversing or overthwarting the whole Circle. And this shallbe called the line of the Zenith, 
The lines vertical & horizontal.  or Uertial point: which also shallbe cut with an other Diameter upon the centre, making right angles with it. And this Diameter shallbe called the horizontal line. These two Diameters shall divide the circle, into four equal parts. After this, you shall make another circle, so much more within the second, that between the circumferences of both the circles, may be contained the numbers of the degrees. Then (the astrolabe hanging before you) you shall divide the one part (being the superior and left part) first into three equal parts, and every part shall contain 30. degrees. Then shall you divide every part of these into three other equal parts, and they shall contain 10. degrees: and every of these divide into two parts, and they shall contain 5. degr●és. This done, put a ruler upon the centre of the astrolabe, applying it to every of the points that divide the said parts, and draw certain lines that pass from the circumference of the first circle, unto the less circumference: and in the spaces of the less circle write the numbers of the degrees, beginning in the horizontal line: and in that space put five, and in the second, t●n, and so forth of the other, until the 90. degrees end in the line of the Zenith. then shall you divide the spaces that are between the first circle and the second, every space into fine, which shall make the 90. degrees. The astrolabe thus made, you shall make the Alhidada or Label. 
The Alhidada of the Ast●olabie.  For the which, you shall take a pla●e of laton, of the breadth of scarcely two fingers, and as thick as the astrolabe: also as long as the Diameter of the astrolabe, and make a line in the midst thereof by the longitude: in the midst of this line, make a circle, so great, that it may touch in the sides of the plate: then cut off this plate on the on● side, that which it hath from the line to the right hand, and on the other side, that it hath from the line to the left hand, leaving the circle whole. This line that shall pass by the centre of the circle, is called Linea fiduciae, (that is) the line of confidence, which is that, that showeth in the degrees, the altitude that is taken. Then shall you take away the ends or corners of the Alhidada that are without the line, so that you touch not the line. This done, you shall make two little rising or raised tables or plates, of the same metal whereof the astrolabe is made, and of the self same thickness that is the Alhidada, or little less, and of the breadth of the Diameter of the circle of the Alhidada, and let them be a thumb in height or breadth. In the midst of these two places by the height, you shall make a line. When these are made equal, and all their angles right, in every line of these that you have made, you shall also make two holes, ●qually distant from the sides or edges of the said plates or tabrets. And of the two holes of every of these little plates, 
The holes of the alhidada.  the one hole must be as big as may contain a great pin: and these shall serve to take the altitude of the Stars. The other must be so subtle and small as a fine sowing neédle: and these serve to take the altitude of the Sun. They must be made in such manner, that the outward part of them be bigger, and less within, of the quantity that I have said. These tablets or erected plates being thus made, they must be sothered in the Alhidada, between the centre & extremities or ends of the same, making in it certain notches where they may be made fast, and sothered: or leaving first in the plates certain sharp points or corners, that may enter into certain holes made in the Alhidada, whereby they may be made fast underneath with pings: And they must be so set, that the line where the holes of the plates are, may fall upon the line of confidence of the Alhidada, so that the one half of the plate be set upon the Alhidada, & the other half without it, or at large. In like manner you shall take good advertisement, that the great hole of the one plate, stand directly against the great hole of the other plate, & be nothing at all awry. This done, you shall bore the astrolabe through by the centre, making a very round hole, that may have in the midst of it the centre of the astrolabe. This hole shallbe of the bigness of a goose quill. And the like shall you make in the centre of the circle of the Alhidada. Then shall you make a pin or nail of the same la●on, the which on the upper part of the Alhidada may have a plain and round head. This pin also shallbe very round and smooth, that it may enter just and close into the hole of the Alhidada and astrolabe. And at the end or point thereof, coming forth on the other side of the astrolabe, must be a hole made sydeway through the pin, close to the plate of the astrolabe, of the bigness of a little nail or pin, that may be put therein, to make fast together the Alhidada with the astrolabe, so that the Alhidada may thereby be turned round about the astrolabe, as appeareth in this figure following.  
To take the altitude of the Sun, 
To take the altitude of the Sun.  hang up the astrolabe by the ring, and set the Alhidada against the Sun, and raise it, or put it down in the quarter that is graduate, until the beams of the Sun enter in by the little hole of the other table● or raised plate, and precisely by the other little hole of the other tablet. Then look upon the line of confidence: and how many degrees it showeth in the quarter that is graduate (beginning from the horizontal line) so many degrees of height hath the Sun. In like manner shall you do to take the altitude of any other Star, looking through the great holes, because this may hardly be seen by the little holes.   

¶ The viii. Chapter, of the definition of the altitude. And how the altitude of the Pole may well be known by the Meridian altitude and elevation of the Sun.  
IT is convenient to define the altitude, b●fore we give rules of the use thereof. The Altitude of the Sun, or the Moon, or of any other Stars, 
What is the altitude of the Planets or Stars.  is the distance that is between it and the Horizon. And this aught to be accounted by the degrees of the great Circle, which passeth by the Zenith, & by the centre of the Sun, or of the Moon, or of the Star, unto the Horizon. And the degrees that are from the Horizon to the Star, or to the Sun, that is the altitude: 
The complement of the altitude.  And the degrees that are from the Centre of the S●arre, or of the Sun, unto the Zenith, is called the complement, or supplement of the altitude. The altitude of the Equinoctial, is ever counted by the Meridian. And the degrees of the Meridian, that are between the Equinoctial and the Horizon, is the altitude of the Equinoctial: and other so many are they, that are from the Zenith to the Pole. 
from the Zenith to the Pole.  For the altitude of the Equinoctial, is equal to the complement of the altitude of the Pole. The degrees of the Meridian that are be●w●●ne the Equinoctial, and the Zenith, is called the complement of the altitude of the Equinoctial, and is equal to the altitude of the Pole. And although we have defined the altitude in general, ye● shall we only profit ourselves by the Meridional altitude of the Sun. The Meridian altitude, is the greatest altitude that the Sun hath every day: 
The Meridian altitude of the Sun.  and this shall be, when the Centre of the Sun is in the Meridian. And the Ark of the Meridian, that is between the Horizon and the Sun, 
The shadows that the Sun maketh at midday.  is the Meridian altitude. So that when we say the altitude of the Sun is taken, it is understood at midday. The shadows that the Sun than maketh, are in three sorts. for either to us it casteth the shadow toward the North part, or toward the South, or pendiculer by a right up line, so that at midday, or noon, nothing that standeth upright, giveth any shadow at all. But forasmuch as there is such variation in declinations, altitudes, shadows, an● paralelles, i● shallbe necessary to give rules for all varia●ions. And these shallbe reduced into four brief and compendious rules the which I have here described, 
Rules for all variations.  that the witty may have profit by them, and the rude learn them: not caring for the rules of the Mariners, because they are so long and tedious. For (as the Philosopher saith) it is vainly done by many, that may well be done by few.  
When the shadow shallbe perpendicular, 
The pe●pendiculer shadow.  it is because the Sun is in the Zenith, and 90 degrees above the Horizon. And then how many degrees of declination the Sun hath so much shall we be distant from the Equinoctial, toward the part where the Sun declineth. And if it have no declination, it and we shallbe under the Equinoctial.  
But when the Sun and the shadows shallbe to us from the Equinoctial, 
The declining shadows.  toward one of the Poles, we shall take away the declination from the Meridian altitude, and then shall remain the complement of the elevation, which complement being taken from 90. degrees, then shall remain that which we be distant from the Equinoctial, toward the same Pole.  
When the Sun declineth from the Equinoctial, toward the one Pole, and the shadows shallbe toward the other, we shall join the declination with the meridian altitude: and if all come not to 90. then subtract them from 90. degrees, a●d we shall have the complement, and so much shall we be distant from the Equinoctial, toward that Pole to the whi●h the shadow falleth. And if they be more in number then 90. then the overplus of 90. shall we be distant from the Equinoctial, toward the Pole where the Sun declineth● And if they be just 90● we shallbe under the Equinoctial.  
When the Sun hath no declination● 
When the Su●ne hath no declination.  we shallbe distant from the Equinoctial the complement of the Meridian altitude, toward the Pole where the shadows are. By these rules (beside the use whereof we have spoken) may be known how much is the greatest declination of the Sun, th● altitude of the Equinoctial, the day, hour, and minute, when the Equinox was: the which is known as followeth.  
Having taken the greater Meridian altitude of the Sommet (which is in the beginning of Cancer) and the less of Winter, 
To know the greatest declination of th●●●nne.  (which is in the beginning of Capricorn) taking away the less from the more, the ●est is that, that is from tropic to Tropike, & consequently par●ed by the midst, is the greatest declination. As for example. 
Example.  I suppose, that being in the City of Cadi●, to find the great Meridian altitude of the Sun (being in the beginning of Cancer) to be 77. degrees, and the lesser Meridian altitude (which is, when the Sun is in the beginning of Capricorn) to be 30. degrees: then taking 30. from 77. remain 28. degrees: and so much is from tropic to Tropike. And the half (which is 23. and a half) is the greatest declination.  
Consequently the greatest declination added to the less Meridian altitude, taking it away from the greater Meridian altitude, that riseth thereof, is the altitude of the Equinoctial. Example 23. and a half of the greatest declination, 
Example.  joined with 30. of the least Meridian altitude, or taken away from the 77. of the greatest Meridian altitude, remain 53. degrees and a half, which is the altitude of the Equinoctial, in the City of Cadiz. Hereof it followeth, 
The true Equinoctial.  that w●en we shall ●ake the meridian altitude in 53. degrees and a half, that day is the true Equinoctial. But if it had one day less, and the other day following it had more, we must take the less from the more, & form the rule of three upon the rest, saying, If 24. minutes (which is that that the Sun declineth in one day) doth yield 24. hours, how much shall those minutes that lacketh of 53. degrees and a half of the altitude of the Equinoctial, yield me? Multiplying & dividing according to the foresaid rule, then that which cometh thereof, shall be the hours after the midday, when it is Equinox.  

Example.  Example of the experience that I made in the City of Cadiz the tenth day of March at midday or high noon, I took the altitude of the Sun, in 53● degrees, and 26. minutes, they lack to be the Equinoctial 4. minutes. another day, the xi. of March, at noon, I took the Sun, in 53. degrees, and fifty minutes: which are more than the Equinoctial by twenty minutes. Then to know at what hour the Sun was in the 53. degrees, and thirty minutes of the Equinoctial, I took away the Meridian altitude that I took at the tenth of March, from that that I took at the eleventh, which is the difference 24. minutes, and I form the rule, saying: if 24. minutes the Sun did rise to me, in 24. hours, then in how much time shall rise unto me the four minutes that failed me at the tenth of March? I multiplied, divided, & found, that in four hours: and so shall you say, that the Equinoctial was in the city of Cadiz the tenth day of March, at four of the clock at after noon, which is understood (according to the Astronomers) at four hours run at the eleventh day of March, at this present year 1545.   

The ix. Chapter, of the making of the cross staff, wherewith the Mariner● take the altitude of the North Star.  
MAke a square s●affe or yard, of the thickness of a ●●nger, more or less, according to the goodness of the wood, and of length six spans, or more. For the longer that it is, the more precise shall it be, and the degrees shall be the greater, whereby followeth the certainty of the altitude. Then take a very plain table, of the length of the sta●●e, and two spans of breadth, or at the least a span and a half: and in the midst of this Table, make a right line by longitude, and in the one end of this line, make another line that may cut it in right angles. And upon the cutting of these two lines, put the foot of the compass, and make half a circle, which may remain on the part of the long line, so that the half circle may have so much Diameter, as you desire the height of the hammer, head, or crossepéece of the staff to be. This half circle being made, you shall draw two lines, equidistaunt to the line which you have made by the midst of the Table. These lines must touch in the extremities or ends of the half circle. Then divide every half of the half circle, or quarter of the circle, into two equal parts, & the two halves that shall end in the first line, divide each of them into 90. equal parts. Then take a ruler, and put the edge thereof upon the centre of the half circle, and upon every of the marks which divide the 90. parts, and so proceed, making punctes in the lines, which you have made equidistant to the first line. Then draw certain right lines, from the punctes of the one line, to the opposite punctes of the other: and so shall the draft be ended. Then take the staff or yard, & put the one end thereof in the centre of the half circle, and apply the edge of the yard to the line that goeth by the midst of the Table: and mark in the yard the marks that are in the said line, by means of the traversing lines, and see also that the marks which you make in the yard, be traversing lines, and make them their numbers, beginning at the end or point of the yard that shallbe to the contrary part, from that which you did in the punct of the half circle. And to know with what degrees you shall begin the yard or staff, and what number you shall mark in the first line of the punct, look how many degrees are from the circle which you divided between the line that goeth to the last mark, and with so many degrees enter, and so consequently shall you place the numbers from five to five, or from ten to ten. When you have thus numbered the yard, then to make the cross piece thereof, take a table or plank of good wood, which shallbe so much in lengthy as shallbe the Diameter of the half circle, & so much in breadth as three times the thickness of the yard, and of thickness two fingers, or little less. On the one side also it must be very plain, and on the other side in the midst it must have a square or quadrature of all the thickness of the plank, and from the square to the ends, it must be made thinner and thinner, so that it hath in manner the form of such pickars wherewith millstones are picked. And in the midst (by longitude and latitude) it must have a square hole, by the which the yard may enter just, and make right angles with the cross piece. And the point of the yard must enter by the plain side of the cross piece, and come forth of the square side thereof. To take the altitude of the North Star, 
To take th● altitude of the Starr●●.  or any other Star on the Sea (for it serveth not on the Land, nor for the Sun, except the Sun shallbe under any thin cloud, & the Horizon clear) you shall put the head of the staff to the corner of your eye, raising it up, or putting it down, until the neither part of the cross piece come with the Horizon: and being so, if the higher part of the cross piece shall come with the star, you must look the plain side of the cross piece in what number of degrees of the staff it falleth, and those degrees shall be the altitude of the Star: as if the cross piece reach not to the Star, you must bring the cross piece nearer to your eye, until the one part thereof come with the Horizon, and the other with ●he Star, and the degrees, which it showeth, shallbe the altitude.   

¶ The x. Chapter, of the altitude of the Pole, known by the altitude of the North Star.  
TO know the parallel in the which the Ship is, over and beside the rules there before of the altitudes of the Sun, it is likewise known by the altitudes of the North Star. These two manners are used, for that more credit is given to two witnesses, then to one: So that if by one arise any doubt, the same may be certified by the other, and also because time may sometime serve for the one, and not for the other: as, to have a cloudy midday or noon, and a clear night.  

The North Star.  The altitude is taken of the North Star, which is a Star in the extremity or end of the tail of the less Bear, being a constellation, 
The les bear.  commonly called the Horn. For this North Star (of the most notable Stars about the Pole) is nearest unto it, & shall therefore show a less circle than any of the other, and so shall his altitude differ little from the altitude of the Pole. This Star hath declination 85. degrees, 
The horn.  and 51. minutes, and the complement to ninety (which are four degrees, 
The distance of the north Star from the Pole.  and ninety minutes) is his distance from the Pole. And although the Mariners hold opinion, that it is not distant more than three degrees and a half, yet to my judgement, more credit ought to be given to the Astronomers, then to the Mariners, for as much as the Astronomers do know the places of the Stars, with their longitudes, latitudes, declinations, and right assentions, more perfectly and precisely then do the Mariners: For they account not only by degrees, but also by minutes and seconds. But let none deceive themselves through my opinion. Therefore, whosoever will precisely know it, let him take the highest altitude of the North Star, which is his being over the pole, and the less altitude, which is his being under it: then take away the less from the more, and the half of that that remaineth, shall be the distance of that Star from the pole of the world.  
And likewise by this experience, may be known the altitude of the pole, and what all the other stars, that go not down under the Horizon, be distant from it. joining the greater altitude with the less, and that shall amount thereof, divided by the half, shallbe the altitude of the Pole: and taking away this altitude of the Pole, from the greater altitude of the Star, or the less from the altitude of the Pole, the rest that remaineth shallbe the distance of the Star from the Pole. 
The Pole is invisible.  And as the Pole is invisible, it can not be seen or known, when the North Star is higher or lower, except it be by the mean of some o●her mark: and for this is considered the position of the former Guards, or watch, being one of the two stars called the Guard, which are in the mouth of the Horn. 
The two stars called the Guards of the North Star.  The Mariners have noted eight positions from the former Guard star, to the North star, which answer to the eight principal winds. And as the Guard is to the North star according to the placing of these positions, so shall it be higher or lower from the Pole. Let us here put the common rules which the Mariners use, 
Common rules of the Mariners differing from the Astronomers.  to comply with those that are of opinion of the three degrees & a half. And for the opinion of the Astronomers (which is the distance of 4. degrees, and 9 minutes) I will hereafter give a circular figure with a movable horn: then the eight winds of the eight positions being marked, and putting the Guard and the North star in every of the winds, it shallbe the distance that the North star is higher or lower from the Pole.  

Common Rules.  
The form Guard being in the East, 
These rules after the Mariner's account do hold, but not after the As●ronomers account, as may appear in the rules next before.  the North Star is in one degree and a half under the Pole.  
The Guard being in the North-east, the North Star is three degrees and a half under the Pole.  
The Guard being in the North, the Star is three degrees under the Pole.  
The Guard in the Northwest, the Star is half a degree under the Pole.  
The Guard in the West, the Star is one degree and a half above the Pole.  
The Guard in the south-west, the Star is three degreé● and a half above the Pole.  
The Guard in the South, the Star is three degrees above the Pole.  
The Guard in the Southeast, the said North Star is half a degree above the Pole.   

The eight principal winds according to four● ly●es.  Note that these eight winds, are made according to four lines. Whereof two are right, which are North & South, and East & West: and the other two are crooked, which are North-east south-west, and Southeast Northwest. When the Guard and the North Star shallbe in the right line, it shall appear clear how they are: and when they shallbe in th● crooked lines, it may be seen, because the Guards are the one by the other in a right line.  
To see by theoric or Speculation, how the North star riseth up, and goeth down from the Pole of the world, I will here describe the said circular figure or instrument, which is a circle, 
An instrument ●o know the rising o● falling of the North star from the pole of the world.  in whose circumference are written the eight winds. The North in the highest place of the instrument, which they call the head, and the South in the neither part thereof, which they call the foot: the East in the right arm, the West in the lef● arm, the four rest between these in their places. And here is to be noted, that the lines which pass not through the centre, are of the winds of their equidistances that pass through the centre. Within this circle, is an other little circle, which describeth the star of the North, by the moving of the first movable, & hath for his centre the Pole of the world, as hath the first. This little circle hath for his Diameter eight degrees and eighteen minutes: as four degrees and nine minutes above the pole, and the other four degrees and nine minutes under it. And they are divided by certain lines equidistant to the East and West. In the centre of this circle, 
The horn of the seven stars  is annexed a horn, with his seven stars, movable round about by all the winds. And seeing them in heaven, 
Advertisement to Mariners in using the figure following.  how, & in what wind they are, even so in this figure shall we see the North star, in what part it is of the degrees high or low from the pole: & that the Pilot or Mariners shall not err. I say that he ought not to put the foreguard in the winds that pass through the centre of the figure, for it shallbe North and South with the pole, and not with the star of the North, as it ought to be, and so of the other winds. And in this manner the star of the North, shall show in the lines equidistant from the less circle, the degrees & parts of degrees that it is higher or lower than the pole of the world: for the same course, differences, and variations, it maketh in heaven.  
¶ This figure is after the Astronomers, Which affirm that th● North star is four degrees, and nine minutes from the P●l●.  
Thus being known how much the North star is under or above the pole, 
The altitude of the Pole above th● horizon.  let us take the altitude thereof: and that of if that is under the Pole, let us join to his height, and as much of it as is above, let us take away, and that shall rise thereof, shall be the altitude of the Pole above our Horizon.   

The xi. Chapter, of the composition and use of an instrument, by the which without observing the South Sun, or midday, is known the altitude of the Pole, and the hour that is.  
WE have given rules, whereby the Pilotte may know in what parallel he findeth himself with his Ship. But he may not know this at all hours, for as much as for the altitudes of the Sun, it is necessary to observe the midday justly, and for the altitudes of the North, it is necessary to observe, that the foremost guard be placed justly with the North, in some of the four lines of the eight winds. And over and beside the rules aforesaid, I have thought good to describe an instrument, 
An instrument to know the parallel and hour by the s●nne.  by the which may be known the parallel where the Ship is, and what the hour is at any time of the day by the beams of the sun.  
Make a round pla●e of La●on, or other convenient metal, of the Diameter of a sp●●ne, or more: For the greater that it is, the more precise shall it be: and make in it two Diameters, that may cut themselves in right angles upon the centre. In the four extremes or ends of these Diameters, leave four round punches or points, that may serve for axis. The one of these Diameters, shallbe called the axis of the world, and the other, the line of East and West. This done, make of the same la●on a semicircular piece, of the thickness of the plate, or little less, and of the breadth of half a ●inger: this must stand upon an edge, so that the co●●ex part may come justly with the half of the circumference of the plate, to the which it must be nailed or sothered in the neither part of the plate, the semicircle being raised, & that the ends thereof may come with the ends of the axis of the world. And this semicircle shall you divide into too equal parts, and every half into 90. degrees, beginning from the half point toward the end of the Axis of the world, which are the Poles.  
In like manner shall you make● two circular pieces, of the bigness of a pe●ce of four rials of plate, which th●y call rundels, for the hours: these must be made fast in the plate by the Poles of the world, which may hold or bear them by their centres. And every of these rundles must be divided into 24. equal parts, and although not all, yet the uppermost part of the plate. And above in the highest point of these divisions, you must write 12. because that there it shall show the midday or noon. And from thence, the afternoon hours must begin their numbers toward the West part, and shall end. 6. hours in the half or midst of the joint of the circle with the plate. In the other joint of the other part, shall begin 6. of the hours before noon, & shall end 12. in the ●ighest point. You must also make another Semicircular piece, of the breadth of a finger, this must be plain or flat, & the concavity or hollowness thereof, equal to the Semicircle of the edge or side of the plate, and in the ends must have two holes, wherein may justly enter the points that come forth of the circle, for the hours, which are the Poles of the world. Also, this Semicircle must have two lines, one on the uppermost part, and the other on the nethermost, which may divide the breadth into two equal parts. This half circle likewise must be divided into two equal parts by longitude, with a traversed line, which shallbe called the Equinoctial, & from this line, to the inward part thereof, must be counted 13. degrees and a half toward the one part, and as much toward the other part of the 90. that every half of the circle containeth. And at every part where end the 13. degrees & a half, make a traversed line, so that from the one to the other, may be 47. degrees. And in this space shall you draw certain lines equidistaunte with them of the midst, that they and the middle line, may divide into 4. equal parts the breadth of the half circle. Then look in the table of the declinations of the sun, what declination have the 5. degrees of Aries, and that shall you account from the Equinoctial toward the one part, and as much more toward the other, making a line that may traverse that of the midst, where that declination doth end and touch in the other two lines. And the same shall you do at 10.15.20.25. and 30. w●ich is the end of Aries, and beginning of Taurus: and then the line shall traverse all the breadth. The like also shall yo● do to Taurus and Gemini, then in the spaces, writ the caractes of the xii. signs, beginning Aries from the Equinoctial, 
The caracts of the xii. signs.  toward the North Pole. And then do Taurus and Gemini end in the greatest declination, beginning Cancer in the other part of it. Then Leo and Uirgo do end in the Equinoctial, where shall begin Libra, Scorpio, Sagittarius: and in the other part, Capricornus, Aquarius, and Pisces, shall end in the Equinoctial where Aries began. This half circle must have an opening, or open place, even and just in the midst from the Equinoctial, unto somewhat more than the greatest declinations, and must be a little brother on the inner part, then without: and not so broad as may come to the two lines, because it would then take away the graduation of the signs. And in this open place must be put a square grain or stub, which on the inner part may come plain with the half circle, & on the utter part may c●me forth a little, where shallbe nailed a square piece of Laton, of the breadth of the half circle. This grain or stub being so nailed with the piece, must have in the midst a hole, 
The hole that representeth the Sun.  so small, as may receive a little pin, and by the centre of this hole, must pass a line, which shall traverse all the grain. And this line shall serve to put the sun (which the hole representeth) in the degree of the sign where it is. This half circle where it goeth in the circumferences of the rundels for the hours, must ●e filed on the one side unto the line that is in the midst, to mark it, and show the number of it. For the placing or setting of this instrument, 
The placing or setting of the instrument.  you must cut a girdle or ring of laton, as thick as the plate, and of the breadth of a fy●ger, or little less: and so large, that of it may be made a circle somewhat bigger than the plate, so that the plate and the Meridian may easily be contained within it. This circle shallbe called the Horizon, which must be divided into four quarters.  
In like m●ner must be m●de two semicirculer pieces, & the ends of them must be nailed or sothered in the points that divide the quarters of the circle: and divide the one from th●ther in two equal parts, making right spherical angles. And in this joint of these two pieces, must be nailed or sothered a Mast●●, the which at the one end is divided into two branches or forks. 
The Foo●e or Base of the instrument.  Then shall you make a base or foot for the same, which in the uppermost part thereof shall have a concavity or hollowness, where may be set a sailing compass or a neédle, touched with the Lode stone, and covered over with a glass. And on the highest edges of this base, the two branches of the Mastel shallbe made fast, and this base, with the Mastel, the half circle, and the circle, shallbe all one piece, which ●halbe called the seat or frame of the instrument. The Horizontal circle in the ends of one half circle, must have two holes, in the which may enter the Axis that are made in the ends of the line of East & West.  
Also you must take good heed when you sother or make fast the Mustel in the base, that the North and South of the plate or Horizon, come with the North and South of the needle that is beneath, having ever respect how much the neédle doth vary from the Meridian, by north-easting or Northwesting. In the joint of the two half circles upon the Mastel, must be a point (called the index or shower) wh●ch shall show in the half circle, 
The Index or shower.  sothered in the place on the ne●ther part the degrees that the Pole is raised above the Horizon.  
For the perfection of this instrument, it shallbe convenient to set the Horizon very play●e and equal at the time of the operation or practising with the instrument, 
The placing of the horizon.  and this may be done in two manners. Whereof the one is, hanging by a fine threéde, at the centre of the plate, a plomet made somewhat pointed at the neither end: so that the Horizon standing plain & level, the point of the plome● may ●al upon the point of the index, 
For the Land.  and this manner is good for the land. But for the Sea, 
For the Sea.  you shall sother the Horizon two Ax●s, little stubbes or ends coming forth. These shallbe put in the two opposite holes of a circle of metal made somewhat strong, and this circle must have other two stubbes likewise coming forth, and equally distant from the two holes. These must be sothered or nailed in two holes of another circle in like manner, and the other circle with other two stubbes, enclosed in a box. If then the box stand even and level, the poised or weight shall cause the Horizon to stand level, although the Ship sway or roll from side to side. The use of this instrument is in this manner.  

The use of the instrument.  When you desire to know the parallel in which you are, and the hour that is, put the line that traverseth the grain, in the degree of the sign in the which the Sun is (which you shall know by the ●able of the place of the Sun, in the second Chapter of the second part) and set the North and the South of the plate, with the North and South of the needle. Then turn the movable Meridian against the Sun, the foot of the instrument standing fast, and raise it, or put it down in the plate, until the beam of the Sun enter in at the hole of the grain, and fall in the centre of the plate, and standing so, behold the index, 
The altitude of th● Pole.  and how many degrees it showeth from the Meridian, so much is the altitude of the Pole. Then look where the movable Meridian showeth in the rundel of the hours, and there shall you see the hour that is.  
Hear followeth the demonstration.   

¶ The xii. Chapter, of the leagues that are run for a degree, according unto di●ers courses.  
IN the sixth Chapter, I promised to give a rule to know the distance from one parallel to another, 
To know the distance from one parallel to another.  sailing by whatsoever line or wind, except the East and West: for the which is to be understood, that the Navigation or course from one place to another (according to the Cosmographers) ought to be by the ark of the greater circle, 
The ark of the greater circle.  for that by this manner shallbe the shortest course, and this greater circle they divide into 360. degrees: and all the distances that are from one place to another, they account by the degrees & minutes of this circle: and so sailing from North to South, to one degree of the variation of the height of the Pole, shall answer another degree of the greater circle in the superficial part of the water and land. And therefore sailing by whatsoever other line, until the Pole doth vary one degree of altitudes, 
The altitude of the Pole varying one degree.  we shall have gone more than one degree of the greater circle: and the degrees that answer to every line or wind, you shall see in the demonstration following, which hath two parallel lines, which are East and West, and the line that cutteth them in right angles, which cometh forth of the centre from the quarter of the circle that is made, is North and South, and then shall you see by this order, all the other winds, half winds, and quarters of winds, reduced to one quarter: 
The quarter serving for the 32. winds of the compass.  For the self same account serveth for North-east and south-west, and Northwest and Southeast, and so of the half winds & quarters of winds that are equally distant from the line of the North and South: and so this quarter shall serve for all the 32. winds of the compass. Without this quarter, hard by the line, you shall find two numbers, whereof the first shallbe of the degrees, & minutes of degrees of the great circle, which is from one parallel to another. The other number, shallbe the leagues, & par●es of leagues that such degrees and minutes do amount unto, after the rate of 17. leagues and a half for a degree. In like manner in the parallel, where the lines of the winds do concur, shallbe set jointly to every line the degrees & minutes of the distance from the line of North and South, and leagues & parts of leagues that such degrees and minutes amount unto. And so it is, that sailing by the line, wind, or point of North and South, until the altitude of the pole vary one degree, is run another degree, which containeth leagues 17. and a half. And by the next line, 
One degree of variation of the Pole.  for one d●greé of the variation of the altitude of the pole, is run one degree, one minute 17. leagues, and 5. six parts. And th●y that run upon that line or point, depart from the line of North, and South, or Meridian line 12. minutes, leagues 3. and a half. By the second line, 
Departing from the Meridian line.  is run one degree 5. minutes, and leagues 19 scant, and in this course, they part from the Meridian 25. minutes, leagues 17. and a quarter. By the third line is run one degree 12. minutes, leagues 21. and a 20. part of a league, and departed from the Meridian line 40. minutes, leagues 11. and two terces. By the fourth line, is run one degre●, minutes 25. leagues 24. and three quarters, and departed from the Meridian, one degree justly, leagues 17. and a half. By the fifth line, is run one degree, minutes 48. leagues 31. and a half, and departed from the line one degree 30. minutes, leagues 26. and one quarter. By the sixth line, is run two degrees, minutes 37. leagues 45. and of the 45. parts of one league, the 11. part, and departed from the line two degrees, minutes 25. leagues 42. and a quarter. By the seventh line, is run five degrees, 
Degrees of the greater circle.  minutes 8. leagues 29. and two ter●es, and departed from the line five degrees, minu●s 2. which are leagues 88 accounting 17. leagues and a half for a degree of the greater circle. And if for every line you desire to know this computation of leagues, after 16. leagues and two terces for a degree, or for more or less leagues or miles, multiply those such degrees by the number of the leagues or miles which ●nter into every degree, & likewise shall you number the minutes that are more than the degrees, by the same number of the leagues that ●nter in every degree, dividing them by sixty, and that that shall come of the division, you shall join with the multiplication of the degrees, and that shall amount thereof, shallbe the leagues, and parts of leagues, that was in those such degrees.   

The xiii. Chapter, how to set or make a prick in the Card of Navigation.  
THe Mariners call the pricking of a point in the Card, 
To know in what part or point the Ship is.  to see and appoint in it, in what point or part of the Sea the Ship is in Navigation. For the performing whereof, it shall be requisite that the Pilot know from what degree, or how many degrees of the altitude of the Pole he departed, and with what wind he saileth. And when he desireth to know where he is, let him know the altitude of the Pole, 
The altitude of the Pole.  by some of the aforesaid rules. And if (taking the altitude) he find himself in the same degrees where he was when he departed, his Navigation hath been from the East to the West, and what he hath gone can not be known but by the judgement of a wise and expert man, according to the s●y●●nesse or goodness of his Ship, with consideration of the more or less time he hath had, as we have said before in the sixth Chapter. 
To find the distance by the Card.  But if ●e find himself in more or less degrees, let him take two pair of compasses, and put the foot of one, in the point or plate where his Ship was when he departed, and the other in the line or wind by the which he saileth, and likewise let him set the one point of the other compass in the graduation of the Card, in that number of degrees that he findeth the altitude of ●h● Pole, and the other point of the same compass in the next line o● East & West: and so with both the compasses, one in the one hand, and the other in the other hand, let h●m go joining them together, taking good heed, that the point of the compass do ●ot serve fr●m the wind whereby he hath sailed, neither the p●ynt of the other compass from the line of East and West, where he set it.  
And following those two compasses by these two lines, until the points of the two compasses join (that is to mean, the point that was set in the place from whence he departed, and the other that was set in the degrees that were found) then where these two points do join, is the point where the Ship is. But (as we have said in the sixth Chapter) they must have great respect to the winds and seas, 
Advertisements t● the Pilots.  and other things which experience showeth them, to know if they have gone directly by that line, or if they have fallen from it, and to what part: the which I remit to the judgement of men of good experience. From thence forward, they shall return to keep the same account, as when they departed from the haven, especially when they change their course.   

¶ The xiiii. Chapter, of the making and use of the Instrument generll, to know the hours and quantities of the day, and at what wind the Sun riseth and falleth.  
MAke a round plate with a ring or a handle above, as in the astrolabe, drawing a line from the ring downward passing through the centre, and another line that may cut it in right angles throng the centre: And this last line shall be called the Horizon. Then shall you give a circle upon the centre, leaving so much space between it and the edge of the plate, that therein may be written the numbers of the degrees: then also make another circle somewhat more within, leaving likewise a space where the graduations may be divided. This done, de●ide one of the highest quadrants toward the left hand into 90. parts, which shall be called the degrees of latitude, beginning the number of them from the ring, and ending the same in the Horizon. Then make another roundel somewhat less than this, in such manner that the degrees and numbers of the greater, remain uncovered. And divide this less, by two Diameters into four equal parts. And at the one end of the one Diameter, leave a point coming forth of the less roundel, cut directly with the same Diameter by the one part, and this shallbe called the index or shower. In this roundel you shall make a circle half, a finger less than the rundel. Then with a compass take. 23. Degrees and a half from the Diameter, which signifieth the Equinoctial: and where as end the. 23. degrees and a half, for every part make a right line from one point to another, so that this be a line of 47. Degrees, and as mu●● 〈◊〉 at ●●e other end of the said Equinoctial. Upon every one of these right lines, you shall make a ha●●e circled, and divide ●u●ry of them into six equal parts, which may answer to six● signs, and every sign into thre● parts, which may 〈◊〉 to the tenths or tenth part●●f degrees: and if the 〈◊〉 be great, you shall divide eu●ry sign into fi●● or 〈◊〉 par●es, so that you may make it perfect and precise. This 〈◊〉, from the points or pricks of the one half circle, to the points of the other, draw certain lines which shallbe equidi●●n● to the Equinoctial. In the ends of these lines, between the less circle, and the edge of the roundel, draw also certain lines, which may reach unto the beginnings and ends of the signs: and in the ●oppe of the ends, or over the ends of these lines, make an Ark, so far distant from the less circle, as is the thickness of the edge of a piece of four rials of plate: And in the space that is left, graduate the signs from ten to ten, or as the division shallbe. The space that remaineth from thence to the edge of the rundel, you shall divide by the half, 
The placing of the twelve signs in the instrument.  and in it shallbe made twelve spaces, where you shall set the signs with their names or caractes orderly, so that Aries be next unto the Equinoctial than Taurus toward the part of the Index, then Gemini: and turning toward the Equinoctial, Cancer, Leo, Uirgo. Likewise on the other part of the Equinoctial, Libra, Scorpio, Sagittarius. And turning to the Equinoctial, Capricornus, Aquarius, Pisces. 
The zodiac.  And thus having signed the Zodiac, you shall also sign or mark the hours in manner as followeth.  
Divide the less circle of this rundel into four equal parts, so that every quarter may have six parts. Reduce this division to the Diameter, putting the ruler upon the points, equally distant from the Horizon. And where it toucheth the Equinoctial, make pricks or points, 
Division of the Equinoctial and Tropikes.  so that the Equinoctial remain divided into twelve parts. Then upon one of the Tropykes give a circle, which may have the same tropic for his Diameter. Divide this circle into 24. equal partest & reduce these divisions to the tropic, as is done in the Equinoctial, & from one tropic to another: then the Equinoctial and the Tropikes being thus divided with this pricks or points, you shall pass with a pair of compasses by every point equally ordered from the Horizon, to the one and the other part: and these shallbe called hours, writing in the ends of them their numbers, beginning the one part in one, 
The hours with their numbers.  and ending it in twelve. On the other part, begin the one in thopposite part, and end in twelve. This done, these rundels shallbe brought to their perfection. Moreover, you shall make a triangle, with a right angle, having two equal sides that may make the right angle. Every of these sides must be as long as is the Semidiameter of the greatest rundel: 
The triangle.  also, upon and about the right angle, you shall make a little circle, which shall have the same angle for his centre, & on the one side of this triangle, set two raised plates, as in the astrolabe: on the contrary side of these raised plates, must be a hole, so far distant from the centre or angle, as is the Semidiameter of the circle of the less rundel. In this hole you must put a threéd, hanging thereat a little weight or plummet, only sufficient to hold the threéd strait, so that it cause nothing of the rundels to turn, or the instrument to decline. Furthermore, in a circle as big as the less of the less rundel, you shall divide into 32. parts the eight winds, 
Division of the winds.  and half winds, and quarters of winds. And being thus redused to their Diameters (as is done in the Equinoctial) you shall translate them in the sides of the triangle, in the which by the centre of his little circle, and by the centre of the rundels, all the three pieces must be made fast with an axes or a nail, so that they may be turned about close and very just. Then put a ring in the handle of the instrument, whereby it may hang, as in the astrolabe: and so shall the Instrument be finished and brought to perfection.  
This is the trace or draft of the Instrument.  
To know at what hour● the Sun riseth and falleth (by the Instrument following) you shall put the Pole of the less rundel (which is the index) to the left hand in the greatest roundel, 
To know at what hour the Sun riseth or falleth.  in so many degrees above the Horizon, in how many degrees the Pole is raised in that land or place. Then put the triangle, (which is the Horizon) in his place: that is to say, if the Sun shallbe in the North signs, put it to the left hand: and if it shallbe in the South signs, to the right hand, and then the triangle shall cut the parallel where the Sun goeth, in .10. or .20. or .30. degrees, or proportionally where it is, and there shall you see in the sides of the Zodiac, the hours when the Sun riseth and falleth. And likewise at what wind the Sun ryseéth and falleth to us, you shall see in the winds of the triangle.  

At what wind the Sun riseth or falleth.  To know by the elevation of the Sun, the hour that is, put the Pole or Index so far distant from the Zenith or handle of the Instrument, as it is in that place or parallel above the Horizon, then turn the triangle toward the Sun, until the beams thereof enter in at the raised plates, and then the threéd with the plomet, shall cut the parallel of the Sun, by the hour that shallbe: and consequently the triangle shallbe distant from the Zenith the degrees that the Sun shall be raised that hour about the Horizon.  
This is the Demonstration.   
FINIS.   

¶ Hear beginneth the Table of this Book.  


The contents of the Chapters of the first part.  THe general distinction of Creatures. 
Folio. iiii.  The definition of the World. 
Fol. v.  The definition of the Sphere. 
Fol. eodem.  The division of the World. 
Fol. eodem.  The number, order, and property of the Elements and Heavens. 
Fol. vi.  The immutability or immobility of the Earth. 
Fol. viii.  The roundness of the Earth and Water. 
Fol. viii.  The motion of the Heavens and Elements. 
Fol. x.  The division of the Sphere into formal parts. 
Fol. eod.  The Equinoctial circle. 
Fol. xii.  The Zodiac. 
Fol. eodem.  The circle called Coluri. 
Fol. xiii.  The Meridian circle. 
Fol. xiiii.  The horizontal circle. 
Fol. eod.  The four less circles. 
Fol. xv.  The five Zones. 
Fol. xvi.  The Longitude and La●itude. And of the proportion which the less circles have to the great circle. 
Fol. xviii.  The circuit or compass of the earth and water, according to the opinions of the ancient & later auctors. 
Fol. nineteen.  The seven. Climates. 
Fol. eod.  Certain principles of this science. 
Fol. xxi.    


The Contents of the second part.  THe course of the Sun in the Zodiac. 
Fol. xxii.  The true place of the Sun in the Zodiac. 
Fol. xxiii.  The declination of the Sun. 
Fol. xxv.  The entrance of the Sun in the xii. signs, and of the Equinoctials and Solstitials which divide the four times of the year. 
Fol. xxvii.  Of the Moon, and her motions and properties. 
Fol. xxix.  The conjunctions and oppositions of the Sun and the Moon. 
Fol. thirty.  The declaration and use of an instrument, by the which is found the place and declination of the Sun, with the days and place of the Moon. 
Fol. xxxi.  The Eclipses of the Moon and the Sun. 
Fol. xxxiii.  Of time, and the definition thereof. 
Fol. xxxv.  Of the year, and the divers beginnings and reckonings or computations had thereof in old tyme. 
Fol. xxxvi.  Of the month, and of his differences. 
Fol. xxxvii.  Of the week. 
Fol. xxxix.  Of the day and night. 
Fol. eod.  Of hours. 
Fol. xl.  The making & use of an universal dial for the day. 
Fol. xli.  Of certain particular Dial's, Mural & Horizontal. 
Fol. xliii.  The composition and use of an instrument for the hours of the night. 
Fol. xlv.  The time of the tides, or rising & falling of the sea. 
Fol. xlviii  Of certain signs which prognosticate tempests, or fair weather. 
Fol. l.  Of the bright & shining exhalations that appear in tempests which the Mariners call Santelmo, or Corpus sancti. 
Fol. li.    


The Contents of the third part.  THe number, order, and names of the winds. 
Fol. liv.  The composition of Cards for the Sea. 
Fol. lvi.  The virtue and property of the loadstone, called in Latin, Magnes, and in Spanish, Piedrayman. 
Fol. lxii.  The making of the Mariners compass for Naviga. 
Fol. lxiii.  The effect and property that the compass hath to north-easting or Northwesting, whereby is known the variation of the compass. 
Fol. lxiiii.  The introduction & principles of the art of Naviga. 
Fol. lxvii  The making and use of the astrolabe, with the which the Mariner's take the altitudes of the Sun. 
Fol. lxviii.  The definition of the altitudes, an● how the altitudes of the Pole may well be known by the Meridian altitude and declination of the Sun. 
Fol. lxxi.  The making of the cross staff, wherewith the Mariners take the altitude of the North star. 
Fol. lxxii.  How the altitude of the Pole is known by the altitude of the North star. 
Fol. lxxiii.  The composition & use of an Instrument, by the which without observing the South Sun or midday, is known the altitude of the Pole, and the hour that is. 
Fol. lxxv.  Of the leagues that are run for a degree, according unto divers courses. 
Fol. lxxviii.  How to set or make a prick in the card of Navigation. 
Fol. lxxx.  Of the making and use of an Instrument general, to know the hours and quantities of the day, and what wind the Sun riseth and falleth. 
Fol. eod.    
FINIS.   

Imprinted at London by Abel jeffes for Richard Watkins, and are to be sold at his shop.  
Cum Privilegio.