The Castle of Knowledge.   Allegorical illustration of the Castle of Knowledge, the trophy that only knowledge can attain. On its turrets are learned men with a quadrant and an astrolabe. On the left stands the figure of Destiny, holding a geometric compass and the 'sphere of Destiny' (an armillary sphere); she faces the blindfolded figure of Fortune, who holds the wheel of fortune aloft. 
Sphaera Fati  
The Sphere of Destinye. whose governor is Knowledge.  
Sphaera Fortunae.  
The wheel of Fortune. whose ruler is ignorance.  

To knowledge is this Trophy set,  
All learninges friends will it support.  
So shall their name great honour get,  
And gain great same with good report.   

Though spiteful Fortune turned her wheel  
To stay the Sphere of Vranye,  
Yet doth this Sphere resist that wheel,  
And fleeyth all fortunes villanye.  
Though earth do honour Fortunes ball,  
And bytells blind hyr wheel advance,  
The heauens to fortune are not thralle,  
These Spheres surmount al fortunes chance.     

The contents in brief of the 4 Treatises of THE CASTLE OF KNOWLEDGE CONTAINING THE EXPLICATION OF THE SPHERE both celestial and material, and diuers other things incident thereto. With sundry pleasant proofs and certain new demonstrations not written before in any vulgar works.  
The first treatise is an introduction into the Sphere, declaring the necessary partes of it, as well for the material Sphere, as for the celestial: And that no partes of it are admitted without profitable use.  
The second treatise doth teach the making of the sphere, as well in sound and massy form, as also in ring form, with hoops: And the proportions of each of them justly described.  
The thyrde treatise doth briefly declare certain things appertaining to the use of the Sphere, and other matters thereunto incidente: without proof or demonstration: and that briefly, for easiness in learning and remembering.  
The fourthe treatise doth approve many things, that were noted in other partes before: and beside then addeth diuers other matters, concerning the necessary use of the sphere, which were not touched before, and doth bring demonstration or other certain proof for the perswadinge of them: wherein are many Tables set forth very pleasant and profitable.  

If ought here want, that you desire,  
remember where this work was wrought:  
In Plutos forge with scarce good fire,  
This rustye Sphere to end was brought.  
But if I may it file agene,  
The rust I trust to scour of clene.    

TO THE most mighty AND MOST PVISSANT princess MARYE, BY the grace of God queen of England, Spain, both Siciles, france, jerusalem, and ireland: defemder of the faith: Archeduchesse of Austria: duchess of Millayne, burgundy, and Brabaunt countess of Habspurge, flanders, and Tyroll. &c.  
AS LOVE OF learning AND zeal unto knowledge( most dread sovereign lady) did provoke me to attempt an enterprise far above mine habilitie, that is, to build a Castle for Knowledge to rest in, after hir long banishment& tedious exile. although I could not be permitted by disturbance of cruel Fortune, to accomplish now my building as I had drawn the perfit: yet in despite of Fortune, thus much haue I done. which is more then ever was done in this tongue before, as far as I can hear. But considering by misfortune this fort lacketh fence, and needeth some good governor to supply that that wanteth, that Knowledge may rest under safe protection, I thought it my duty to make most humble suit unto your excellent majesty, that it might please your highnes to accept this poor Castle into your gracious tuition: that not only in time of your majesties reign, but by your highnes special defence, Knowledge might bee maintained and revoked from exile. unto which suit I am the more boldened, through remembrance howe god in despite of cancred malice and of frowninge Fortune, did exaulte your majesty to that throne royal, which of iustice did belong unto your highnes, although the musers of mischief wrought much to the contrary. In which matter as Knowledge did detect the malice of other, and taught your true subiectes their duty to their sovereign, so Knowledge yet diuers ways shall further your majesty. And therefore am I encouraged to sue to your royal excellency, not only for to take into your highnes protection this Castle of knowledge, but all Knowledges friends, which in hir maintenance do keep continual war against pestilent ignorance, the subuerter of realms: which knoweth no virtue, honesty, nor duty, and therefore meaneth no truth, how so ever she flatter. yet doth she often times show great countenance of friendship, when she meaneth nothing less. Here could I paint forth ignorance in hir right colours, but unto your majesty it is needless, whom God not only hath endued with excellent knowledge, but also hath aided with such prudent Councellars, that it may seem arrogancy in any such as I am, to make explication, or in manner more then only insinuation of any doubtful matters. It may therefore please your majesty, for love unto Knowledge, and favour to your highnes subiectes, to accept this simplo Castle into your graces defence, and so shall I bee animated to fynishe the rest, and to publish it under your majesties name. whom God of his mercy increase in all honour royal, and true felicity, and continue prosperouslye and long amongst vs. Amen.  
Your majesties most humble subject, Roberte record physician.   

INCLITISSIMO CARDINALI POLO, CANTVARIENSI ARCHIEPISCOPO &c. Reueren dissimo Archiepiscopo Eboracensi, Nicolao, summo Angliae Cancellario. ac vniuerso sacrae Regiae Maiestatis Consiliariorum Praeclarissimorum Senatui, dominis maximè suspiciendis.  
APOLLOPHANES clarus ille sophista, qui in Heliopoli Aegypti civitate vna cum Dionysio Areopagita eo ipso tempore fortè degebat, quo Seruator hominum Christus crucis mortem sustinuit, quum admirandam illam eclipsim conspexisset, respondisse dicitur: {αβγδ}. Dionysius vero altius quodammodo adspirans, {αβγδ}( inquit) {αβγδ}. Adeo certa quidem ratio est coelestium motuum, vt si quid praeter consuetum in coelo eluceat, novi cuiusdam ac insoliti eventus indicium certissimum esse conuincatur. add quod qua est benignitate Deus optimus maximusque, non vult homines inaduertentes opprimi, nisi eorum supina admodum inertia, aut contumax planè malitia divinas eas admonitiones vecordius aspernetur. Erunt( inquit Christus) signa in Sole& Luna. divinae quidem in nos philanthropiae certissima testimonia, ac nostrae, si neglexerimus, vesaniae argumenta irrefragabilia. Si ingrati igitur in deum dici horreamus, praesertim in nostra ipsorum causa: imò si in ipsos nos iniurij esse, quod vitium naturae aduersissimum censetur, nolimus, coelum assidue contemplemur, divinam in eo potentiam suspiciamus, prouidentiam admirantes amplectamur, sapientiam adoremus& exosculemur. siquidem dicente Propheta, {αβγδ}. atqui ne quis ad formam coeli,& motus tantum referat, {αβγδ}( inquit) {αβγδ}. Serenitatem itaque vestram rogo, ac per pietatem obtestor, per celsitudinis apices, honorumque titulos, quos diuina fauente clementia adepti estis, obsecro: vt quod alij multi ex summa prudentia in vobis probant, id vos vicissim in aliis exoptetis. adque ea studia alios, ingenua precipuè indole praeditos, à vanis ludicrisque exercitijs, ne dicam improbis planeque impijs, reuocetis. Penes celsitudinem excellentiasque vestras est, subditorum studia moderari, exercitia praescribere, impetus effrenatos coercere. Vos oculi, aures, adeoque mens ipsa Regiae Maiestatis estis. Vos regni sydera post solem ac lunam ipsam splendidissima collucetis. Vos omnes probi tanquam patriae parentes, imò terrestres deos cernui adorant: vestris vestigijs aduoluuntur: opem vestram nisi assiduè senserint, actum planè de se jure optimo putant. At haec studia fortassis quibusdam malè feriatis ingenijs parum reipublicae commoda, eoque vestro favore aut subsidio indigna videri possunt. Aliter long existimauit Atlas rex, qui ind sibsaeternitatis nomen meruit, coelumque humeris sustinere praedicatur, quod Astronomiae studiosissimus, sydera obseruarit sedulò. Hunc Eusebius Enoch esse arbitratur. Hic inter Titanos praecipuus erat. quos si rectè intucamur, veneratione, nedum admiratione dignos censebimus: quod industria maxima altissimos montes scandentes, ibique in defessi pernoctantes, sydera obseruando, munia cuiusque vera animad uerterint, primique ostenderint ea unius summi Dei imperio parere, nec deos esse: vanamque g●… ilium deorum opinionem arguerint. eoque Iouem coelo deturbare conatos eos poëtae asserunt. quo nomine quamtum illis debeat syncerior religio, pij omnes agnoscunt. Liceret hic, ni longioris commemorationis tedium vitarem, refer Orionem, Hyperionē, Endymionem lunae amasium, Ganymedem, Adonim, Aeolum, Phaëtontem,& Ptolemaeos, omnes principes viros,& astronomiae studiosos, vt qui obseruationibus inuigilarint, motusque fyderum notarint. Alfonsi vero regis praeclarissimi non unquam intermorituram famam, ex hac arte multo celebriorem redditam, omnes norunt. Quin cesso artem omni laud maiorem amatoribus eius summis enixius obtrudere? Haec est illa maxima secundum Theologiam scientia, solo silentio praedicanda. Vestrae itaque celsitudini tam eam quam alumnos eius omnes, precipuè vero Recordum, supplex commendo. Deus vobis omnia secunda donet, ex animi sententia.  
Celsitudini excellentiaeque vestrae deditissimus Robertus Recordus Medicus.   

THE PREFACE TO THE READER.  

If reasons reach transcende the sky,  
Why should it then to earth be bound?  
The wit is wronged and leadde awry,  
If mind be married to the ground.   
THEREFORE,  
WHEN SCIPIO beheld OVTE of the high heauens the smallenes of the earth with the kingdoms in it, he could no less but esteem the travail of men most vain, which sustain so much grief with infinite dangers to get so small a corner of that little ball. so that it yrked him( as he then declared) to considre the smallness of that their kingdom, which men so much did magnify. Who soever therefore( by Scipions good admonishment) doth mind to avoid the name of vanity, and wish to attain the name of a man, let him contemn those trifelinge triumphs, and little esteem that little lump of clay: but rather look upward to the heauens, as nature hath taught him, and not like a beast go poringe on the ground, and like a scathen swine run rootinge in the earth. Yea let him think( as Plato with diuers other philosophers did truly affirm) that for this intent were eyes given unto men, that they might with them behold the heauens: which is the theatre of Goddes mighty power, and the chief spectakle of al his divine works. There are those visible creatures of God, by which many wise philosophers attained to the knowledge of his invisible power. There are those strange constellations, by which Job doth prove the mighty majesty and omnipotency of God. There are those pure creatures, which wax not weary with labour, neither grow old by continuance, but are as fresh now in beutye and shape, as the first day of their creation. and as apt now to perform their course, as they were the first hour that they began. And though time wholly depend of it, yet time can not utter any force in it▪ yea though all other things in the world by time be consumed, and even the most hard metals freted into dross, yet the liquid heauens not only govern time itself, but utterly stand clear from all corruption of time. Oh worthy temple of Goddes magnificence: Oh throne of glory and seat of the lord: thy substance most pure what tongue can describe? thy beauty with stars so garnished and glytteringe: thy motions so marvelous, thine influence strange, thy tokens so terrible, to stonishe mennes hartes. thy signs are so wondrous, surmountinge mannes wit, the effects of thy motions so diuers in kind: so hard for to search, and worse for to finde. Thy greatness so huge, thy compass so large, thy rollyng so swift, and yet seemeth slow: thy stay so unknown, thy place without name: thy spheres are more wondres, and so is thy frame. Thy lights are so liking to comfort mennes minds, no beast is so brutish, but that he still fyndes, thy warmenes to work him great solace and ease: thy colour to comfort his sight and his brain. Thy stars in such order, thy circles so fine: thy perfit form is painted with many a sign. Oh marvelous maker, oh God of good governance: thy works are all wondrous, thy cunning unknown: yet seeds of all knowledge in that book are sown. The signs of the times who can them comprise? the tokens of troubles what man could devise? And yet in that book who rightly can read, to all secret knowledge it will him straight lead. The star in the east did govern the Wisemen, and taught them the very region where christ should be born. And farther by it they understood, that he was the true king of Jews, and saviour of jsrael. And though many saw the star as well as they, yet few or none knew the signification but they yet did God at the beginning ordain the stars to be as signs and tokens of times alteration: and namely of such strange effects as seldom come in ure, and therefore are known but to few men. These works the more strange they be, the more ought men to esteem the fruit of them: to magnify the knowledge of them, and to study to understand the mean to attain them, but most of all to honour, praise and glorify the author of them. who willeth nothing to happen so suddenly on the most wicked, but by some signs and tokens he giveth warning of them. of which thing who so ever standeth in doubt, let him peruse the state of times, and he shall see wonderouse things. Before the flood of Noe although God did by special revelation utter his mind to his servant Noe, yet did he also by wonderful signs and strange conjunctions, express the same to the whole world. for all the planets were in coniunction in waterye signs. so that no nation might excuse themselves, for that they were so far distant from Noe, that they could not hear his preaching. sith all nations might see the heauens and the tokens in it, although but few in every nation could skill of them. And though Noe could not in person go into all partes of the world, yet was that office supplied by the heauens, of whose revolutions it is written by david the prophet: They haue no speech nor language, so that their voice can not bee heard. yet did their course extend into all the earth, and their words into the extreme bounds of the world. So was there never any great change in the world, neither translations of Imperies, neither scarce any fall of famous princes, no dearthe and penurye, no death and mortality, but GOD by the signs of heaven did premonishe men therof, to repent and beware betime, if they had any grace. The examples ar infinite, and all histories so full of them, that J think it needless to make any rehearsal of them now: especially seeing they appertain to the judicial part of Astronomy, rather then to this parte of the motions, yet shall it not bee prejudicial any ways, to repeat an example or two. As namely before the building of Rome, there was a very notable eclipse of the son, declaring that the liberty of the world began then to decay, when Rome began to rise: which should subdue all the world near hand: as in effect afterward it did succeed, increasinge still by little and little, and continuing for a long time, till the goths in the time of Arcadius and Honorius, did spoil that city, and subdue their power. At which time also strange signs did appear in the air, and in the sky: which seemed not only to signify the devastation of the Imperye of Rome, but also the subduing of all the west provinces, by strange invasion of barbarous nations. Many other strange eclipses both of son and moon, beside the appearing of sundry sons, and strange shapes of the moon, and the stars diuerselye disordered, with Rainbowes of marvelous forms, comets of diuers kindes, and other wonderful signs, which ever were messengers of as wonderful effects, of new innovations, strange transmutations, and sometime utter subuersions, not only of small provinces, but also of great kingdoms, yea and of many regions at ones. And therefore saith M. Manilius.  Nunquam futilibus excanduit ignibus aether. 
The earth doth ever feel grief and thirteen,  
When those strange sights in heaven be seen.  
But who that can skill of their natures, and conjecture rightly the effect of them and their menacynges, shall be able not only to avoid many inconveniences, but also to achieve many vnlikelye attempts: and in conclusion be a governor and rulare of the stars according to that vulgar sentence gathered of Ptolemye:  Sapiens dominabitur astris. 
The wise by prudence, and good skill,  
may rule the stars to serve his will.  
J mind not to discourse in declaring the profit and commodity of astronomy, but only to admonish briefly the reader, that he may think the study worthy his travail, and to know it to be the most necessary study that can be, for any man that desireth perfection of wisdom. What benefit doth come by it to the true knowledge of husbandry and navigation, J am assured the very simplest in those artes do partly perceive: and the cunningest in the same do so fully understand, that they judge themselves naked and bare without it, and utterly destitute of all excellency in their arte. in physic the use of it is so large in judging duly of complexions, in prescribinge right order of diet and conversation, in governance of health, for just ministration of medicines in time of sickness, and in right iudgement of the critical daies, that without it physic is to be accounted utterly imperfecte. For proof whereof although there be infinite places in Hippocrates and Galene, and diuers other good writers, yet he that hath read in Hippocrates but that one book of air, water, and Regions, and Galen his third book of critical daies, can not be ignorant howe necessary an instrument Astronomy is unto physic, as both those books do testify at large. But omitting the testimonies of famous writers( which would make a wonderful volume of themselves, if they were written only together) J will use a simplo plain proof manifest to all men, and therefore most apt for to persuade all men. first to begin with sowinge of grain, with graffynge and plantinge, who is so rude, but knoweth that without these be dulye done, and in their seasonable time, men can not conveniently live on the earth? And bow are their times known, but by the rising and setting of certain notable stars? peradventure some man will answer, that by the months of the year all men do know their times without farther Astronomy which answer is such, as if a carpenter or mason should say, that he can work with his compass, rular, squire, plumb rule, and such like instruments, without any knowledge in geometry. but how ridiculous an answer this were, all men can judge. Likewaies, if a master of a ship would say, that he can sail and govern his course by his compass and his card, with his quadrant and his other instruments, without any knowledge in cosmography or astronomy, would not all men that hear him, deryde him, or think him mad, for speaking so vndiscreatly, especially such as know( as few ar ignorant therein) that all those instruments are made by those artes, and appertain to them? So if the distinction of times do depend of Astronomy all together, and the months would soon run out of their courses, if the aid that it hath by that arte were neglected, so that michaelmas day would happen in the Spring time, and the An nunciation of our lady would fall after harvest( as the truth is, it would do, if astronomical account were not) who can show himself so mad as to deny the necessary use of astronomy, in due keeping the times of the yeares? The ecclesiastical history doth declare at large, and other writers in great number do testify, that great controversy hath been in the church, for the right observation of Easter, which controversy could never be decided but by the knowledge of astronomy. And of late yeares in diuers councils redress hath been sought for the just observation of it: considering that if error be in it, all other movable feasts, are wrongly kept by that occasion, and lent displaced so, that some time it hath been kept sooner then it ought, and at other times later then it ought. which fault can never bee redressed but by astronomy. Whereby it appeareth also manifestly, that in ecclesiastical matters Astronomy hath a great use. but that is so well known, that every man almost doth confess it. And generally who so ever doth take benefit by the dew distinction of the year, he can not choose but aclowledge that the same commodity doth come by Astronomy. if J should specially and perticularlye discourse in every kind of science and artes, and show how they are aided by astronomy, J should make my preface over long, and repeat things that all men doth know. in lawe for contracts and bargains the time is most necessary to be observed: but especially if they depend of movable feasts, wherein astronomy must discuss the doubt. in Grammar, logic and rhetoric howe needful it is, and in histories also, J need say nothing, but remit all men to the reading of those books, which are used in those artes, whereby it shall appear, that without the principles of astronomy those books can not bee understand. Then for vulgar artes how the knowledge of ebbs and studs doth profit, many men, but specially mariners can testify: and namely such as understand, what error cometh by the difference of the true account therein and the vulgar account. again for loppinge of trees and wood fall, and diuers other observations in husbandry, the consideration of the son and commonly of the moon doth greatly help. wherefore J may conclude, that in all artes and sciences, in lawe, physic and divinity, in mariners arte and husbandry, the profit of astronomy is exceeding necessary. But above all other things the testimony of christ in the scripture doth most approve it, when he doth declare that signs of his coming, and of other strange effects shall be seen in the son, moon and stars. Also for alteration of wether he testified that many did mark the face of heaven, and pronounced truly of the wether, and therefore blameth them that they could not mark and judge the signs of the coming of the son of man. But here possiblye some men will object the asking of the prophet: fear not the signs of heauen-wherevnto J may duly answer: that those words of Hieremye do forbid honouring of them as goddes, as the text is plain. for oftentimes in the scriptures fear of God is taken for honour of God, and so is it here, else other ways might J answer that the true servants of God which haue reposed the love and fear of God in their heartes, are never afeard of any tokens that God sendeth, but rejoice to see them, and glorify God for them. But because in this case there be many divines that can better de clear those things then J, which am a man of an other profession, J will remit that matter to them. only admonishing all men, that the son, the moon and the stars, were ordained of God to serve all nations that be under the heauens, as Moses doth testify. Then seeing God hath made them for mannes commodity, and to be distincters of times, and for signs and tokens, for aid of mennes knowledge, let not men be unkind to God again, but lift up their eyes to heaven and behold the good gifts of God: Note diligently their marvelous motions, and studiouslye considre their wonderful alterations, with perpetual constancye and inviolable order: so shall men never bee doubtful of Goddes providence toward them, of his daily provision for them, when they see that he hath made such an vnexplicable frame to serve only for mannes use, for whose sake all other creatures also were made. in token therfore of thankfulness, let us sing an hymn unto that God, praisinge his name, and magnifiynge him forever and ever.  

The world is wrought right wonderouslye,  
whose partes exceed mennes fantasies:  
His maker yet most meruailouslye  
Surmounteth more all mennes devise.   

No eye hath seen, no ear hath heard  
The least sparks of his majesty:  
All thoughts of heartes are fully barde  
To comprehend his Deitye.   

Oh lord who may thy power know?  
What mind can reach the to behold?  
in heaven above, in earth below.  
His presence is, for so he would.   

His goodness great, so is his power,  
His wisdom equal with them both:  
No want of will sith every hour  
His grace to show he is not loath.   

behold his power in the sky,  
His wisdom echewhere doth appear:  
His goodness doth grace multiply,  
in heaven, in earth, both far and near.   
FINIS.   

AN ADMONITION FOR THE orderly trade of study in the Authors works, appertainyng to the mathematicalles.  

The ground is thought that steady stay,  
Where no foot faileth that well was pight:  
Whereon who walketh by certain way,  
His pace is like to prosper right.   


1.  The ground of Artes who hath well tredd,  
And noted well the slyppery slabbes,  
That may him force to slide or fall,  
He hath a staff to stay withall.   


2.  Then if he trade that pathway pure  
That unto Knowledge leadeth sure:  
He may be bold tapproche The Gate  

3.  Of Knowledge and pass in thereat.   

Where if with Measure he do well treat:  

4.  To Knowledges Castle he may soon get.  
There if he travail and quainte him well.  

5.  The Treasure of Knowledge is his each deal.   


5.  This Treasure though that some would haue,  

3.  which Measures friendship do not crave,  

2.  Nor walk the Patthe that leadeth the way.  

1.  Nor in Artes ground haue made their stay,  
though brag they may, and get false famed,  

4.  In Knowledges court they never came.    

certain faults omitted out of the corrections.  
10.29, proof of my words. And in the mean season to proccede as I began: you must. 212.1, differeth not. In this table the first. 279.17. deferentes. 280.28, within the shadow. 281.15, in every common almanach. 283.21, alway runneth. 284.10. And the rather.   

 Woodcut illustrating two astronomers at work outdoors, with an armillary sphere and an astrolabe.   

THE first TREATISE OF THE CASTLE OF KNOWLEDGE. which is an induction to the necessary partes of the Sphere, as well celestial as material.  SCHOLAR. 

The desire of knowledge.  THE TIME seemeth long( bee it never so short in dead) to him that desirously looketh for any thing: for as the obtaining of it bringeth great pleasure, namely the thing itself being profitable, so the want therof causeth displeasure and continual grief till the desire be either fully satisfied, other partly( at the least) accomplished.  master. 
And sometimes we see, that when the desire is partly performed, and the pleasantness of the same ones tasted of, the desire thereby nothing assuageth, but contrary ways greatly increaseth: and the more it getteth, the more it desireth. so that in this point may knowledge well be compared to covetousness: for as the covetous mind with getting is never satisfied, so knowledge by knowing doth covet still more: And as it increaseth, so doth it still learn the vileness of Ignorance, and profit of Sciences, and therfore can not rest from searching more knowledge, as long as it spyeth any spot of ignorance.  scholar. 
This oftentimes as I haue considered, maketh me to muse what mind is in them, which care for no knowledge, nor esteem any science. 
The grosenes of ignorance.   master. 
This is the greatest point of all ignorance, not to know the grossness of ignorance, and not to understand the benefit of knowledge, and with this fault are a great number spotted. The next is their fault, which perceive sufficiently what vileness is in ignorance, and what profit in knowledge, and yet of a certain negligence partelye, and partly for other pleasures, they omit to travail any whit for knowledge, and content themselves with wilful ignorance: but as these men do trouble the good state of the world, so the talk of them will hinder the talk of the worlds knowledge, which is the thing that you so much long after: and therefore beste it is, that wee let them lie still tomblinge in the ditch of ignorance, and that wee travail forward toward the Castle of knowledge. But first let me hear what is your chief desire.  scholar. 

The occasion of this book.  sith my last talk with you about the knowledge of the world and the partes of it, I haue readd dyvers books that entreat of that matter, as namely Proclus sphere, joannes de Sacro bosco, Orontius cosmography, and diuers other, whose words in many things I remember, but of the matter I haue sundry doubts, and therefore desire much your help therein. For although I haue consulted with diuers men therein, yet me thinketh they tell me but the same words in like sort as I read them before, or little other ways altered, but light of understanding, I haue gotten little yet.  Master. 
Then prove again, peradventure your chance may be better: that which at the first seemeth hard, may at length become easy: for use maketh masterye, all men confess. And, The best things are not most easiest to attain. begin in that order as your Authors do.  Scholar. 

The diversity of writers.  their ordres bee as dyvers as their names be, so that I know not whose order is best. For Proclus in treatinge of the Sphere, defineth first the Axe three of the world, before he had shewed other what the world is, or what he calleth a Sphere, or what need the world hath of any Axe three. Therfore I turned to joannes de Sacro bosco our country man, which beginneth first with the definition of a sphere, but nothing like to that sphere, which I before had bought, as an apt instrument to learn by. Then see I Orontius disagree from them both: and generally, eueryeone from other, so that I know not where to begin.  Master. 
As touching those writers, I will say no more now, but although eueryeone of them haue some things that exactly scanned may be misliked, yet he that hath done worst, is worthy of thankes, for his studious pains in furtheringe of knowledge. And seeing you doubt of their order, let the thing itself minister order. What is it that you desire to know?  Scholar. 
I see in the heaven marvelous motions, and in the rest of the world strange transmutations, and therfore desire much to know what the world is, 
The argument of this book.  and what are the principal partes of it, and also how all these strange sights do come.  master. 
Then is the world the thing that you would know first, sith all these other things are incident to it. What do your authors call the world?  Scholar. 

what the world is.  Orontius defineth the world to be the perfect and entire composition of all things: a divine work, infinite and wonderful, adorned with all kindes and forms of bodies, that nature could make.  Master. 
This definition doth much agree with those that bee written by ancient authors, and namely Aristotle which defineth it thus.  {αβγδ}. Mundus est compages ex coelo& terra,& reliquis in ijsdem contentis naturis. 
The world is an apt frame of heaven and earth, and all other natural things contained in them. The like words hath Cleomedes and others. So that the world is that entire body, which containeth all things that ever God made, and man can see, nothing excepted but God himself only, which is not comprehensible by any worldly means. This work is so pure and wonderful in beauty, that it beareth the name of cleanness, 
whereof the world is name.  both in greek and latin, that is 〈◇〉 in greek, and Mundus in latin. and thereto alludeth Sibyll in her verses, speaking of the dissolution of the world, saying: {αβγδ}. Erit mundus immundus, pereuntibus hominibus. The world( saith she) shal be vnclean, or lose his beauty, when all men shal perish.  scholar. 
And so doth that sentence lose his beauty by the translation, for there can bee no such allusion of words in the english of that sentence, as there is in the other tongues.  Master. 
You say truth, except a man would rather allude at the words, then express the sentence, for so might it be translated thus: It shall bee an vnworldlye world, when all men shall perish: But here the sense is lost: for this name world, 
Diuers significations of that word world.  hath not the like derivation of cleanness in english, as the latin and greek names haue in their tongues: neither can I well tell whereof this english name is derived, although I remember some other significations of this word, as first it is used in Scripture for a name of long continuance of time, when we say: world without end. and, through world of worlds: which signifieth for ever. Also this name doth signify sometimes a great wonder, as when wee say: It is a world to see the craft that some men use under colour of simplicitye. now if any man will contend, that this word world doth principally betoken a wonder, and that the world for the wonderful shape of it, took that name, as the chief wonder of all wonders, I will not greatly repined, but then must I needs wonder, to see the chief worldly men to wonder so little at this wonderful wonder, and to bend all their study to the centre of the world, I mean the earth, which in comparison to the whole world is not only a parte without all notable quantity, but also least adorned with marvelous works, and most subject to all frail transmutation and change, still replenished with continual corruption. And yet on it only doth the greatest number set all their study. For it they sustain great travail and toil: for yt they chide, quarrel and fight: to get it they venture life and limb, and when they think most assuredlye that they haue gotten the earth, then in deed the earth hath gotten them, and most commonly then doth the earth consume them, when they think themselves full maisters of yt.  scholar. 
By these mennes travail( I think) it came to pass, that the earth doth usurp the name of the world, as though it were all, and that besides it were nothing.  Master. 
Thereof cometh that common proverb of a covetous man: All the world is to little for him. where he in deed seeketh nothing but the earth, 
The smalenes of the earth to the whole world.  which earth in comparison to the whole world beareth no greater view, then a mustard corn on Malborne hills, or a drop of water in the ocean sea. for of all the partes of the world, the earth is the least, and that without comparison, as hereafter I shall not only tell you, but also prove it by invincible reason. And therefore to proceed in our matter, I think it beste not only to make discourse lyghtlye of the principal partes of the world, but to do it in such a brief sort, as the mind may conceive it soonest, 
The best order in teaching.  and the memory also retain it longest: and therefore will I omit all proofs, till we haue ones generally drawn the image of the whole world, so shall not your memory be troubled with sundry things at ones, as in learning a science which seemeth sumthing strange, and in conceauyng the reasons of it, which in declaring, seem much more strange.  Scholar. 
In dead I haue felt the discommodity of such hasty desires: for where I haue sought reason, before I understood, whereto that reason tended, I haue troubled my mind, and hindered my knowledge. wherefore it may please you in your order to procede.  Master. 
I haue all ready said, that of all the partes of the world the earth is the least: 
The order of the elements.  whereby you may conceive, that within it is nothing: for so should that( what so ever it were) be lesser then the earth. but without the earth, doth the Waterlye, which covereth a great parte of the same: about them both, doth the air run, and occupieth( as we may easily consider) much more room, then both the sea and the land: above the air, and round about it,( after the agreement of most wise men) doth the fire occupy his place. And these four, that is, earth, water air and fire, are name the four elements, that is to say, the first, simple and original matters, whereof all mixed and compound bodies be made, 
All things compound ar made of the four elements.  and into which all shall turn again.  Scholar. 
Oftentimes haue I heard it, that both man and beasts are made of earth, and into earth shall return again: but I thought not that they had been made of water, and much less of air or fire.  Master. 
Of earth only, nothing is made but earth: for an herb or three can not grow( as all men confess) except it be helped and nourished with air convenient, and due wateringe, and also haue the heat of the Son, and generally, sith all thing is maintained by his like, and is destroyed by his contrary, than if man can not be maintained without fire, air and water, it must needs appear, that he is made of them, as well as of earth, and so likewaies all other things that be compound.  Scholar. 
This talk delighteth me marvelously, so that I can not bee weary of it, as long as it shall please you to continue it.  master. 
This talk is not for this place, partly for that it is more physical then astronomical: and partly because I determined in this first parte, to omit the causes and reasons of all things, and briefly to declare the partes of the world, whereof these four elements, being vncompounde of themself, that is simplo and unmixed, are accounted as one parte of the world, 
The elementes are simplo. The elementes do alter daily in their parts The sky. The order of the spheres. The seven planets.  which therfore is called the elementary parte, and because those elements do daily in crease and decrease in some partes of them( though not in all partes at ones) and are subject to continual corruption, they are distinct from the rest of the world, which hath no such alteration nor corruption, which parte is above all the four elements, and compasseth them about, and is called the sky, or Welkin,& also the Heauens: this part hath in it diuers lesser or special parts, name commonly Spheres: as the sphere of the moon which is lowest, and next unto the elements: then above it, the sphere of Mercury: and next to it the sphere of Venus: then followeth the son, with his sphere: and then Mars in his order: above him, is jupiter: and above him, is Saturne. These seven, are name the seven planets, every one having his sphere by himself severally, and his motion also several, and unlike in time to any other. But above these seven planets, is there an other heaven or sky, which commonly is name the Firmament, and hath in it an infinite number of stars, whereof it is called the Starrye sky. and because it is the eight in order of the heauens or spheres, it is name also the Eight sphere. This heaven is manifest enough to all mennes eyes, so that no man needeth to doubt of it, for it is that sky, wherein are all those stars that we see, except the five lesser planets, which I did name before, that is Saturnus, jupiter, Mars, Venus and mercury.  scholar. 
The son and moon also must bee except out of that number, for they haue their spheres by themselves, as well as the other planets.  Master. 
truth it is. but because no man doth account them as stars, therefore they need none exception, where mention is made of stars only, where as the other five smaller Planets( which I name before) ar so like to other stars, that no man, but such as are of good experience in Astronomy, can discern them from the other stars, 
Howe the Planets are known from other stars.  although many men do make a difference of them by twinkelinge, affirming that the Fixed stars do twinkle, and not the planets, with other differences difficult to observe, and scarce certain in distinction. But this is their most certain difference, that all those stars, which be in the firmament, do stand and continue in one form of distance each from other, and change not their places in their spear, and therefore be they called Fixed stars: for although they go round about the world in 24. houres, that is every day ones, yet they keep their places in their sphere, and turn only with their sphere: or( as Aratus saith) they be drawn with their heaven, where as the seven planets are not only carried round about the earth with the like motion of heaven every day, but they do move of themselves, and do change their places in their own spheres, and for that cause are they called planets, that is to say, Wanderynge stars.  Scholar. 
Oftentimes haue I heard this, but yet can I not tell howe to perceive it.  master. 
That shall be referred to the fourth treatise, where I will show you the proof of all that you shall think doubtful.  Scholar. 
Yet I beseech you let me know this, why are those heauens called Spheres? for( in my phantasye) they are nothing like that instrument of sundry cirkles, which is commonly called the Sphere, sith neither can I se in them such cyrkles as are in that material sphere: neither is there in the material sphere any such representation of such dyvers heauens, neither of such variety of stars.  master. 
This doubt was moved before now, by joachim Ringelbergh, in a treatise that he wrote of the Sphere, but it shall be answered easily by yourself, after a little declaration of the celestial spheres. And for that cause, I will omit it till anon, and will first declare certain other accidents of the heauens, and of the other partes of the world.  
Hitherto you haue heard only the names of the partes of the world, and of their situation, howe they be placed in order. now for the form and shape of them, you shall understand, that the whole world is round exactly as any ball or globe, 
The form of the world and his partes.  and so are all the principal partes of it, every sphere severally and ioyntlye, as well of the planets, as of the Fixed stars, and so are all the four elements.  depiction of the planetary spheres. And they are aptly placed together, not as a number of round balls in a net, but every sphere includeth other, as they be in order of greatness, beginning at the eightesphere or firmament, and so descending to the last and lowest sphere, is the Sphere of the Mone: under which the four elements succeed: first the fire, then the air: next followeth the water: which with the earth jointly annexed, maketh as it were, one sphere only.  Scholar. 
This I do well understand in words, and the easier by this picture, which I find in every book of the Sphere, but that I see there more spheres, then you speak of: for in some books mention is made of nine spheres: and in other are ten spheres name, where you set forth but eight.  Master. 
The cause of this diversity will I in the fourthe treatise declare: in the mean season, I think it best to tell you of no mo spheres, then are perceptible by sight, for so many are we certain of. And therefore understand you thus, that as the eihhte sphere is the greatest, and hath none other without him that may be seen, so the earth is the least, 
The earth is the centre of the world.  and hath none other within him, but it standeth in the middle and in the centre of the whole world, and of every one of these spheres, and therfore it is called the Centre of the world: so that although the earth in itself haue a great and notable quantity, 
The earth hath no quantity in respect to the world.  yet in comparison to the firmament, it is to bee esteemed but as a centre or little prick, yea in dead much less than any notable star that you see,& if I shall speak boldly that which I intend hereafter to prove certainly, the earth is lesser then the least star in the firmament which is commonly seen, but yet is it greater thē Venus or Mercury, yea greater then the moon.  scholar. 
This affirmation seemeth to me impossible, or at the least contrary to sense: for the Mone seemeth bigger much then any star, yea somewhat bigger then the son.  Master. 
Content yourself to credite me, till time serve for the proof of my words, and in the mean season, to procede as I began. You must think, that the earth and the water annexed together in one globe, are of no notable quantity, in comparison to the firmament, and that it stan death as the centre of the world, 
The earth hath no motion.  and hath no motion out of his place, neither yet circular moving about his own centre, but resteth( as we may say) quiet without all such moving, like ways must you think of the other elements, which of their own nature haue none other motion then a ston or a light feather, so that they may be accounted all four to be without natural motion.  Scholar. 
Yet in the water and in the air we see every day notable moving. and sometime I haue heard of moving of the earth, by earthquakes: and as for the fire that we see, it always moveth and fly ckereth in burning.  Master. 
And so you haue seen a ston move swiftelye, when it fell from any high place. but these motions haue an end quickly, except they be continued with violence, as hereafter I will sufficiently declare. But as the ston although it will move in falling, yet in his place lieth quiet without motion: so the earth of itself, and the other elements must be accounted quiet by nature, and without motion.  

The motions of the heauens. ¶ The heauens contrary ways haue such a natural motion that never resteth night nor day, neither can be stayed by any violence. This motion wee se in the heauens daily by their moving from the east to the west, and from the west to the east again, about the earth, ones every 24. hours, and therfore is this motion name the Daily motion, for it is the measure of a natural day, 
A day.  commonly accounted. and this motion is likeways called of ancient writers the motion of the First firmament, according to which motion you see the son in the day time, and the stars in the night time, and the moon both in the day and the night, to pass from the east into the south, and so into the west, and at the end of 24. houres to come again into the east: whereby you may easily understand, that this motion is common to all the spheres of heaven.  Scholar. 
This may all men see, that can see any thing. yet haue I heard of some so grossly witted, that they doubted which way the Son and the moon did come into the cast again, as though they did not think that the sky did move about the earth.  Master. 
such gross ignorance happened somrymes to famous men, for lack of due consideration of that, which all men may see, as I will in place convenient more largely note.  scholar. 
Yet one doubt I haue, of which I wolde gladly be rid, and that is of the moon: for as you say, and by sight wee perceive, all the stars with the son and moon go round about the earth in 24. houres, 
A diuers motion in the Mone.  save that the moon is slacker then all the rest, for she is every day later in rising by an hour, then she was the day before: but howe that cometh to pass, I do not understand.  Ma. 
This doubt is well moved, and in good time, for by it will I take occasion to instruct you not only in the true knowledge of it, but also of other sundry motions in all the heauens: for in every one of them doth there appear a like motion, contrary to the daily moving of the Firmament, which in the moon is most swiftest, and therefore may be perceived daily of all men: but in the son it is not so swift, and therfore not so easily perceived: yet all men see a great alteration in the moving of the son in one year: 
A scuerall moving in the son.  for sometimes he is higher and nearer over our heads, and sometime farther from our heads, and lower in the south: yea sometime he shineth with us almost 18. hours,( as in the middle of the summer) and in the middle of Winter he shineth but 6. houres or little more: this every child doth see, although they know not the reason thereof.  Scholar. 
Yet the reason of that is easy enough to be conceived, for when the day is at the longest, the son must needs shine the more time, and so must it needs shine the lesser time, when the day is at the shortest: this reason I haue heard many men declare.  Master. 
That may well be called a crabbed reason, for it goeth backward like a crab. The day maketh not the son to shine, but the son shining maketh the day. And so the length of the day maketh not the son to shine long, neither the shortenes of the day causeth not the Son to shine the lesser time, but contrary ways the long shyninge of the son maketh the long day, and the short shining of the son maketh the lesser day: else answer me, what maketh the dayes long or short?  scholar. 
I haue heard wise men say, that summer maketh the long dayes, and winter maketh the long nights.  Master. 
They might haue said more wiselyc, that long dayes make summer, and short dayes make winter.  scholar. 
Why all that seemeth one thing to me.  master. 
Is it all one to say. God made the earth. and the carthe made God▪ covetousness over cometh all men. and all men overcome covetousness.  scholar. 
No not so, for here the effect is turned to bee the cause, and the agent is made the patient.  Master. 
So is it to say, summer maketh long dayes, where you should say: long dayes make summer.  scholar. 
I perceive it now, but I was so blinded with the volgare error, that if you had demanded of me farther what did make the summer, I had been like to haue answered, that green leaves do make summer: and the sooner by remembrance of an old saying: that a year should come, in which the summer should not bee known, but by the green leaves.  Master. 
Yet this saying doth not import that green leaves do make summer, but they betoken summer: so are they the sign and not the cause of summer.  scholar. 
So I perceive now that the long shinynge of the son doth make the dayes long. But now can I not tell what causeth the son to shine longer one time of the year, then an other.  Master. 
That is it that drove wise men to search, and mark the motions of the son, whereby at length they found, that the son hath an other course, contrary to the daily motion of the sky. And as the moon doth accomply she her proper course( which is from the west into the east, contrary to the daily motion) every month in the year, 
A year.  so the son doth end his course, in his proper motion, but ones in the year. And to express it aptly, I must say, that the true term of a year is nothing else, but the very time of the course of the son from a certain point in heaven, till his return to the same point again. 
A month.  And a month is the just time of the proper course of the moon, from change to change: and every quarter of the moon maketh a week. 
A week.  of which I will speak more in the next treatise, with the declaration of the diversity for the beginning of months and Yeares. But now to continue our principal matter the more ordrelye, I would haue you repeat the chief articles of our talk hitherto.  scholar. 
This is the sum of all your doctrine hitherto. 
The first repetition.   
1. That the world is that entire body, which containeth in it all the heauens and the elements, with all that in them is.  
2. The partes of the world ar two especial, the heauens which are eight in number, and the elemenents which are .iiij. in kind.  
3. The order and situation of all these partes, as well elements as heavenly spheres, beginning at the highest, and proceeding to the lowest, is this. the Firmanent, Saturne, jupiter, Mars, the son, Venus, Mercury, and the moon.  
THE four elements. fire, air, Water, and earth. and ever the higher encloseth all that is under it.  
4 The world and all his principal partes are round in form and shape, as a globe or ball.  
5. The earth is in the middle of the world, as the centre of it:& beareth no view of quantity in comparison to the world.  
6. The earth hath no motion of itself, no more then a ston, but resteth quietly: and so the other elements do, except they be forcibly moved.  
7. The heauens do move continually from the east to the west, and that motion is called, The daily motion: and is the measure of the Common day.  
8. The Mone hath a several motion from the west toward the east, contrary to that moving of the daily course, and that motion is the just measure of a month, and every quarter doth make a week.  
9. The Son also hath a peculiar motion from the west toward the east, which he accomplisheth in a year, and of that course the year taketh his measure and quantity.  
Now then it may please you to procede to farther explication of the appearances which are noted in the heauens, and to show the manner of their motions.  Master. 
To the intent that you may understand all things the more easily, 
A material sphere.  I think it good to describe unto you a material sphere, which shall contain in it such notable circles only, as haue special use in the declaration of the heavenly motions, and such as reason shall drive a man to appoint, as certain bounds of the motions in the heauens: yea such I say, as yourself shall by interrogatories be constrained to confess needful to that knowledge which you desire.  scholar. 
If nothing bee placed in that sphere but that which must needs be had, then can I not account any part of it superfluous. And again, if it serve sufficiently to instruct me in that I desire to know, I can not justly blame it in any point as insufficiente, so must it needs be a perfect instrument, void of default, and without superfluitye.  Master. 
So shall it be, for so much as this parte of knowledge requireth. Now then to begin. ye do believe that the world is round.  scholar. 
Yea for sooth.  Master. 

The makig of a Globe.  Then must that instrument also be round, which shall aptly express the form of the world.  Schol. 
Truth it is.  Mast. 
Can there be any thing more round then a circled?  scholar. 
No truly.  master. 
And doth not two half circles make a whole circled?  scholar. 
It can not be denayed.  Master. 
Then take half a circled, and fasten it on an axtre or on any diameter, and then turn it round about, first letting the half circle hang downward under the diameter  Geometrical diagram. as here you se it  Geometrical diagram. figured, in the half circle A B, C. then turn the half circle right up over the diameter, as here also is represented in the half circle A, D, C. do not these two positions make a whole circle?  Scholar. 
Yes surely.  Master. 
Then set the half circled so, that the diameter may stand still firmly fixed, and the half circle may turn round about. Do not you imagine now that every dyvers position of this half circle with the contrary place against it, doth make a whole circle.  scholar. 
Yes verily.  Master. 
And because there is no place round about that diameter, within the reach of that half circled, but that half circled hath passed it, there can no void place be assigned but it is occupied and filled with half a circle, and every half circle with his contrary doth make a whole circle, so doth this whole revolution of the half circled make a just cyrcular body.  

Here is the like form of that work.   diagram expressing the form of a sphere.  scholar. 
So it appeareth truly.  master. 

A Sphere is defined.  This circular body is name a sphere, as it may appear by the description that euclid maketh of a sphere: which is this in greek, as himself wrote it, in his eleventh book of geometry.  {αβγδ} 
which into latin may well be translated thus.  Sphaera est figura comprehensa ex circumductu semicirculi, donec eo redeat, vnde moveri incoepit, manente interim immota semicirculi eius diametro. 
And thus it soundeth in englishe.  
A Sphere is a sound figure, made by the turning of half a circled, till it end where it began to be moved, the diameter of that half circled continuing steady all the mean while. This description dooeh joannes de Sacro bosco expound thus: that a sphere is a round and sound body made by the turning of half a circled.  scholar. 
So that a sphere is nothing else but a round and massy body closed with one plate form, which you in your pathway do call a Globe.  Master. 

The centre of a Globe or Sphere.  You take it right. But now must you mark, that as a circled is made about his centre, so a globe also hath his centre, as you may easily understand, from which center all the lines that may be drawn to the plate form, or utter parte of the globe, are all equal together, according to Theodosius definition, which saythe thus: A sphere is a massy body, enclosed with one plate form, and in the middle of it there is a prick, from which all lines drawn to the said plate form, are equal each to other, and that prick is the centre of the globe and so saith euclid also.  {αβγδ}. Idem centrum sphaerae est, quod& semicirculi. 
The centre of a globe is the same centre that a semicircle hath, by which the globe was made.  scholar. 
It must needs bee so: and likeways the diameter of them both must needs be all one, as I think.  master. 
You say not much amiss. Yet must you put a difference in a globe, 
A Diameter and an Axe three differ.  between a Diameter and an Axe tre. For every right line that passeth from side to side in a globe, and toucheth the centre, is aptly called a diameter. so that as ther may be many diameters in a cyrkle, so may ther be as many also in a Globe: But of all that multitude, one only is called the Axe three, and that is it on which the globe turneth. This difference did joannes de Sacro bosco overpass not ignorantly, but negligently, or else witting: but so did not euclid, which defineth them both thus.  
An axe tre  {αβγδ}. Axis Sphaerae est, recta illa stabilis linea, circa quam semicirculus rotatur. 
 diagram showing a sphere on an axis.  
The Axe three( saith he) is that right line which moveth not, but the half circle moveth about it. These words haue respect not only to the making of a Globe or Sphere, but also to the use of it. But now the diameter is defined by him thus:  {αβγδ}. 
A diameter  Dimetiens vero Sphaerae est recta quae{qu} linea per centrum acta,& vtrinque desinens in sphaerae superficie: 
 Geometrical diagram.  
The diameter of a Sphere, is any right line that is drawn by the centre, and ended in the plate form of the sphere.  scholar. 
This difference must needs seem reasonable, sith there may be so many diameters drawn as a man listeth, but Axe trees there can be but one in one globe.  master. 
When a globe turneth round, are there any mo poyntes then two in that globe, on which it doth turn?  scholar. 
By proof it appeareth, that all partes of the globe move, except the two ends of that Axe three, whereon it moveth, and they move not out of their place.  Master. 

Poles of a Sphere.  Those two points are name the poles in a sphere, whereby also you may understand, that there can be but two poles in one sphere: mark this well, for it will serve your turn in place convenient. now apply all these to the world, which in his whole substance is round, and therefore aptly may bee called a sphere: you see it turn about round, and therefore must it haue two poles, on which it turneth so. Also because it is round, it must haue a centre( which I did affirm before to bee the earth) and by this centre, we may imagine a right line to run from the one pole to the other, which right line must be called the Axe tre of the world.  scholar. 
For the centre of the world, it must needs be somthinge: for I perceive a globe can not be, but it must necessary haue a middle prick or centre, no more then a line may be made which hath no middle, or a circled that hath no centre: which both appear unpossible. Also for the pools, they appear needful, or rather of necessity to follow the movings of heaven. For in all round things that move roundly, there be such two points that seem not to move: but why there should be any axe three required in the world, I see no reason: for if the mighty power of God did not stay the world, there could bee no Axe three able to bear it.  Master. 
Your imagination in this point is to gross. I said not that the Axe tre was made to stay the world, but that it passeth as a line only from the one pole to the other: and is not without great and profitable use, both in doctrine, and also in practise, for placynge of instruments, as you shall know better hereafter. But now hear howe Proclus doth apply these to the world.  {αβγδ}. 
which words our worthy contrye man D. Linaker, translateth thus.  Axis mundi vocatur dimetiens ipsius, circa quam voluitur. Axis extrema, poli mundi( seu vertices) sunt nominati: horum alter Septentrionalis, alter Austrinus dicitur. 
The Axe three of the world, is name the Diameter of it, about which it turneth. 
The north and south Poles.  and the ends of that Axe three, are called the Poles of the world. of which poles one is name the north pole, and the other the South pole. The North pole is always seen of us where as we dwell, and the south pole is never seen in this our contrye, but is ever more under our Horizonte, and that as low, as the north pole is high above our Horizonte.  scholar. 
I haue been taught to know the north pole, and I haue marked it oftentimes, whereby I perceived a great number of stars to move about it, and were sometimes higher then it, and sometimes lower then it: now on the east side of it, and now on the west side: but that pole star seemed not to stir out of his place at any time: whereby I gather, that he is never out of sight to us, when the stars appear, and that is all the night. but what becometh of him in the day time, I can not tell.  Master. 
I will clear you of all such doubts before I leave you: 
The Horizonte.  but in the mean time I marvel you found no doubt at the name of the Horizonte.  scholar. 
That name I learned to signify that circle, which goeth along by the edge of the ground, and parteth that parte of the world which we see, from that part which we se not:& when the Son riseth, then is he in our horizonte,& so is he, when he is going down as low as we can see him.  Master. 
This is not greatly amiss. the like expressing 
Here the Horizonte is represented by the line A. C.   Geometrical diagram. of it doth Hyginius use in his first book, and in the .iiij. also of his astronomy: but Proclus in his Sphere, doth define it thus.  {αβγδ}. Horizon vero circulus est, qui conspectam mundi partem ab inconspecta dirimit: itaque in duas partes vniuersam Sphaeram secat, vt alterum hemisphaerium supra terram, alterum sub terra relinquat. 
The Horizonte is a circle which parteth that parte of the world that wee see, from that which wee see not: and it divideth the whole 
And here the Horizonte is the edge between the light parte( which standeth for that which wee see) and the dark part which doth signify that which wee can not see of the sky.   Geometrical diagram. sphere of the world into two equal partes, in such sort, that half of that sphere is ever above the ground,& half always under the earth. This circle you perceive to be necessary in the material sphere, seeing it hath so great use in the heavenly motions, that by it we judge the risynges and settings of the son and the moon and all other stars. what say you then for the noon steede of the day, from which you reckon all your houres, as it appeareth both by the clockes and dials? for as the clock striketh one next after noon, 
The meridian circled  and so in creaseth forward in the number of houres, so likewaies are your hours marked in the dialles.  scholar. 
I think it very meet to haue the south point well known, as well for this, as for standing dialles, and for knowledge of the time of the night by the moon, and by other stars.  master. 
Then must there be a circled appointed for that use, which is called therfore the Meridiane circled, and may be name well the noon steede circle. 
The Nonesteed circled  This circled is thus defined by Proclus.  {αβγδ}. Meridianus circulus est, qui per mundi polos& punctum, quod nobis supra verticem eminet, ducitur. in quem cum solincidit, medios dies, mediasque noctes efficit. 
The Meridian is a circle drawn by the poles of the world,& the point right over our heads. in which circled when the Son is, he maketh the middle of the day,& the middle of the night.  
now farther to procede to other partes needful in the sphere. you do se, that twice 
The Meridiane circle here is resembled to the circled, A, B, C, D.   Geometrical diagram. in the year the daies& nights ar equal,& the Son riseth in the just east,& goeth down in the full west, where as in the summer the Son riseth north-east, and setteth northwest:& at nonetide is very high over our heads: but in the winter, contrary ways the son riseth south east,& setteth south-west:& at nonetide is very low. think you not that these three bounds of the course of the Son would be well noted, and haue their peculiar circles, for distinction of those times?  scholar. 
I think nothing more needful then that.  Master. 
These three circles( with two other that I will next speak of) are name the five Paralelles: and the middle circled of those, is name the equinoctial, because that when the son is under it, the dayes and nights are equal in all the world, except only two places. This circled is thus defined by Proclus.  
The Equinoctial circled  {αβγδ}. Aequator, circulus is est, qui maximus aequidistatium circulorum statuitur, ita nimirum ab Horizonte dissectus, vt alter eius semicircultie supra terram, alter sub terra condatur: in hoc sol duplex aequinoctium, vernum autumnaleque facit. 
The equinoctial circled is the greatest of the five parallel circles, and is divided so equally into two partes, by the Horizonte, that the one half of it is above ground, and the other is under the horizonte: and when the son is in this circled, he maketh the daies equal with the nights, ones in the spring time, and again in the harvest. This equinoctial circled and the other seven that follow, to be declared, do move all as the sky moveth. but the Horizonte and the Meridian do not move with the heaven, but stand stedye, and keep their places.  scholar. 
That seemeth reasonable, else could not men know the rising, setting, and noonesteed of the son. but howe shall I know this equinoctial circled in heaven, seeing I can not see any such circled there?  Master. 

Howe to know the place of the circled equinoctial  mark the course of the son about the eleventh day of march, or else about the fourteenth day of september, and so may you best understand the place of this circled, for at those two times the son runneth directly under the equinoctial circled, and doth( as it were) describe it by his motion, in four and twenty-howers. And if you list do mark the rising of the son that day, you may know the precise point of the east, and at night he setteth in the just point of the west.  scholar. 
I would I knew as good marks of the other circles.  Master. 
So will I give you in their convenient places and times good orders to know them al: and first I must tel you, that these other two circles, which I name before( with the equinoctial) are called the two tropic circles after the greek derivation, 
The knowledge of the ij. tropics  and may be called in english the son bounds, because the son doth never pass them, neither towards the north, nor yet toward the south: but when he toucheth any one of them, he doth tourn his course toward the other. as for example: All the time from the middle of December until the eleventh day of june, you may perceive the son to rise higher 
Examples of those circles and other that followeth.   diagram of the circles of latitude on the celestial sphere. 

A, C. the Horizonte.  
** The poles of the world.  
G, H. The equinoctial circled.  
B, F, one tropic, and  
E, D. the other tropic.  
A, 
The summer tropic.  I, the artike circled,  
C, K. the antarctic circled.   and higher, and that day he is at the highest that he can go towards our heads, and then doth he by his course describe that summer tropic, after which day he draweth again lower and lower every day, till the twelfte day of December, for then he is at the lowest, and that day he doth describe the Winter tropic. now mark howe Proclus defineth them.  
The winter tropik  {αβγδ}, 
Linacer nimium coactè commune no men utrique tropico ae stiuo uni tribuit, Plimum importunè secutus. * Solstitialis autem circulus is est, qui omnium, qui à sole describuntur maximè septemtrionalis habetur. in quem quum se sol receperit, aestiuam ceciprocationem peragit, longissimusque totius anni dies, breuissimaque noxerit. post hancautem reciprocationem, nequaquam vltra versus septemtriones solem progredi, quin potius ad diver sa mundi regredi cernas. vnde& Tropico graecenomen. 
The summer tropic is the most northerly circled of all thē that the son describeth: in the which when the son is, he maketh his summer turn, at which time is the longest day of al the year, and the shortest night: for after this summer turn, you se the son go no more toward the north, but turneth to the contrary coast of the world, and therof is that circled name( in greek) a tropic: that is to say, a returning circled, or a circled of return.  
The son aftter he beginneth to turn, may be perceived every day, or at the least every week, and chiefly at nonetide to wax lower& lower, until he come to the Winter tropic, and there he turneth again, as by the definition of that tropic you may understand.  
The winter tropik.  {αβγδ}. Brumalis circulus is est, qui omnium circulorum qui à Sole circumactu mundi describuntur, maximè ad austrum pertinet: in quo sol brumalem reciprocationem facit, maximaque totius anni nox, minimusque dies efficitur. post hanc metam nequaquam vltra progreditur* sol, 
Intellige versus austrum quod& graecè additur.  said ad alteras mundi partes revertitur: vnde tropicus hic quoque, quasi versilis, appellatur. 
The winter tropic, saith Proclus, is the most southerlye circled of all them that the son doth describe, by the revolution of the world, in which when the son is, he maketh his Winterly turn, and then is the longest night in all the year, and the shortest day, for after this Winter turn, the son is not seen to go any farther toward the south, but tournith to the contrary coasts of the world, and thereof is this circle also name a tropic or circle of return. And thus haue we the three circles that are principally noted for the course of the son. 
The south and north circles.  now are there other two which be parallels with these three, whereof the one is more southerlye( to us) then is the Winter tropic, and the other is more northerly, thē is the summer tropik, which whether they be needful or not, their use may declare. I remember, that you said, you had oftentimes beholden the north pole, where you might see many stars about it, that never go under our horizon. do you not think it good that all those stars were enclosed in a circled to be discerued from al other, which rise sometime above the horizon, and sometime again do set under the same?  scholar. 
Yes verily, it were pleasant to know.  Mast. 
And profitable also, as you shal hereafter perceive. Now contrary ways, 
The use of the arctic and Antarctik circles  there are other stars, that are never seen of us in this country, and yet much mention is made of them in writers, were it not good that their bound were marked, that all other may be known from them?  scholar. 
else might men often look for such stars as they read of, and should loose their labour, for they shall not see them.  Master. 
And yet are there goodly bright and notable stars, which are not seen here, but in south spain, in Barbary, in Guinea and calicut, and many other countries, they appear fair and pleasant to behold.  Scholar. 
I pray you, what call you those circles that encloseth those stars?  Master. 
They are name after the coast of the world where they bee. So that the circled which encloseth all those stars that be about the north pole, is name the Arctyke circled or north circled: and the contrary circled in the south, is called the antarctic circled by the greek composition, as you would say, Contrary or against the arctic circled: and it may well be called the South circled. But now hear howe Proclus defineth them.  
The arctic circled.  {αβγδ}. Septentrionalis circulus est is, qui omnium quos perpetuo cernimus, planè maximus est, quique Horizontem solo puncto contingit, totus supra terram interceptus. intra hunc quaecunque clauduntur astra, nec ortum nec occasum norunt, said circa polum uerti tota nocte cernuntur. 
The arctic cirle is the greatest of all those circles which do always appear, and toucheth the Horizonte in one only point, and is all together above the earth, and all the stars that bee within this circled neither rise neither set, but are seen to run round about the Pole all the night.  
Thus haue you the fourth parallel, now resteth the fift which is described thus of Proclus.  
The Antarctik circled.  {αβγδ}. Antarcticus vero circulus aequalis& aequidistans Septentrionali circulo est,& Horizontavno puncto contingens. totus praeterea sub terris mersus, intra quem sita astra semper nobis occulta manent. 
The antarctic circled is equal and equidistant to the arctic circled, and toucheth the Horizonte in one only point, and is all under ground, and all the stars that be in it, are ever more out of our sight.  
These are al the parallels which are wont to be set forth in the material sphere, and that agreeably of all men, save that touching the two last circles there is a difference, of which I will instruct you at large in the next part of our talk, and omitting it for this time, will go forward to other three circles which yet remain, 
The zodiac.  and are needful to our sphere. because our chief consideration consisteth about marking of the motions of the son, the moon and the other planets, howe they change their places in the sky, and therfore make diuers appearances to us that behold them, and mark their courses, and yet all they haue( as it were) one common path or way, from which they serve not, but keep themselves still within the limits of it: how think you is not that path of theirs well to be marked, and worthy to haue a notable name?  scholar. 
Mary that is the principal point( as I take it) of all the rest: for without knowledge of that, nothing else can be known.  Master. 
That common path of the Planets, wherein all they haue their course, is called of Astronomers the zodiac: which is, 
The .xij. signs.  as you may englishe it, the circled of the signs: which signs are the greatest and notablest partes of that circled, and were invented for the more exact distinction of the motion of the planets monethlye. For as there bee but twelve months in the year, so there are twelve partes of the zodiac distinct by several names, and correspondent to every month, although they vary something now from their first application, whereof hereafter I will instruct you sufficiently. and now will touch them briefly as this place doth require. Their order in the zodiac and their names ar these that follow, in greek and latin, which may bee englished as I haue under written, and are often times mentioned of our english poets.  
{αβγδ}. {αβγδ}. {αβγδ}. {αβγδ}. {αβγδ}. {αβγδ}. Aries. Taurus. geminy. Cancer. lo. Virgo. the ram. the Bull. the twins. the crab. the lion. the Virgin. ♈ ♉ ♊ ♋ ♌ ♍  
{αβγδ}. {αβγδ}. {αβγδ}. {αβγδ}. {αβγδ}. {αβγδ}. Libra. Scorpius. Sagittarius. Capricornus. Aquarius. Pisces. the Balance. the Scorpion. the Archer. the goat. the waterman. the Fishes. ♎ ♏ ♐ ♑ ♒ ♓  
And because that their names always can not bee placed in small instruments, there ar certain figures devised for their names, which I haue also set under their names, that you may the better know them. 
The degrees of the signs.  These signs are all of one length, each being the just twelfte parte of the zodiac. And for exacter knowledge of the motion of the planets every day, each sign is divided into thirty equal partes, which are called Degrees, so that in the whole circuit of the zodiac there must bee 360 degrees, which agree almost with the dayes of the year.  Scholar. 
And thereby I gather, that as the Son doth move throughout all the zodiac in a year, so every month he moveth, he runneth one sign,& every day nere one degree.  Master. 
You gether well, but this must you mark also, that by this same nombre of degrees all the circles in the sphere are divided, so that of every circled great or less, 
what a degree is in measure.  a degree is the 360 parte and not any measure certain, as a foot, a yard, a mile, or such like.  scholar. 
I understand you thus: as a quarter is no measure certain, but sometime is referred to one thing, and sometime to an other, and yet still it betokeneth the fourth parte of that whereunto it is referred, for when we say: a year and a quarter: an hour and a quarter: a yard and a quarter: a quarter of a foot: in all these sayings, the quarters differ. so when wee say: a quarter of corn: a quarter of cloth: a quarter of pepper: a quarter of allame: by the accustumed measures all men understand our meaning, and yet these quarters differ, and be in common meaning, a quarter of a weigh, or eight bushels, a quarter of a yard, a quarter of a pound, a quarter of a hundreth.  Master. 
So is a degree the thirtieth parte of a sign, and a sign the twelfte parte of any circled. howe be it, commonly& chiefly the name of signs, is attributed to the zodiac.( which many do call the Thwarte circled) This zodiac is thus described of Proclus.  
The zodiac.  {αβγδ}. Obliquus circulus is est, qui duodecim signa continet, ex tribus aequidistantibus circulis constans: quorum dvo latitudinem signiferi determinant, vnus per media signa ductus vocatur. hic adeo duos pares& aequidistantes circulos attingit, Solstitialem in prima Cancri parte, Brumalem in Capricorni principio. Latitudo Signiferi continet partes duodecim. Dictus estautē hic circulus Obliquus, quod aequidistantes( ad inaequales angulos) intersecet. 
The thwarte circle( or zodiac) is the circle of the twelve signs, and is made of three circles, whereof two are the bounds of his breadth, and the third is called the Middle sign circled,( because it goeth by the middle of the signs in the zodiac) and it toucheth two equal 
This whole circled representeth the zodiac, and the middle circled signifieth the ecliptic line.   diagram of the zodiac. circles of the parallels: that is to say, the summer tropic in the first point of the crab called Cancer, and also the winter tropic in the first degree of the goat, called capricorn. The breadth of the zodiac, containeth twelve degrees. This zodiac is called a Thwart circled, because it crosseth the parallel circles, going overthwart them. By these words of Proclus you may understand, that the zodiac doth not go directly between the two poles of the world, as all the five parallels do, but is drawn cross the sphere, so that his middle( in breadth) doth touch the two tropics, and that middle line is called of latin writers the ecliptic line, 
The ecliptic line.  because there can be no eclipse of son or moon, unless the moon be under that line: as hereafter I will declare in place convenient. But touching this zodiac( of which wee spake last) I said it was divided into twelve signs, according to the twelve months of the year. And because every quarter of the year may bee the more exactly known a sunder, this zodiac is partend into four partes principal, every part( as it must needs follow) containing three signs.  scholar. 
This is a very apt agreement of arte unto nature: for as the whole zodiac agreeth with the whole year, so for the four quarters of the one, there is four quarters in the other: and for the twelve monthes of the year, twelve signs in the zodiac: and for the thirty dayes of the month, thirty degrees in every sign. But I pray you sir, doth the beginning of these signs answer to the beginning of our year?  Master. 

The year when it be ginneth.  The beginning of the year is diuers in dyvers nations, as I will show you an other time, with the reason why we begin our year in january: but for this time it shal be sufficient, to declare the agreement of our year with the Astronomers year. The Astronomers begin the twelve signs of the zodiac at Aries, and lykewaise do they begin the year that day and hour, that the son entereth into that sign of Aries, which is now at the eleventh day of march: 
The spring of the year  and from thence they reckon the spring of the year three months, while the son is in the first three signs. Then at the eleventh day of june; they account the end of the spring, and the beginning of summer, because then the son entereth into Cancer, 
The summer  which is the fourthe sign. and while the son passeth other three signs,( which maketh the second quarter of the zodiac) they account the second quarter of the year, which we call summer,& that endureth till the 14 day of September, at which time the Son entereth into Libra, where the third quarter of the zodiac doth begin,& so with it beginneth harvest, which is the third quarter of the year, 
harvest.  and continueth till the twelft day of December, and then doth the Son entre into Capricorn. 
winter. & Winter beginneth, being the 4 and last quarter, which continueth till the eleventh day of march, where the old year endeth, and a new year beginneth.  Scho. 
These 4. signs, Aries, Cancer, Libra& Capricorn, seem to haue a certain prerogative, that they begin the 4. quarters of the year, therfore they would be well noted in the zodiac.  Master. 
You say well, and yet they haue other notable qualities, for in the beginning of Aries and Libra, the son maketh the daies equal with the nights.& these 2. points ar name the equinoctial points. In the first part of Cancer, the day is at the longest, and beginneth to shorten by the descending of the son from our heads,& when the son doth enter into Capricorn, the day is at the shortest,& then the son beginneth to return to us again,& the day doth thē begin to increase. and these 2. points ar called the ij. tropic points: 
The colours.  wherefore as these 4. points are notable, so are ther ij. circles appointed for their limits, the one going by the beginning of Aries& Libra, and the other by the beginning of Cancer and Capricorn. these ij. circles ar called colours, 
tropic colour.  whereof the one only which passeth by Cancer and Capricorn, is described of the greeks, the reason thereof I will show you in the fourthe treatise. But this first colour, which is called the tropic colour, is thus described by Proclus.  {αβγδ} 
λ. significat. 30. quae semissis est circuli maximi divisi in 60. partes, quod Procl{us} facit. Vt perperam quidā α. hic p λ. substituerint.  Sunt& per polos ducti circuli quos nonnulli Coluros vocant: iis accidit, vt in ambitus suos mundi polos recipiant. Coluri autem dicti sunt, quod partes aliquas in se minimè conspectas habent. reliqui enim circuli in mundi circumactu integri cernuntur, said colurorū partes quae piam quae videlicet ab 
Antarctico legendum, contra exemplarium omnium consensum.  Arctico sub Horizonte latent, cerni non possunt. Signantur autem hi circuli per tropica puncta, diuiduntque per 
duas ad modum aptè Linacer transtulit loco λ. literae, {per} semissim hic significare, suprà admonui.  duas aequas partes circulum qui per media signiferi ducitur. 
 diagram of the colures circles on the celestial sphere.  
The circles that go by the poles are those, which some men call colours: they haue the poles of the world in their circumference. And ar name colours in greek, that is trunked circles, because some partes of them come not into our sight. for the other circles by the turning of the world are all seen, but some parts of the colours are not seen, that is, those partes which are in the antarctic circled, and remain under our Horizonte. 
The equinoctial colour.  These circles are deawen by the two tropic points of the eclipte circled, and so divide it into two equal partes. The equinoctial colour goeth by the poles of the sphere, and by the .ij. equinoctial points of the zodiac, in Aries and Libra. Thus haue you now all the circles needful for a material sphere. let me hear howe you do remember their names.  scholar. 
If I should not remember them, I did but lose my labour, 
A good lesson.  and occasion you to spend your time in vain: for I know that in this science and in all other, he that coveteth to run still forward, and remembreth not that, that is gone before, shall never attain that which remaineth behind, but while he delighteth to much to see the end, he deceiveth himself of the fruitful end of knowledge. much like a man that is delighted in hearing a cunning song of music, but when it is done, doth remember nothing of it, so is his profit and pleasure both ended, when the song is ended. Therfore( if it please you) I will repeat the chief points that I haue learned sythe my former repetition.  master. 
do so then.  scholar. 
This it is as I remmembre, 


The second repetition.  1 first you taught me what a sphere is, and howe it is made, also what is his Centre, his axletree, his Diameter, and his Poles, and what the Poles are name.  
2 next you declared two circles, that is the Horizonte, and the Meridiane circled, which( I perceive) stand still, and turn not with the world, but keep their places.  
3 Then did you describe five parallel circles, the equinoctial, the two tropics: the summer tropic, and the winter tropic, and then the other two parallels, that is, the north circled, and the south.  
4 After that, you shewed me what the zodiac was, and the twelve signs that be in him, and of their division.  
5 And last of all, you described the two colours, which divide the zodiac into four equal and principal partes, according to the four times of the year.    master. 
This good remembrance declared your good will to knowledge, which I shall with as good a will help to further. Now you look( I think) to be instructed in the use of all these things, and to understand thereby the celestial motions, and the diuers appearances that thereby do ensue: how be it, because that a material instrument is a great help for them that begin to travail in this arte, and doth as an image represent to the eyes those things, which by only hearing, were very hard to conceive, besides many other commodities, which shall be uttered in their place, I think it most convenient order, first to teach you the manner howe to make such a material sphere, as may serve both to learn by, and also to work by, in practising the observations needful to this arte.   

THE second TREATISE OF THE CASTLE OF KNOWLEDGE wherein is taught the making of the material sphere, as well in sound or massy form, as also in ring form with hoops.  MASTER. 
ALTHOVGHE THERE BE MANY and wonderful instruments wittily devised for practise in Astronomy, as the Astrolabe, the plain sphere, the Saphey, 
Instruments of Astrronomye.  the quadrant of diverse sorts, the Chylynder, ptolemy his rules, Hipparchus rules, Tunsteedes rules, The Albion, the Torquete, the Astronomers staff, the Astronomers ring, the Astronomers ship, and a great number more, which hereafter in time you may know, yet all these are but parts, or( at the most) diuers representations of the Sphere. wherefore as the Sphere is the ground and beginner of all other instruments, so is it most meet that we begin with it, and the rather because it doth more aptly represent the form of heaven, then any other instrument can do. What a Sphere is, you haue learned before: and howe a material Sphere or Globe may bee made round, you may conjecture by the same description of euclid. Therfore must you haue an instrument of steel made like a Semicircle, which in the inner circumference must haue a sharp edge apt to cut and pare smooth, 
The turning of a Globe.  and( as I may say) by true working to justify your Globe, which first may bee made as round, as any Turner can do it. and then shall your instrument not only duly examen the Turners work, but correct it exactly if it be amiss.  
This is the form of that instrument, and it is thus made justly. first draw a right line as long as you will haue  diagram of an instrument for making a globe. the diameter of your sphere, and an each longer, or more. Then open your compass according to the half diameter of the sphere that you would make, and draw half a circled, so that the fixed foot of your compass be set in the middle( as you may nearlye guess) of the said line, and with the other movable foot make the semicircle, but not fully complete to the diameter, for there must bee two holes made as big as a wheat straw or bigger, according to the bigness of the Globe, for clothe these 
An other form of the same work.   diagram showing the making of a globe. holes must the Turners spyndles pierce, that must bear the Globe while it is in turning: but you must take good heed, that those holes bee so made, that the foresaid line do pass exactly clothe the very middle of them, for so much as you miss in making those holes, so much will your sphere bee false in every quarter. again you must take heed that your instrument do not bow inward without those holes toward both the poyntes, except it bee in true compass, but better it is to file it somewhat a slope outwardelye. What more is to be done, I leave it to the studious devise of your own practise. for such things are better taught by hand, then by mouth.  scholar. 
I wolde I could as well use it, as I could devise to make it just round.  Master. 

To find the Poles in a Globe.  When you haue your globe so justified in roundness, mark well the two Poles of it, which you may easily do by the same instrument, whereby you did justify it, for the spindles that passed through the two holes of your instrument, do touch the two poles exactly.  scholar. 
That can I easily do.  Master. 
Then must you haue a pair of compass aptly made for to draw the circles in your Globe, and the points of the shanks in that compass must bow somewhat inward( as here you see an example) and the points of it must bee very fine and hard, that they may grave deeply, and yet make a fine and small circled. for the finer that your circles be, the exactlier will the divisions be made, and the less error will bee in the making  diagram of a pair of compasses. and using of the same Globe. 
A compass for a Globe  Then set one foot of the compass in one of the Poles of the Globe, and open the other so wide, as you think will suffice to reach to the middle of the Globe, toward the other Pole, and with that foot make a light mark in the Globe: and keepynge your compass vnchaunged, put one foot of it in the contrary Pole, and turn the other foot toward the foresaid mark, 
To make equinoctial circled.  in the middle of the Globe, and if the foot touch it exactelye, then is that middle duly found: but if the compass reach to far, or to short, make with yt an other light mark, and the true middle between those two marks is the just middle of the Globe or Sphere, as by your compass a little opened more or closid( as you see cause) you may prove.  scholar. 
That can I do well enough, by experience learned in often practisynge the conclusions of your pathway.  Master. 

The pathway.  That pathway will lead you rightly to this work, if it bee well travailed as it ought to bee before you come to this work. But to procede with our Sphere: When you haue found the just middle of the Globe between both the Poles, then open your compass accor dynge to the distance of that middle mark, and one of the Poles, and set one foot of the compass in the Pole( which you list) and with the other draw a circle round about the Globe. which whether it bee truly done or not, thus may you prove: remove the foot of your compass into the other Pole, 
Proof.  and with the movable foot try the former circled,& if the compass run justly in it, then is that circled truly drawn between both the Poles, else haue you erred: and therfore grave not that circled to deep, till you haue examined it. 
The dividing of the equinoctial  And when you haue found it true, then without alteringe of the compass, set both feet of it in the said circled,& they will take the fourth part of the same circled, as by remouinge it four times, you may know.  scholar. 
That haue I learned in the pathway also, and if I haue myssed, 
Proof.  it is by the grossness of the poyntes of my compass, or else by mine own gross negligence, which both I can quickly examine and amend, as the case requireth.  Master. 
After that you haue marked out those four partes of that circled, dyuide each of them into three even partes, and so haue you that circle divided into twelve equal partes: mark those partes with little cross lines, or else draw an other circled within a corn breadth of that other, on which side you list, but let it be somewhat less grauid then the first, that the first may bee known for the true circled, and this second circle to serve but only for the marks of division in that other: and so draw a line at every twelfte parte, from the one circle to the other. Then dyuyde every one of those partes into three lesser partes, and each of them again into even halves, and so haue you in all, 72. parts made of that circle. After this, divide one of those partes into five lesser portions, equally, and by the same example diuyde all the other 71. partes, and so haue you in the whole circled, 360. partes, which you shall mark with numbers of figures, from 10. to 10. beginning where you list.  scholar. 
Those I may call degrees, as I remember by your former lessons. and I must mark them thus. 10.20.30.40. and so unto 360.  Mast. 
So it is: And this circled thus drawn in the middle between both the Poles, is the equinoctial circle in that sphere. Now to make the two Tropiks, 
To draw the two tropics.  open your compass so▪ that they may extend to 66. degrees and an half of the said equinoctial circle. and then set one foot of the compass in which Pole you will, and with the other foot draw a circled on the Globe, which shal stand for one of the tropiks, and setting the foot of the same compass unaltered, in the other Pole, draw about it an other circled, for the other tropic. Now appoint names for the Poles, 
The Poles.  callyinge one the South pole or antarctic pole, and the other the North pole or arctic pole: and then the tropics of necessity will take their names: for that tropic which is next the North Pole, must be the tropic of Cancer, that is, 
The tropics.  the summer tropic, and the other that is next to the south Pole, must needs bee the tropic of capricorn, or the winter tropic. Then mark where you began the noumbrynge of the degrees in the equinoctial( which may well be called the beginning of the equinoctial) and set one foot of your compass in that beginning, 
The tropih colours.  opening the other foot till it will reach unto 90. degrees justly, and first hold the one foot steady in the beginning of the equinoctial, and draw a circled with the other foot, and if that circled touch both the Poles of the Globe, then is it truly drawn. 
Proof.  but it should go also by the end of the 270 degree of the equinoctial, and if it miss any whit, examine it well, and amend the fault, before you work any farther. 
A general rule.  which rule you shall observe still, for else of one fault neglected, many other may ensue.  

The Equinoctial colour.  This done keep your compass at the same wydenesse, and set one foot in the equinoctial circled, at the end of 90 degrees, and holding it steady, with the other foot describe a circled, 
Proof.  which shall pass by both the Poles of the Globe, and by two points of the equinoctial, that is the beginning of it, and the end of 180 degrees. and if you haue missed, amend it by and by. This last circled is the colour equinoctial, and the other last before drawn is the colour Tropikall, or Solstitiall, or the tropic colour. These two circles shall you divide into 360 parts each of them, 
The division of the colours.  beginning your numbrynge at the equinoctial, and reckoning toward the Pole, in every quarter of them severally, so shall you never reckon above 90. But it is easily known, that four times nynetye doth make. 360.  Scho. 
But in this order of numbrynge, the common form of account is not kept, as it was in the equinoctial: for when I haue reckoned in one quarter 90. degrees from the equinoctial to the Pole, then if I go forward in the same circled, the next number beyond the Pole is nynetye again, and so that second quarter decreaseth from 90 to 10, going backward, and then the thyrde quarter increaseth from 10 to 90, and the fourth quarter decreaseth again from 90 to 10.  Master. 
So must it be in these circles for most aptenesse in account, 
Proof.  as you shall perceive hereafter. now shall it be convenient to mark in what degrees the two tropics do cut those colours, for if you haue not erred, they touch the middle of the four and twentieth degree in every quarter of the colours. And if you haue done well, then procede to the making of the zodiac, which you shall draw thus. Open your compass to the same wydenesse that you did for making the colours, or the equinoctial,& then reckon from one of the poles( which you will) 23 degrees and an half, in any one of the colours, 
Pole Circles 〈◇〉.  and it will light in 66 degrees and an half, by cause the numbers from the poleward go backward.( as you confessed before) then with a lesser compass( for it shall bee meet that you haue diuers sorts) draw a circled of that circuit abouteche Pole, setting the fixed foot of the compass in the Pole, and stretching the other soot unto 66 degrees& a half. After this look whether these circles do cut like degrees in every quarter of the colours: and if it do, your work is right, else it must be redressed. These circles may well bee called Pole circles, or Polar circles. Then take your greater compass opened( as is before declared) to the wydenesse of a quarter of the equinoctial, 
The drawing of the zodiac  and set one foot of them in that poyncte where the Polare circled that is about the north pole, doth cross the tropic colour in that quarter, which goeth from that same Pole, to the 270. degree of the equinoctial, and holding that foot steady, with the other draw a circled about the Globe. 
Proof.  This circled will touch the two tropics in two of those places, where they cross the tropic colours: and also it will cross the equinoctial in two points, that is, in his very beginning, and in the end of the 180. degree. now to prove whether it be truly drawn or not, by an other means, 
An other proof.  set one foot of that compass( with which you drew the zodiac) in that point which is directly contrary to the first place, where you stayed hit: that is to faye, in the crossynge of the fouthe Polare circled, and that quarter of the tropic colour, which goeth from the South pole to the 90. degree of the equinoctial, and on that point prove whether the movable foot of the compass will exactly agree with the foresaid circled, which yf he do, it is well drawn, else is there some error, which must bee amended. This circled thus drawn, is the ecliptic circled, which goeth by the middle of the signs and of the zodiac. and these two poyntes wherein the fixed foot of the compass was stayed, 
The Poles of the zodiac.  are the Poles of the zodiac. But considering that the zodiac( as you heard before) hath in it twelve degrees of breadth, that is, on each side of the ecliptic line six, therefore open your compass to 84. degrees only, that is six degrees less then a quarter of the equinoctial, and set one foot of it fixedly in the one Pole of the zodiac, and with the other movable foot draw a circled, which will be a parallel to the ecliptic circled, distant from it in all partes by 6 degrees, and with the same compass unaltered, draw a like circled on the other Pole of the zodiac, which shall bee a parallel to the other two, and they three do make the full zodiac in length and breadth.  scholar. 
I understand all this very well, but I muse what those Polare circles mean, 
The Polare circles, and their use.  of which I heard no word before in the first treatise.  Master. 
I did of purpose omit them before, because they ar name of diuers men, as of joannes de Sacro Bosco and other later writers, for the circles arctic and Antarctike, contrary to Proclus, and all the greek writers, and I pourposed( and so do I still) to reserve the discussing of that repugnance, to the fourthe treatise, yet here was such just occasion ministered to use their help in finding the poles of the zodiac, by which poles they are described every day, by the revolution of the heauens, that I could not willingly neglect them: for although I might finde the poles of the zodiac without them, yet they bring a proof of the work with them, as before I haue shewed, and also they enclose all such stars as are within 23. degrees and a half of the Pole, and are the limits of the motion that the Poles of the zodiac do make about the poles of the world, as you shall better perceive hereafter. And because their names should not bee confounded with the circles, arctic and Antarctike, I think it most meet to call them only Polare circles, or Pole circles, which name the other circles may not justly challenge, especially because they are not fixed( as the Pole circles are) but be changeable as the regions change. which thing I will declare more largely hereafter, but now for the drawing of the circles arctic& Antarctike, that is( as I name them) the north circled, and the south circled, 
Circles arctic and Antarctik.  you must learn the elevation of the region for which the Globe is made, and according to it must you draw those circles, which thing because as yet it is not easy for you to do, I will in example of our own country show their description, namely for the vniuersitye of Cambridge, which standeth in even degrees of 52. Therfore reckon from one of the Poles 52. degrees in any colour, and it will light on 38. degrees( because the numbers go backward) and there set one foot of your compass, extending the other foot to the next Pole, where you shall stay it, and with the other foot describe a circled first about the one Pole, and then about the other: and those two circles shall stand for our circles arctic& Antarctike. And thus hath the Globe all those circles which were accounted needful unto it, except the Horizonte and the Meridiane circled, which are not so well placed in the Globe as without it, because they ought not to move with the Globe.  scholar. 
Where shall they be made then?  Master. 
That will I show you, as soon as I haue ended the Globe, which yet is not done, for the signs in the zodiac are yet vndrawen. First therefore ye shall draw by the ecliptic line within a corn breadth of it, 
The division of the zodiac.  an other circled as you did by the equinoctial, it forceth not on which side, but let the ecliptic line be more notable then it. Then consider that the zodiac is all ready divided into four equal quarters by the two colours, now it is meet to divide every quarter into three equal partes, and so haue you twelve partes in the whole zodiac, which stand for the twelve signs, which shall be distinct by lines drawn over thwarte all the breadth of the zodiac.  scholar. 
Those are not easy to draw, but error may quickly be committed, in making them wider in one place then in an other.  Master. 
Therfore to avoyde that error, thus shall you do. Open your compass equally with a quarter of the zodiac. then keep one foot of it steady in each division, one after an other, and with the other draw a portion of a circled cross overthwart all the breadth of the zodiac,& thus shall you do it exactly, 
Proof.  and in so doing, your compass doth try and examine the former division: for if at any setting of your compass it reach to short, or to far, and not justly on the thyrde sign, then must you correct your first division. When you haue drawn these twelve signs, thē must you divide every one of them first into two parts equally, and each of them again into three even partes, and lastly, every one of them into five just portions, and so haue you in every sign, thirty partes or degrees.  scholar. 
This division is like the dividing of the equinoctial and the colours, so that I may conceive the one by the other.  Mast. 
In dead they ar all three like in their general division, but yet in placing of their numbers, they differ each from other, for the equinoctial had his numbers continually proceeding from 1. to 360. The colours, stay their numbers at every quarter, never proceeding above 90. but the zodiac stayeth in a lesser number, for at every sign, his numbers change: so that from the beginning of each sign to the end of the same, you shall mark them from 10. to 10. thus: 10.20.30. and so like in all the zodiac no number is greater then 30.  scholar. 
I perceive that, sith you told me before, that every sign severally hath 30 degrees.  Master. 
Those divisions shall you mark with a little line drawn from the ecliptic circled to that other which is drawn within a corn breadth of it: yet at every ten degrees it will do well to draw the line somewhat longer from the ecliptic, that those degrees may be the easier to see and to reckon, and so may you do at every five degrees, but somewhat shorter then that other, and so shall you haue the degrees more notably distinct in sunder. now resteth no more but to give every sign his name, which you may do other by writing it at length, or else by setting their Characters and figures for their names, which I before haue set forth unto you in both forms.  scholar. 
That is easy enough to understand, but how shall I know their places?  Master. 
That is as easy also, if you mark the order of the circles. but for a full plainness you may begin at the tropic of Cancer, where the sign of Cancer doth begin, and in that quarter of the zodiac, which is on your right hand, and descendeth toward the equinoctial, set these three signs, Cancer, lo, Virgo, and so procede forward as the signs succeed in order: then will the second quarter haue Libra, Scorpius, and Sagittarius: and the third quarter, Capricornus, Aquarius and Pisces: and to make up the fourth quarter, ther resteth Aries, Taurus and geminy.  scholar. 
You name the second quarter of the zodiac to be the first, and so cometh it to pass, that you call the first quaiter the fourthe, as I remember your former doctrine.  Master. 
You may perceive, that I name them now not in their custumable order of quarters, but according to the order of this work, else if you can discern the place of Aries from the place of Libra, you may best begin with quarters of the zodiac The quarters of the year. The signs in every quarter of the zodiac, aunsweryng to each quarter of the year. 1. spring. Aries, Taurus, geminy. 2. Sommmer. Cancer, lo, Virgo. 3. harvest Libra, Scorpius, Sagittarius. 4. Winter. Capricornus, Aquarius, Pisces.  
Aries,& thē not only the signs, but the quarters will keep their accustomend order, as here in a table it doth appear: where I haue also annexed the quarters of the year for readiness of remembrance,& for the better occasion to mark the motion of the son in each of those quarters. And thus haue we ended the globe or sphere, with al the circles in it customably used, whose picture here you may se, as it will be drawn in flat form. 


A, C. is the Equinoctial circled.  
E, K. the tropik of Cancer.  
Q. L. the tropik of Capricorn  
Q. K. The zodiac.  
B, and D, The ij. Poles of the world.  
F, I. The arctic circled.  
P, M. The Antarctike circled.  
G, H, and O, N. The two Polare circles.  
G, and N, The ij. Poles of the zodiac.     diagram of the astronomical circles on the celestial sphere.  

The makig of the Horizonte.  Now for the horizon& the Meridiā thus shal you do. Take 2. square bords of a quarter of an inch thick,& let the one be in breadth 3, inches,& the other one inch& a half more then the diameter of your globe, in the middle of the broder board take a centre,& on that centre make a circled, scarcely a corn breadth wider thē your globe is, which you shal thus find out. Open your compass as wide as ij. signs in the zodiac, or 60. degrees in the Equinoctial, any other of his great circles, and that compass will make a circled just in bigness with any great circled of your Globe, therfore make you the circled in the square board, almost a corn breadth wider then that circled of your Globe. And without alterynge of the compass, make the like circled on the middle point of the narrower board. Then haue you taken the just measure for the inner part of your horizon, and also of your Meridian.  scholar. 
I doubt not but I can do that with a little labour by often trial where the middle of the board is. but is there no way to finde the place of the centre quickly?  Master. 
Yes truly, and that may you do diversly, but one ready way is this. 
To find the middle in any square.   
draw with your ruler a right line from corner to corner, or if you list, make it only about the middle of the board, as you can aim with your eye, but be sure that you draw it long enough, then turn your ruler to the other two corners, and make a line cross that other, and where they do cross, there is the middle of the board, on which, as on a  diagram of the construction of a celestial sphere. centre you may make your circles. 
The Pathway of Ge ometrye.  This work might you easily gather out of the 35 conclusion of the Pathway.  scholar. 
I see now continually more and more, that the pathway serveth to other uses, then I took it.  Master. 
It is a common instrument to many arts, and infinite conclusions: and if you procede to farther knowledge of higher artes, without good exercise in it before, you do as a carpenter that goeth to work without his tools. But now to proceed, When you haue drawn this circled on both those boards, on the same centre make an other circled in each board, a corn breadth wider then that other: and after that an other somewhat wider, as you may aim two corn bredthes: and then the fourth wider then the thyrde by a quarter of an inch: and yet again one other a quarter of an inch wider then the fourth. and these five circles shall you make in both the boards, and you shall divide them both in one manner, after this sort.  
divide the innermost circled save one, into 4. quarters first, and after that, every quarter into three partes, and each of those partes into 30. as you did before in dyvers circles of the Globe. then set your ruler to the centre, and to every division,  diagram of part of a celestial sphere. and make a line from that second circled to the third: but at every 10. degree you shall draw the line longer, that is unto the fifte circled, and at every fift degree, you shall draw the line to the fourth circled, so shall you both place your numbers best, and also reckon them most surely and most speedily in all uses of them.  scholar. 
All this I can do by the former examples, if I knew how high the numbers shall proceed. for in them I remember ther was 3. varieties before, each unlike to other.  Master. 
And in these shall be somewhat diuers from them all. for here shall be set double numbers, but yet the fyrsts placynge of the numbers shal be like as it was in the colours, I mean in each quarter 90. and those numbers shal be set in the space, between the thyrde circled and the fourthe. Then shall you set the like numbers between the fourthe circled and the fyft, but not in like order, for their order shal be contrary to the other, so that where 10. stood in the first order,& then 20, and so increasyng to 90. in this 2. order you shall set 90, and thē 80,& so decrease unto 10. as here in example you may se, where I haue drawn the Meridian line sufficiently divided, for the use of the sphere: but thē the horizon must haue other things drawn in it, as in this figure following you may se. for in the inner part it is divided like unto the meridian, but then without those divisions it hath a certain small space all black, left for a partition, without which ther are drawn 3. other circles, each one a little wider then other,& the widest is uttermost, and that last circled is as large as the board will permit, so that the whole breadth of the horizon is an inch& a half, for because the whole board was 3. inches wider thē the globe. And the Meridian shalbe but 3. quarters of an inch broad, seing his board was but 1. inch& an half wider thē the globe. Now for the division of the utter part of the horizon, you shall dyuide the uttermost of the three circles into eight partes only: The second circled shalbe divided into 16. parts And the third or innermost of those 3. shall be partend into 32. partes, which do betoken the points of the Shypmans compass. or the 32. winds notable in sailyng, as some men list  diagram of part of a celestial sphere. to call them. If your Horizonte bee large enough to receive their names, you shall writ them at length, else may you writ letters for them, as your own phantasye liketh.  
Their names are these following, agreeable to those places, and letters, which I haue drawn in the horizon.  

THE NAMES OF THE thirty AND TWO points IN THE ship compass, which bee the winds names that Mariners sail by.  {fleur-de-lys} north. ↑ south. ☓ east. ✚ west. A. west and by north. B. west northwest. C. northwest and by west. D. northwest. E. northwest and by north. F. north northwest. G. north and by west. H. north and by east. I. north northeaste. K. Northeaste and by north. L. Northeaste. M. Northeaste and by east. N. east northeaste. O. east and by north. Q. east and by south. R. east southeast. S. southeast and by east. T. southeast. V. southeast and by south. X. south southeast. Y. south and by east. r. south and by west. Δ south Southeweste. z Southeweste and by south. θ south west. ξ Southeweste and by west. Π west south west. Σ west and by south.  

The foot of the Horizonte.  And thus now is the horizonte fully drawn. That Horizonte must you set vpon a foot, that it may stand like a round table: and that foot must be made of two half circles of wood, somewhat thycker then the Horizonte, but of the same compass in the innermost parte, and they must be joined so, that the one may cross the other, with right corners, and themselves bee fastened on a strong foot, that may bear all the whole frame, with the Globe. The joining of them unto the horizon is diversly to be imagined, for if their heads be flat, then must you haue nailes or else pings, that must pierce the horizon and enter into their heads, otherways there may be left certain tenants on their heads, and then must you make like morteyses agreeable to them, in the Horizonte, to receive those tenants.& so may there be imagined diuers other forms, which I leave to your own devise.  scholar. 
If I might see their form I should be much easyed in framynge it.  
 diagram of part of a celestial sphere. 
The form of the foot of the Horizonte.   Master. 
Here is the form, with their sockets,& one namely for the Meridiane, in that arm also that goeth from East to west. Howe be it, it shall be best, to fasten those arms under the Horizonte in the south east, south west, north east, and north west, and so shall the Meridiane sink beste into the Horizonte, with an easy socket in the meeting of those arms, so that the just half of the Meridiane only may appear above the oouer edge of the Horizonte: in which thing practise shall instruct you farther. As for the foot, make it as you think beste. But now must you cut out of both, the Meridiane and the Horizonte all that is within the innermost circled, and so must you pare away all that is without the uttermost circled, to make them both like just circles. Also you must make in the Horizonte two sockets, one by the south line, and the other by the north line, so that the one side of those sockets which is toward the east, shall touch the south and north lines, and the other side shall go westward from both those lines, as much as the thickness of the Meridian is: and the length of each of those sockettes shall bee agreeable to the just breadth of the Meridiane, so that the Meridiane may entre justly into those socketts, and turn in them without stressynge.  

The form of the foot unto which the arms are fastened that bear the Horizonte. which therfore wolde be made large, that it may bear the Globe with al his circles steddilye.   diagram of part of a celestial sphere.  Schol. 
This trobleth me somewhat, because the sockettes be not iustelye one against the other, but both stand toward the west half of the Horizonte.  Master. 
It wolde trouble you worse to remember that the Globe must be fastened to the Meridiane on the two poles,& both they placed within the Horizonte.  scholar. 
That is strange in deade, for so should the globe bear more toward the west, then toward the east: and so all were misframed.  Master. 
To avoid all that, you shall make two small clampes of thin brass plate, 
The hanging of the glob in the Meridiane.  and bow them so in the middle, that when they are tacked to the side of the Meridiane in two contrary points, just over that line where 90. is set, they may receive in their bought the poles of the globe. I mean here by the poles two short pings, which shall go through those clampes of brass, and be fastened or driven into the two Poles of the Globe, except you will take the pain to pierce a hole through the globe, from one Pole to the other, for so may you make an axletree to run clothe both the clampes and the whole Globe, which is all to one effect. And by this means shall the Globe not only hang in the just middle of the Horizonte, but also the one side of the Meridian( which hath the divisions in it) shall point exactly the south and north partes of your Globe, which will be most exactly seen, if you consider the thickness of your axletree, and frame your clampes so, that the one half of the thickness of the axletree, may be let into the side of the Meridian.  scholar. 
I think I do conceive the true meaning of your words, howe be it to bee out of all doubt, I will be bold to see your Globe, at some convenient time.  Master. 
So shall you do well, for many things in the making, and in the use also of instruments, are better perceived by a little sight, then by many words▪ and thus haue I ended the making of this Sphere.  scholar. 
Yet is this sphere unlike to that, which is commonly used, by the name of the Sphere, and is made all together of hoops.  Master. 
You shall understand that this is the true sphere, which I haue described, and that other( which you mean) ought rather to be called an Armylle or ring sphere, then absolutely a sphere, 
The Armylle or ring sphere.  for it is but a part of this other Sphere: I mean, that it doth contain only the circles of the sphere and not the substance of it. And therfore do the many men call that a pierced sphere, and is name in Latin Sphaera pertusa, where as they call the other sphere, a Sound or massy Sphere, that is in latin, Sphaera solida▪ but seeing that it is not only commonly received by the name of the Sphere, but the use of it is very apt in teaching, and it is more easy to bee made in slyghte form for young learners then is the soonde sphere, and for other considerations, which now I omit, I will also describe the composition of that Armylle sphere. 
The making of the Ring sphere.  first you shall make of wood or of brass( as you list to bestow the coste) four hoops of one bigness in compass, the one of them being three times so broad as any of the other, as your eye may aim. Then divide each of those circles into 360. partes, one of them according as you did divide the equinoctial in the former sphere, 
The equinoctial. ij. colours.  and the other two like unto the two colours, and the fourthe which must be the brodest of them, you shall divide, as you learned to divide the zodiac in the other sphere. And when they are thus divided, 
The zodiac.  you shall call them by the names of those circles whose division they follow, wherefore if the zodiac haue more breadth then twelve degrees are in length, you shall abate the overplus, allowing it but 6. degrees in breadth on each side of the ecliptic line, which as you remember before, did run by the middle of the zodiac.  scholar. 
Then I perceive I must make in this zodiac an ecliptic line, and all the signs with their divisions, as I learned in the other zodiac.  Master. 
You shall make them as like as you can devise. Then shall you join the two colours so together, that the one of them may cross the other,( as they do in the Globe) with right and equal corners, observing well that the places of their crossyng be in the just points where 90. is set, in each of them: and those places must be called the Poles of the sphere. Then put on them both crossewaies( like a girdle) the equinoctial circled( so that it do cross them exactly with his middle, 
The Poles.  in those points where the number of each quarter doth begin, and that the beginning of the equinoctial, in number be against the just middle of one of them, that is, of it that standeth for the equinoctial colour, and then shall the 180. degree of the same equinoctial stand justly on the middle of the same colour, in the contrary point: and the other colour which is the tropic colour, shalbe joined with the 90. degree,& the 270. of the equinoctial, 
The .ij. tropics.  in ij. contrary points. Then shal the 2. tropic circles be set on the colours equidistantly to the equinoctial, so that they be fastened on the 23. degree& a half from the Equinoctial, whereby you may easily conceive, that they must be somewhat lesser then the equinoctial, that they may join closely to the four colours. Then must you haue two other circles of one bigness, that may join justly with the colours, 52. degrees from the equinoctial, on each part equally distant: and those must be called the arctic, and Antarctike circles, 
The arctic and Antarctik circles  or the South circled,& the north circled. Beside these you shall make two other lesser circles of equal bigness, which shall be set on the colours also equidistante from the other parallels: and they must be fastened with their middle on the 66. degree& a half from the equinoctial on both sides, that is 23. degrees& a half from each pole, and therfore I think meetest to call these circles peculiarly, Pole circles. This being done, 
The Pole circles.  you haue 2. colours and 7. parallels fixed on them. now must you set the zodiac a slope ways cross the equinoctial, so that his middle line, name the Ecliptyke line, may touch the middle of each tropic, and that may you try by the utter edges of the breadth of the zodiac, 
The zodiac.  for the one must touch the 29. degree and an half, and the other the 17. degree and an half from the equinoctial. And thus is this sphere plainly made, whose picture I haue here set, as it will bee drawn in a flat form. Then if you make two small holes clothe both the colours, 
The Axtre The Meridiane and Horizonte.  in the places of their crossynge, where the Poles of this Sphere are, and put a small axe three clothe them, you may thereby join this Sphere to his Meridiane first, and then place it in the Horizonte, as you didde place the Globe: for those two circles, are like in both these Spheres. 
The Proportion of the circles in a sphere.   Geometrical diagram.  scholar. 
I understand al things here in well enough as I think, save y t I doubt somewhat of the quantity of the parallel circles. for although I know by trial I may at length make them meet, yet would I gladly know their measure before hand, if I might, for so shall I be sure to work most certainly.  Master. 
Your desire is good. and all be it that the writers of the Sphere haue omitted it, as they haue done many things else, yet will I give you a rate of proportion drawn out of the tables of cords and Arkes, called commonly in latin Tabulae Sinuum.  
first you understand, that the equinoctial, the zodiac and the two colours must be of one compass, that is of one bigness, although not of one breadth, for the zodiac must be in breadth twelve degrees, and the other circles as small as they may be, and bear any stress, for the smaller they be, the better they are, and most apt for the use of the sphere. The other syxe parallels would be made as small as they may bear conveniently, and in length they must haue three dyvers rates, which I will set forth, both in measure, and also in number, to the intent that you may alter the measure to what bigness that you list, by the help of the number.  
And lo here is there forms.  
1. The equinoctial with his division.  
 diagram representing the equinoctial line.  
2. The colours both of one form.  
 diagram representing the colures line.  
3. The zodiac with the 12. signs, and his breadth of 12. degrees.  
 diagram representing the colures lines.  
4. The length of the two tropics.  
 diagram representing the tropic lines.  
5. The proportion of the arctic and Antarctike circles.  
 diagram representing the Arctic and Antarctic circles.  
6. The proportion in length of the two Polare circles.  
 diagram representing the Polar circles.  
Here you see six several forms.  
The first representeth the just length of that plate or hoop, that shalbe the Equinoctial, and in it is the divisions set forth as they ought to succeed in order, with their numbers agreeablye.  
The second is the form, that serveth for the two colours with their numbers and divisions, as they should be set.  
The third is the draught of the zodiac with his just breadth of six degrees, and the twelve signs set forth with their degrees orderly. And these three circles be all of one length.  
The fourth circled doth represent the due length of the two tropics, which must be shorter then the equinoctial by 30 degrees, for it is equal to 330 partes of the same: so that the length of the tropic doth bear the same proportion to the equinoctial, as 11 doth to 12.  
The fift plate, resembleth the measure of the circles arctic and Antarctike, and is in length equal with 222. degrees of the equinoctial, which proportion is as 37. to 60.  
The sixte plate setteth forth the just measure of the two Pole circles, which is equal to 144. degrees of the equinoctial, and so it beareth to him the same proportion that 2. doth bear to 5. and each of those circles parallels are divided like unto the equinoctial, into their 360. degrees.  scholar. 
This is so plainly set forth, and so certenlye, that I see no doubtfulness now in the whole work, for the making of it: for these plates are so made, as if they were of metalle, and should haue both the ends soudred together. so that if any man will make them of wooden hoops, he must allow so much more in the length of each of them, as will suffice for to bind them fast in compassed form. But these hoops of this length will make but a very small Sphere, yet by the same form of the numbers, and their proportion, I may make a sphere of what bigness that I will.  Master. 
So may you do certainly. and if you will haue a Sphere twice so much in compass as these hoops would make, or thrice, or 4. times, and so forth, this measure also may serve you, taking for each circled so often times the length of the like here in this patron, as you will haue your Sphere greater then this in number of times.  scholar. 
And so I perceive, if I would make an other three times and an half so big as this, I ought to take the measure of each circled three times and an half. and so for all other proportions.  Master. 
truth it is, save that you must augment the breadth of the zodiac only in like number of times: But as for the other circles, they are broad enough if they be not to weak, for the smaller they be, the better is the Sphere, sith their breadth doth serve only for strength, and for to receive the divisions as here you see.  
And thus haue I described unto you both sorts of Spheres, that is the Globe or massy sphere, and the pierced sphere or Armille. One other form of Sphere there is, which excelleth both these forms, and is wonderful apt for the teaching and expressinge of the Theorikes of planets, therfore I will reserve it to that place.  
Here needeth no repetition, because all standeth in woorkynge of the former lessons before repeated, and therfore this second treatise shall end here.   

THE third TREATISE, wherein IS BRIEFLY TAVGHT the use of the Sphere, for certain conclusions of daily appearaunces and other like matters.  MASTER. 
NOW you look TO hear somewhat of the use of the Sphere, as you shall do anon: And for an induction thereunto, you must diligently know the plagues of the world, 
The plagues of the world.  amongst which there are four principal, that is, the east, the west, the north and the south: and between these are there other diuers, which are sufficiently set forth in the horizon of the Globe, as much as shall at this time bee needful.  
You must know also, 
The parallels in the earth.  that every one of the parallels in the heaven hath a like circled in the earth proportionably drawn, and answering to those that are in heaven, in just rate of distance. So is ther first an equinoctial in the earth exactly drawn under that equinoctial in heaven, 
The earthly equinoctial.  and it divideth the whole earth into two equal partes, between the south and the north, so that it pointeth precisely the middle of the earth, in that respect: 
The middle of the earth  and all the partes of the earth from that earthly equinoctial toward the north, is called the north parte of the earth: and of the world likeways all that is beyond that circle towards the south, 
The north part of the earth. The south parts of the earth.  is called the south partes of the earth.  scholar. 
Yet wee do call that parte only north, that is north from us: and that wee call south, that is south from vs.  Master. 
You must consider that there is two forms of speaking in such talk, the one vulgar, and commonly used, as well of the unlearned as of the learned, and that maketh not the comparison to the whole world, which few men doth know, but it regardeth principally their own country, which they do best know. The other talk is general in form of speaking, because it hath respect to the whole earth, and yet is it not general in knowledge, for few men can aptly skill of it: so that both are true in their due use, but the one is less known then the other.  scholar. 
So I perceive then, that although in common talk we do call spain south, and likewaies other countries, yet is not that true in comparison to the partes of the whole world, but in comparison to us, for our common talk hath chief relation in such things to our own country. But I pray you then, where is the middle of the earth, from which we must make our account, and unto which we must haue regard in all such general talk?  Master. 
That will I tell you anon, but first we must end that matter that we began withall, touching the parallels on the earth, whereof I haue name yet only 
An example of the parallels in earth agreeably to the parallels in the sky.   diagram representing the parallel circles in relation to the celestial sphere. the Equinoctial, but now must you imagine other 2. parallels next unto it, the one toward the south,& the other toward the north, 
The tropics on the earth.  which may answer to the 2. Tropiks. And for a general knowledge first, understand this, that al nations over whose heads the son doth run directly, when he is in the highest point toward the north that is in the beginning of Cancer, where he describeth the tropik of Cancer in the sky, al those people I say dwell just in the course of the like tropic in earth: And contrary ways, all those people over whose heads the Son passeth directly, when he is in the Winter tropic, they dwell in the course of that south tropic in earth, and haue the son right over their heads that day that he entereth into the first degree of capricorn.  scholar. 
By these examples I can imagine the south and north circles in the earth to be under the Antarctike and arctic circles in heaven, 
The other parallel.  and so two Polare circles in earth under the two Pole circles in heaven. Then are there seven parallels in earth, answering to seven other in the sky.  Mast. 
That is sufficient. howbeit for this time I will omit the circles arctic& Antarctike, because in mine opinion, they make no Zone in earth, though all the greeks in appearance do say the contrary, but I will bring invincible reason for my purpose, when we come to the scanning of repugnant sentences, especially when I do disagree with the greeks, which are the fathers of wit. but in this point of the five Zones, I like much better our own country man John de Sacro bosco as I will now only affirm, 
joan. de S. Bosco zonarum restaurator & in the fourth treatise will prove it substantially. Therefore to continue our matter as we began: there are made by these v. parallels, v. large rooms in the heaven, and other v. in the earth, 
The five zones.  agreeable to them in heaven, which spaces are called Zones.  Scholl. 

Example of the zones.  By your favour, ther are six Zones, if every space between the parallels be accounted for one zone, and that doth not only the account of thē by memory declare unto me, but also the sight of them in this figure, which is commonly name the figure of the Zones.  Master. 
neither doth the account deceive you, neither yet the sight of the figure, but want of knowledge of their natural qualities, which therefore I will tell you by and by, though these parallel circles do sufficiently distinct them, as their notable bounds, 
The qualities of the five zones.  yet by the qualities bee they distinct also. for as reason doth lead you, all the space between the 2. tropics,  diagram classifying the climates between the circles of latitude, illustrated by the four winds at the corners. 
MERIDIES.  
A ZONA FRIGIDA.  
B ZONA TEMPERATA AVS.  
C ZONA TORRIDA.  
D ZONA TEMPERATA BOR.  
E ZONA FRIGIDA.  
SEPTENTRIO  must needs bee esteemed very hot, because the son runneth always between thē, so that in the middle between the two Tropiks is the equinoctial line, from the which the Son is never fully 24. degrees so must it seem to be as hot there in the middle of winter, as it is in spain in the middle of summer, and for this cause all the old Cosmographers did think that that country might not be inhabited for heat: and therefore called all that space between the two Tropykes, the burning Zone, 
The Burning zone.  called in latin Zona torrida. And of each side of it, they noted two Zones, one under each Pole, which they called the frozen zones,( and are name in latin, Zonae Frigidae) where for extreme could, 
The frozen zones.  they thought that no man might dwell. and between those frozen zones,& the Burning zone, they appointed two Temperat zones,( called Zonae temperatae of latin men) which were partakers of the heat on the one side, 
The Temperate zones  and of the could on the other side, so that of both, there was made a temperate mixture. Now se you that between the equinoctial and the one tropic, there is no other quality, then is between the same equinoctial and the other tropic, wherefore all men( except only Polybius) did account the space between the tropics but as one Zone: so that the equinoctial is the bound of no Zone, but passeth by the middle of the Burning zone.  scholar. 
now I see( as I haue had at other times often occasion) that we learn many things when we be children, which we understand not all when we bee men, for by this talk I remember that both in yield& Vergile I learned the distinction of those 5. Zones, but what was to be understand by them, I never know till now. And now I see reason that between the 2. tropics, all may well be accounted the burning Zone, where no man can dwell, as both my authors affirm.  Master. 
They had spoken more modestly, yf they had said that ther had been painful dwelling for heat.& likwaies of the could Zones, that ther is hard dwelling for could: but of this will I more exactly reason in an other place, and for this time( as the truth by experience is known) I suppose that all the 5. Zones haue their inhabitants, though not so plentifully as the two Temperat zones now haue, especially this temperat zone that we dwell in. Who is it that hath not heard of the isles of Molucca, and of Samatra, where the Portingales get the great plenty of rich drugs and fine spices? and all that haue been there, confess that those places ar right under the equinoctial line: and calicut is but little from it, for it is  diagram representing the circles of latitude on the celestial sphere. 


A. C. The Horizonte.  
B. The point over the head.  
*. The Poles of the world.    
The zodiac and the other circles doth appear of themself.  more thē 19. degrees beyond the tropic of Cancer toward the south so that it is within 5. degrees of the very equinoctial line. Now therfore I think it most apt place for my purpose to begin at these countries, over whose head the equinoctial doth rightly pass, so that they must needs see both the Poles in their Horizonte.  Sc. 
That doth reasonably follow, because half the heaven justly appeareth above the horizon, and the other half is under the horizon. And also I perceive that if I set the sphere so that the equinoctial stand full nought, then will both the Poles be in the very Horizonte. as this position of the Sphere doth show.  Master. 
You consider it right. And because the equinoctial doth cross the horizon with right angles( for all 4. angles are equal) therfore is this placing of the sphere called a right sphere: 
A right Sphere.  so that all other nations, which haue the one Pole above their Horizonte, must needs haue the other Pole under their Horizonte, and the equinoctial declinith from the point right over their heads, that way as the hidden Pole is, whether it be toward the South, or else toward the north.  scholar. 

The use of the material sphere.  All this seemeth easy to me, as long as I behold this material sphere? but when I do not confer it with your words, then your sayings appear the more doubtful.  Master. 
For that cause did I teach you the making of it, before I instructed you in the use of it, knowing how great a help the sight of the eye doth minister to the right and speedye understanding of that, which the ear doth hear. But again to our matter: in all places where the equinoctial doth decline from the point over the heads of any inhabitants( which point is commonly called the Zenith) there the equinoctial maketh unequal corners with the horizon, 
The Zenith  and therfore is that called a Bowyng sphere, 
A bowing Sphere.  or a Leanynge sphere; because the equinoctial boweth or leaneth toward one side of the horizon, more then toward the other side.  scholar. 
I haue heard it called a Crooked sphere also.  Master. 
That name is unapt for this arte, for there can bee no crooked corner between the equinoctial and the Horizonte, which might make that name meet for the matter: and( as I haue said) the Sphere taketh those several names of his diuers position,  diagram representing the zodiac on the celestial sphere. 


A. C. The Horizonte.  
B. The Zenith.  
*. The Poles.    
The zodiac, the equinoctial and the other circles do appear of themself.  and according to the corners that the equinoctial doth make with the Horizonte.  
And this may you consider herein, that there is no Zone but one that can haue a right Sphere: and to speak precisely, but one tract in that zone, which is the very middle of the burning zone, right under the equinoctial where as there be innumerable places that haue Leaninge spheres, which you may call obliqne spheres or Declininge spheres, if you delight more in latinelyke names then englishe.  scholar. 
So I perceive that both we and all other nations which dwell not right under the equinoctial line, must be name to haue a Leaning sphere. And this I consider reasonably, that in some countries the sphere doth lean and bow more then it doth in other, which difference I wolde gladly understand.  Master. 
The diversity in leaning of any sphere, is agreeable to the elevation of the Pole in every country, so that where the Pole is highest above the Horizonte, there the sphere leaneth most: and where the Pole is lower and nearer to the ground, there the sphere leaneth lesser.  scholar. 

The height of the Pole  Howe shall I judge truly the height of the Pole?  Master. 
That true and exact iudgement will I not treat of as now, to avoid interruption in teaching: it shall be sufficient for this place to show you a plain and easy form, with the use of an instrument that may help you somewhat in marking the height of the son and moon and any other stars that you list. and the manner of it is thus.  
You shall take a quadrant  depiction of a quadrant. ( whose composition I haue taught amongst other instruments in the Gate of knowledge, but this which you se here, is the form of the most plainest sort) and by the two sights of it, you shall mark the height of the north star commonly called the Pole, and when you se it through both the sights, thē mark what degree the line of the plommet doth touch in the margin, and, that may you call Latitude of that region, or the height of the Pole, for this time and place where no preciseness is required. for now it is sufficient for you to understand generally, that there are such diuersyties of elevation of the Pole in diuers countries: and thereby may you understand, that all Spheres bee not alike in their position. As for example. In the south partes of england about Sowthehampton, 
Southehampton.  the Pole is not fully 51. degrees high, and in the isles of Orkenaye, beyond Scotlande, the Pole is above 62. degrees high: this may easily bee tried by them that list to travail, but if you list to go no farther then york, 
york.  you shall finde the elevation above 54. degrees, and so at Edynburghe shall you finde the elevation about 57. degrees. 
Edynburgh  And thus within your own country may you understand a great diversity, whereby you may conjecture the diversities that bee in other partes of the world.  scholar. 
This is so appearaunte to them that will travel any thing for knowledges sake, that they cannot pretend any ignorance, but wilful ignorance: but herein I finde one doubt, that maketh me to muse, 
The alteration of the Horizonte  for in trauelyng thus from one place to an other, whereby the Pole is diuerslye changed in his elevation, I can not think that the Pole itself doth change his place, but that rather the horizon doth alter, from which we must take the measure of height of the Pole.  Master. 
You say well, for in dead there is no such motion in heaven, that may make the Pole so notably to change his place: but as we do change our standing, so doth there appear a new Horizonte, which causeth the Pole to seem higher. if we go toward the north, for then wee see more of the sky( that ways) above our horizon, then we did see before: but if we go toward the South, then will the Pole seem lower and lower, still as we go Southward: not because the Pole changeth, but our horizon changeth: for now wee see more of the sky toward the south, and less toward the north: but yet generally as much as wee leefe in the one parte, so much wee win in the other coast, so that evermore we may see half the sky. 
Whether the Horizonte do move or not.   scholar. 
Then this is my doubt, how I shal understand your former words: for I remember you said that the horizon was a circled immovable, and did not turn as the circles in heaven do:& now you haue plainly declared that the Horizonte doth change, which can not be without moving of it.  Master. 
You haue answered your own question, if you mark it well: for the Horizonte moveth not as the circles in heaven do move: that is to say, it goeth not round about the earth by a daily course, but it standeth steady while the heaven moveth, so that if you never change your place, your horizon will never move. And to speak more exactly: the horizon moveth not, though you move never so far: but rather should we say, that you are come into an other Horizonte, when you are come into an other country.  scholar. 
It must needs appear so, now that I do consider the matter more earnestly: for when I am at London, I see the same Horizonte that all other men there do see: then if I go to york, I see the horizon of york, and not of London, so that the horizon of London remaineth as it was, and so doth the horizon of york, whether I tarry or go. And thus I perceive great alteration in the Horizonts between south and north, whereby the pole is diversly altered in height above the horizon. What if I go eastward or westward, shall I not finde the like alteration?  Master. 
It must needs appear yes. for the same reason that causeth you to change your horizon between south and north, the same will cause it to change between east and west. And for declaration thereof, answer me to this question: Do you think that there is any such country far east from us, 
Example of calicut.  as the Portingales report calicut to be?  scholar. 
It were as much folly to make a doubt of it, as it were to make a doubt of Babylon, or jerusalem.  Master. 
And do you think that the son doth rise to us and to them at one time?  scholar. 
It can not be. for this much I may gether by that I haue learned already, that the rising of the son and of all other stars, is the appearing of them above the Horizonte, so that they rise to us, when they begin to appear above our horizon: and they rise to them in calicut, when they appear above their Horizonte. And further I gether now by your brief admonition of the change of the Horizontes, that as between south& north in our own country, we may perceive notable diversity, so may wee consider the same much more in so great a distance, as calicut is noted to be from us, which I haue heard to be name above 15000. miles, and that is far greater( yea 20. times) then all the length of england and Scotlande together. wherefore I gather that the diversities of the Horizontes must be twenty times so much, as was between southampton and the north parte of England.  Master. 
The distance is not so much, nor the difference so great, but by means that the Portingales do sail a marvelous compass in going thether, they account the distance by that compassed course, which is far from our talk now, for we must ever take right distance by a strait line, as often as we do speak of any such matter. how be it for examples sake, suppose it to be. 6000. miles east from us, 
The diversities of the day in dyvers Regions.  it seemeth to be more then a quarter of the whole compass of all the earth,( as I will prove it in the next treatise) and therfore must the son at the least rise 6. houres to them sooner then it doth to vs. do you perceive that?  
 diagram representing the lines of midnight on the celestial sphere. 


A.C. The Horizonte of London.  
B. The Meridian of it.  
A. The east to London, and the nonesteede to calicut.  
D. B. The Horizonte to calicut.  
D. The east to calicut, and the line of midnyghte to London.  
C. The west to London, and the line of mydnighte to calicut.     scholar. 
The Son( as all men knoweth) doth compass all the earth in 24. houres, then must it compass half the earth in 12. houres, and a quarter of the earth in 6. hours. this is as plain as can be:& thē it must needs follow, that if they bee a quarter of the earth more toward the east then we, they must see the Son 6. houres sooner then wee.  Master. 
And likewaies they that dwell farther east then they, as the inhabitants of Molucca do, must needs see the son before them: and those that dwell more westerly then they do, as at jerusalem, or at Constantinople, must haue the day spring later then they that be at calicut. And thus you may consider, that the Horizontes do change as well between east and west, as it doth between south and north: As this figure sheweth for London and calicut.  scholar. 
That is plain. for if all those places had one Horizonte, then should the son rise to them all at ones.  Master. 
And as their morninges do differ, so must their noonetyde differ also.  scholar. 
No man that hath reason can deny that.  Master. 
Then must their Meridian circles differ in like sort, seeing they be the limits of the nonetide.  scholar. 
So I perceive that between east and west, the Meridianes do change, as well as the Horizontes: and hereby I understand, that when it is son rising at calicut, it is not day with us, by 6. houres: and when it is noon with them, it is 6. of clock in the morning with vs. and so of all other houres, which all appeareth by the former figure. houres, which all appeareth by the former figure.  Master. 
This standeth for the declaration of diversities of dayes in diuers regions: but yet you haue not heard what causeth the diversities of dayes in one region.  scholar. 
Yes for sooth. I remember that you reproved me for saying that the long daies caused the son to shine long: and you turned that sentence, affirming, that the long shinynge of the son doth make the daies long, and the short shinynge of the son, doth make short dayes.  Master. 
And are you satisfied with that reason?  scholar. 
I think it reason good enough.  Master. 
The reason is good, but not enough, sith farther reason is to be given. What maketh the son to shine long? can you tell?  scholar. 
By your help I trust to know it.  Mast. 
Set your Sphere before you, and first turn it so that both the Poles may  diagram representing the zodiac and circles of latitude on the celestial sphere. touch the horizon, which is the situation of the right Sphere. Then do you se that the horizon doth cut not only the equinoctial circled in 2. equal halves, but likeways doth it cut both the tropics, equally into 2. even partes, so that there is as much of each of them above ground, as there is beneath the Horizonte: and contrary ways. wherefore it must needs appear, that the son when he runneth in any of those three circles, is like time above the horizon, as he is under it, so must the daies and the nyghts be equal, not only when the son is in the equinoctial circled, but also when he is in any of the both tropykes: but this equality of dayes and nights, when the son is in any tropic, is privately appropred to the right sphere: for in all other varieties of the Bowinge spheres, then is the greatest difference in all the year, between the day and the night, when the son is in any of the tropics. as for example: Set the sphere to what elevation that you list. that is to say: Raise the Pole as many degrees above the Horizonte as you will.  scholar. 
I haue set it now( as here you see) to the elevation of 52. degrees, which you say is the elevation at Cambridge.  Master. 
And now may you see that the equinoctial only is equally divided by the Horizonte, and that the two tropics are very vnequallye diuyded, so that the tropic of Cancer hath almost three quarters above the Horizonte, and little more  diagram representing the zodiac and circles of latitude on the celestial sphere. then a quarter under the horizon, where contrary ways the tropic of capricorn, hath almost three quarters under the ground, and little more then one quarter above the horizon: whereof it must needs follow, that when the son is in the summer tropic, he is almost three quarters of the natural day above ground, and little more then one quarter of the same day under ground.  scholar. 
I know your mind very well, and I do gather thereby, that when the day is at the longest, it is almost is. hours day, and but lytte more then six hours night. And contrary ways in the shortest of winter, the day is little more then six hours long, and the night almost is. hours. And farther I hear you call the whole space of 24. 
A natural day.  hours a natural day: But I know not yet the reason of that name.  Master. 
By that name of addition, the whole day of 24. hours is distinct from the artificial day, which is from son rising to son setting: 
An artificial day.  and that artificial day is most commonly understand, when men speak of the day. therfore for a difference it is good to use such an addition. But now for the better practise, set your globe to some other elevation.  scholar. 
I trow I haue set the pole high enough.  Master. 
Let it stand. What is the number of the elevation?  scholar. 
I do see between the Pole and the horizon in the  diagram representing the zodiac and circles of latitude on the celestial sphere. Meridian dyvers numbers, but I take that number only, which touchith the horizon, and I take that also of the two orders of numbers, which descendeth from the Pole, and that is here now 71.  Master. 
That is the latitude or elevation of the Pole at Wardhouse, where our new venteterers into Moscouia do touch in their voyage: but now mark the variety of the tropiks to the horizon: The tropic of Cancer is( as you see) more then four degrees above the horizon clear, so that the whole 2. signs of geminy and Cancer, with 5. degrees of Taurus, and as much of lo, doth never set under the horizon.  scholar. 
Then while the son is going through those signs, from the 25. degree of Taurus, to the 6. degree of lo, it is continual day, because the son doth not set under their horizon. but I pray you how long time is that?  Master. 
It is from the 7. day of May until the 19. day of july; 
The longest day at Wardhous is 73. diaes continual.  so that it is continual day with them by the space of 73 of our dayes, which is almost two months and an half.  scholar. 
This is marvelous strange to me.  Master. 
Yet shall you hear more strange matter then that: set your Sphere so, that the equinoctial may be justly in the horizon, and the north Pole right up in the place of the Zenith.  scholar. 
That haue I done, as here you may see.  Master. 
now mark how much of the zodiac doth never go under that horizon.  scholar. 
Howe shall I perceive that?  
 diagram representing the zodiac and circles of latitude on the celestial sphere.  Master. 
turn the Sphere round, as it should move naturally on his own poles, but stir not the Horizonte.  scholar. 
Hereby I perceive that 6. signs, Aries, Taurus, geminy, Cancer, lo, Virgo, do never set under the horizon, but continue always above it.  Master. 
Then while the son is in those six signs, he can not bee out of their sight, that dwell within that Horizonte.  scholar. 
It is truth, yf any body do dwell directly under the Pole.  Master. 
It is not now my purpose, to prove what partes of the earth be inhabited,( for that appertaineth to Geographye) but to declare howe the son doth show in all partes of the world, as well on the sea, as on the land: and as well in wyldrenes, as in populous countries. Whereby it doth appear sufficiently, that under the Poles of the world, it is half a year continual day, and the other half year, 
The length of the day under the Poles of the world.  continual night, because so long again the son is not seen above that Horizonte.  scholar. 
This is as true as can bee. the reason of it is so certain and manifeste, that I could not better understand the state of that place, if I were there to see it, then I do by this beholding of the Sphere, and the motion of it. And this( as I take it) is a marvelous excellency in knowledge, 
The excellency of knowledge.  to bee able so certainly to judge of things absent, as if they were present: to bee able to tell what hour of the day it is in all the partes of the earth, and when the son riseth and setteth in all nations under heaven.  Master. 
you wolde account this knowledge more marvelous, if you understood other more wonderful conclusions in it, which hereafter I will utter as I shall haue occasion convenient: but in the mean season, I will show you two or three conclusions, appertaining to our present matter which we haue in hand.  
As the houres of the day are dyvers in dyvers regions, so the shadows that the son causeth in their dialles, and all other shadows, doth disagree many ways, not only from our shadows, but also one of them from an other. again the times of the year are not alike through all the world, but when it is summer to us, it is winter to some other: and when it is spring time with us, it is summer in an other country: and when it is harvest with us, other people haue summer: so when it is Winter with us, some nations haue summer: yea when the spring time beginneth with us, it is harvest in some countries, and in other countries it is midsummer at the same time: but when it is midsummer with us, it it harvest no where in the world, but mid winter it is then in two diuers partes of the world.  scholar. 
This talk is marvelous, and in mine opinion the greatest marvel is, that you can understand the shadows of their dials or any other things, in all partes of the world.  Master. 
peradventure it would seem more marvelous if I should say, that by the knowledge of the shadow of a staff, or any thing else that standeth upright,( if I hear it truly reported) I will tell you in what part of the world that shadow was marked. And think you this no marvel, to tarry within england, and yet to measure all the compass of the earth, as certainly, as any man can do it, by going round about the earth?  scholar. 
These things do exceed credit, save that other things, which before I judged impossible, and now I know them certainly, do persuade me to think many things possible by learning, that seem unpossible to the ignorant, though their wits be never so good. I hear such men say sometimes, that learned men and far trauelers may be per mitted to talk at their pleasure, sith no man can comptroll them.  Master. 
By those words they signify, that they do not credite all that learned men do writ or say: wherefore I will constantly say to them, that if they wolde vouchsafe to employ sometime in learning, they should be easily persuaded, not only to believe such things as now they think impossible, but also to know them so certainly, as they know howe many fingers they haue. But to persuade you in the mean season, 
three conclusions.  I will presently show you some of these three conclusions before name, I mean for the general knowledge of the times of the year: for the declining of shadows in diuers nations: and for the order to measure the whole earth, and yet go not out of England.  scholar. 
If I may understand but the general form of those three, I will trust hereafter to attain all the rest more certainly.  Master. 
I will begin with the last, which seemeth most hardest, and I will allege nothing, but that which you shall grant unto.  scholar. 

The declaration of the first conclusion for measuringe of the whole earth.  Then shall your proof bee as certain as I can wish.  Master. 
Can you with a quadrant mark the elevation of the Pole above the Horizonte?  scholar. 
That is easy enough.  Master. 
Then mark it first at Southehampton, or in some other more easterlye place, on the south shore of England. after that go to newcastle beyond york, and there take the elevation with your quadrant again, and mark it well, and the difference of those two elevations shall you set in your table, and by it you shall writ the number of miles diligently and truly taken between those two places, where you took those two elevations.  scholar. 
This can I do with diligence, although it bee as hard to mark the miles truly( the reports of them being so diuers) as it is to work truly with the quadrant, but diligence will avoid error in them both.  Master. 
Then go forward to Edynburghe in Scotland, and mark the elevation there: likeways go to the most northerly point of Catnesse, and take the elevation there also, always marking the difference of every two places in miles of equal quantity, and also the difference of the degrees of the Pole in each of those places from other, and set them in your tables in order the one by the other, as here for examples sake only, I haue set them.  
The places. The elevation of the Pole. The difference in degrees. The distance in miles. Southehampton. 51. 0. 0 0 000. Newecastell. 55. 0. 4. 0. 240. Edynburghe. 57. 0. 2. 0. 120. Catnesse point. 62. 0. 5. 0. 300 The sum of all     11. 0. 660.  
Here you see for Southehampton, where the first elevation was taken, no miles set, because it is the beginning of your journey, but the elevation of the Pole there is 51. degrees: then at Newecastell the height of the Pole is 55. degrees, and that is more then the other by four degrees, so that four degrees must be set down for their difference in degrees, and their distance in equal miles, is 240. now to see howe many miles do the answer to a degree, I do divide 240. by 4. and the quotient will be 60. wherefore I say, that 60. miles in earth( by this trial) doth answer to one degree in heaven. Then at Edynburghe I find the eleuation of the Pole to be 57, that is two degrees more then it was at newcastle, and the distance between them in miles, is 120, which if I dyuide by 2, the quotient will be 60. as it was before: so that one of these works doth confirm the other, because they agree so justly.  scholar. 
I understand all this, as by declaring of the third work it shall appear to you. At Catnesse point, the Pole is 62. degrees above the horizon, which maketh 5. degrees more then it was at Edenburghe, and the space between those two places is 300. miles: now if I divide 300. by five, there will amount 60, which quotient doth agree with the other two before found: so it appeareth that in all england, 60. mile in earth, answereth to a degree of latitude in the sky.  Master. 
prove you also the whole difference in degrees with the whole distance in miles.  scholar. 
The whole difference in degrees between southampton( where the Pole is 51. degree high) and Catnesse point,( where the latitude is 62.) doth amount unto 11. degrees, and the distance in miles is 660: now dividing 660. by 11, the quotient appeareth 60. agreeably as it was in all the other works.  Master. 
What if you did go farther north, 19. degrees more? I mean so far north that the Pole were 81. degrees high above the Horizonte, howe many miles think you would that place be from south hampton.  scholar. 
That can I quickly account by the Golden rule of proportion. The difference between those 2. places in degrees is 30. then seeing I found before, that 11. degrees gave 660. miles, I set the numbers thus in their form of work, and then I multiply 660 by 30, whereof cometh 19800: which I must divide by 11, and the quotient will be 1800.  Master. 
think you this a true work?  scholar. 
This work is true and without any doubt, so that the measure of miles in england were true, which wee take for our ground.  Master. 
And if that measure bee not true, yet by that manner of woorkynge you may attain to a very true rate of miles between south Hampton and Catnesse.  scholar. 
That is no great matter, neither so hard to bee done.  Master. 
And it is no greater matter, in both those places to take the altitude of the Pole.  scholar. 
That is true also.  Master. 
So that if this rate be not true, ther may be found a true rate by diligence.  scholar. 
Yea surely.  Master. 
And by that true rate you could finde how many miles doth answer to 30. degrees in the sky.  scholar. 
easily.  Master. 
Well then: Take this for a true rate, till you can finde an other more certain. And now answer me: How many miles are in compass roude about the whole earth?  scholar. 
Nay that is impossible for me to discuss yet, till I haue farther knowledge.  Master. 
Se how easy a thing seemeth impossible to you.  
Howe many degrees is there in the compass of the whole sky?  scholar. 
That can I certenlye say to be 360: for as I learned before, a degree is no standing measure, but a rate of proportion, and doth betoken the 360. parte of any circle.  Master. 
You say well. Now if the whole circumference of heaven be 360. degrees, I demand of you, howe many miles doth answer to 360. degrees?  scholar. 
That may I do as in the former work, setting the numbers according to the rule of proportion . Then multiplying 1800, 
The compass of the hole earth.  by 360, there riseth 648000, which I must divide by 30, and so the quotient will bee 21600, whereby I know that 21600 miles, doth answer unto 360. degrees in the sky. And so it should seem that those are the just number of miles about the earth.  Master. 
You need to make no doubt thereof, except you doubt whether there be any part of the earth without the circuit of heaven: or else that you doubt, whether the earth be in the middle of the world.  scholar. 
The first doubt were to foolish, and for the second( all bee it I doubt nothing of it) yet I adsure myself by your promise; of the full proof thereof in the next treatise.  Master. 
And other doubt there can be none, but this: Whether the earth and the sky bee both round. which both I will so substantially prove unto you, that no reasonable man will doubt of it.  scholar. 
Then am I certified in the possibility of the most doubtful conclusion of the three, which you proponed: It may please you to proceed to the other two.  Master. 

The declaration of the second conclusion, for declining of shadows  You do consider that this conclusion being true, they that dwell 5400 miles from us, do dwell a quarter of the earth from vs.  scholar. 
That must needs be so: for four times 5400. doth make the whole circuit of 21600. miles.  Mast. 
And so they that dwell from us any manner of way, 10800 miles, they dwell half the compass of the whole earth from vs.  Scholar. 
It followeth so by the former reason.  Master. 
It is well known by the nauygations of the Portingales and spaniards, that there is almost south from us, certain places inhabited about 6300. miles, as namely at the streight of Magellanus. 
Magellanus straight. The scape of Good hope.  Also at the great forelonde of Affrike, commonly called the scape of Good hope, are there diuers regions replenished with inhabitants, and they be from us southward above 5200. miles: then northward wee haue good knowledge of dyvers countries beyond us above 1200. miles, which both joined together, do make from the great forelonde of Affrike aforesaid in the south, unto Wardehouse in the north parte of norway, about 6400. miles, which is more then a quarter of the compass of the earth: but from Wardhouse to Magellanus streight, it is above 7500. miles, by which distance of miles, you may easily gether how many degrees of the heaven each of those places is from us, and from the equinoctial.  scholar. 
Therein I pray you, that I may prove my new cunning. The scape of Good hope is from us southward 5200. miles, that is in degrees of the sky 86 ⅔, according to the former rate of 60 miles to each degree. from which number of 86 ⅔, if I abate so many degrees as we be north of the equinoctial, which are 52 degrees, then doth there rest 34 ⅔ degrees. So that it appeareth hereby, that the said forelonde is 34 ⅔ degrees south beyond the equinoctial.  Master. 
Now for Magellanus streight, prove the like work.  scholar. 
It is 6300. miles southward from us: then by the rule of proportion, agreablye to the former rate, it must yield in degrees 105, out of which abatyng our distance north from the equinoctial,( which is 52 degrees) and so remaineth 53. degrees. thereby I understand, that they are so far beyond the equinoctial southward. Now will I prove for Wardehouse, how far it is north from the equinoctial. It is from us toward the north 1200. miles, which must yield in degrees, after our former rate 20, from these 20. degrees I may not abate 52 degrees for our latitude, as I did before.  Master. 
It were against reason, seeing that the latitude of Wardehouse is greater then our latitude is, and lieth on the same coast of the equinoctial: for in the former examples the two places were on the contrary coast of the equinoctial from vs.  scholar. 
I see it well now, so that by reason I must needs add it to our elevation, and so ther amounteth 72. degrees, which is one degree more then you did affirm it to haue in latitude, in your former declaration.  Master. 
The cause is this: that rate of 60 miles to each degree doth serve in going precisely from south to north, but neither is Wardhouse just north from us, but somewhat toward the east. neither yet in the other two examples any of both places was directly south from us, for the Forelonde of Affrike beareth toward the east, and the Streight of Magellanus bendeth toward the west, yet for this time it may serve as well for our purpose, as if it were more precisely done.  scholar. 

An order in teaching.  Yet I think in teaching there should bee used nothing but certain truth.  Master. 
What so ever is taught to be retained for a truth, ought to be a very certain truth in deed: and they do not well that in such manner do teach first untruths for truths. but where induction is made by examples, it is often times more or at the least, no less expedient to use examples not exactly true, then to take only precise true examples, for thereby it appeareth the proof to bee of greater force, if it will procede in an example which is not precisely true. And in these examples we haue so large scope of trial, that we need not stick for two or three degrees, for I intend not to speak particularly of any city that is under one certain degree, but of whole provinces, which occupieth diuers degrees in their latitude: as you understand that the whole isle of britain doth occupy from 51 degrees, unto 62, which containeth 11 degrees. But now to come to our purpose: thus much you understand, that beyond the equinoctial, yea and beyond the tropic of capricorn also, there be inhabitants.  scholar. 
Yea that ther be, above 29 degrees besouthe the tropic of capricorn: for that tropic is but 23 degrees and a half beyond the equinoctial: and ther be inhabitants 53. degrees beyond the equinoctial, as before is shewed.  Master. 
Well if there dwell men but 6 degrees besouth the tropic of Capricorn( for I said before, I would not stick with you for a few degrees, sith I would make my proof the more forcible) then I demand of you, which way doth the son stand from them at noontide?  scholar. 
It must needs be always north from them at noon, as it is always south from us at noon, seeing they are beyond the south tropic, toward the south, as we are beyond the north tropic toward the north.  Master. 
Then consider two places that stand just south and north( because you like well a preciseness in examples) as Venice that famous city standeth north almost from the scape of Good hope: Now consider the matter thus: in these two places there is one common meridiane line, sith they do stand almost just south and north the one from the other: then when the son is in the Meridiane line of Venice, is he not also in the Meridrane line to them that dwell at the said scape of Affrike?  scholar. 
Yes truly.  Master. 
Then those two places haue their noon tides at one hour.  scholar. 
So haue they.  Master. 
And at Venice their shadow goeth always at noon toward the north& never toward the south, because it is far north from the northerly tropic, called the tropic of Cancer, and so is the foresaid scape of Affrike far south, beyond the south tropic, which is the tropic of capricorn: wherefore( as you haue confessed) their shadow at noon tide, must needs go all times of the year toward the south.  scholar, 
So I see that those two places haue a contrary property, touching their shadows.  Master. 
That is parte of the thing that I did intend to show unto you: but yet they both do agree in this point, that all times of the year their several shadows do incline toward one coast.  scholar. 
That is true. for at Venice it goeth stil north, and at the scape of Good hope, it runneth always south.  Master. 
These sort of people are name of the greek Cosmographers {αβγδ}, 
{αβγδ} Heteroscij Single shadowed.  Heteroscij, because their shadows goeth still toward one coast.  scholar. 
As though there were other people, whose shadows did sometime go southward, and other times northward: I mean their shadows at noon, for else all nations haue in one day, at diuers houres, much diversity in their shadows.  Master. 
Ye understand the time well. and you shal perceive as well, that ther be such places, which change their shadows.  
You confess that men dwell beyond the tropic of capricorn southward: and other you know to dwell beyond the tropic of Cancer northward:& think you it not agreeable to reason, that between these two peoples there do dwell dyvers nations in so great a plot of ground?  scholar. 
I think yes. and I hear say, by our own country men, which travail to Guinea, that they went beyond the son, which always I took to be a lie of liberty permitted to far trauelers, but now I perceive it may be true in one sense.  Master. 
Ther are 2. places of that name, and both are beyond the tropic of Cancer, toward the south, and the one of them is almost directly under the equinoctial circled: and because you haue name that country which our nation doth well know, take it for your example. They of Guinea beeynge nigh under the equinoctial, haue the son some times north from them at noon, as when he is in the tropic of Cancer: and other times they haue the son south from them, when he is in the tropic of capricorn. and must not their shadows change in like sort?  scholar. 
It can not otherways be. And so I see, that when it is midsummer with us, then doth their shadows go sourth ward, to as many as dwell between both the tropics: and in our myd winter, their shadows goeth northward.  Master. 

{αβγδ} Amphiscij Double shadowed.  Those people are name of the greekes {αβγδ}, Amphiscij, because the noon shadows goeth both ways, sooth and north.  scholar. 
And farther I gather, that there is no quarter in the horizon, but their shadow runneth that ways sometime in the year.  Master. 
You say truth. but the chief regard is here given to the shadow at nonetide, whereby you may conceive, that sometime they haue almost no shadow: for when the son at noon is right over their heads, then their shadow is right under their feet, and not on any side.  scholar. 
It must needs be so. for seeing the son is some times north of them, and sometimes south from them, he must needs twice in the year bee right over their heads, ones in going southward, and again in coming northward.  Master. 
To help your memory and conjecture take this figure for a presidente and example, where I haue set the line A. C. for the horizon, and D. B. E. for diuers places of the son at noon. Now if you call A. the north point of the horizonte  Geometrical diagram. zonte, and C. the south point, then when the son is in D. toward the north from their heads, their shadow goith to F. toward the south. And when the son is in E. toward the south, then is their shadow in G. bendig toward the north: likewaies the son being right over their heads in B, their shadow must rest in H. right under their feet. but I see by your countenance that your mind worketh in some strange imagination: and I conjecture it to bee for that I haue drawn the shadows beneath the Horizonte, as you take it.  scholar. 
You haue truly conjectured my phantasye.  Master. 
because this place serveth not to declare conclusions of bye matters, I will exhybite to you this other figure,  Geometrical diagram. where the shadows do run on the Horizonte, agreablye to your phantasye, the letters of demonstration remaining as they were before, and both these tend to one end.  scholar. 
But here are but two shadows.  Master. 
Where wolde you haue the third set?  scholar. 
Right under the tower that giveth the shadow.  Master. 
But it may not reach from the foot of the tower, neither toward one coast, nor other.  scholar. 
No, that it may not.  Master. 
Then the footer of the tower doth cover it so, that you can see no shadow at all.  scholar. 
That is most certain.  Master. 
Yet remaineth ther an other sort of people, which differ in one point from these other two sorts, by reason that their shadow in one day runneth round about them, and goeth toward all coasts of the horizon wherefore the Greekes do call them {αβγδ}, Periscij. 
{αβγδ} Periscij. round shadowed.   scholar. 
Is ther no english nor latin names for these sorts of properties?  Master. 
The latin men borrowed of the greeks, both their knowledge and also many names of arte, because there is not the like grace of facility inborn position, in the latin tongue, as there is in the greek tongue, and therefore haue I given them no english names, because no one word can aptly express these properties, except I would triflinglye make such an imitation, to call them, One shadows Two shadows, and Round shadows: or else, which is not much unlike, ye may call them Single shadowed, Double shadowed, and Round shadowed.  scholar. 
That imitation seemeth strange yet were it better to make new english names, then to lack words: therefore I will not refuse to use them, till I can learn more apt names. but I pray you, where do those men dwell, that haue their shadows running so about them?  Master. 
Within the Polare circles: for all people whose zenith is within 23 degrees and a half of any of both the Poles, haue their shadows running round about them. but as I shewed you before, the nearer they dwell under the Pole, the longer is their day: and therefore the oftener doth their shadows run about them for where the day is but 24 houres long, there the shadow runneth but ones about: and where it is half a year long, there it runneth about 183 times: and in all other mean places raccodingly.  scholar. 
This is manifest enough by your former declaration of the length of the dayes, and the course of the son. And farther I perceive that when they that be under the north pole haue their shadows thus running about them, then they that dwell under the south pole haue no shadows at all, for it is continual darkness with them.  Master. 
You say well, 
light and darkness under the Poles.  concerning the son light, touching them that dwell directly under the Poles, but yet they haue the light of the Mone every month more then 14. dayes together.  scholar. 
Then do they not want light( though they lack the son) but only half a month together, when the moon is in that half of the zodiac, which is out of their Horizonte.  Master. 
That is well considered of you. And yet every month they lack not light, though both the son and the moon also bee out of their sight: for as you see with us, that we haue light before the son rising, and after the son setting, so haue they such a light by the beams of the son 50 dayes continually after they haue lost the sight of the son, and so haue they the like light 50. daies continual, before the son doth rise to them.  scholar. 
Then they want not the son light but only 82. daies, although they see not the son in half a year, and yet half that 82. daies they haue the mone in their sight, as I perceive by your former lessons: for seing she goeth about the zodiac every month, she must needs bee half that time in that parte of the zodiac which is always above their Horizonte. This contemplation delighteth me much, to mark places absent, as if I were present, and to see their alterations by reason more certainly, then I can do by sense, if I were there presently.  Master. 
Yet will I withdraw you from this matter, till an other more convenient place: and now will I procede to the third conclusion mentioned before: that is the general knowledge of the times of the year, in all parts of the world. When the son is at the highest with us, 
The third conclusion is declared.  it is at the lowest with diuers other nations, namely to all them that dwell other under the equinoctial circled directly, other south from it: and therefore all those nations haue mid winter, when wee haue mid summer. But amongst them all there is one region, which is as far beyond the equinoctial toward the south, as we are toward the north.  scholar. 
That region is about Magellanus streight, as I gether by the second former conclusion.  Master. 
In deed the streight of Magellanus is in that region, for here I mean by a Region that which the greeks do call a Climate, which is in form like to those Zones, which I did describe before, 
A Climate.  save that there are more such Climates or regions, then there are Zones: for the climates may well be accounted 48 between the two polare circles, 
The number of climates  which containeth but three of the Zones. but of those climates I will say no more at this present, but that every region where the longest day is half an hour longer or shorter then it is in any other region, must bee accounted in a several climate from it: so that under the equinoctial the longest day is but 12. houres, and with us in the middle of england, it is about 18. houres: wherefore we must account that the middle of england is in the 12. climate from the equinoctial northward, and they that dwell 66. degrees and a half north, or south from the equinoctial, because their longest day is of 24. houres, that is twelve hours longer, then it is in the middle of the world under the equinoctial( from which all those accounts of Climates do begin) they must be judged in the 24. Climate.  scholar. 
Then are there 24. climates on each side of the equinoctial, between it and the polare circles, yet I remem brethat the common authors make mention but only of 7. on either side, which maketh but 14. in all.  Master. 
That shalbe answered anon, where I will set out the order and reason of the diver sity of the climates: but for this time it shall suffice that you consider this, that all places within one Climate, haue the times of the year alike exactly, 
The qualities of contrary climates.  and their dayes still of like quantity the one to the other, and they that dwell in the contrary climate, as many degrees on the other side of the Equinoctial, the haue both the times of the year contrary, and also the quantity of the daies disagreeable, for when it is summer in the one climate, it is winter in the other and when the day in the one doth increase, the night in the other doth increase after the same quantity just.  scholar. 
Then for example: In the country about Magellanus straight, it is summer when wee haue winter: and when our day is at the longest then is their night at the longest.  Master. 
truth it is, and when wee haue spring, then is their harvest: and so is it common to all them that dwell ahoue the earth within those two climates, yet is there this difference, that in our climate and theirs also we may imagine four quarters equally distinct: the first quarter being that which we dwell in, 
every Climate hath 4 quarters  and in the contrary climate, our meridian circled limiteth the first quarter,& also the third quarter in both places, so that in this first quarter in both climates, the times of the day and night at a like: for when it is noon to us, it is no one to them: and when it is midnight to them, it is midnight also to vs.  scholar. 
Then likewaies when the son riseth to them, it riseth to us, and so setteth at one time in both Climates.  Master. 
Ye are far deceived, for then of necessity must it follow, that their day and ours at one time should be of( one quantity, which is not true, as I said before, but the reason of that shalbe shewed anon, yet is it true, that their houres agree with our houres if their meridian circled agree with ours. And the same meridian circled under ground doth li●… te in both these climates, the 3 quarter also where it is noon when we in the first quarter haue midnight, and they haue midnight anour noon. Now may you easily conceive by your own mind, the places of the other two quarters.  scholar. 
order enforceth them, the one to be in our west, and the other to be in our east.  Master. 
That distinction is sufficient for you at this time, and it is precisely true, if you mean the east, where the son riseth at the beginning of the spring time, or of the harvest, wherefore for that time I will make mine example: When the son riseth to us in the spring time, it is noon with them that dwell about calicut, and when the son is in our Meridian line, then doth he set to them: so that when the son doth set to us, 
calicut. Peru.  it is midnight to them about calicut;& thē is it noon to the famous country of Peru: Again at that time the son riseth to thē that be in the isles of Molucca. 
Molucca.  whereby you may gether that Peru& calicut be in 2. contrary coasts of the earth, and therfore seem to go with their feet the one against the other, and their heads the one from ward the other, which sort of people therefore are called of the Greeks and latins also {αβγδ}, Antipodes, 
Antipodes.  as you might say Counterfooted, or Counterpasers. Now to our purpose. all people that haue midnight when other haue noon, do differ in sunder by half the compass of the heauens, one way: yet may they not be called Antipodes, except they differ in distance every way a quarter of the sky, and must haue one meridian circled. So that our Antipodes must be under our meridian circled, and must be half the compass of that circled from vs.  scholar. 
Then as wee are 52. degrees north from the equinoctial, so must they bee 52. degrees south from the equinoctial, in that parte of the Meridian circled, which is under our Horizonte, and then haue they myddenyghte when wee haue noon: and hereby I perceive that they haue mid night when it is noon at Magellanus straight.  Master. 
In deed it is day then at Magellanus streight, but not nigh noon, for Magellanus streight is much to far toward our west: but for examples sake that error may be permitted, and especially because there is no land but sea, where you should mean that noon to bee: so can you give it no proper name: but retaining that name for example of the true place, you may consider three forts of people, that is to say, ourselves, and those that dwell by east Magellanus streight, under our Meridian circled, which haue noon when we haue noon, 
Antipodes.  and the third sort which are under the same Meridian, but haue midnight when we haue noon, and are as far south from the equinoctial, as we are north, whom I name our Antipodes, and so ought they to be called in respect to us, and we are Antipodes to them also: But now comparing them with those other by east Magellanus strait, they ar called each to other {αβγδ} Perioeci, as you may say, like dwellers, because they dwell under one Meridiane circled, and under one parallel also, and be like in distance from the equinoctial circled.  scholar. 
There are many places in every such region or climate, but there are but two properly under one Meridiane, and the one of them hath midnight when the other hath noon: so the times of the day doth differ with them yet I perceive that they haue the seasons of the year agreeable, because they dwell on one side of the equinoctial. Then must it folewe that those which unto us be Perioeci, 
Perioeci, likdwellers  are An tipodes to them that dwell by Magellanus straight under our Meridian.  Master. 
You say well. and we unto them by east Magellanus straight, under our Meridiane, are called by the greekes and latins {αβγδ} Antichthones, 
Antichthones, Counterdwellers.  as you would say Counterdwellers, or Counterclimates.  
And thus haue you three sorts of inhabitants by comparing the one with the other, whereof always Perioeci( that is Likedwellers) haue like times of the year, but not of the day. Antichthones or Counterdwellers, haue like times of the day, but not of the year. Antipodes or Counterpasers, haue neither the parts of the year, neither of the day agreeable together, but contrary in both, how be it ther is a farther consideration for exactness of this knowledge, which I will hereafter declare to you in place more convenient: but hereby may you gather the diuersityes of times of the year, and also of the dayes, according to the diversity of the inhabitants comparing them all other to your own country, or one of them to an other, as occasion shall serve, and oportunitye of matter. And thus will I end for this time, if I may perceive by your repetition of this thyrde treatise that you remember all things therein declared.  scholar. 
I were else to blame. but as I haue learned in it many several things, so for the order of the arte these I note as chief matters. 

1 
The repetition of the third treatise.  first the distinction of the plagues of the world, accordingly as they be set forth in the horizon of the Sphere.  
2 Then the parallels on earth, agreeable to the parallels in the sky, of like names, and distance proportionable.  
3 Thirdly the distinction of the. v. Zones, by their qualities and limits, and of their inhabitants.  
4 The diversities of Spheres according to their diverse inclinations, but two are the general distinctions, that is a right Sphere, and a Bowinge Sphere.  
5 Fyftlye, you gave me a brief order to take the height of the Pole, or any other star or Planete.  
6 Then followed the diuers alterations of the Horizonte, as well between east and west, as between south and north.  
7 Seuenthlye, there was declared the causes of the diversities of the daies, first in diverse regions, and then in one region.  
8 The difference between a natural day, and an artificial day.  
9 The quantity of the longeste day in certain partes of the world, and namely under the Poles of the world.  
10 How by this excellent Arte a man may measure all the compass of the earth, and yet abide still in one country.  
11 A distinction of sundry inhabitants, according to the diversities of their shadows, which are three principally.  
12 Then lastly followed an other distinction of inhabitants, according to the agreeablenes and diversities of times of the year, and the quarters of the day, and these you name by three several names also, which are names of comparison, because they take not those names, but in comparison to other nations.    
This I remember to be the sum of this last treatise.  Master. 
You remember it well, and understand it also well, as it may appear by your repetition. Therfore now shall you depart for a time, and you shall read over again your authors of the Sphere, which you did name before, and now mark whether you can understand them, and as your return, I will instruct you more exactly in all the premises, and other diuers conclusions, which now I haue omitted of purpose.  scholar. 
I am most earnestly bound unto you for your great gentleness, which I pray god to requited, sith I cannot, and who will else I know not.  Master. 
Farewell then, and remember your own profit▪ scholar. The author of all profit, continue and increase your profit, that you may haue quiet time to travail for the profit of many.   

THE fourth TREATISE OF THE CASTLE OF KNOWLEDGE WHEREIN ARE THE proofs OF ALL that is taught before, and other diuers notable conclusions annexed thereto▪ but nothing in a manner with out demonstration and good proof.  scholar. 
IF THE INEXPLICABLE benefit of knowledge did not enforce me to forget all bashfulness, I might think it to much shane, so often to trouble my Master from his earnest studies, and to stay him from his profitable travell with mine importune crauynge of knowledge, namely sithe I can not recompense any parte of his pains: yet his gentleness is such, that he seeketh more the profit of other, then his own pleasure or peculiar commodity: and therfore will I boldly entre into his house. Are you at home sir?  Master. 
I am always at hove for my friends, if I bee not with them from home: yet some times I can not be at home for myself.  scholar. 
The less for me and such as I am, that often trouble you more for our own commoditye, then for your gain.  Master. 
I seek to gain no more then competentelye may serve my necessary uses, with convenient regard to my charges: but if I offend any ways in couetinge monnye, I adsure you it is to bear the charges in setting forth such monuments of knowledge, as were marvelous profitable for all men, very pleasant to many men,& yet esteemed only of wise men. but sith I cannot do the good that I would, and other want will which haue goods in excess, I must do as many other doth, wish good to all men,& help them as I can. And for your parte I look none other recompense but this, that you always be thankful to your Master. and as he helpeth you freely, so do you help other again, and hide not the knowledge privately, which may profit many publicly. but now to your matter: haue you perused the authors of the Sphere which ar commonly read?  scholar. 
To read them all, it were to much for my life time, and the profit not so great, as I hear many men say: for as the noumbre are infinite, so the later writers do most commonly but repeat that, that two or three of the ancients haue written before. wherefore as I learned that the beste writers of them for my study, were Proclus, joannes de Sacro bosco, and Orontius the french man, so I haue read them, and out of them haue I collected a table of their most notable matters, which as yet I understand not, or else do desire to hear the demonstrations for their proof.  Master. 
You haue done well in both points. for as the number of writers are infinite, so haue I found great tedious pain in reading a great multitude of them. notwithstanding as you shall hereafter seek further knowledge, so must you read more writers in that matter: wherefore amongst a great noumbre wo orthye the reading, I will name a few unto you, which I wish you to study: and the residue I leave to your own discretion. Cleomedes the greek author, is very worthy to bee often read: but beste in his own tongue, for the latin book is much corrupted. Also euclid his book entitled Phaenomena, and Stoffler his commentaries upon Proclus Sphere: which book I wish were well recognized( as it hath great need) then might it serve in steede of a great number of other books. dyvers english men haue written right well in that argument: as Grostehed, Michell Scotte, Batecombe, Baconthorpe, and other dyvers, but few of their books are printed as yet, therefore I will stay at those three for this time. As for Plinye, Hyginius, Aratus, and a great many other, are to bee read only of masters in such arte, that can judge the chaff from the corn. and Prolemye that worthy writer and miracle in nature, is to hard for young scholars, except they be first instructed not only in the principles of the Sphere, but also well traded in Euclides his geometry, and also well exercised in the Theorykes of the planets. But now let me see the table that you haue collected. 

1 The order and movings of the nine Spheres.  
2 The spaces of their revolutions by their proper motions.  
3 The form of heaven is round, and his mouynges circular.  
4 The earth is round in form, and the water also.  
5 The earth is in the middle and Centre of the world, and is but as a point in comparison to the firmament, and doth not move any ways.  
6 The compass of the earth, and the diameter of it, what they make in common miles.  
7 Of the circles in heaven what is their just quantityes, their number, their order, their distance, and their offices.  
8 why the zodiac hath that name, and whether any such forms bee in the sky.  
9 The diuers significations of a figure, and the declyninge of them. There are two Horizontes, one sensible, and the other only judged by reason, and what the quantities of them both are.  
10 The Greekes and the latins do not agree in the description of the circles arctic and Antarctike, and what are their reasons.  
11 Whether there bee any dwellers in the untemperate Zones.  
12 What bee the circles vertical and circles of height, the circles of hours, and of the twelve houses.  
13 Of the rising and setting of the signs and other stars, both in the right sphere, and also in the Bowing sphere, after the Astronomers.  
14 Of the Latitude of the son and the twelve signs from the east and west.  
15 Of the rising and setting of the stars, after the mind of the poets.  
16 Of the diversity of natural daies, as well as of Artificial daies in diuers partes of the earth.  
17 The diversities of hours, whereof some ar equal, and other unequal according to the course of the son.  
18 The height of the son above the Horizonte at all hours, and in all regions.  
19 The diuersyties of shadows, whereof some be called right shadows, and other be called Turned shadows.  
20 The distinction of the circles parallels necessary in cosmography, with the proportion of their degrees, to the degrees of the equinoctial.  
21 The distinction of Climates and the number of them, and howe large in breadth each of them is.  
22 Of the Longitude and Latitude of regions and other places, and how both these ought to be taken.  
23 The description of the milk way in the sky, which is commonly called Watlynge street, and what is the cause of that colour in it.  
24 The number and names of the chief signs and figures that be in the sky, and why they be so called.  
25 Of the circles and movings of the planets, and namely of the eclipses of the son and the moon.    
These be the titles of such matters as I haue noted in them most meet for this time, sith many other things are sufficiently taught in the former treatises, and some other things, namely in Orontius book, appertain to cosmography, which I perceive by your sayings, you mind to reserve for a peculiar treatise of that matter, and therfore I haue omitted them here.  Master. 
So might you haue done some other things also, which you haue noted here: howe be it I will use my liberty therein, to express in convenient largeness those things, that be meet for this place, and the rest will I touch with as convenient briefnes: referringe the other to their more convenient places.  scholar. 
sir I know right well, that your iudgement is as well to be followed in the order of teaching, and choice of matter, as it is to be esteemed in the teaching and explication of all doubtful cases.  Master. 
In order of teaching is more credit to be given to a master, then in affirming of any doctrine: for the order is by long experience best known of such men: but for affirming of any doubtful doctrine, no man ought to say any more then he can show good reason, for thapprouyng of the same. And now to your matter. although you follow the order of joannes de Sacro bosco in many of your propositions, yet will I begin with your third proposition, and refer the two first to a more meet place, sythe the proof of them can not well bee understand, without a great number of other conclusions, which must first be proved. And for to begin with the declaration of the ro undnes of the sky, and his circular motion, I think it good to follow that order which mouyd men first to observe this kind of arte.  

The first occasion to think the world to be round.  At the first beginning of the world, when this arte was unknown, men marked the rising of the son and the moon, and other notable stars, as the brood hen, which is called of many men the seven stars, and other like: and perceauinge them to rise always about the east, and so to ascend by little and little to the south, from whence they did descend again softly to the west, where they did continually set: and the next day again they perceived them to begin their accustomend course and so continued like as before: wherein although they saw some diversity, yet they perceived that diversity to bee uniform, and after a year to return to the old state again. by this occasion they began to ymagine that this manner of moving could not bee but in a round and circulerre form, and also in a round and circulerre body.  

The second occasion.  Then to understand this matter the more exactly, they observed the movings of such stars as never go under ground, which be about the north pole:& ther they perceived by diligent marking of thē, especially in the long winter nights,& that at sundry times, that they turned round about one point in the sky: and those stars that were nigh to that point did make but a little compass in their moving, and the farther that any stars were from that point, the greater was the circled of their revolution. 
The third occasion.  Then thirdly they marked certain notable stars, which did rise and set, but yet were not far from those other stars, which do never rise nor set, and they might well perceive that they did continue but a little while under the horizon out of sight, where as contrary ways, those stars that were farther from that point or Pole, did remain longer time under the horizon, out of their sight, whereby they were enforced to think, that these varieties and forms of moving could bee in none other manner of body then in a round form, and that the same moving was circular and round, as it did manifestly appear in the north parte of the sky, where the stars continually move round about one point, and do never set under the horizon. And that point about which they noted this motion to bee, they called( as reason enforced them) the Pole of the world. 
A Pole.   scholar. 
What doth that word signify?  Master. 
It hath his name of turning: as you wolde say, a turn point. and it doth betoken the end and extreme point of any axletree, howe be it by special prerogative the name is appropred to the ends of the Axetre of the world.  scholar. 
This picture doth some  Geometrical diagram. what represent the motion of the stars about the north Pole.  Master. 
You say truth. howbe it aptly it can not be perceived in flat form but in a round body, as a globe is: but in that point( me thinketh) ther is no better instrument then the sky itself, where every man may learn that listeth to mark, and there bee certain notable stars in that place and namely Charles wain, which is called also the great bear, whose motion is so evident, that every child may mark it: 
Charles wain.  And twice in the year, that is in the middle of February and in the middle of August, they serve for a just horologe: so that the finger in a clock doth not more aptly point the hours, then doth that figure of Charles wain.  scholar. 
There can he no more apt declaration of the roundness of the heaven, and of his circular motion, then the sight of those stars which move so roundly, and keep their quarters in heaven so precisely. and yet I haue heard of certain great clerks, that in no case thought it reas onable to affirm such a form of roundness, or such a round motion in heaven: but most of all I marvel of that famous man Lactantius Firmianus, which doth affirm( as I haue heard) that the heaven is not round, but flat and plain. 
Lactantius Firmianus his error.   Master. 
Many scrupulous divines by miss understanding of scripture, haue abhorred the study of astronomy, and also of philosophy, and often times do more sharply then discreetly rail at these both, and yet understand they not any thing in either of them both. such men are to hasty to bee good iudges, that will so quickly pronounce sentence, before they haue any good evidence, and will determine the case, before they understand the matter. for how can any man understand well or judge rightly that thing that he knoweth not? yet such drowsy dreamers haue oftentimes deceived many wise men, with their appearante reasons, but yet none but such, as either were given to hate the name of philosophy, or else at least had no time, or none habilitie to get understanding in it. By some such men I may think that Lactantius was seduced: and the more easily, for that he had conceived a deadly hatred against all philosophers and against philosophy itself: 
Lactantius opinion of the form of heaven. lib. 24. c. 3  but I will let him and his followers pass, and return to the matter.  scholar. 
Yet if it please you, I wolde gladly hear his reasons, that he maketh for approving his opinion, seeing he is name so great an orator and so famous in learning, that many men will believe him without any reason.  Master. 
Who so ever will believe him in this point, must do it without reason: for he allegeth no reason for his purpose, but taketh it as a certain truth, thereby to improve the opinion of the Antipodes, as I will more largely declare anon in proving the roundness of the earth. But seeing he could bring no reason for his opinion, you shall hear some reason against his phantasye, and then judge as you can.  

That the sky is not flat.  first I reason thus: If the heaven be flat and plain as a board, then howe so ever it stand, one parte of it must needs be nearer to the earth then any other parte of it. and that parte by all lykelyhod must be right over our heads, is not that so?  scholar. 
I can not imagine else any form of situation: and  Geometrical diagram. that doth appear partly in this figure, where A. B. C. standeth for the sky, and lieth flat over the earth, which is here represented by D: and now I see that B, which is right over D, is much nearer to it then A. or C, or any other point in that flat plain form, which is set to represent the flat sky.  Master. 
now then what will Lactantius say, or any man for him? doth this heaven moueor not?  scholar. 
He can not deny that which we may see with our eyes, that both the son, the moon, and all stars do move every hour continually.  Master. 
Yet peradventure he might say, as some other like contemners of philosophy haue said, that the stars and planets do move in the sky, as fishes do swim in the water: and that they go forward though the heaven stand still.  scholar. 
I remember I haue heard of that saying, and that a famous writer of late doth maintain that opinion.  Master. 
What will they say then, doth keep the stars in such a just order and equality of distance? which never altered any one whit sith the beginning of the world, is it possible that the stars should mouein the sky as fishes do swim in the water, or as birds fly in the air, as some term it, but that the stars must stragle in their course, as the fishes do, and as the birds also do?  scholar. 
I haue seen both fishes in the water, and fowls in the air, to keep a meruallous certene course in their flying and swimming, and namely fishes that go in gaols, as herringes commonly do, and other fishes diuers times, and wild goose also and storks in their flying, whereof I haue often mused.  Master. 
You may often see such notable sights; yet if you mark them, you shall see much alteration in their flying, as well as in the swimming of the fishes: whereby you may think their order not to be constant, but sometimes one flieth a little faster, and an other a little slacker: and sometime they serve on the one side, and sometime on the other. but were it not a sonde ymagination, to think that stars do fly and follow one guide as birds do, and in 5000. year space to keep their places so precisely, that they vary not one minute of a degree?  Schoollar. 
In dead it were marvelous, and so are all Gods works.  Master. 
Yet is there one invincible reason against that opinion, 
The Mylky way called of the greeks Galaxia  gathered of the figure of the Milkye way in heaven, which many men in England do call Watlyng street, comparing it to one of the great high ways in england that is called Watlyng street. This Mylkie way, if it served for none other purpose, yet doth it seem worthy the noting, for the exact consutation of the said opinion, and for that cause it might seem to bee made by God, which hath wrought man ye means to lead men unto truth. This way is in the sky itself, as all men hath confessed, and their eyes do testify, and the stars that bee in it are always seen to keep their places in it: so that it must needs follow, that the same ways doth move with the stars, and then consequentlye the sky must needs move also.  scholar. 
Yet it may be said, that the stars which bee in it do move always so certainly in it, that it may seem to move, as though it stand still.  Master. 
Did you ever mark the same milk way?  scholar. 
Yea verily, and that often.  Master. 
And did you perceive in it any boughts, corners, partitions, or such other like marks, whereby you might know one part of it from an other?  scholar. 
That haue I done also, in so much that in some places it seemeth to be divided into two ways.  Mast. 
That is true. And think you if the stars did move in it, and it stand still, that these stars which now be by the partition of those branches, must not within four or five hours be passed far from that place?  scholar. 
It should so follow, yet that is not so: for I haue marked the contrary oftentimes, that they keep those places still.  Master. 
Then do not the stars move from their places, but as those places move with them.  scholar. 
It appeareth now to plain to bee made doubtful any more.  Master. 
Yet will I prove it better: did you ever mark any notable place of that milk way at the beginning of the night in the east, or in any other coast of haven?  scholar. 
Yea for south.  Master. 
And haue you marked whether that place hath gone any farther westward that night?  scholar. 
I haue marked it well, and haue perceived that it hath moved a great way from his first place: and who so ever listeth to try it, let him at six of the clock in the deep winter mark any notable places in it, and at ten of the clock the same night, he shall perceive it to haue gon westward more then a quarter of the sky.  Master. 
Your words are true, meaning a quarter of the sky above your Horizonte: and by this you see, it can not bee avoyded, but that the sky doth move as well as the stars.  scholar. 
It is most manifestly proved, so that Lactantius himself can not deny it, unless he will deny that his own senses may judge in sensible things.  Master. 
Then if the heaven be flat, as he doth imagine it to be, and it doth move westward, as all men doth see, other the must say that the sky is infinite in length, and that wee never see any parte of it again after it is ones past our sight: and thereby affirm, that there be infinite many sons and as many moons, and an infinite number also of all other planets, and of all several kind of stars, or else he must declare which ways that the son, the moon, and the other stars do come into the east again.  scholar. 
He can not say that they come backward the same way that they went forward, for then wee should see them in their returning: and to say truth, there can bee none other form of moving, but in round form, that may bring them into the east again: But peradventure he may say, that though the sky be flat and plain in form, yet it hath a round motion.  Master. 
Some other man may say so: for he thinketh the contrary as his words import, for in reproving Astronomers, he saith: Ex motu syderum opinati sunt coelum uolui. By the moving of the stars they imagined that the heaven doth turn round by which words he seemeth to mean that the stars move, but not the sky  scholar. 
That is fully improved before.  Master. 
If it were not, I might reason with him thus: seeing he affirmeth as reason enforceth him, that the stars do move, and will not confess that the sky turneth round, then( as I declared before) one parte of the sky which is over our heads, is nearer to the earth then the both ends be.  scholar. 
That appeareth plain, except he wolde say against all reason, that the earth were as large as the sky.  Master. 

an argument against the flatness of the sky. The maior or maxim.  Yet though he would say so, my reason shall proceed in full strength, sith some partes of the sky by his meaning must needs bee farther from us then some other. Therfore I frame my reason thus: All things that men can see, seem greatest when they bee nighest unto men, and the farther they bee from their sight, the lesses they show.  scholar. 
I think no man so childish to deny that. for every hour our sight doth approve that it is so: if we see a man a far of, he seemeth no bigger then a little child: and a great ship far in the sea, doth show no bigger then a crow sometimes.  Master. 

The minor.  Then taking that for a maxim in argument, I annex this minor, that the stars moving it that imagined flat sky, are most nighest to us, when they bee over our heads: and they are farthest from us, when they be in the east or in the west: 
The conclusion.  wherefore I infer the conclusion, that the stars must seem greatest, when they be over our heads: and they must seem much lesser, when they be in the east or west.  scholar. 
This conclusion is plainly false. for our eyes do testify the contrary, sith always the son, the moon and the stars do seem greatest at the rising in the east, and at their setting in the west. And they show smallest, when they be nighest over our heads.  Master. 
If the conclusion be false, and the argument good as Lactantius can not comptroll it, then I may object to him his own rule: Necesse est falsa esse, quae rebus falsis congruunt. It can not be chosen but those must be false sentences that do agree with false matters. and so must they needs bee self premises, that do infer a false conclusion.  Scholar. 
In good faith I think neither Lactantius, neither any man else is able to avoid this reason, except he will avoid that fonde opinion of imagining a flat sky, and the standing of the same vnmouable: yet if any man wolde say, that the heaven were square, or of any other form of diuers angles, as here you se many varieties in these figures. 
An other reason by auoi ding of emptiness which nature cannot bear   Geometrical diagrams. How might I aptly reprove their opinion, if they will affirm farther, that the sky with such a form doth move round? for by saying they might avoid the danger of this last inconueniene.  Master. 
While they might seem to avoid one danger, they fall into an other: as for a proof. I turn those figures round, whereby in dead it appeareth, that every part of them keep still their own distaunces vnchangeably from the centre, but yet is one parte more nearer the centre then an other parte is, and every parte in their turning seemeth to describe a circled about the centre, each circled in bigness according to the distance of that parte whereby it is described, and so the greatest circles are made by the extreme angles, of every figure.  Scholar. 
All that is easily perceived, at the first sight in turning the figures about.  Master. 
Then if the heaven bee cornered, it may haue no less room to move in, then the compass of the uttermost circled doth require.  Scholar. 
That appeareth certain, for else it would stay by those corners, or else break the corners in the turning, whereof nether is to be fantasied but of fools, whose thoughts are pardonable in all those that refuse not their common fellowship, but not in other, although for their woorthines they might be Wardens of that company.  Master. 
Then if for their motion they require so large a circled, as may compass their corners, there appeareth void room against every side, in which room what shal be set to avoid emptiness, which nature can not bear?  scholar. 
Let them answer that liketh that fantasy, for I can imagine nothing, except I should name air, but that by his nature can not ascend so high.  Master. 
You guess well, that it must be some subtle and liquid thing, that might change his place as fast as the heauens do turn: for in turning, the corners will come anon where the emptiness is now, and so successively each change place with other. but air you say can not come thither, sith it may not ascend so high: the like may you say of fire and water, and much more of thearth. again if they could ascend, how should they pierce through the substance of the heauens? beside that being elements, and therefore corruptible and subject to daily alterations, they are vnmeet to be matched with the unchangeable substance of the heauens.  Scholar. 
This is reason enough against that imagination, sith nature can not suffer it to bee empty, and nothing else but part of the sky can supply it.  Master. 

The third reason for apt moving  Yet considre farther: sith the motion of heaven of all other must bee judged the most swiftest, which in 24. hours doth run so large a race, that is many fold greater then the compass of all the earth, so that every hour it runneth many thousand miles, doth not this swift motion require that form, which is of all other most apt for moving?& doth it not repugn to such forms as be full of corners,& therfore unapt to move swiftly or uniformly?  Sc. 
It appeareth plain madness to dream ones the contrary.  Mast. 
Then all men know that as cornered bodies be most unapt for to run, so is a round globe most apt for all other.  Sc. 
every common turner can skill in that reason,& know that a little altering of the one side, maketh the boul to run biasse ways.  Master. 
If the reason be so plain that common artificers can skill of it, it were to great a folly for learned men to doubt of it.  Scholar. 
They that doubt of it, never weighed their opinion with any reason, as I may think, for these reasons suffice to persuade any man.  Master. 

The fourth reason for capacity.  Yet ones again way this for thee for me of heaven. sith it encloseth all things, and is the greatest of all other, were it not meet that it should haue the greatest form which is most large and apt to compass and enclose all other?  scholar. 
It is both meet and necessary also.  Master. 
Then is it well known of young scholars in geometry, that as of all flat forms of like circumference, the circled is the greatest, so of all sound forms of like circuit the Globe is most largest, and therefore most aptest for the form of the sky, which encloseth all things that man can see.  Sch. 
I might be ashamed to demand any more proof for the roundness of heaven or his circular motion, yet are the reason so pleasant, that I delight much in the hearing of them, and therefore can bee content to employ as much time in hearing them, as you think good to bestow in framynge them.  Master. 
I could occupy you so a great time: but I think it not best to stay thereon to long, sith wee haue many other matters to prove, and at other times we may talk hereof again. These reasons which you haue heard do prove not only that the motion of heaven is round, but also that the round form doth best agree to the sky, for largeness of capacitye, for aptness in moving, for avoiding of emptiness, and for the just appearance of the stars in uniform bigness, which I think sufficient for this time.  scholar. 
There be two things by the way which I desire much to hear more largely declared: the one is for the appearance of stars, which seem most greatest at their rising and setting: the other is, for the avoiding of emptiness, which as I haue often heard, so would I gladly ones understand.  Master. 
The first of them appertaineth to perspective, and the second unto natural philosophy, so that both do require an other place and time: yet because I haue alleged it for this present matter, although the reasons why it is so, may not well here be repeated, yet that it is so, shall be briefly declared. 
All things show great through vapours or gat.  In a mystie morning as you walk, all things  diagram illustrating how objects appear larger when viewed through mist or water. that you see, seem greater through the gat, then in deed they be a penny in the water seemeth broader then it is, and the deeper that it lieth, the greater it appeareth: so the son and the Mone and all other stars being nigh to the earth, do show through the vapours that ascend from the ground, and therfore appear greater then they be:& if the vapours be many, the stars show the bigger: the cause is, the interruption and reflection of the sight beams by the vapours& the water.& liker is the cause in seing through glass which occasioned weke sights to seek aid of spectakles  Sch. 
Many use that aid, that know not the reason thereof.  Master. 

Nature abhorreth emptiness.  So many draw water at a plompe, that know not the cause, why the water do the ascend, which is only natures work to avoid emptiness. And many men use bellows to blow the fire, which know not the reason of their first invention, and therefore can not mend them if they be hard to draw. many men also draw waters by fountains higher then the spring, yet few of them do know what is the reason of their work, and therefore few can amend it, if the fault be any thing doubtful. A great number of other like things could I show, where natures abhorfulnes to permit any emptiness, doth cause strange effects, in things that are used of many men, and well known of few men. But ass it appertaineth not to this place to discourse largely in those matters, so an other time shall serve for them. And now let us proceed in our purposed attempt, to see what proofs I can bring for the roundenes of the earth: wherein I will begin with a distribution disjunctive, containynge many opinions touching the form of the earth: and each of them will I substantially improve, 
Diuers opinions of the form of the earth.  save that only which affirmeth it to bee round, and that will I so fully approve, that I doubt not but you shall think yourself fully satisfied. some men considering that as for the sky not form was so meet as a round form, because of his swift moving, so for the earth which standeth so steddilye, they judged no form so meet as  diagram of a cube. a Cube form, which they esteemed most stable of all other: and therefore many ancient Philosophers by the form of a Cube did secretly signify constancy and stableness: 
Why fortune is pictured standing on a globe.  and contrary ways by the form of a globe they express changeable alteration, and continual moving.  Scholar. 
That I may perceive by the placing of Fortune on a rolling globe, in token of hir inconstancy& voluble changinge. And therefore haue I often phantasied, that dice, 
Why dice be made in cubik form.  which is the image of Fortunes inconstancye, and serveth onely for fortunes plays, might beste haue been made in form of a Globe, for they are as unconstant as fortune herself.  Master. 
Ther seemeth in Fortune two diuers natures, 
Diuers fortune.  the one is light and alway flickerynge, the other is heavy, and therefore more stable, so that oft times we see them that haue a light and pleasunte fortune, as lightly lose, that they lightly gained: but where heavy fortune setteth hir foot, seldom can she be removed, hir steps are so stayed: but to express more exactly the nature of the cube resembled in the dice, both in form and in effect, you shall mark well the meaning of that old proverb: Iacta est alea, The dice is cast. or the lot is drawn. or fortune is past. by which saying is declared, that the thing that is ones done, can never again be undone, although it may be altered, and so constancy in that appeareth most certain. for as your chance on the dice being ones cast, you must be content to stand to it: so fortune when it is paste, can not bee altered. And that is the cause why all men use to say, when they express their stay in living: such is my fortune. Yet many learned men put difference between changeable chance, and stable fortune, calling the first Fortuna, and the other Fatum: so that destiny is stable, though fortune change right often. But thus I forget our purposed intent, with so many digressions of other bye matters.  scholar. 
I found no fault not thought no time lost, sith the matter is pleasunte and somewhat to our purpose.  Master. 
Well, this was their imagination, that thought the earth to be of a cubyke form, for that they judged it the most steadfast form.  

The second opinion.  Then an other sort devised a three cornered form like he rygge of an house where tone side lieth flat, 
A rygge form.   Geometrical diagram. and the other two lean a slope. And this form they judged better for two causes. first they thought that it was more steady then a cube form, because it hath a broader foot, and a lesser top: and secondly for that they thought it a more apt form to walk on, and more agreeable to the nature of the earth, where some times there riseth high hills, and sometime again men may see great vales descending.  scholar. 
This imagination is gross enough.  Master. 
And so gross is the iudgement of the that follow not, or search not for true reason, but content themselves with a light conceived fantasy.  scholar. 
And in this they be deceived, that they account this form more apt to walk on: for the flat of the cube is plainer,& therefore more apt to walk on, then is a slope ground.  Master. 
If the sixth parte of the earth were only inhabited, then would it appear so in deed: but if you go any farther, then haue you unapt plainness to walk on in their imagination, which go so down right, that they do fear falling. again they think this rig form meetest for the standing of the sea, and for running of riuers: for in the first form, if the sea should rest on the overmost plain, then wolde it over run all that plain, and so flow over all the earth: where as in this second form it might rest about the foot of the earth, and yet the slope rising will not permit it to over run all the earth. And so for riuers if there be no slopenes( as in a cube there is none) then can not the rivers run well.  

The thyrde opinion.  A thyrde sect thinking to amend 
A plain flat.   Geometrical diagram. these both, imagined the earth to be plain and flat: for so they fantasied that it would rest most steddilye, and so was it very easy to walk on.  scholar. 
We are more beholding to those men, for devising our easy walking, then we are bound to them for their wise doctrine.  Master. 

The fourthe opinion.  The fourthe sect, fearing least by this opinion they should lose the sea and all other waters, imagined the  Geometrical diagram. form of the earth more apt to hold water, and deuifed it hollow like a bowl.  scholar. 
Those men were very studious for staying of water, more then they were for framyng of their wits.  Master. 
Yet this vain folly didde seem to them great wisdom.  scholar. 
save that I do credite your report, I wolde never haue thought, and much less haue believed, that ever any such mad imaginations had been phantesied of any men.  Master. 
Who listeth to see the monstrous opinions of such dreaminge doters, may read them often touched in Aristotle his natural books, and abundantly in plutarch his book De philosophorum placitis, and in Galene and Eusebius in books of the same matter peculiarly written. But these 4 opinions which I haue here rehearsed, are briefly noted in the first book of Cleomedes sphere, though not in like order: and save that in the second opinion I judge his print corrupt, and that for {αβγδ}, I do read and translate {αβγδ}: as it may well be gathered by his own confutation, which will not agree so well for confuting al stiple sormes or spire forms, but as mens iudgment ought to be free, so if any man list to follow that print, I will not withstand him.  scholar. 
Although some of these opinions are so gross that they need no confutation, yet I pray you repeat the confutations that Cleomedes doth use.  Master. 
I am well content, and better pleased to allege them in his own name, then to ascribe them to myself, for diuers causes. first he beginneth with the third opinion, and reproveth it thus. 
he reprose of the third opinion.  If the earth were flat and plain, then should all nations haue one horizonte: for in a plain flat form, there can be no just cause of alteration of the horizon.  Scholar. 
That followeth most certainly.  Master. 
Then must the son and moon and all other stars rise to all people, when they rise to any one, and so must they set( each one in his course) to all men at one instant.  scholar. 
That will follow also.  Master. 
If the son rise to all men at ones, and set likeways at one time, then must the day begin to all people at one,& all nations must haue night at one time precisely.  scholar. 
That is false as all men confess: for at jerusalem( which is well known) it is day three houres sooner then with us, and so is it night sooner by three hours also. But in calicut( as learned men affirm, and trauelers thither, do confirm) it is day 6. hours sooner then with us, and it is night 6. hours sooner to them again then to vs.  Master. 
Your sayings are true if they be well taken: but and if this conclusion bee false, as it is in deed, then must that opinion be false, whereof this conclusion is inferred.  scholar. 
So doth it well follow, and is fully proved.  Master. 
One strong reason for the variety of hours is gathered by the eclipses duly observed, and namely of the moon,, for as it happeneth at one instance of time, so is it not one hour to all nations. As for example: 
Examples of eclipses.  This year of 1556, the eclipse of the moon shall be with us the 17 day of Nouembre at 3. of the clock in the morning, and to them at calicut it shall be at 9. of the clock in the morning: yea we shall see the moon in the south-west, and they shall not see her at the same instant, for she will be to them under the horizonte in the north-west. like ways in the year of 1562. there shall be a great eclipse of the moon with us, which shall endure above three houres and an half, and yet shall they at calicut see no part of it, by reason that the moon shall be far under their horizon before that eclipse begin. And in like manner this last year 1555. was there a great eclipse of the moon the fifte day of june, at three of the clock in the morning, yet in calicut there was none eclipse seen then, for the moon was set under their horizon two hours almost before the eclipse began. But in the year of 1551. when we had the eclipse of the moon at 9. of the clock at night, the 20. day of February, they at calicut saw that eclipse at three of the clock in the morning the next day, as the Portingales that were there can testify. whereby it is manifest, that their horizon doth not agree with ours, and thereof doth it follow that the earth is not flat. But now to return to Cleomedes again,( unto whose words I haue added but the examples of the eclipses) his second reason against the flatness of the earth, is this.  

An other reproof of the flatnes of the carthe.  If the earth were flat and plain in form, then the Pole must needs appear at one height to all parts of the world, and the artike circled( which encloseth the stars that never set) should be but one to all nations. But both these things appear plainly false: for as unto us about London the Pole is not fully 52. degrees high, so if you go northward, you shall finde the Pole to rise higher and higher, till it bee fully 90. degrees high. and in going southward, the elevation of the Pole waxeth lesser and lesser, till you come to the middle of the earth under the equinoctial, where the pole is of no height, but is equal with the horizon. Also in all these places, you shall haue several arctic circles.  Scholar. 
That must needs follow the diversity in the eleuation of the Pole, as it hath been sufficiently declared before  Master. 
As the first improbation doth reprove the flatnes of the earth between east and west, because it regardeth chiefly the rising and setting of the son and other stars, and their course between east and west, so this second confutation improveth the opinion of plainness between south and north. So doth it follow, that the earth is flat neither one way neither other, but both ways hath some certain rising, which anon I will prove to be a just roundenes.  

The third confutation  A third reason is alleged by Cleomedes, touching the equality of daies to all nations, which should of necessity follow if the earth were flat, and all people had one horizonte, but because it is so little disagreeable from the first reason of one Horizonte, and one time of rising and setting of the son, I haue joined them both in one, as before it doth appear. These three reasons are plain enough. The fourth reason which Cleomedes doth make, is not so easy, yet is it as certain as any of the other: and therefore I will show you what it is, seeing you desire to hear his own arguments, although I determined before to allege such reasons only, as might appear easy to understand.  Scholar. 
If it be not over much obscure, it may please you to declare it in the most plainest form ye can.  Ma. 
I will only alter his order in the propositions, adding that which is not easy to be gathered, to make it the easier to your understanding. This is it.  

The fourth confutation of the plain nes of the earth.  If the earth were plain, it should follow, that the whole diameter of the world from one side of the sky to the other, should be but 100000. furlongs, that maketh 12500 miles, which saying appeareth so absurd, that no man will grant it. but if any man would do it, this argument following shall confute him. First therfore I reason thus. If the earth be plain, then al places in the earth ar as far a sunder, as their Zeniths, or vertical points be in heaven. This maxim must I add unto Cleomedes, to make his reason the more plain.  Scholar. 
But this maxim do I not understand, wherefore I beseeke you both to prove it, and declare it.  Master. 
I am content.  
You know by the former treatises, that the Zenith is the point right over the head of any people, whose Zenith it is: whereof it must follow that every diuers place in carthe, must needs haue a several Zenith in the sky.  Scholar. 
That is plain.  Master. 
Then imagining the earth to be flat, the lines that doth ascend from any two places, unto their Zeniches in the sky, must needs be parallels, as here in this  Geometrical diagram. picture doth partly appear. for if the circled be set for the sky, and the flat square within it for the earth, then take two places in the earth, as A and B. the zenith to A is C,& must needs be right over it, and therfore the line that is drawn from A to C, must be a just plumb line,& perpendiculare to the flat earth. And likewaies the zenith to B is D, which must needs be right over it, and therfore the line that goeth from D to B, must of necessity be a perpendiculare and plumb line to the flat earth also. Then if both those lines be per pendicular to one flat plain, or to one line standing for that plain flat, all the angles that they both do make with the thyrde line A B, must bee right angles, according to the definition of a perpendicular line. now if all their angles be right, then are they all equal according to the fourthe grauntable request in the second book of the Pathway, that all right angles be equal each to other. And if all their angles be equal, then must their match angles be equal of source: whereby it doth follow according to the is. theorem of the second book of the Pathway, that those two perpendicular lines be parallels, seeing that on 2 right lines, as A C and B D, there is drawn a thyrde right line A B, crossewayes, and maketh two match corners of the one line, equal with the like two match corners of the other line.  Scholar. 
Hereby I haue not only gotten the understanding of your proof, but also I perceive a farther use in he theorems of the Pathway, then I knew before.  Master. 
I will prosecute my proof. sith those two lines bee parallels, and equally distant, then is there as much space between A and B, as there is between C and D.  Scholar. 
Thus is your maxim sufficiently proved, and fully declared: for A B betokeneth the distance of the two places in earth and C D, standeth for the distance of their zeniths in the sky.  Master. 
now therefore will I return to Cleomedes argument. They that dwell at Lysimachia( in Grece)& they that dwell at Syene( in the south parte of egypt) haue between them in distance 20000 furlongs( that is 2500 miles) wherefore it must solowe that their zenithes in the sky be no farther a sonder, seeing they be limited by two perpen diculers equally distant: but it is well known by good proof of instruments, that Syene is under the tropic of Cancer directly, and Lysimachia is under the head of the North dragon, which 2 places in the sky are justly pro ued to be a sunder the 15 part of the whole compass of heaven, that is the first part of the diameter of the sky. Whersore if 20000 furlongs be the first parte of the diameter, the whole diameter must be but 100000 furlongs:& the whole compass of the sky must be but 300000 furlongs, and of these furlongs it is proved, that the earth containeth in compass 250000. so is the heaven little bigger then the earth in compass which absurdity may easily be confuted by the son, which in comparison to the sky, is a very little parte of it, and yet is bigger than the earth mannye fold: whereby any man may see what absurditye followeth that opinion, to think that the earth is flat.  Scholar. 
I do meetly well understand this reason, but I should better haue conceived it, if I had known the two places which he allegeth for examples sake. 
A like reason.   M. 
Then will I for your pleasure make the like argument by example of 2 places which ar better known to english men. you know the castle of arundel.  Scholar. 
The name is ancient and famous.  Master. 
And new castle upon Tine is well known to you also.  Scholar. 
So is it.  Master. 
To go the next way between these two places it is 270 english miles. 
Arundel castle.  And the Zenith of arundel castle( which is the just point of the latitude of it) is 50 degrees and 30 minutes, as ones I remember I took note of it in riding that ways. The Zenith also of Newcastle is from the equinoctial 55. degrees, so is the difference between their zeniths 4 degrees and 30 minutes. Now( as I haue declared before) If the earth be flat and the perpendicularre lines bee parallels and equidistant, that go up from these two places to their zeniths, then is 4 degrees and 30 minutes, just equal in quantity to 270 miles.  Sc. 
That is true, as it is proved before in the third treatise.  Master. 
You are far deceived: it is declared there, that 270 miles in earth, must answer in proportion to four degrees and an half, and not that they are equal together.  Scholar. 
I perceive mine own negligence in marking the propretye of speech. I should haue said, that as four degrees and an half is the eight score part of the whole compass of heaven, so 270 miles is the eight score parte of the circuit of the earth.  Geometrical diagram.  Master. 
That is true: but yet these 2 partes are as far unequal in quantity as heaven& earth ar unlike in their compass, wherefore to the intent that from henceforth you shall not mistake it again, I will by lineary demonstration set before your eyes the declaration and difference of them both more plainly then curiously.  
Here in this figure you see two circles drawn upon one centre, their common centre being G, from which there are drawn to the uttermost circled two right lines G A,& G D, these lines do cross the lesser circled in 2 points E and F, fro which two points I haue drawn two parallels, unto the circumference of the greater circled, which two parallels be B E, and C F. now may I say, that because these two circles be made vpon one common centre, and two lines drawn from that centre to the circumference of the both circles, because A G D is one common angle in them both, therfore are there arch lines enclosed between those two right lines like in proportion.  Scholar. 
I perceive it well: so that if the arch line A D in the greater circled, be the sixth parte of it, then is E F the arch line of the lesser circled, the sixth parte of his own circled, in like manner. but yet that arch of the lesser circled is not so great as the like arch in the bigger circled.  Master. 
Then what say you of the arch B C, in comparison to the arch E F, which both arches are between two lines parallels?  scholar. 
They must needs bee equal, seeing there is just as much distance between E F, as there is between B C.  Master. 
So may you now perceive what difference it is to say, that two arches of two several circles, are like in proportion; and to say that they are equal in quantity.  scholar. 
now I perceive it plainly, that although 4 degrees and an half( as your former reason did import) be like in proportion to the whole circumference of heaven, as 270 miles are in comparison to the compass of the earth: yet it followeth not that they should be equal together.  Master. 
But supposing the earth to bee flat, then it followeth as I haue declared before, that they are equal in quantity, seeing both beetoken the distant of one couple of parallels. And thē it followeth, that seeing 4 degrees& a half is the four score part of the compass of heaven, if I multiply 270 miles( which is equal to it) by 80, therof will amount the number of miles that make the compass of heaven, which are 21600 miles. now to know the diameter of it, I take the two received numbers for the proportion between the circumference of a circled and the diameter of it, which are 22 and 7,( as in the Pathway is declared more largely) and by the rule of proportion I work in saying: if 22. give 7, what shal 21600 yield? and there amounteth 6872 8/ 11, which must be the whole diameter of the sky, if the earth were flat.  Geometrical diagram.  Scholar. 
That is to great an inconvenience for any man to affirm. for thereby I se it would follow that if we go any way from our own country, 3436 miles, we shal come hard to the sky, which is to childish a fantasy, sith not only reason, but daily travell declareth the contrary. again I remember that in the third treatise you declared that the earth was so much in compass, which must needs bee many fold less then the heauens, which ar so far distant from the earth on every side.  Master. 
Thus are all Cleomedes reasons against the flatnes of the earth fully alleged,& somewhat largely declared: Now will I proceed to the confutations which he useth against the other opinions, following his own order. wherefore next doth follow the confutation of them which say that the earth is hollow like a bowl. 
The consutation of the fourthe opinion.  Against whose fantastical imagination he reasoneth thus: If the earth were hollow as a bowl, then should the son, the moon and all stars in their rising appear sooner to them that dwell in the west, then to them that dwell in the east: which thing is contrary to daily experience.  Geometrical diagram. For declaration of which saying by lineari demonstration I think good to draw a figure, wherein you may aptly se the force of his reason. The uttermost circled of the figure doth represent the sky, and the inner most half circled standeth for the imagined holownes of the earth,& the half roundelet A B, representeth the massy substance of the earth, the right line K L, expresseth the diameter of the world, and therfore the right horizon of the earth, K being the east and L the west. Now for explication of Cleomedes reason: If the earth were hollow, as here the form of it is drawn, then when the son is risen, in the east about E, it would appear to them that dwell in the west by B,& not unto them that dwell in the east by A. for the brow of the hollow ground by C, doth hid the Son yet from them, so that he must ascend as high as F, before they that dwell in the east by A may see him. Again when the Son goeth down, by this opinion he should set to them that dwell in the west by B, as sone as he came to G, by occasion of the brow of the ground by D. and yet they that dwell in the east by A, should see him a great while longer: for that brow of ground by D, will not yet hinder their sight, until he be descended as low as H. So should they that dwell in the west see the son soonest in the morning, and they that dwell in the east should see him latest at evening.  scholar. 
This thing is so false, that every child knoweth the contrary.  Master. 
Yet of that opinion doth there follow farther inconueniency, 
An other reproof of the same opinion.  as Cleomedes doth show: for by this fantasy, they that dwell in the south should see the north Pole more higher above ground, and so should haue a larger arctic circled, then they that dwell in the north, as by the same figure it may be declared.  Scholar. 
I perceive it well: for if I make K to be the south, and L the north, then it appeareth in this form of the earth, that they which dwell in the south by A, may see as low as H: and they that dwell in the north by B, can see no farther north then G. which is so far against reason and daily experience, that it must needs appear to be a vain fantasy, that bringeth for the so mad and monstrous conclusions.  Master. 

Yet an other confutation of the same opinion  Yet doth there follow more fonde conclusions of it: for by this opinion all nations that dwell within that holownes, should see less then half the sky, less then half the zodiac, and less then half the equinoctial, whereof it would follow( beside other absurdities) that they should haue their night commonly longer then their day, because that parte of heaven which they se is less( especially to them that dwell in the bottom of that holownes) then that part which is under their horizonte: Yea they that dwell in the bottom of that holownes, can never haue their day so long as their night, because they do see so little a portion of the sky. As a man that is in a deep trench or in a pit, can see but a little of the heauens. And thus hath Cleomedes sufficiently confuted those two opinions: which kind of confutation Ptolomye doth use also against both those opinions.  Scholar. 
Then must they needs be good: 
Ptolemye.  for as I hear all learned men say, Ptolemye is the father of that arte, and proveth all his words by strong and invincible reasons.  Master. 
No man can worthily praise Ptolemye, his travell being so great, his diligence so exact in observations, and conference with all nations, and all ages, and his reasonable examination of all opinions, with demonstrable confirmation of his own assertion, yet must you and all men take heed, that both in him and in al mennes works, you be not abused by their authority, 
authority of writers.  but evermore attend to their reasons, and examine them well, ever regarding more what is said, and how it is proved, then who saieth it: for authority often times deceiveth many men, as here by and by in Cleomedes it shall appear, whose arguments in confuting the other two opinions ar nothing substantial: which chanced other because he saw the fondenes of these opinions so great, that he sought no great reasons to confute them, other else hastinge in his writing caused him to use the less diligence in framynge his reasons. but now will I repeat them.  

Cleomedes argument against the first opinion.  If the earth were of cubike form, then should all nations haue syxe hours day only, and 18 hours night, seing ther be round about the cube four sides, so that on each of them the son should shine 6 hours only: this is a very weak argument.  scholar. 
Yet unto me it seemeth a strong reason: for seing that the Son doth go round about the sky and about the earth also just in 24 hours, it must needs follow that he spendeth only 6 hours in every quarter: and a cube hath but four sides in his compass,( although it haue 6 sides in all) wherefore in mine opinion it is well concluded, that every one of tose four sides, do see the son 6 hours justly.  Master. 
Often haue I read in Galene, and more often haue I seen it by experience, that better it is for men to want all arte of reasoninge clean, then to haue such confidence in a mean knowledge therof, that may occasion them to deceive themself, and to seduce other. You are fully persuaded that this argument is good: whereby it appeareth that you espied not the want of that mean proposition, which should make the argument good, which must be this: that every quarter of the sky, agreeth to one quarter of thearth.  scholar. 
That not only I think to be true, but yourself affirmed it also before this time, as a true sentence.  Master. 
And so will I do still, affirming it of the true form of the earth, but not of this imagined cube form.  Scholar. 
Why, is there any difference in the quarters of any forms? is not a quarter of a cube the fourth part of it, as well as a quarter of a Globe is the fourth part of the globe?  Ma. 
Yes, but yet doth not the quarters of the cube so agree with the quarters of a globe, as the quarters of two globes agree together.  Scholar. 
That I understand not.  Mast. 
Then will I declare it manifestly by lineary demonstration.  Geometrical diagram. mark these figures. Here you se first for the true opinion, 2. circles drawn one with in the other vpon one centre, and the same are divided into four quarters each of them, so that the four quarters of the lesser circled, E F G H, do answer agreeably to the four quarters of the greater circled A B C D, but in the second figure, where the cube is made in lieu of the earth, the quarters do not agree, as you may perceive by the draft of the right lines, agreeable to each side of the cube: for every side of the cube hath almost half the circled above his horizontal line. wherefore if you will haue a cube drawn in a globe, in such sort that the quarter of the one in compass shall agree to the like quarter of the other, that cube must be so great, that his  Geometrical diagram. corners may touch the globe on each side, so must it bee as great a cube as may bee made within that globe. And I am sure you will not say that the earth is so great in comparison to the sky.  Schol. 
Now I se mine own error, and the fault of Cleomedes argument.  
 Geometrical diagram.  Master. 
And if any man would excuse Cleomedes, he must say, that Cleomedes did make that reason against such as affirmed two errors at ones, that is the cubike form of the earth,& the greatness of it also to bee such, as might touch the sky with every corner: but if this had been his meaning he might easily haue expressed it so: but what so ever he ment he framed the confutation of the second opinion in the like sort. for this is his argument.  

Cleomedes confutation of the second opinion.  If the earth be of a three cornered form, then should the son show 8 houres justly on each side of it, and so would it be to al people 8 houres day,& 16 houres night: which thing is to appearant false: so can not that opinion be true. for declaration of this argument I haue drawn first a circled for the sky, and then a small triangle form D E F, unto whose three  Geometrical diagram. sides I haue drawn 3 streight lines, representing three several horizontes. but it appeareth at the first sight, that each of those horizontes do contain above them almost half the sky. So that in this quantity of the earth, Cleomedes reason taketh no place, neither generally in any other but one, where the three corners of the earth may touch the sky, for which form I haue drawn the great triangle A B C.  Scholar. 
Yet although Cleomedes arguments bee not sufficient to confute their opinion, that would say the earth were of any of these both forms, their opinion is false nevertheless. think you not so?  Master. 
Yes verily: for a weak confutation of an untruth doth not make that untruth to become true. And because you shall not think that these opinions haue any sure ground, I will repeat Ptolemye his confutation of them both, by one unfallible reason.  

Ptolemy his confutation of the first and second  You see in both these imagined forms of the earth, that there can be no more horizontes, then there be sides in the figure.  Scholar. 
That is certain: for all that dwell on one plain side, must needs haue one horizon: wherefore if the form of the earth were four square in his compass, then could ther bee but four Horizontes, that way: I understand it between east and west, and in all varieties there can be but syxe, sith a cube hath but six sides: likeways in the three cornered form, there can be but three diuers horizonts between east and west.  Master. 
You say well. And seeing all that dwell on one plain side haue all one horizonte, they must haue day all at one instant both for the son rising and also for the setting, so can ther be no more variety in the beginning and ending of daies, then there are sides in the figure of the earth, which by the first opinion must be but 4, and but 3 by the second opinion, where as the contrary is well known by daily experience, as well as by reason, that every 15 degrees in distance westward maketh the day an hour later: and contrary ways every 15 degrees of distance estward, causeth the day to be rather by one hours space.  Sch. 
That is proved also before, in confutation of the third opinion, and namely by examples of eclipses. But what if any wolde affirm that the earth were made of many flattes, as of 24( for an example) between east and west, then should there be no more horizontes, then there bee hours in one natural day, and yet so the difference of hours could not confute them.  Master. 
You must think that learned men can as well mark the difference in every minute of an hour, as the common people can observe diversities in hours: yea the learned observations are more exactly taken thē the 60. part of a minute of an hour, wherefore seeing it is so well proved by sundry observations, and especially by eclipses, both of the son and the moon, that every mile distance between east and west, doth make a several horizonte, there can bee no other form of the earth aptly assigned, but a round circular form. And by the like reason, by the orderly ascending of the Pole, in going northward, and by the uniform descending of it in going southward, it must needs appear that there can bee none other form of the earth between south and north, but a round form also.  Scholar. 
now can I end your argument of the distribution disjunctive, which may be framed thus.  

The collection of the argument  The earth must haue some form, either cubike, three cornered, flat, or hollow, or some such like, other else a round form, but his form can not be cubike, nor threcornered, neither flat, neither hollow, nor any such like, as before is fully proved, wherefore it must needs be round.  Master. 
It followeth well. for it is not possible that in any other imagined form of the earth, the horizontes should alter toward every coast so uniformly, and the dayes differ so proportionably, the Pole to be elevate so rateably, or to be depressed so orderly, and all other appearances to answer so agreeably. 
A roller form.  Yet some men( as Ptolemy doth report) had invented an other form like a roller, or a round pillar, whose ends should lie north and south, by which form although they thought none of the varieties of appearances might bee hindered, yet in that form the elevation of any one of the Poles could haue but two varieties for ever more it must appear other over their heads, as to them that dwell on the flat eandes of that roller, or else to all other that dwell about the compass of the roller, it must still appear in their horizonte, so should ther bee no stars about either Pole always appearant above ground, neither all ways hid under ground, but all stars should rise and set to all them that dwell about the roller. And again they that dwell on the flat ends of the roller, should haue but one horizon, so large in distance of ground, as the whole thickness of the earth is: all which imaginations are both well known to be vain,& also easy to be confuted by the former reasons, which serve so largely, that you can imagine no form other then round, but those reasons will confute it. wherefore your argument doth proceed well.  

That the water is round by diuers profess  Yet farther for the roundenes of the water also, and namely of the sea, you may frame arguments by the like form of appearances: for where so ever you bee on the sea, you shall see half the sky justly, and the farther west that you go, the later doth the son rise: and contrary ways the farther east that you sail, the sooner in the morning will the son appear to you. whereof I will declare unto you a notable example, and a just proof.  

An example of the roundness of the sea by a ships ceurse.  Imagine a ship swift of sail to be at the scape of Cornwall ready to make sail toward the west directly, and to haue a great gale of wind, it is possible that she may run 240 miles in 24 hours: for I haue been at the trial of a greater course, therefore I speak( as men say) within my bounds: after which rate she shall run in 16 hours 160 miles. Now let hir hoist sail at the son rising, and let the time of the year be somewhat before midsummer, or little after, when the artificial day from son rising to son setting, is 16 hours long: by this means at the end of 16 hours, she shall be west of the scape of Cornwall where she began her course 160 miles: and then shall the son be at setting to their sight that dwell at the said scape, but the ship shall haue the son above four degrees high at that instant, by reason that she did run with the son, and that the roundenes of the sea doth change the horizon so many degrees in 160 miles.  Scholar. 
although this example bee pleasant, yet it passeth mine understanding, sith that I believed hitherto, according to your former doctrine, that 160 miles would not haue altered any ways three degrees, seeing 60 miles do answer to one degree.  Master. 
That saying is true all ways for the elevation of the Pole, for going between south and north in all places; but for going between east and west, it serveth only for the middle of the world, that is under the equinoctial circled: and in all other places, the farther you bee from the equinoctial, the fewer miles answer to each degree, by reason that the parallels grow lesser still toward the Poles: yet the least of them is divided into three hundreth and sixty degrees as well as the greatest, whereof hereafter I will instruct you more exactelye. in the mean season, you shall understand, that for the latitude of the scape of Cornewalle, every degree requireth only 37 miles: 
How many miles answer to a degree at the south coast of england.  which being multiplied by 4, maketh but 148: and therefore I said above 4 degrees did answer to 160 miles, as the truth is.  Scholar. 
now I perceive somewhat better the reason ther of by the proportion of the parallel circles in the Sphere. and surely this proof is pleasant, and easy enough to bee tried.  Master. 
A like example may this be. Suppose at the same time of the year when the day is at the longest, 
A like example of a ships course.  that there is a swift ship at the west point of the isle of island, where the longest day is 20 hours from son rising to son setting, in those 20 hours, that ship might sail westward 200 miles. Then considering that at that latitude which is above 63 degrees, there answereth but 27 miles to a degree. when the ship is at the end of his course, the son will set to them that bee in island; and then shall the ship haue the son 7 degrees and almost a halse, above the horizon,( which maketh half an hour in time) so that by the roundness of the sea, they haue changed their horizon so much in twenty hours saylinge. now turn his course and let the ship haue like wind homeward again the next day, and let him make sail at the son rising, then shall it bee after son set half an hour, before she shall arrive at the former port: by reason that the son rysse half an hour later to the ship, where shee was in the west, then it did to them at island: and therefore must it set half an hour rather at island, so hath the ship lost half an hour, by coming eastward against the son.  Scholar. 
I understand that. As 15 degrees doth answer to an hour, so 7 degrees and a half maketh half an hour: wherefore if the ship sail just twenty hours, and that artificial day is just 20 hours long, then shall they come to their port in iceland half an hour after son setting, because it was half an hour after son rising in iceland, before they began to make sail.  Master. 
This variety could not happen, except the water also were round as well as the earth. 
An other proof that the water is round.  And for farther proof of the roundness of the sea, daily experience doth teach us, if we would diligently observe it, howe that when a ship doth draw toward land out of the main sea, the low ground doth not appear at the first unto the ship but the tops of high hills and cliffs: like ways they that be on the land and look to the ship, they see the top of the ship first, and after that, the masts, sails, and shroudes before they can see the hull, and body of the ship. Now I demand of them that think the water to be flat, what is it that letteth the sight, so that it can not as well see the lowere ground from the ship, or the hull of the ship from the land.  Scholar. 
They can name nothing but water: for there is nothing else between them, able to stay the sight. But then peradventure they will say, it is the waves of the sea, which rise very high often times.  Master. 
That were to childish an answer, sith the like doth appear, and that most exactly, in a great calm, when the sea seemeth as plain and as smooth as a board: so that they must show some such thing, as is higher between them then any of both their syghts, when the sea is as quiet as can be.  Scholar. 
Then is there nothing but water. But then it seemeth to me, that if the water did rise round, the farther the ship were from the land the higher she should be, and therfore the better might be seen.  Master. 
Your imagination hath small ground of reason: for although the earth and the water both ioyntlye and severally bee round of nature, and therefore haue in dead no place higher then other in their circumference, yet all vulgar men shall think by apparance that that place is highest where they stand,& that from them on ethe side ther is a round descente, until by imagination they come to the right contrary point where their Antipodes be, whom they shall think to be right under thē, where as those Antipodes haue the contrary imagination, that they dwell on the highest parte of the ground, and that their sea is highest, and so both descendeth compassedlye unto the contrary point to them again. and thus every other sort of people think that they dwell on the highest parte of the land, and also of the sea,( if they dwell on the sea) and they shall think that both the sea as well as the land doth descend from them each ways.  Geometrical diagram. As in this circularre form of the earth and sea, the men that dwell by A, think themselves to dwell highest of all other, so that on each side of them the land& sea seemeth to descend,& therefore they judge the ship that is by B, to bee lower then they, where as that ship, contrary ways, seemeth to them that be in it, to bee on the highest parte of the world: and therefore they think that the land by A, is lower then they are. again they that dwell by C, and the ship that is by D, are of like imaginations, each in his fantasy thinking himself highest, and the other lower. And so of them that dwell by A and by C, each meruayleth how the other can go, and his head downward: yet in deed none is lower then other, sith each of them is equally distant from the centre of the earth, which is the lowest place of all other. and therfore no way is accounted lower except it be nearer to that centre. whereby also it may appear contrary to your saying, that although the sea bee round, yet shall not the ship seem to ascend still, but rather seem to descend, though in dead it doth none of both, but moveth circularly about the centre of the world, so that it can not aptly be called a right motion, but a compassed motion that a ship maketh, save that it is tolerably to be born in vulgar speech, because every small arch of a great circled, seemeth to be a right line to the sight of the eye. And in this figure is somewhat represented the declaration how the compassed form of the water doth let the sight to see the ship, and like ways how that they on the land may se the top of the ship when they can not see the hull, and they in the bull of the ship can not se those places on the land, which other in the top of the ship may see, by reason that their sight is above the height of the water. And this may stand for a convenient proof.  Scholar. 
So doth it appear manifestly, now that my former misconceaued fantasy is reproved. And so I remember when I haue looked after a ship that departed from the port where I stood, first I lost the sight of the hull as though it had sunk into the sea, and yet I saw the top still: but at length I lost the sight of it also, as though all had sunk into the water. which by your declaration I perceive doth follow of the roundness of the water: for other reason I can find none.  Master. 
Although you could find other reasons never so many, yet this reason doth enforce that effect. this is the reason that Ptolemy, Cleomedes, and after them joannes de Sacro bosco, and other also do allege, 
A physical reason for the roundness of the water.  but the same John hath an other reason more physical thē geometrical, borrowed out of natural philosophy, which is this: Seing that the water is a body of uniform substance, the partes of it must be of like condition as the whole body is: but the partes of water doth all ways couette a round form,( as wee see in every drop that falleth from any thing, or standeth on anythinge) wherefore of just congruence the whole body of the sea and water must needs covet the same form.  scholar. 
In deed all drops that fall from the air in a mild rain, when men may mark it, do fall in a round form, and so the drops that fall from the eaues of the house, or from any thing else, yea and the drops of dew that stand upon any leaves of herbs, or other like thing.  Master. 
For a farther experience, fill any vessel brym full of water, and you shall perceive by trial, that the water is higher over the middle of that vessels mouth, then it is by the brimmes. And again pour out water on a board or on a ston, and you shall soon see that it will show in a round form, and will be deeper in the middle, then it is by the sides.  

Erasmus Rheinhold.  Yet farther reasons there be alleged, which were to tedious to repeat: but two of them I can not omit, which are declared by Erasmus Rheinholt a man not only of great learning, but also of as great honesty in seeking to profit all men by his travail, although sometime he wanted leisure to examine some of his writings, as it may appear by one of those two reasons, which is this.  

An other reason.  By the long course of every great river( saith he) it may appear that the water doth covet a round form, else could it not so much rise in roundness, as it doth in running so long a course. for example he bringeth the course of the great river Danubius, which springeth in the Alpes, beesyde Vlma in Swicerlande, and entrith into the sea Euxine, above Constantinople, which is from Vlma 312 germany miles, that is 20 degrees, which is the eighteenth part of the whole circuit of the earth: whereby it must needs follow that the middle of that river is higher then the fountains or the mouth, by 13 germany miles( that is 52 english miles) in plumb height. for declaration whereof he maketh this demonstration linearye, supposing A E B C, to be as one of the greatest circles about the earth, whose centre is D. this circled must be imagined so to pass agreeably to the course of Danubius, that A may represent the fountains of it, and B the mouth of it, so E shall stand for the middle parte of the riuers course and A E B, for the whole  Geometrical diagram. course. Now is it said before, that between A and B are 20 degrees, then if you draw a right line from the one to the other, as here you se A F B, it will be lower under the middle of the arch, by the length of the line E F, which is almost the 60 parte of the semidiameter of the earth, and maketh justly 52 english miles, somewhat less then 57: which is the 60. part of the semidiameter of the earth.  Scholar. 
This reason seemeth pleasant, but I perceive not the reason of the just quantity of the line E F.  Master 
That dependeth of the arte of sins and cords and is very certain without any sensible error, of which in an other place ye must learn the use. And in dead as you say, this reason is pleasant, and the author much to bee praised and loved, and as much is it to be lamented, that the shortness of his life would not permit him to haue recognized his works again: wherefore that he can not do by prevention of death, I trust some of his friends will do: for although they be but little faults, yet pittye it is that in so good works there should remain any little spots, as in this argument there are two, which yet hinder not the argument. And although it might bee truly said that the height of the middle of Danubius is not 52 mile, and is but 36 mile, yet is the form of his argument good, for that height is sufficient to prove that the middle appeareth much higher then the fountains of it: the cause of this ouersyght was, that he did esteem the course of Danubius to run by one of the greatest circles of the earth, which is not so: for it hath in latitude from the equinoctial 46 degrees, so must the parallel of his course bee little more then two third parts of the greatest circled: but as this is somewhat to strange for you yet being unexpert in the arte of cords and sins, and in the knowledge of cosmography, so I will let it pass with this light admonyshmente, wysshynge that he had also more aptly expressed his meaning, and the use of his terms, for auoidinge of slanderouse tongues, for it might now bee answered him, that Danubius is no higher in one place, then in an other, seeing all distance of height is to bee accounted from the centre: and the middle of the river by E, is no farther from the centre D, then is the fontayne A, or the mouth B.  Schola. 
Marye that objection is certain, and therefore is his error manifest, and his argument of no force.  Master. 

Erasmus Rheinholt excused.  You triumph to much before the victory. his argument is better then you do considre it his intent was to prove that the water doth not run by a right line and dounwarde still, as the vulgar sort doth imagine, but that it runneth circularlye. wherefore it followeth well against the vulgar opinion, to say that the water of Danubius is higher in the middle of this his course, by so many miles in height plumb upright, then it should be by their imagination So is there none other fault in this point, but the want of distinction of the true opinion of highnes and lownes, from the wrong taking of the same names, whereby those which do not know his great learning, and might happen to hear his argument, would judge that other he were wonderfully deceived, other else that he did to much abuse his terms: but if death had not prevented him, he would haue declared his meaning, I doubt not, as I haue declared it.  

Erasmus Rheinholt his second argument.  now to his second argument. he proveth that there can be no such holownes in the sea, as there is between two hills for seeing the sea is a heavy body, and presseth toward the centre of the world, every parte of it will do the like if it be not stayed. And the water being a lyquide and fluxible body, can not be stayed by his own partes: wherefore it followeth that there can remain no valyes nor dales, nor hollow partes in it, but it shall quickly be filled with water. and therfore wee see, that nothing can be more plainer then is the top of water, sith every part so exactly joineth with other, in fyllinge up all vnequalitie: whereof it followeth, that if the top of the water be just equal and like distant from the lowest part of the world,( which hath been often declared to be the centre of the earth) then must the face of the water needs be round, according to the definition of a circled.  Scholar. 

Why the water doth not cover all thearth.  That followeth well in deed: for as each parte of the circumference in a circled is equally distant from the eentre, so if all partes of the face of the water be equally distant from the centre, it must needs be circular, as the circumference of a circled is. But if it be so round, and ought to haue his place above the earth, how doth it happen that it doth not cover the whole face of the earth? and so should there be no earth seen.  Master. 
Haue you forgotten what you read in joannes de Sacro Bosco, for to answer that question?  Scholar. 
In deed he saith that the other three elements do compass the earth round about, save that for the preservation of man and beasts, the dryness of the earth doth withstand the moisture of the water.  Master. 
That reason savoureth more of the determinations theological, then of the demonstrations mathematical, wherefore I will add thereto a proof by good demonstration that it can not compass the earth round: 
That the water 1. can not compass the arth II.  for which purpose first I say, that the water being enclosed within the bounds of the earth, can not be so great as the earth is. again considering that one portion of water being mixed with 4 times so much earth, would make it all soft and slabby, it may not be thought that the water of the sea and of all ryers and springs joined together, is so much as the first parte of the earth. 
III.  furthermore if you consider the firm stableness of the earth, and the unstable swaruynge of the water, you wolde think that if the water were able to match the twentieth parte of the earth, it would make the earth more unstable then the nature of the earth, and the preservation of earthly creatures could bear. Yea it would be a weak ground to bear so wonderful a weight as it doth, 
IIII.  if the quantity of water were notable, in comparison to the quantity of the earth. 
V.  Yet now for farther trial, suppose( as I think it true) that on the flat face and circumference of the earth, there is as much water as land, so might it appear that the water were as much as the land, as many men do affirm.  Scholar. 
And most part of learned men( as I haue heard say) do vouch that as a most certain truth.  Master. 
It is true, as I judge also, yf they mean like cosmographers that half the face of the earth( as I said) is covered with water, but then imagine what depth may that sea be of.  Scholar. 
No man can tell.  Master. 
Yet by trial of mariners it hath been found in few places, a hundreth fathoms deep, which is little more then the tenth parte of a mile.  Scholar. 
That not withstanding, it may bee deeper in some places.  Master. 
For a supposition, imagine it were in all places a mile deep, taking one place with an other.  Sch. 
I think that to to much a great deal, considering that all known partes are not in the deepest, accounting one place with an other, as good mariners can testify, above 40 fathom, and so groweth shallower still to the shore.  Master. 
The more that that supposition exceedeth truth, the stronger shall the proof be of the smallness of the water in comparison to the earth.  Scholar. 
Then for trials sake, I suppose it were so.  Master. 
How deep think you now the earth to be?  Scholar. 
I remember you said before, that 57 mile was but the 60 parte of the semidiameter of the earth: then must the whole earth be in thickness 6840 miles.  Master. 
That is agreeable to that rate: but as I said before, the diameter is 6872 8/ 11. And now if you abate one fifte parte of that depth, the rest will make the side of a cubike form, almost as great as the globe of the earth: as it appeareth in the works of geometry.  Scholar. 
The fift parte of 6872 is 1374. which being deducted from 6872 there resteth 5498.  Master. 
That number is somewhat to little, but 5541 is very nigh the side of a cube, equal to the globe of the whole earth, therefore multiply it cubikly, as you haue learned in arithmetic, and then shall you see, howe many miles square are in the whole globe of the earth.  Schol. 
If 5541 be multiplied by itself, it maketh in square number 30702681, which being multiplied again by 5541, doth yeld 170123555421: which is the cubike number to 5541, and so consequently must it be that cube which is equal to the earth, in his whole globe.  Master. 
So is it very nigh. But now for the quantity of all the sea, this way must you work. first to know all the plate face of the earth, you must multiply his circumference by his diameter, as it is declared in the pathway, and so will there amount 148450909: which is the full perfit form of all the face of the earth: whereof presupposing( as the truth doth enforce us) that half the same is sea and water: then doth it follow, that the whole perfit face of the sea and water is 74225454 miles and a half in all together, which is not the 2000 parte of the earth.  Scholar. 
But must not this number be multiplied by the depth of the sea?  Master. 
seeing that depth is not in one place with an other above one mile, and 1 doth neither multiply nor divide, it will remain as it is.  Scholar. 
Then dare I think farther, that the depth of the sea being not a quarter so much generally, the earth must needs bee 10000 times so great as the sea, and all other waters.  Master. 
Your words err not much from the truth: and therfore by this reason it doth appear, that the water being so little in comparison to the earth, can not aptly compass the earth. And by this it appeareth also how childishlye they do err, that think the water to bee ten times so great as the earth: for if it were but twice so great as the earth, it must of necessity cover all the face of the earth: yea I will say constantlye, if all the water were as much as the hundreth parte of the earth, it would over run all the earth, and cover it clean: which I may easily prove, but not briefly: and seeing the same thing is all ready declared in the pathway, I will omit it here, sith it is a more appropred proof for geometry, then for astronomy: and now will I return to the prosecutinge of our former matters, accounting this sufficient for the declaration of the roundness of the earth and also of the water severally, and now will I add one reason to approve that both they do make one perfect round globe. 
That the earth and water together do make a perfect globe.   
every gross and sound body doth give a shadow like unto his own form the earth is a gross and sound body, therefore must it give a shadow like his own form: but in all eclipses of the Mone, which are caused by the shadow of the earth, his shadow is always constantly round, whether the shadow do run east, west, south, or any other ways mixedly: wherefore it followeth, that the form of the earth is round, which giveth that round shadow.  Scholar. 
How shall a man understand that the shadow of the earth is round?  Master. 
In the eclipse of the moon, other all the mone is darkened, or else but one part of hir: If all the mone be darkened, then doth the darkness begin on the east side of the moon in circularre form, and increaseth still in the same form, till all the whole moon be eclipsed, and then decreaseth the darkness again, so that the west side of the mone is darkened, but the darkness vadeth by little and little, and yet still in circularre form. And if the moon be darkened only in one parte, whether it be the south part, or the north parte, yet still is the shadow round in form: where as if the earth were square or cubike, other three cornered, or of other such form, the shadow wolde so appear in the mone as by the third and fourthe figure, you may partly perceive.  
 diagram of the eclipses of the moon. 
Examples of the first form where all the moon is eclipsed at the full eclipse.   diagram of the eclipses of the moon. 
Example of the third and fourth forms.   
 diagram of the eclipses of the moon. 
Examples of the third and fourth forms.  
Examples of the other two sorts, of one parte eclipsed.  
The south parte.   diagram of the eclipses of the moon. 
The north parte.   

That the earth is but a prick in respect of the sky.  But I will omit this matter till anon, because it is not easy to understand without farther explication of other matters incident thereto. And because I haue begon to speak of the shadow of the earth: I will allege one argument more, taken by the same shadow to approve the smallness of the earth in comparison to the sky. wherefore thus I frame mine argument.  
The son is but a very small portion in comparison to the whole sky, and yet the son is manifold bigger then the earth: wherefore the earth must needs bee but a very small thing in comparison to the heauens.  Scholar. 
Your arguments is good, and the maior is manifest to every mans sight: but how do you prove the minor?  Master. 
every dark body giveth shadow according to the quantity that it beareth to that shining body, which giveth the light, so that if the shining body be equal to the dark body, thē doth the shadow run in form of a pillar, or of a roller, like big at both the ends: but if the bright body be greater then the dark body, then doth the shadow grow lesser& lesser in spire form, or taper fashion, and at length doth end in a sharp point. contrary ways, if the light body be lesser then the dark body is, then doth the shadow grow greater and greater, still as it goeth from the dark body, and is smallest at the beginning; contrary to the taper form, which is greatest at the beginning: and this form may be called maundforme, or bell form, because it is like a maunde basket, or a bell.  
Examples of these three diuers shadows. 
The pillar form.   diagram of a shadow cast by the earth. 
The Taper form.   diagram of a shadow cast by the earth. 
The Bell form.   diagram of a shadow cast by the earth. A representeth the son or other light body. B the earth, or any dark body, and C the shadow.  Scholar. 
This may stand as a sure maxim, sith both reason& sense do testify it to be true.  Master. 
Then do I infer farther: that if the son were lesser then the earth, the shadow of the earth would grow greater and greater, and would be infinite in length: whereby it would darken the most parte of the stars, every night:& very often it would shadow the mone, and that for a long space together. as you may gather by this figure,  Astronomical diagram. where A representeth the son in lesser form then the earth, which is signified by the circled marked with G, & the shadow that cometh by this form, is marked with D, which occupieth a great part of the sky, and therefore would darken all the stars is so much space of the sky, which is nigh hand a quarter of that hemisphere that is above our horizon. And as the shadow turneth about according to the motion of the son, so in four and twenty hours all the stars that be nigh unto the zodiac, should suffer eclipse: which thing is contrary to daily experience, for wee see there( about the zodiac and against the son) the stars very bright.  Scholar. 
This reason doth suppose, that the stars do receive their light of the son, which thing was not yet proved by you, although I think it to be true, yet in a good argument, no doubtful sentence may be alleged.  Master. 
Then seing this place doth not conveniently permit so long a digression to prove that, I will use the mone for an example, which appeareth so manifestly to borrow her light of the son, that according as she receiveth the light from him, so doth shee appear greater or lesser in light, according to hir distance from him. and when so ever she cometh into the shadow of the earth, she loseth her light, other fully or in part, accordingly as she passeth and toucheth the shadow of the earth. wherefore as long as the moon should be within that shadow, she must needs be in the eclipse: and the shadow being so great, she should be eclipsed not only every month at the full, but she should continue almost four dayes to gether in that eclipse, seing that shadow doth occupy as much of the sky, as shee doth move by hir proper course in four dayes.  Schol. 
That absurdity is to manifest to grant unto: and yet the greatness of the shadow infereth no less, sith it occupieth so much of the sky.  Master. 
The like inconvenience will follow, if the son and the earth were both of one greatness, as are B& G in the former figure, for so wolde the shadow run of one bigness like a roller, as is represented by E, and would darken diuers stars, and namely all that bee in the middle of the zodiac, and the moon should both oftener be eclipsed( then in dead she is) by the greatness of the shadow, and would tarry longer in the eclipse, by that same reason, then good reason would allow. But seing we perceive no stars directly against the son to be eclipsed, neither yet the mone, in such form as that pyllerlyke shadow would cause, we must needs think that the shadow is much abated, before it come to the sphere of the moon, and is clean consumed before it come at any of the stars, which kind of abatement could not be, but where the light is much greater then is the body that maketh the shadow, as is C in comparison to G.  Scholar. 
So must it follow, that seeing the son is the light body, and the earth giveth the shadow, of necessity the son must be greater then the earth.  Master. 
Yea in deed, and that many fold.  Scholar. 
Then of more force must the earth bee a very small body in respect to the whole sky, which is infinitely greater then the son, as every child may perceive.  Master. 
Yet haue I farther matter of proof, that the earth is not only a very small body in regard to the sky, but is without any view of greatness in that comparison.  
If the earth had any notable quantity in respect of the sky, 
The second reason for the quantity of the earth. &c  then must the diameter of the earth haue as great a quantity, in comparison to the diameter of the sky. for as in two circles the proportion of the diameters is equal to the proportion of the circumferences, so is the proportion of the shorter to the longer, greater then is the proportion of their two perfit forms: but in two globes the proportion of the shorter diameter to the longer, is much greater then is the rate of their perfit forms: and yet much more greater then the proportion of the lesser globe to the bigger.  Scholar. 
That is sufficiently proved in Geometry, wherefore you may proceed with your conclusion.  Master. 
If the diameter of the earth haue notable quantity in comparison to the diameter of the sky, then the stars which ar over our heads, be nigher unto us by a notable quantity, then when they be in the east, or in the west.  Scholar. 
In deed they are nearer by the semidiameter of the earth: which of itself must needs bee accounted a notable quantity.  Master. 
But if it shall be so accounted in regard to the half diameter of the sky, then must the stars over our heads seem bigger by a notable quantity, then when they are in the east or west.  Scholar. 
That reason is not only approved by geometry, but also by common sight and daily experience, that the nigher any thing is to the sight, the greater it seemeth: and the farther from the sight, the lesser it sheweth.  Master. 
There is no such diversity perceived in the quantity of the stars, but that they appear still constantly of one bigness: wherefore it must follow, that their distance is all one in all partes of the sky, and then doth not the semidiameter of the earth make any notable diversity in distance: wherefore it must be thought that the quantity of it is not sensible in comparison to the semidiameter of heaven, neither the circumference of it in comparison to the circumference of the sky, and much more may not the whole quantity of it bee accounted sensible in respect to the whole quantity of the world.  Schol. 
That followeth well: for as I learned in Geometry, if the diameters of any two Globes, be in such proportion that the greater do contain the lesser a thousand times, then be their circumferences in the same rate: but the perfit form of the greater, is 1000000 fold greater then the lesser: and the whole substance of the bigger globe, doth contain the smaller globe, 1000000000 times.  Master. 
undoubtedly it may bee perceived by sight as well in dialles, as other greater instruments made for observations, that the semidiameter of the son his sphere is more then a thousand times longer then the semidiameter of the earth, else wolde not the shadows agree so exactly as they do: for they move as duly and orderly about the centre of all such instruments, as if their centre were the very centre of the world. which thing could not be, if those two centres did differ notably, in respect to the sphere of the son. And if it were not, that an introduction doth not admit the exact proofs of the arte, I could hereby declare the proportion of these two semidiameters so exactly, that you should confess that proof to bee right certain and good. But now will I procede to the declaration of this third reason by linearye demonstration, although it be somewhat obscure, without other help.  
In this figure, which representeth the three notable circles in a dial, 
The third reason.  that bee made by the course of the son, in the three notable places of the zodiac, that is in the two tropics and in the equinoctial, the uttermost ark B L C, representeth the tropic of capricorn, and is here made no bigger, then the quarter of a circled, by cause the son doth shine but syxe hours unto us, when he is in the sign. the equinoctial is set as half a circled, because the son being in it, doth shine to us 12 hours, and is here limited by E I F.  Geometric diagram. The tropic of Cancer containeth three quarters of a circled, because that when the son is in it, then is there 18 hours from son rising to son setting: and that circled here is signified by G K H. The centre of this dial is A, and the style that giveth the shadow is D A, whose top being D, doth describe those cantylles of circles, in such preciseness, as if that dial stood in the centre of the earth. and like ways the distinction of the hours is such exactly in that dial, as if the centre of the dial, were the very centre of the world.  Scholar. 
I do conceive good reason of proof hereby, but yet I think I shall perceive much more, when I shall understand the just use of those dials, as well as of other several instruments of like use.  Master. 
You say truth: and therefore will I pass from this third reason, and come to the fourthe proof, which is this.  

The fourthe reason for the smallness of thearth.  If the earth were of any bigness in comparison to the world, then should his semidiameter bear some view of byggenesse to the semidiameter of the sky. and so consequently the horizon that we haue on the over parte of the earth, should not divide the sky into two equal partes, for that part which should be under the horizon, would always be the greater, and the lesser parte above the horizonte, as in this figure it doth appear.  Geometric diagram. where A C D B is the circled of the sky, and the lesser circled is the earth, the centre B, being common centre to them both. and E F is the semidiameter of the earth, as E A is the semidiameter of the sky. now if E F bee notable in quantity in comparison to E A, then will the line C F D( being the horizonte on the top of the earth) differ notably from the line A E B, being the diameter of the world, and the horizonte to the centre of the earth. And so shall not that horizon C F D divide the world into two equal halves, but the over part above the horizonte shall be lesser then the other parte that is beneath the same horizonte, which thing is contrary to daily experience, and to all observations: for we may see in the long winter nights those stars that be in the horizon in the east at the beginning of the night, to be in the same horizon in the west, at the end of twelve hours; and contrary ways those stars that did set in the west, when those other did rise in the east, shall rise again when the other do do set. And so of the son and the moon when they be in contrary points of the zodiac.  Scholar. 
That is at the full of the moon.  Master. 
In deed then are they right opposite the one against the other: but if the moon be at the full, long before the son setting, then will she rise somewhat after the same: and contrary ways if she be at the full after the son setting, then will she rise somewhat sooner, by reason that she moveth eastward every hour 33 degrees. And although unto them that be meanly acquainted with the motions of the planets, the declination of the moon and hir latitude, may occasion some doubtefulnes to rise, yet unto the learned, those many fold varieties in the motion of hyr and tother planets, do confirm the principles of astronomy more adsuredly: but this will I omit till an other more convenient time.  Scholar. 
This is well proved now, that the earth in comparison to the whole world is but as a prick or a mote, and likeways in comparison to the other spheres.  Master. 
You must except the spheres of the three planets  Geometric diagram. which bee beneath the son. for unto them the diameter of the earth beareth a notable quantity: for the semidiameter of Venus Sphere, is but 167 times so long as the semidiameter of the earth: and the semidiameter of Mercury his sphere is shorter much, for it is little more then 64 times the semidiameter of the earth, but the moon hath hir semidiameter only 33 times and a half longer then the earths semidiameter: all which proportions with the residue, I haue set forth in this figure, whereby you may perceive, that unto the semidiameter of each sphere, is annexed the number that importeth howe often it containeth the semidiameter of the earth. that is to say: the son his semidiameter containeth it 1120 times, Mars 1220 times, jupiter 8876 times, Saturne 14405 times an: d the eight sphere or starry sky. 20110 times.  Sch. 
I remember that Faber on the Sphere doth account those distances by miles, which is a pleasant matter to red.  Ma. 
In that place Faber followeth the account of Alphraganus the Arabitian, which speaketh of miles much longer then the Italian miles be: for 6 of the Italian miles do make but 5 of Alphraganus miles: of which diversity at an other time I will instruct you, namely in the treatise of cosmography: where I will set forth diuers varieties and appearante repugnances of sundry writers, for the measuringe of the earth: and prove it to be a disagreement more in words then in meaning: and to come by reason of their diuers miles, or other in constant measures. And because you like that table so well, lo here is an other drawn according to the rate of 60 miles to each degree. But here by the compass is understand the inner concavity of each sphere.  
The eight Spheres. The miles that their semidiameter containeth. The miles of every sphere in compass. ☽ The moon 115278. 724604 4/ 7 ☿ mercury. 220500 2/ 33 1386000 4/ 231 ♀ Venus. 573872 8/ 11 3607200 ☉ The son. 3848367 3/ 11 34189737 1/ 7 ♂ Mars. 4192363 7/ 11 26352000 ♃ jupiter. 30501163 7/ 11 191721600 ♄ Saturne. 49500818 2/ 11 311148000 The eight sphere. 69105272 8/ 11 434376000  
And his conuexitie or utter compass is equal to the concauitye of the next sphere above it.  Scholar. 
If the whole circuit of the sky bee 434376000 miles, and the same compass is 360 degrees, then must it needs follow, that every degree of that sky containeth just 1206600 miles, as by division it may be sufficiently well proved. But howe is this supposition of distaunces approved to be true?  Master. 
That proof dependeth of more knowledge, then this introduction teacheth, and therefore must be referred to a higher treatise. But in the mean season admitting this supposition, you may easily tell, howe many miles the son and the moon are in breadth, seeing each of them is accounted about 31 minutes by their diameter, each in the middle of his own sphere.  Scholar. 
now I understand the form of working for trial of this matter. first I must search how many miles make a degree in each of those spheres, and then take a parte proportionable of that numbre agreeable to 31 minutes& a half. Therfore to begin with the son. As his whole sphere in the middle is in compass 25270868 miles, so tryinge it by division, I finde that every degree in that sphere doth contain 70197 miles nigh hand. Then say I by the golden rule, if 60 minutes( which make one degree) do require 70197, what do 31 and a half make? After just multiplication and division, as that rule doth import, I finde the whole diameter of the son to contain in miles, 36853: where as the earth( as before is noted) doth contain in his diameter but 6872 miles. So that thereby it appeareth, that the son is more then 5 times so broad as the earth is overthwart.  Master. 
That is well limited. for else if the flat of the greatest circled of the whole earth might appear unto us, as the flat form of the son doth, the flat form of the son ought to be accounted about 29 times so great as the earth is, in like form. And the whole globe of the son must needs be about 155 times so great as the earth in his whole Globe.  Scholar. 
I perceive that doth follow by two rules of geometry, whereof the first is this.  
In what proportion so ever the sides of any two squares be, those squares are in the square of that proportion: so that if the sides be as 2 to 1, the squares are as 4 to 1: and if the sides be as 3 to 1, the squares are as 9 to 1. &c. The second rule is this: In what rate so ever the sides of any cubes be, the cubes do bear the like rate cubikly multiplied. as if the sides be as two to one, the cubes are as 8 to 1: and if the sides be as three to one, the cubes are as 27 to 1. &c.  Master. 
This is well applied of you, that you can frame your common rules in Geometry to such special matters. And now may you prove the like in the moon.  Sc. 
You say, that the circumference of the sphere of the mone is 724604 miles, and 4/ 7: then dividing it by 360, ther will amount the quantity of one degree: which yieldeth in this rate 2012 miles and 71/ 90: but accounting the breadth of the moon 31 minutes and a half, the miles that answer unto it, are but 1057: whereby it followeth, that the diameter of the earth being 6872, is 6 times and a half greater then the diameter of the moon. And therfore the flat of the earth in his greatest circled, is above 42 times so great, as the like flat form in the moon: and the whole globe of the earth is 273 times so great, as the whole globe of the moon.  Master. 
In this account you take the innermost circumference of the sphere of the moon, and in the like account many other take the uttermost circumference, but it appeareth more reasonable to take the middle distance between them both, which is 1055302.( as here by example doth appear ) and in that place of distance to take the rate of hir diameter.  Scholar. 
So it seemeth most indifferent reason. And then the measure of one degree will be 2931 71/ 180 and of that there will answer to the diameter of the mone( being accounted 31 minutes and a half) 1539 miles. now if I divide the diameter of the earth( which is 6872) by it, there will be in the quotient 4 and a half almost: so will it appear that the diameter of the earth is 4 times and a half almost so long as the diameter of the moon: and the flat of the earth 20 times so large as the flat of the moon. And the whole earth nynetye times so great as the globe of the moon.  Master. 
Yet according to the common account, the earth is but 39 times so much as the moon: but hereof and of many other things that seem above the reach of mannes wit, I will an other time instruct you farther. for it is no meet matter for an introduction. And this is brought for examples sake only, that you might understand the order of such sort of woorkynge, and thereby learn to try your authors sayings. But now it is time to proceed to other matters, and to declare the true place of the earth, and to prove that it standeth in the middle of the world, which thing although it may sufficiently bee gathered by that that is written before, 
That the earth is in the middle of the world.  yet I will declare certain invincible reasons for confutation of them that mysseplace it. And to begin with all, there can be but three dyuersities of places in general, without the centre of the world: for other it must bee beside the axletree of the world, and yet equally distant from both the Poles, or else it must bee on the Axe three of the world, and yet nearer to one Pole then to an other: or thyrdlye it must bee beside the Axe three of the world, and also nearer to the one Pole then to the other. beside these three varieties there is left but one more( which is the true placynge of it) and that is to be on the Axe three of the world, equally distant from both the Poles: wherefore if the first three opinions bee reproved as false, this fourthe must needs remain as only true. And now for the confutynge of the three first opinions I will use Ptolemyes arguments, augmentyng them with a larger explication.  

The confutation of the first opinion  If the earth were out of the centre of the world, and yet stood in the middle between both the Poles, then should not the Horizonte cut the sky into two equal halves. And thereof would follow, that in the right sphere the day and the night should not be of one length.  Geometric diagram. As for example: If you would imagine the earth to stand as L doth in this figure, then would the horizon be the right line E L F, and so the parte that is under the horizon is greater then the other parte of the sky above the Horizonte: wherefore in the right Sphere the night must needs always be longer then the day. but if you would imagine the earth to stand where M, is set vnderneth K, which is the very centre of the world, then would that Horizonte G M H, which answereth to that centre, be under the true horizon of the centre of the world, that is the right line A K C. And so should the night always in the right sphere be shorter then the day, because the greater parte of the sky is above the Horizonte, and the lesser parte under it. And by the like reasons in al other bowing spheres ther should bee no equality between the day and the night: and if there were any, it should not be in that time when the son were in the just middle between the two tropics,( that is under the equinoctial line) because that the equinoctial line is not equally partend by the horizon, but the greater parte is above the horizon, after the one supposition, and after the other supposition it is under the horizon of the earth.  Scholar. 
This I do understand well, accounting the circled A B C D, to represent the equinoctial line.  Master. 
And farther you may perceive( as all men, in all ages, and in all nations do confess) that the increase of the dayes from the shortest to the mean, and from the mean day to the longest are not only agreeable between themselves, but are like also exactly to the decrease of the daies from the longest to the mean, and from the mean to the shorteste. which thing could not bee, except that the middle circled between the two tropics( which is ryghtlye called the equinoctial circled) were equally divided by the horizonte into two just halves. And farther: seeing there can be no position of such obliquity( except it be right under the Pole) but some one circled of the sons course must be divided equally into two partes by the Horizonte, so that when the son were in that circled, the day would be equal with the night: which thing as all nations confess, happeneth at one time to all men, and that is when the son is in the beginning of Aries or Libra, precisely under the equinoctial line: wherefore not only that circled doth rightly agree with his name, but also it followeth that the same equinoctial line is equally partend into two just partes by the Horizonte. And therefore the earth must needs bee judged to bee in the centre of the world.  
furthermore, if the earth were supposed to bee toward the east or toward the west, 
An other confutation of that first opinion.  from the middle of the world,( as in this figure it is set toward the east, which is limited by A) thē as the space toward the one side is shorter thē the space to the other side from the earth, so the stars would seem bigger in that nearer part, and lesser in that farther parte.  Geometric diagram.  Sc. 
Which thing is before reproved, and by daily experience may be confuted.  Master. 
Therfore can not it be a true opinion, that infereth so false a conclusion. And yet there would follow of it more absurdity: that from the morning until noon should bee shorter time, or else longer then from noon until night.  Scholar. 
That must needs follow also, seeing that noon is that time of the day, when the son is in the circled which goeth right over our heads from south to north, which here in this figure is represented by the right line B E D, as I gather by your former doctrine.  Master. 

An abridged argument of all the premises.  You guess well. and by the contrary of all these you may conclude thus: that seeing the time before noon is equal to the time after noon, and the stars appear neither bigger nor lesser in the west, then they do in the east: And that when the son is in the equinoctial line, the dayes are equal to the nights, it followeth certainlye, that thee earth can bee no ways out of the Axe three of the world.  
And now for the second opinion I reason thus.  

Against the second opinion.  If the earth were on the Axe three of the world nigher to the one Pole then to the other, then would the Horizonte only in the right Sphere dyuide the sky into two equal partes, and in no form of bowing sphere, as by this figure you may gather, where E standeth for the earth, and A E C for the right horizon. B E D and F E G for two obliqne horizontes, in 2 several bowing spheres: and K limiteth the centre of the world.  Geometric diagram.  Scholar. 
Here I see manifestly that only the right horizon doth divide the greater circled( which is set for the sky) into 2 equal partes, and none other: whereby it would follow, that wee which dwell 52 degrees northward from the equinoctial line, should see much less then half the sky: but that is false, as it hath been often times proved, wherefore I perceive that opinion can not be true.  Master. 

An other argument against the second opinion.  Yet an other argument against that opinion, may this be. Yf the earth were nigher to the one Pole then to the other, when the son is in the just east, the shadows of any things in earth, would not run full west: but all shadows in earth run full west, when the son is just east:( and contrary ways) therefore can not the earth bee nigher to one Pole, then to the other.  Scholar. 
This argument is good, and the minor is well known to every sensible man: so is there no doubt but of the maior.  Master. 
For the proof of it, I set this figure.  
where the great circled A B C D betokeneth the horizon, and the lesser circled E F G H, standeth for the earth. The centre of the world is E: the east is D: and the west is B: the south is A: and the north is C. In the earth the line F G, standeth as a parallel, with the right  Geometric diagram. line BED, and the right line DH runneth cross thē both, and maketh an angle on the centre of the earth, equal to the angle by D: whose largeness is agreeable to the imagined distance of the centre of the earth from the centre of the world. wherefore the greater that that distance is, the larger is the angle of that declination, and the lesser distance, causeth a lesser angle: but yet if the distance be any thing, then will that angle of declination be notable enough.  Scholar. 
The rest is easy to considre: I mean that all shadows run in a right line from the light body, that causeth that shadow: so that the son being in D, which is the just east, wolde cast the shadows in the earth, not to F( which is the west in the earth) but to H, which is almost north-west: and therefore is your maior duly proved, and the second opinion fully confuted: but how may the third opinion be answered?  Master. 

Against the third opinion.  The third opinion is, that the earth standeth out of the axe three of the world, and also nearer to the one pole then to the other: so doth it contain both the other opinions: wherefore seeing they both are reproved, this third must needs see me falser then ony of them both, because it includeth all the untruth of them both. And therfore to conclude with Ptolemye, 
A confirmation.  the increase and decrease of dayes could never be so rateable and justly proportioned as they be, if the earth stood any where else, then in the very centre of the world. And farther more the eclipses of the moon should not happen, 
An other reason. ( as now they do) at the precise hour of full opposition, if the earth were not in the very centre of the world: for considering that all the three bodies of the Son, the moon, and the earth must needs be in one right line( as in the doctrine of those eclipses it is taught) there is no place in the world, where the earth may stand in that right line common to all such eclipses, but only the centre of the world:  Geometric diagram. as for examples sake I haue noted 4 several eclipses of the moon: the first was in the year of Christes incarnation 1551, the 20 day of february, when the son was about the 12 degree of Pisces, and the moon about the 12 degree of Virgo. The second eclipse was in the year of 1553, the son being in the eleventh degree of lo, and the moon in the eleventh degree of Aquarius: The third eclipse happened on the fifte day of june, 1555, the son being in the 23 degree of geminy, and the mone in the 23 of Sagittary. The fourth eclipse, shal be this year 1556, the 17 day of Nouembre, at which time the son shalbe in the fifte degree of Sagittary, and the moon in the fifte degree of geminy. now if you list to take more examples, for farther trial you may so do. yet two several eclipses serve as well for this proof as 10000. And then drawing lines for each eclipse from the place of the son to the place of the moon, all those lines must needs pass by the earth, and there is none other point, whereby they all( or any two of them) can pass, but only the centre of the zodiac,( which is the centre of the world) therefore must that centre of necessity bee accounted the place of the earth. And this may suffice for this time touching the earth and his accidents, principally appertaining to astronomy: for although many other things are to bee considered in it, they appertain rather to philosophers or Cosmographers, then to Astronomers, and namely in the doctrine of the principles. 
Whether the earth move or not.  As touching the distinction of the zones, I haue said somewhat before,& somewhat more will I say anon. But as for the quietness of the earth I need not to spend any time in proving of it, sith that opinion is so firmly fixed in most mennes heads, that they account it more madness to bring the question in doubt. And therfore it is as much folly to travail to prove that which no man denieth, as it were with great study to dissuade that thing, which no man doth couette, neither any man alloweth: or to blame that which no man praiseth, neither any man liketh.  Schol. 
Yet sometime it chanceth, that the opinion most generally received, is not most true.  Master. 
And so do some men judge of this matter, for not only Eraclides Ponticus, a great Philosopher, and two great clerkes of Pythagoras school, Philolaus and Ecphantus, were of the contrary opinion, but also Nicias Syracusius, and Aristarchus Samius, seem with strong arguments to approve it: but the reasons are to difficult for this first Introduction,& therfore I will omit them till an other time. And so will I do the reasons that Ptolemy, Theon& others do allege, to prove the earth to bee without motion: and the rather, because those reasons do not proceed so demonstrablye, but they may be answered fully, of him that holdeth the contrary. I mean, concerning circularre motion: marye direct motion out of the centre of the world, seemeth more easy to be confuted, and that by the same reasons, which were before alleged for proving the earth to be in the middle and centre of the world.  Scholar. 
I perceive it well: for as if the earth were always out of the centre of the world, those former absurdities would at all times appear: so if at any time the earth should move out of his place, those inconveniences would then appear.  Master. 
That is truly to be gathered: howe bee it, Copernicus a man of great learning, of much experience, and of wonderful diligence in observation, hath renewed the opinion of Aristarchus Samius, and affirmeth that the earth not only moveth circularlye about his own centre, but also may be, yea and is, continually out of the precise centre of the world 38 hundreth thousand miles: but because the understanding of that controversy dependeth of profounder knowledge then in this Introduction may be uttered conveniently, I will let it pass till some other time.  Scholar. 
Nay sir in good faith, I desire not to hear such vain phantasy, so far against common reason, and repugnant to the consent of all the learned multitude of writers, and therefore let it pass for ever, and a day longer.  Master. 
You are to young to be a good judge in so great a matter: it passeth far your learning, and theirs also that are much better learned then you, to improve his supposition by good arguments, and therefore you were best to condemn no thing that you do not well understand: but an other time, as I said, I will so declare his supposition, that you shall not only wonder to hear it, but also peradventure be as earnest then to credite it, as you are now to condemn it. in the mean season let us proceed forward in our former order, wherein by order of your table I should speak of the circles in heaven, both of their number, how many they be, and also of their quantities, how great they are, 
Of the circles in the sky.  which is to be understand in comparison to the equinoctial, or some other great circled. Then of their order, and their distance a sunder: and likewaies what is their offices, whereunto they serve. of all which things, although I haue all ready said enough for so brief an Introduction, yet because in their number there may be some disagreement, and in their quantities. distances and order there may bee some variety, at the least in diuers places, therefore I will speak a little of them again. 
Equinoctial  First for the equinoctial, there is but one clothe all the world, and he is equally distant from each Pole, and therefore is called the Girdle of the sky: his office was declared before to bee the lymite of the middle of the world, in which the Son maketh the dayes equal to the nights. Also he declareth the true east and west, and is not only the common measure whereby all other circles are judged in quantity, but also it is the true measure of motions celestial, and the very rule to judge all ascensions by, 
the tropiks  as hereafter more largely shall appear. next unto this circled are there 2 tropic circles, one on each side of it,  depiction of a quadrant. whose distance a sunder may well be marked by a quadrant set so in place convenient, that it may stand just plumb with the flat of the horizon, and be turned full south. Then observe many daies about the middle of june the highest point that the son will ascend unto, and shine duly clothe those two sights in the ruler, moving it higher or lower, as occasion serveth, till it stand exactly pointinge the height of the son at no one being at the highest. The like observation shall you make diuers dayes before, at and after the middle of december, till that you be assured of the just height at noon of the son, being at the lowest then toward the south. The points of these two observations well marked in the edge of the quadrant are the true places of the two tropics: and the distance of those two marks a sunder by number of degrees, is the very true distance of the two tropics. In the just middle between these two tropics is the place of the equinoctial circled. Example. With us, where the pole is 52 degrees high, the winter tropic will be 14 degrees and a half above the horizon. the summer tropic 61 and a half. and the equinoctial just 38 degrees in height. 
The greatest declination of the son  And the number of degrees that are between this equinoctial and any one of the tropiks is name the Greatest declination of the son, which in our time is about 23 degrees and 28 minutes. The other points of declination of the degrees in the ecliptic line from the equinoctial circled, because they be many in numbre and diverse in use, I think it good to express in a table which hereafter shall serve you for sundry uses.  Scholar. 
The like table is in Orontius.  Master. 
Not even the like, as by conferring you may perceive: but for the use of it, take what degree you list of any sign, and by this table you may know his declination from the equinoctial circled. The signs are written partelye on the head of the table, and partelye on the foot of the same. The degrees in the first 
THE TABLE OF DECLINATION PARTICVLARLY FOR EVERY DEGREE of the ecliptic line, and so for the son.    Aries, Libra, Difference. Taurus, Scorpius. Difference. geminy, Sagittarius Difference.   deg. degr. min. min. deg. min.   degr. min.   deg. 1 0 24 24 11 50 21 20 23 12 29 2 0 48 12 11 20 35 28 3 1 12   12 32 20 20 47 11 27 4 1 36.   12 52 20 58 26 5 1 59   13 12   21 9 10 25 6 2 23   13 32   21 20 24 7 2 47   13 52 19 21 30 9 23 8 3 11   14 12 21 40 22 9 3 34   14 31   21 49   21 10 3 58   14 50   21 58   20 11 4 21   15 9 18 22 7 8 19 12 4 45   15 27 22 15 18 13 5 8 23 15 45   22 23 7 17 14 5 32 16 3   22 30 16 15 5 55   16 21 17 22 37 6 15 16 6 18   16 39 22 44 14 17 6 41   16 56   22 50 5 13 18 7 4   17 13   22 55 12 19 7 27 22 17 29 16 23 1 4 11 20 7 50 17 46 23 5 10 21 8 12   18 2   23 10   9 22 8 35   18 17   23 13   8 23 8 57   18 33 15 23 17 3 7 24 9 19   18 48 23 20 2 6 25 9 41   19 2   23 22   5 26 10 3   19 17   23 24   4 27 10 25 21 19 31   23 26 1 3 28 10 47 19 44   23 27 2 29 11 8   19 58   23 28 0 1 30 11 29   20 10   23 28 0 degr. degr. min.   degr. min.   degr. min.   deg.   Virgo. Pisces. Difference. lo. Aquarius. Difference. Cancer. Capricorn. Difference.   column do serve for the signs that bee on the head of the table, and the degrees in the last column do serve for the signs in the foot of the table, and the common angle against the sign: and the degree that you seek for, doth contain the degrees and minutes of the declination due to it.  Scholar. 
I perceive it well: if I would know howe much the tenth degree of lo doth decline from the equinoctial, I must look in the columpn over lo right against the numbre oftenne in the last column, where I find 17.46.  Master. 
That is 17 degrees, and 46 minutes, which is the declination of the 10. degree of lo from the equinoctial circled.  scholar. 
I must always understand that 60 minutes do make a degree: so these 46 minutes are ¾ of a degree and 1/ 60 more. But what is the use of this table?  Master. 
That shall you know in the next treatise. in the mean season to procede with the parallel circles: there followeth next, the arctic and Antarctike circles, 
The Artik and Antartik circles  which are in number two, and there office is to enclose those stars, which ever appear above our horizon, or never appear above the same, as before is declared: but because every seueralle Climate hath those circles disagreeynge from other Climates, therefore their distance from the other circles parallels can not bee certain,( but for one region certain) neither yet their quantities, neither their order: for where the elevation of the pole is less then 66 degrees and a half, there are those circles lesser then the tropics, and are in order between them and the Poles, being always distant from the Pole just so many degrees as the Pole is in height above the horizon in that region.  Scholar. 
It can not bee other ways. And therefore it followeth, that where the pole is more then 66 degrees and a half in height, there the tropic is above the Horizonte, as at Wardehouse you declared it to be: and therefore in that climate the arctic circled is greater then the tropic of Cancer.  Master. 

Of the fiuc zones against the Greekes.  Hereby appeareth the ouersighte of most parte of the Greekes in limiting the Zones: for they appoint the arctic and Antarctike circles for bounds of the Temperate Zones on the one side, and the tropics on the other side: whereof neither bound can be well admitted, after their own explication of the qualities of the Zones. for if the temperate Zones shall be called those Zones that be inhabited, as they do so name them, then because there was known inhabitants innumerable besouthe the tropic of Cancer, it must needs follow, that the tropic can be no bound of the temperate Zone: but yet otherways accounting the distinction of the Zones, not by that they are inhabited or vninhabited, but by the variety of the motion of the son in respect to them, and by other accidents of shadows, there may be good reason to make the tropics bounds of the temperat zones: mary there is not the like reason for the arctic and Antarctike circles. for confutation therfore of that opinion, I make this argument.  

An argument in Ferio.  No uncertain and variable bounds can limit any certain place: the temperate Zones are places certain, and the arctic circled with the Antarctike are changeable, and uncertain limits, Therfore can not they be the bounds of the temperate Zones.  Scholar. 
This is a good argument, made in Ferio, the fourth mood of the first figure. And the maior is most true, sith nothing can more disagree, then certain and uncertain, stable& unstable, being contraries together. The minor hath 2 partes in it, which both seem as true: for as long as the son keepeth one yearly course, so long the regions must remain as they were, and that is for ever, other still temperate, other still untemperate. And so is that part of the minor true. The other part for the inconstancy& khan gablenes of the circles arctic& antarctik, must needs be true by their definitions, approved of the same Greekes: for every region hath a several Actike circled. wherefore I marvel much that the Greekes being so wise men, and so greatly learned, should be so much ouerseen and so foroly deceived: but peradventure ther are but few of that opinion, and such as were least learned.  Master. 
Parmenides, Aristotle, Cleomedes and Proclus may not be accounted unlearned, and yet they with many other haue written that as truth. But hereby may you perceive what folly it is, when men receive any doctrine as true, and do not well weigh it, but credite the authority of the first teacher. So it appeareth in this matter, that because Parmenides, which was a great Philosopher, had first taught that which was a great Philosopher, had first taught that distinction of the zones, all the rest did follow his opinion as a plausible doctrine, without examination of it, till Posidonius began to espy that error& to confute it: as Strabo doth declare in his second book of Geographye, which place in the latin translation is so evil expressed, that no sentence in it importeth any sense: wherefore as well for the commodity of you as of other, I will somewhat amend that place, wisshinge them that haue leisure and learning to help to amend many other faults of that good book and other like. The latin translation is this.  

A place of Strabo amended.  Ad Septentriones, neque penes omnes existentem; neque eisdem vbicunque. Quisnantemperatas quae immutabiles sunt diuideret? Cum igitur non penes vniuersos sit septentrionales esse, nihil esset ad argumentum. si enim penes habitatores temperatae omnes, ad quos dicitur, so los temperata? Quod autem non vbique eodem modo, said mutari, been comprehensum est. ipse autem in zonas partiens, quinque ad coelestia quidem utiles esse asserit. Ex his duas circumstantes subter polos vsque ad eas quae septentrionales habent tropicos, diuersarum vmbrarum esse ab aliis duabus, quae deinceps sunt vsque ad habitantes sub Polis. Quae vero inter Tropicos est, vtrinque umbras habere.  Scholar. 
Other the matter is very obscure, or else there wanteth light in the declaration of it.  Ma. 
Ther is little sense in all these words: & that sense that may be gathered of it is very false. And yet is the greek book both vn corrupt( except it be in a word or two) and full of perfect, sensible and pleasant sentences. this is it.  

The prited book hath 〈◇〉 falsely.  {αβγδ}, 
The greek book hath 〈◇〉 falsely.  {αβγδ}.  
which I do translate thus.  
Arcticis vero circulis( vt qui nec apud omnes existant, nec ijdem vibique perseuerent) quis unquam temperatas Zonas( quae immutabiles sunt) terminaret? Caeterum illud quod non apud omnes existant Arctici circuli, nihil facit ad reprehensionem. quum satis sit, si modo sint apud omnes incolas temperatae ipsius zonae, ad quos solos temperata dicitur. quod vero adiecit, non vbique servare eos eandem rationem, said varie mutari, hoc quidem rectè adsumptum est. Atque ipse Po sidonius dum Zonas destinguit, quinque inquit utiles esse ad coelestes obseruationes. quarum duae, quae Polis subiacent, umbras circumfluas habent, undè Perifciae dicuntur: ibique finiuntur ubi tropici ipsi pro arcticis circulis habentur. has sequuntur aliae totidem, eo pertingentes, ubi Tropici verticibus incolarum imminent, atque in his umbrae me ridianae in unam plagam porriguntur semper, hinc Heterosciae vocan tur. quinta vero quae inter tropicos jacet, in vtrunque latus vicissim umbras mittit, atque Amphiscia nuncupatur.  
Which words may be englished thus. What man( saith Posidonius) would assign the arctic circles to be as bounds to the tempera te zones? seing those circles ar not in every Climate: neither do they continue uniform and of one sort to all countries. These words( saith Strabo) that they be not in every climate, maketh nothing to the reproof. for it is sufficient that they be incident to all the inhabitants of the temperate zone, in respect to whom alone that temperate zone beareth his name: but those other words, that they keep not one vnforme manner in all places, but are diversly changed▪ that is well alleged. Also Posidonius himself when he distincteth the zones, doth say, that five zones are needful and sufficient for celestial observations: whereof two which be under the poles, are called Perisciae, or Round shadowed, because their shadows run round about them. And these zones extend to that place; there the tropik circles and the arctic circles are all one. After these there do follow two other, which reach from thence unto those partes, that are directly under the tropiks: and these haue their noon shadow running one ways still▪ and therfore are called Heterofciae, or Single shadowed. The fift zone lieth between the tropics, and casteth the noon shadows 2 ways, wherefore the Greekes call it Amphiscion, that is Double shadowed. Scholar. By this translation( which is worth a paraphrasis) I do not only perceive the sense of these words, which before were dark, partly for the hardness of the matter, and partly for the hypallage, in changinge of the speakers person, but also I espy the monstrous shape of the old translation. And by this I gather also that Strabo would not haue the Temperat zones to be bounded by the arctic and Antarctike circles.  Master. 
His mind appeareth more manifest anon after where he blameth Polybius, for assigninge those circles as bounds of the zones: whereof one should be enclosed with in that circled, and the other should extend from it to the next tropic then he concludeth thus: that those unconstant circles, may be no bounds of certentye.  
{αβγδ}  
Dictum enim est, quod per signa transmigrantia, ea quae non mutantur, terminate non convenit.  
For I haue said before, that changeable limits may not be appointed as bounds to vnchaungable places.  Sch. 
Thus it appeareth, that the distinction of zones by the arctic and Antarctike circles were no constant distinction. and so is authority of one sort repelled by thauctoritie of an other sort.  Master. 
You may not weigh the matter by authority, for so should that former doctrine continue still, seeing I alleged for it Parmenides, Aristotle, Polybius, Cleomedes and Proclus,& against them only Posidonius and Strabo, which may seem the weaker in number: but then considre that the first sort bring only affirmation for their testimony, and bare authority: the other, confute them by good reason and substantial arguments, which are far to bee esteemed above any authority.  Scholar. 
Then credityng reason against authority, I must say, that the Zones must be otherways divided, peradventure as I did learn of you before, agreeable to John de Sacro bosco his mind, whom you called the restorer of the Zones.  Master. 
Yea in deed: for although Posidonius and Strabo did teach the like distinction, yet did they not so openly name the true limits, howe bee it in effect they mean the same: for when Strabo saith, that the could zone doth reach to that place, where the tropic is the arctic circled, he doth mean that there, where this first Zone endeth, and the temperate Zone beginneth, the Pole is 66 degrees and a half above the horizonte, and so must the same Pole bee from the top of their heads in that place 23 degrees and a half: in which distance because the Poles of the zodiac do describe a circled, therfore doth John de Sacro bosco call that circled the arctic circled, in that confounding▪ it in name with an other circled of the Greekes: wherefore I think it more reasonable for avoiding confusion, to give it a several name, and call it the Polare circled, and the other to be called still the arctic circled, 
The Polare circles.  as the greeks long before did name it. And this distinction of the zones by the two tropics, and the two Polare circles doth distinct exactly those three varieties of shadows before mentioned. which is a certain and notable difference, not imagined by men which may err, but wrought by the son, which can not err. But here must I admonish you of an other error, 
An other error.  gathe read not of grounded reason, but of fantastical imagination, by occasion of which, this fonde distinction of zones was imagined.  
because the elder greeks had no trade into the south parts of Afrike, neither the Ethiopians again into Grece, and farther by reason the son runneth still over their heads, that dwell between the tropics, many of the latins as well as of the greeks phantasied that there did dwell no inhabitants, neither could dwell there for the vehement heat: wherefore they called it the Burned Zone. And of like occasion where they moved to account two other zones, that be nigh the poles, to be vninhabited for could, by reason that the son doth never come nigher to them then the Tropik circles: but how much herein they were deceived, it may be declared not only by reason, and by experience, but also by authority of many of their own writers, as namely Eratosthenes, Posidonius, Polybius, and Ptolemye. but as this is a matter more agreeable to the treatise of Geographye or Cosmography, then of the Sphere, so will I overpass it for this time, and will return to the rest of the circles of the sphere, amongst which the zodiac as principal, 
The zodiac.  doth offer itself, as the common theatre and stage of all the planets motion, and of the chief signs and celestial figures.  Scholar. 
Are there I pray you such figures in the zodiac, as Astronomers do describe?  Master. 
There are some that affirm no less, and testify that they haue in a clear air perceived them: but for the rest of the form, I will say nothing now: only this I do affirm which I know, that all the stars which astronomers do name to be there, may easily be seen there, and in like form as they do place them.  Scholar. 
If the forms of beasts be not there, why do they call it by that name of zodiac, which name is derived as many do affirm, of {αβγδ}, that signifieth a beast.  Master. 
The signs do bear the names of beasts, and therfore may that circled take the like denomination also: but yet I denied not that the very forms were there, but that they are not easily seen in such exact shapes as they be portured, and as some mem writ that they haue seen them: but howe so ever it bee, the certainty is, that the 12 signs are contained in that zodiac, and therfore doth Tullye with other latin men call it Signifer, that is, the circled of the signs: but why those names were given to every sign rather then other, doth not appertain so much to this treatise, as to that judicial arte, which hath more ground of reason then many men think.  Scholar. 

What is to bee in a sign.  When you say that the son is in any sign, you do not mean( I am sure) that the son hath wart so high from his own sphere, into the sphere of the Fixed stars, where the zodiac and the signs be, but that the son is directly under the same sign, and in a right line between that sign and the centre of the earth.  Master. 
You say well. That is the common understanding, when we speak of the place of the son: but because other planets do decline from the middle of that zodiac, some times toward the north, and other times toward the south, therfore haue all astronomers appointed a convenient breadth to the zodiac, according to the declination of the Planets: howe bee it properly they do call that the Latitude of the planets, 
The latitude of planets. Their declination. Their longitude. The second signification of a sign.  when they serve from the ecliptic line: and the Declination of them is their distance south or north from the equinoctial line: so do they call the motion of them in Longitude, their distance by their natural course from the beginning of Aries, which is the beginning of the zodiac. And now appointing the latitude of the zodiac to bee twelve degrees( although some planets may run in latitude on the one side almost 8 degrees) because that quantity is most received, then is every sign twelve degrees broad, and thirty degrees long. and so maketh a long square: from the corners of which long square, you may imagine lines to be drawn to the centre of the earth: and what so ever cometh within the bounds of those lines, is accounted to bee in that sign: and this is the second signification of a sign. 
The thyrde signification of a sign. Arcturus. The Pole star.  A third signification ther is, which we use when we say that the bright star Arcturus is in virgin, where as in dead he is above 30 degrees north from the ecliptic line: which is far out of the breadth of the zodiac: and so we say that the pole star is in Taurus, which is from the ecliptic line 66 degrees. and likeways we name all the stars in the sky to bee in some sign, bee they never so far from the ecliptic line, and the zodiac. Therfore to know what is understand by the name of a sign in this signification, you must imagine 6 circles to be so drawn about the Globe, that they may pass by the beginning of all the signs( for every circled will serve for two signs being contrary one against the other) and so shall the whole zodiac and all the globe also be partend into twelve equal partes, yf you haue drawn those circles rightly& that they do pass al by the two poles of the zodiac. Now mark how those 2 lines that do enclose any sign, ar widest a sonder in the middle of the zodiac, and from thence toward each pole of the zodiac they come nearer and nearer, till they touch in the Pole itself. All the space between any two such semicircles from one Pole to the other, is name a sign in the thyrde signification: so that what so ueuer stars bee within that space, are name to bee in that sign which is within the same space: of all these three diuers forms of signs here may you see examples. of the first by A, where the son standeth under the sign of Cancer. of the second form you haue an example by B, and of the third sort you haue two varieties, one by, C and an other by D. So that what  Astronomical diagram. so ever Planet doth come within the bounds of that figure B, is name to be in the sign of Taurus:& what so ever Planete or fixed star is within the compass of the figure C, is judged to be in Cancer: as the moon is ther represented to be and all the stars there portured,& so may you judge of any other sign. now this may suffice for the explication of the zodiac, 
The colours.  after whom followeth next the colours, which take their names in greek of vnperfectnes, because they bee never seen all above the ground in any obliqne sphere: whereby it appeareth, that good John de sacro bosco was much deceived in comparing them to the compassed bowing of a wild bulls tail, as though they took their names thereof: but men must bear with the ignorance of that time, for lack of knowledge in the greek tongue. These colours serve principally for the distinction of the four chief points in the zodiac, as before is declared. and because the point of the intersection or crossinge of the ecliptic line and the equinoctial, doth sufficiently express two of those points in the beginning of Aries and Libra, therfore the greekes do assign commonly but one colour, for the other two tropic points, and none for these equinoctial points. How be it, because they serve also for the declinations and latitudes of fixed stars and planets, I think it better to describe them, then to omit them. And thus haue I lightly touched all the circles that be fixed in the sphere, and move with it. now remaineth other two, which stand still always and move not, of which the first is the Horizonte, and the next is the Meridiane. The horizon is of two diuers sorts. the one doth extend on every side unto the firmament, 
The Horizonte. The celestial horizon  and serveth as it were pecularly for the partition of the heauens, and divideth the sky justly into two halves, whereof the one appeareth unto us above that Horizonte, and the other is hid from us, under the same horizon: this horizonte hath his name of the sky, and is called the Celestial horizon, and his diameter is as large as the diameter of the eight spher, which is the farthest and highest part of the sky that we can see: this large horizon our sight doth enforce us to acknowledge as a just horizon, although reason can finde in it some want of exact preciseness. And therfore Proclus doth not well distinct this horizon from the other, by naminge the other a sensible horizon, and affirming this to be considered only by reason, where as in deed we need reasons help more in judging the other horizon, which I think most aptly to bee called the Earthly horizon, 
The Earthly horizon  because it serveth for sights on the earth and water only, and reacheth not unto the sky: no, his semidiameter exceedeth not( as Macrobius saith) 180 furlongs, that is 22 miles and a half: and his whole diameter comprehendeth but only 45 miles in length. So that if any man do stand on a plain ground or on the sea, he may see round about him every ways 22 miles and a half: that is in round compass of the whole horizonte 141 miles& 3/ 7.  Geometric diagram. I mean that seing the right line A, C, is 45 miles, the whole circled A B C D, must bee accounted 141 3/ 7 miles in compass. This asking of Macrobius is more nigher to the truth then Proclus assertion, which is that the diameter should be in this horizon, 2000 furlongs, that is 250 miles, whereby he meaneth that a man may see every way in: a plain 125 miles from him: which assertion every mariner doth know to be false: for it is well known by often and good observation, that in plain ground, or on the sea, they can not discern. well above 20 miles, and therefore do all mariners call that distance commonly a Kenninge: 
A kenning.  which is as much as a man may well see: yet from a hill or high ground men may see farther, and especially they may see other hills or clyffes, but that is no certain view, nor just kenninge: yet in that sort men may see 60 miles, or at the most 80 miles: but 125 miles is to great a distance, for to view any thing from a high place, and therfore of more force it is to excessive a distance to view any thing in an equal plain, 
A demonstration against proclus.  as the horizon must needs be, for declaration whereof, I suppose this figure to represent the whole globe of the earth,  Geometric diagram. and the earthly horizon to be expressed by the right line F B G: unto which line ther is an other drawn as a just parallel, which is H K L. of like length precisely with the earthly horizonte, and two other lines joining them at the eandes, making a long square of all right angles, so that two of those angles do light on the circumference of the circled of the earth. Then draw I a right line from E which is the centre of that circled, unto B, and an other from the same centre E unto G: whereby ther is made two triangles E B G, and E K L. now presupposing that B is the place where we stand on the earth, and H and 〈…〉 unto which the Semidiameter of 1000 furlongs of our earthly horizon, doth extend on both sides: and from the one of them is drawn a right line to the other, that line must needs fall within the circled.  Scholar. 
That is true, according to the 47 theorem of the pathway.  Master. 
Then must the line K E, be shorter then the line B E, and so B and K, are notably distant.  Scholar. 
That is certain.  Master. 
And because the right line F B G, is parallel to the right line H K L, there must be as much distance between G, and L, as there is between B and K.  Scholar. 
That followeth by the definition of parallels.  Master. 
Then as K, is notably under B, so must L be notably under G: that is to say under the horizon, and therfore can not be seen.  Scholar. 
It is against the definition of an horizonte, that any thing under it should be seen.  Master. 
Then if the semidiameter of the Horizonte shall extend no farther then that a mean quantity may be seen on the earth, it may not be so long as Proclus hath limited it. Also by the two triangles aforesaid, whose angles are like, and therfore their sides proportionable,& other ways diversly, by the former figure, it may be domonstrate, that the right line E G is much longer then E L, which is the semidiameter of the earth, so that the horizon in so much distance is far higher then the earth is there, and therfore can not bee aptly called a Sensible Horizonte, nor an Earthly Horizonte, as Proclus meaneth. But is appeareth that Proclus did rather in this doctrine follow some other mennes opinion then his own reason, as he doth also in the declaration of the change of the Horizontes and the Meridianes, for between east and west, he saythe that the Meridianes change at the end of 300 furlongs: but between south and north he doth assign no change unto the Horizonts within 400 furlongs. In which words there are two errors included: the one that the horizonts be not like in change between east and west, and between south and north.  Scholar. 
Nay he speaketh only of the Meridianes( I trow) between east and west, and not of the Horizontes.  Master. 
As though we might change the one, and not uniformly change the other.  Scholar. 
truth it is, that seing the meridiane doth cut the Horizonte with right angles, they both must needs other stand both still, other change both a like: wherefore this first error can not be excused.  Master. 
And the second error is as manifest as it: for thereby he supposeth that the Climates do change by equal quantity of furlongs or miles, which error is to manifest: for nigh unto the equinoctial, 2150 furlongs northward do cause increase but of a quarter of an hour in the longest day. And with us in the south parte of England, 700 furlongs north ward doth cause increase of a quarter of an hour in the longest day, and in the north partes of Scotlande, 320 furlongs do give as great an increase: in Iselande 4 furlongs yieldeth the like increase: and so still the farther north you go, the smaller space of ground bringeth the like increase in the longest day.  Scholar. 
Hereby I perceive, that who so ever will travail in these sciences with profit, must lean rather to reason, then to authority, else he may be deceived.  Master. 
That rule is general in all artes.  Scholar. 
And if Proclus rule be not certain, what rule may I haue more certain? M. For the alteration of the Horizonte between south& north, because not only the climates do change therwith, but also the quantities of the daies, I will anon before the doctrine of the ascensions, give you a table general for all climates in the earth. And as for the change of the horizontes or of the meridianes between east and west, you 
A TABLE FOR THE DIFErence of hours according to the distance of miles from east to west, under the equinoctial.  The distance of miles. The minutes of an hour. The distance of miles. hours. The minutes of an hour. The distance of miles. hours. The minutes of an hour. The distance of miles. hours. The minutes of an hour 15 1 465 0 31 915 1 1 1365 1 31 30 2 480 0 32 930 1 2 1380 1 32 45 3 495 0 33 945 1 3 1395 1 33 60 4 510 0 34 960 1 4 1410 1 34 75 5 525 0 35 975 1 5 1425 1 35 90 6 540 0 36 990 1 6 1440 1 36 105 7 555 0 37 1005 1 7 1455 1 37 120 8 570 0 38 1020 1 8 1470 1 38 135 9 585 0 39 1035 1 9 1485 1 39 150 10 600 0 40 1050 1 10 1500 1 40 165 11 615 0 41 1065 1 11 1515 1 41 180 12 630 0 42 1080 1 12 1530 1 42 195 13 645 0 43 1095 1 13 1545 1 43 210 14 660 0 44 1110 1 14 1560 1 44 225 15 675 0 45 1125 1 15 1575 1 45 240 16 690 0 46 1140 1 16 1590 1 46 255 17 705 0 47 1155 1 17 1605 1 47 270 18 720 0 48 1170 1 18 1620 1 48 285 19 735 0 49 1185 1 19 1635 1 49 300 20 750 0 50 1200 1 20 1650 1 50 315 21 765 0 51 1215 1 21 1665 1 51 330 22 780 0 52 1230 1 22 1680 1 52 345 23 795 0 53 1245 1 23 1695 1 53 360 24 810 0 54 1260 1 24 1710 1 54 375 25 825 0 55 1275 1 25 1725 1 55 390 26 840 0 56 1290 1 26 1740 1 56 405 27 855 0 57 1305 1 27 1755 1 57 420 28 870 0 58 1320 1 28 1770 1 58 435 29 885 0 59 1335 1 29 1785 1 59 450 30 900 1 0 1350 1 30 1800 2 0 shall understand that 15 miles difference from east toward west, doth make the son rising, the none stead, and son setting, to be later by one minute of an hour. and so 30 miles 2 minutes: 120 miles 8 minutes: 225 miles. 15. minutes. which is a quarter of an hour. And for examples sake more then for any other cause I give you here this table, which you may easylye increase by the like form, until you haue accomplysshed the whole 24 hours, yf you list. howe bee it he that is ready in account of arithmetic, needeth not any such tables of aid. This table is calculate only for such places as differ not above 1800 miles between east and west, having no difference or very little in their distaunces between south and north, as touching this consideration. And it serveth only for the middle climate of the world under the equinoctial circled. for every other climate, yea and every degree in latitude of each climate, must haue a several table, which may not well be set forth in this brief introduction, but an other time shall serve hereafter for it, yf you call on me and put me in mind therof, else the necessity of provision for my family will make me forget such promises: howe be it by cause you shall not think that I haue done more for them that dwell under the equinoctial( or nigh unto it in Guynea or in calicut) then for our own country, I haue drawn the like table for the elevation of 52 degrees, whose use is even one with the other before. wherefore if I know the distance of miles between any two places under this latitude of 52 degrees, or nigh thereto, as soon as I haue found out that number of miles in the table under that title, in the next column on the right hand, I may see howe many minutes they do differ in their hours.  Scholar. 
So that the miles exceed not 1110, for this table hath no greater number.  Master. 
If you list by this president, you may increase the table as much as you will.  

A TABLE OF THE DIFFERENCE of hours, according to the distance of miles from east to west; for the elevation of 51 degrees, 55 minutes.  The distance of miles. The minutes of an hour. The distance of miles. The hours. The minutes of an hour. The distance of miles. The hours. The minutes of an hour. The distance of miles. The hours. The minutes of an hour. 9 ¼ 1 286 ¾ 0 31 564 ¼ 1 1 841 ¾ 1 31 18 ½ 2 296 0 32 573 ½ 1 2 851 1 32 27 ¾ 3 305 ¼ 0 33 582 ¾ 1 3 860 ¼ 1 33 37 4 314 ½ 0 34 592 1 4 869 ½ 1 34 46 ¼ 5 323 ¾ 0 35 601 ¼ 1 5 878 ¾ 1 35 55 ½ 6 333 0 36 610 ½ 1 6 888 1 36 64 ¾ 7 342 ½ 0 37 619 ¾ 1 7 897 ¼ 1 37 74 8 351 ½ 0 38 629 1 8 906 ½ 1 38 83 1/ 4 9 360 ¾ 0 39 638 ¼ 1 9 915 1/ 4 1 39 92 ½ 10 370 0 40 647 ½ 1 10 925 1 40 101 1/ 4 11 379 ¼ 0 41 656 ¾ 1 11 934 1/ 4 1 41 111 12 388 ½ 0 42 666 1 12 943 ½ 1 42 120 ¼ 13 397 ¾ 0 43 675 ¼ 1 13 952 ¾ 1 43 120 ½ 14 407 0 44 684 ½ 1 14 962 1 44 138 ¾ 15 416 ¼ 0 45 693 ¾ 1 15 971 ¼ 1 45 148 16 425 ½ 0 46 703 1 16 980 ½ 1 46 157 ¼ 17 434 ¾ 0 47 712 ¼ 1 17 989 ¾ 1 47 166 ½ 18 444 0 48 721 ½ 1 18 999 1 48 175 3/ 4 19 453 ¼ 0 49 730 3/ 4 1 19 1008 ¼ 1 49 185 20 462 ½ 0 50 740 1 20 1017 ½ 1 50 194 ¼ 21 471 ¾ 0 51 749 ¼ 1 21 1026 ¾ 1 51 203 ½ 22 481 0 52 758 ½ 1 22 1036 1 52 212 ¾ 23 490 ¼ 0 53 767 ¾ 1 23 1045 ¼ 1 53 222 24 499 ½ 0 54 777 1 24 1054 ½ 1 54 231 ¼ 25 508 ¾ 0 55 786 ¼ 1 25 1063 ¾ 1 55 240 ½ 26 518 0 56 795 ½ 1 26 1073 1 56 249 ¾ 27 527 ¼ 0 57 804 ¾ 1 27 1082 ¼ 1 57 259 28 536 ½ 0 58 814 1 28 1091 ½ 1 58 268 ¼ 29 545 ¾ 0 59 823 ¼ 1 29 1100 ¾ 1 59 277 ½ 30 555 1 0 832 ½ 1 30 1110 2 0  Scholar. 
because examples do make rules manifest, I pray you let me prove one example. London and bristol are 94 miles a sunder, and as I haue heard you say, they are not much different in latitude: I desire to know their difference in hours, therfore I seek for 94 under the title of distance of miles, and I can not find it there, for 92 and a half is to little, and 101 ¾ is to great.  Master. 
And in like rate is there difference of minutes: for 10 minutes is to little, and 11 minutes is to great. but to guess most nearest: as 92 and a half is nigher to 94 then 101 ¾: so is 10 minutes more nearer their true difference then 11. And for this time this may suffice, although I can give you a precise rule by the part proportionable to finde out the just parte of every minute, but that were more curious then profitable in this place: Therfore will I leave it, and declare unto you, how you may make the like table for any latitude of even degrees.  Scholar. 
I do perceive by these two tables, that it I haue ones the first number which must be set against one minute of time, then must I double it for two minutes, and triple it for three minutes, and so forth, still multiplying the first number of miles by the number of minutes against which it shall stende.  Master. 
You take it well, and therfore seeing you doubt only of the first number, I will give you a table by which you may easily find out that first number for all degrees of latitude of any region. And this is it. where in the first column you see placed the degrees of latitude, and in the second column are set the miles with their fractions, which serve for one degree of longitude, in each of those dyvers latitudes. By this table may you make any table for any elevation of hole degrees, according to the example of the former two tables.  Scholar. 
That do I perceive now very well, and can do it, I doubt not, sufficiently for any Climate, yf I were as 
A TABLE declaring how many miles do answer to one minute of time, in every several latitude.  Degrees of latitude. Miles agreig to i. minute of time. 0 15 1 14 230/ 240 2 14 79/ 80 3 14 47/ 48 3 14 77/ 80 5 14 113/ 120 6 14 11/ 12 7 14 71/ 80 8 14 41/ 48 9 14 40/ 60 10 14 37/ 80 11 14 87/ 120 12 14 162/ 240 13 14 37/ 60 14 14 133/ 240 15 14 117/ 240 16 14 101/ 240 17 14 83/ 240 18 14 4/ 15 19 14 11/ 60 20 14 23/ 240 21 14 11/ 240 22 13 100/ 120 23 13 97/ 120 24 13 160/ 240 25 13 143/ 240 26 13 29/ 60 27 13 11/ 30 28 13 50/ 240 29 13 29/ 240 30 12 119/ 120 31 12 103/ 120 32 12 173/ 240 33 12 139/ 240 34 12 21/ 48 35 12 69/ 240 36 12 2/ 16 37 11 47/ 48 38 11 197/ 240 39 11 79/ 120 40 11 59/ 120 41 11 77/ 240 42 11 7/ 48 43 10 233/ 240 44 10 10/ 24 45 10 73/ 120 46 10 101/ 240 47 10 11/ 48 48 10 9/ 240 49 9 101/ 120 50 9 77/ 120 51 9 53/ 120 52 9 7/ 80 53 9 1/ 240 54 8 40/ 60 55 8 29/ 48 56 8 93/ 240 57 8 41/ 240 58 7 10/ 20 59 7 87/ 120 60 7 ½ 61 7 13/ 48 62 7 1/ 24 63 6 97/ 120 64 6 69/ 120 65 6 81/ 240 66 6 1/ 10 67 5 207/ 240 68 5 140/ 340 69 5 ⅜ 70 5 31/ 240 71 4 53/ 60 72 4 19/ 30 73 4 31/ 80 74 4 2/ 15 75 3 53/ 60 76 3 101/ 240 77 3 ⅜ 78 3 7/ 60 79 2 207/ 240 80 2 29/ 60 81 2 83/ 240 82 2 7/ 80 83 1 109/ 240 84 1 17/ 30 85 1 37/ 120 86 1 11/ 240 87   47/ 240 88   21/ 40 89   21/ 80 90   0 certain of their bounds. 
Of the climates.  but that may I learn by such tables as Orontius and dyvers other haue set forth all ready.  Master. 
In deed both Orontius and other haue set forth such tables, which may suffice for an Introduction, but Orontius extendeth not his table above the latitude of 66. degrees and a half, so there resteth unto the north Pole 23 degrees and a half, 
The famous adventure unto Moscouia by the north Ocean.  which coast hitherto hath been known to very few men, but now of late by the famous adventure of that worthy company of our Englishe merchants for Moscouia, that cost is discovered unto 75 degrees of latitude nigh hand: and our hope is that if they do continue as they haue valiantly begun, they shall disclose those unknown people which dwell directly under the Pole, or at the least ways discover that climate, such as it is, to the full satisfaction of that importune desire, which hath forced many thousands to wish, that which not one yet( that we know) could attain: whereby they shall not only profit their country, but shall procure to themselves great riches and treasure: and that which is most to bee desired, immortal same. Wherefore for my parte to further their knowledge in the atchiuinge of their worthy attempt, as I haue all ready in this book given some light, so will I( God wyllinge) hereafter give more light: and for an earneste thereof I will now exhibyte to you a table of the Climates extended to the very Pole, whereby you may learn not only the beginning and end of every climate, but also the just quantity of the longest and shorteste day in each of them, and in all other places to the Pole self: the reason whereof you shall better understand by the diversities of the ascensions.  
But because( as I said before) that every Climate differeth from other, by the space of half an hour in the quantity of their longest day, therfore did the greekes and namely Ptolemye, for a more preciseness make a certain distinction for every quarter of an hours difference, which he calleth only by the general names of parallels, as it doth at large appear in the sixte chapter of the second book of his Almagestes, whereof at any other time I will more largely entreat. And for this present time will only set forth the sum of that matter in a table, whose first column doth contain the number of the parallels as Ptolemye did distinct them. The second column containeth a more exact partition of those parallels according unto the increase of the longest day, by a quarter of an hour, which Ptolemye observed not, after he came to is hours of length: but I observe still, until 24 hours of length. after which time and place, because the increase of the longest day is greater and greater continually, I think it not good to make so curious a table for every quarter of an hour, but( as Erasmus Reynhold doth) to make the distinction thence forth by half a degree of difference in elevation of the Pole, as by the table you may see.  
In this table are set for the 96 parallels justly: and but 38 by Ptolomies partition: the cause whereof, I will show you an other time. Of these parallels are made 24 climates between the equinoctial circled& the tropic of Cancer. each differinge from other by half an hour, as the last column of the table declareth. but the elder Greekes did not know very well those North countries, and therefore did they assign only 7 climates according as I haue set them annexed to the first column of this table.  

A TABLE FOR THE IVSTE distinction of Climates, with the quantities of their longest dayes, and the elevation of the Pole.  The number of the 7 climates according to the old Greekes. Parallels after Ptol Parallels more exact elevation of the Pole. The quantity of the longest day. The Climates. The names Parallels after Ptol. Parallels more exact elevation of the Pole. The quantity of the longest day. The Climates. De. Mi. H. M. De. Mi. H. Mi. 1 1 0 0 12 0 1 of the 7 climates after 25 25 58 27 18 0 13 2 2 4 18 12 15 26 59 15 18 19 3 3 8 34 12 30 2 some chief place in thē 26 27 59 59 18 30 14 4 4 12 43 12 45 28 60 40 18 45 1 5 5 16 44 13 0 3 by Meroe 27 29 61 18 19 0 15 6 6 20 34 13 15 30 61 53 19 19 2 7 7 24 11 13 30 4 by Sienc. 28 31 62 25 19 30 16 8 8 27 36 13 45 32 62 55 19 45 3 9 9 30 48 14 0 5 by Alexandria. 29 33 63 22 20 0 17 10 10 33 46 14 15 34 63 47 20 15 4 11 11 36 30 14 30 6 by the Rodes.   35 64 10 20 30 18 12 12 39 3 14 45 36 64 31 20 45 5 13 13 41 23 15 0 7 by Rome 30 37 64 49 21 0 19 14 14 43 32 15 15 38 65 6 21 15 6 15 15 45 31 15 30 8 by Ponte Euxine.   39 65 22 21 30 20 16 16 47 21 15 45 40 65 35 21 45 7 17 17 49 1 16 0 9 by Boristhenes. 31 41 65 47 22 0 21 18 18 50 34 16 15 42 66 58 22 15   19 19 51 59 16 30 10 by england.   43 66 7 22 30 22 20 20 53 17 16 45 44 66 15 22 45   21 21 54 30 17 0 11   32 45 66 21 23 0 23 22 22 55 36 17 15 46 66 25 23 15   23 23 56 38 17 30 12     47 66 29 23 30 24 24 24 57 34 17 45 48 66 31 23 45                   33 49 66 31 ½ 24 0    
Parallels after Ptol. Parallels more exact elevation of the Pole. quantity of the longest day.   Parallels after Ptol. Parallels more exact elevation of the Pole. quantity of the longest day. Deg. Mi. day. Ho. Deg. Mi. day. Ho. 34 50 67 0 23 11     74 79 0 127 19 51 67 30 33 17 75 79 30 130 17   52 68 0 41 14     76 80 0 133 13 53 68 30 48 6 77 80 30 136 8   54 69 0 54 3     78 81 0 139 3 55 69 30 59 12 79 81 30 141 21 35 56 70 0 64 11     80 82 0 144 14 57 70 30 69 4 81 82 30 147 7   58 71 0 73 13     82 83 0 150 0 59 71 30 77 17 83 83 30 152 16   60 72 0 81 17   38 84 84 0 155 8 61 72 30 85 14 85 84 30 158 0 36 62 73 0 89 8     86 85 0 160 15 63 73 30 92 22 87 85 30 163 5   64 74 0 96 10     88 86 0 165 19 65 74 30 99 21 89 86 30 168 9   66 75 0 103 9     90 87 0 170 23 67 75 30 106 11 91 87 30 173 13   68 76 0 109 16     92 88 0 176 2 69 76 30 112 20 93 88 30 178 16   70 77 0 115 22     94 89 0 181 5 71 77 30 118 22 95 89 30 183 19 37 72 78 0 121 22     96 90 0 186 7 73 78 30 124 21  
Howe be it because you shall know what names thelder greeks did give them( which names hath been retained ever sith that time) I haue here drawn a like table as your other authors haue set forth, that you may the better confer the figure with the table, and the more easily understand the one by the other. in which figure the circled A, B, C, D,  diagram illustrating the globe. representeth the horizon,& the right line A C, standeth for the Meridiane line. 
The names and order of the Climates.  A is the north pole and C, the south pole. B the east,& D the west. B D betokening the equinoctial, and of the tropic of Cancer, GH, the tropic of capricorn. and al the other lines are the bounds of the climates each in his order. The first Climat taketh name of Meroe, a famous island in Ethiopia under Egypt, enclosed by the river Nilus. the second Climat is name of Syene, a city of Egypt, lying directli under the tropik of Cancer. The third Climate is called after Alexandria, a notable city& an ancient university in egypt also, lying on the north shore of it. The fourth climate beareth the name of the Rodes, an iceland better known then kept, and yet better lost then kept so dearly. The fifte Climate is expressed by the name of Rome, a city in italy well enough known.  
The sixte climate is called after the Euxine sea, commonly called Ponte. The seventh Climate reacheth from the parallel that passeth by the mouth of the river Boristhenes, and extendeth to the parallel that runneth by the south partes of england, as Ptolemy witnesseth in the second book of his Almagestes. And although more may bee said of the Climates, yet I will reserve it to the treatise of cosmography, and at this time will say no more, but that on the other side of the equinoctial toward the south, there are the like parallels, and the like Climates, 
The south Climates.  with the same quantities of distance from the equinoctial, and the like increase of daies.  Scholar. 
The distance of any Climate or parallel from the equinoctial is equal all ways with the elevation of the Pole above the Horizonte, as I may easily conjecture: so that when I know the one, I must needs know the other: and that maketh me now to think that yf I know any elevation of the Pole, I may by this table easily declare howe far that parallel which serveth for that elevation, 
The use of the table of Climates.  is from the Equinoctialle circled: and howe long the longest day is in that place: and if it chance that the latitude of any region which I do seek for, bee not in this table iustelye expressed, I must then guess by the proportion of those two numbers, between which it standeth, what the precise length of the longest day is.  Master. 
this table itself sufficeth for each quarter of an hour between the longest night of 24 hours, and the longest day of 24 hours: but for more exacter partes of time, I would not wish you to travail yet, till I may hereafter give you full rules for it: especially seeing this quarter of the hour is the difference of the whole day, which must be partend into two partes, and the one half quarter to bee assigned to the difference of the son rising, and the other half quarter the difference of the son setting.  Scholar. 
That difference is more precise then our clocks or dials do serve unto, and therfore I may well enough bee satisfied with it for this time: wherefore I pray you now proceed to the Ascensions.  Master. 
The use of the name of the Ascensions, hath great diversity in it, 
Of the ascensions.  therfore I must by division and definition distinct so those diuers varieties, that you may justly know them each in his kind. And first, for the name of Ascension in general, it doth betoken the rising of any stars or signs( what so ever they be) above the horizon. But now is there dyvers observations of several persons touching the rising of the stars, for Astronomers use to observe their rising in form, that is to say, whether they rise right or obliquely, not regarding( in that consideration) the difference in the time of the day: where as the cunning mariners, and authors of husbandry, yea and good Physicians also as well as Astronomers do mark their rising at two times principally, that is when they rise just at the son setting, or else just at the son rising.  Scholar. 
If Astronomers do nonsider only the first form, then these other forms do not appertain to this treatise, which is of astronomy peculiarly.  Master. 
although those risinges and settinges of the stars which Physicions and other good writers of husbanddrye and writers also of navigation, do oft times speak of in their writings, as being such, which in ancient calendars haue been set forth plainly for all men to understand, and so might bee at this time also, yet he that should well set them so forth, ought to bee skilful in astronomy, else can he not do it worthy the reading, and therefore it belongeth to Astronomers to determine their true times. Howe bee it because poets haue oftener made mention of such rysinges, then Astronomers haue done, therefore doth joannes de Sacro Bosco and others also call them Ascensions poetical: not as feigned matters, but as things often remembered in poets books. And as I said, they put difference between the rising of those stars in the morning with the son, and the rising of the same at the son setting. The first manner of rising with the son, they call in latin, Ortus Cosmicus, Mundanus and Matutinus: which may well bee name in english the morning rising: the other sort which in English ought to bee called the evening rising, is name truly in latin ortus Vespertinus or Acronychus, and not Temporalis or Chronicus.  Scholar. 
Yet many do call it so, and joannes de Sacro bosco sheweth a reason of that name, because( saith he) that Astronomers use that time after the son setting best for marking the course of the stars.  Master. 
Ignorance of the greek tongue hath hindered much many good wits: which may often appear not only in good John de sacro bosco, but also in many writers within these 300. yeares especially: but wee must wink at such faults, which rather were the faults of the time, then of the persons. and for this name Acronychus, is easily turned into Chronicus. The first name is often read in Ptolemye and other greek writers, and is name of the beginning of the night, which name by ignorance was turned into Chronicos in greek, and so accordingly was called Temporalis in latin, and then an imagined reason clotted thereto: likeways also in the thyrde kind of rising and setting, whereof the same author doth make mention, hit appeareth that he was somewhat deceived, for that owghte not to bee called properly rising of any star when it getteth out of the son beams, and may show or shine at evening or morning. 
The thyrde kind of setting.  but it ought rather to be called Apparition or appearynge of that star. And contrary ways when any star is so nigh unto the Son that the son doth take away or hide the light of it, it ought to bee called the Hydynge or occultation of that star, and not the setting of that star, sith setting and rising haue proper relation to the Horizonte, and yet doth he and mennye other contrary to the learned Greekes call the first, the Sonnelye rising of the star, and the other, the Sonnelye setting of him where as Ptolemye and the learned Greekes call the one {αβγδ}, that is in latin Apparitio, the showing of the star. and the contrary is called in greek {αβγδ}, and in latin Occultatio, the darkenynge or hidynge of the star. which chance happeneth commonly to any star being within 15 degrees of the son. this passion is called of many men Combustion: 
Combustion. Oppression.  Other contract the name of combustion to syxe degrees, and call this Oppression. but of all these, I will an other time declare my full mind, for the just knowledge hereof appertaineth to a higher Arte. And so will I hereafter give you a table declaring the morning and evening rising and setting of all the most notable stars, for the matter is not so easy as it seemeth to bee.  Scholar. 
I understand it thus: that when the son is in any parte of a sign, those stars which be in the same parte of that sign, do rise with the son, and those which be in the like degree of the contrary sign, they rise at the son setting.  Master. 
Your taking is true, for such stars as are nigh unto the ecliptic line: but yet such stars as be far from the ecliptic line, may rise or set with the Son, although they be in an other sign then the son is,& so may they rise or set before or after the son, although they be in one degree of any sign with the son. And here may you not forget that the star that setteth with the son, 
The evening settig The morning settig  is name to haue an evening setting: and the star that setteth in the west at the son rising, is judged to haue the morning setting: whereby it followeth, that the star that hath the morning rising, hath also the evening setting: and he that hath the evening rising, hath the morning setting: thus haue I spoken rudely and lightly for this time, but in the table of these risinges and settinges, you shall haue a more exact form of knowledge set out for you, touching this matter. And now to return to those ascensions which be peculiarly called astronomical, first, for the definition you must understand, that Ascension astronomical is the certain limitation of some point of the equinoctial circled, 
Ascention astronomical  which riseth iustelye with any star, and largely taking the use of that name. It betokeneth also the ark of the equinoctial circled, which lieth between the beginning of the same equinoctial at Aries, and extendeth to the just degree that riseth with any star or sign. Thirdly the ascension of a sign or constellation( which includeth a certain measure in length,) is that just ark of the equinoctial, which doth pass the horizon with that whole sign or constellation.  
This ascension is commonly divided into two kinds, the one is called right ascension, and the other obliqne or Crooked ascension. right ascension, is defined to bee that, 
right ascention. crooked ascention.  with which a greater portion of the equinoctial doth ascend. And that is called Crooked or obliqne ascension, with which a lesser portion of the equinoctial doth ascend.  Scholar. 
I hear you speak of a lesser portion and a greater portion, but where unto those comparisons ought to be referred, I can not tell, except I shall refer the one to the other.  Master. 
That may you not do, for so one ascension  depiction of two globes. might bee called right& crooked also, at the least in diuers comparisons: but that can not be, neither is it permitted by any astronomers  Scholar. 
How may it appear that such absurdity would follow?  Master. 
To the intent that I may allege nothing, but that which shall not only be certain and true, but also shall be manifest to you, I will first instruct you in the understanding of those Ascensions, and after that I will return to the proof of these my words. And for the better understanding of both definitions, I will name unto you a third Ascension, which must be as the rule of those other 2, and that is the mean ascension, for seeing you can not well refer greater and lesser but other to one common mean, or else each to other: and I haue said before( and will prove it anon) that they can not be compared together, 
The mean Ascension.  therfore must they bee referred and compared to one common mean, which I call the Mean ascension, because that with it ther ascendeth not so much of the equinoctial, as with the right ascension, nor so little as doth ascend with the crooked ascension. and for this cause may it well be called a Mean ascension. Again it may be called a mean ascension, because it is without all excess: for the portion of the equinoctial which ascendeth with it, is equal to it in preciseness of degrees, so that neither of them exceedeth other.  Scholar. 
It seemeth reasonable that all excesses being referred to any one thing, do approve that one as a mean between them, namely when the excesses decline to both extremities, as more and fewer, greater& lesser do. but in al this kind of doctrine, the words are more easy to bee understand, then the matter. Therfore except ye do with examples declare these varieties of Ascensions, I doubt it will be long before I shall well conceive them and rightly distinct them.  Master. 
You haue learned before, that there is two varieties of Spheres, a right Sphere, and a Bowing sphere: and as in each of these the equinoctial doth keep one uniform ascension, that is to say, that in 24 houres justly all the equinoctial doth ascend, and so consequently in every hour of the day 15 degrees of the equinoctial do pass the right horizon, so the zodiac which is the circled of the signs, by means of his obliquity, doth not keep uniform ascension any where in any position of Sphere. for although the whole zodiac do ascend justly in 24 hours, yet in every hour, unequal portions of it do ascend, and that diversly, according to the diversities of the Climates. 
Certain general rules in a right Sphere.  But in a generaltye of differences, you may take these general rules.  
In the right sphere, every quarter of the zodiac hath an equal or mean ascension, with every quarter of the equinoctial, beginning the quarters at the 4 principal points, which I haue before set forth: for if you should take three signs in other partes of the zodiac, their ascensions will not agree with a quarter of the equinoctial, sith there is no one sign that doth equally agree in ascension with the like portion of the Equinoctial, that is to say, with 30 degrees in it.  Scholar. 
This rule is in joannes de Sacro bosco, and in Orontius also.  Master. 
Then you believe it the better.  Scholar. 
Yea in deed.  Master. 
Then tell me whether the ascension of one of those quarters of the zodiac, ought to be called a Right ascension, or a Crooked ascension.  Scholar. 
Neither of both, as I do understand their definitions, seeing the ark of the equinoctial that ascendeth with them, is neither greater neither yet lesser then they, as these definitions do import, but is equal with them, and therfore it seemeth to me more apt to call it a mean ascension after your definition.  Master. 
You say truth, and therefore is their doctrine imperfecte, that make but two ascensions, where three ought to be distinct,( and themselves name three in use, and but 2 in distinction and definition) namely seeing( as Tullye hath said) it is the greatest fault that can be, to omit any member in division: but to omit their faults in omission, and to return to their better declaration. This second rule do they also approve, yea and natures order doth necessary infer the same, that every two signs or partes of signs equal in quantity, and like distant from any one of the 4 principal points, haue equal ascensions each to other.  Scholar. 
That is to mean, that Taurus, and Aquarius haue equal ascension, because they are equally distant from the equinoctial point of Aries.  Master. 
And so haue Taurus and lo, because they differre equally from the tropical point of Cancer, and so of all the other. But to the intent that you may the better understand all this that is said, and the rest that is to be said, I haue here set forth in a table the just numbers of degrees of the equinoctial circled, which do answer to the degrees of every sign in their ascensions in the right Sphere. So that if you desire to know the ascension of any degree of any sign, first seek out the sign, and then in the first column look for the noumbre of the degree, against which in the common corner vnderneth the sign you may see the number of the degrees and Minutes of the equinoctial, that do ascend with that degree of the sign. And those degrees be accounted from the beginning of the equinoctial at Aries, and so orderly after the natural course of the signs. whereby you may perceive, that Aries, Taurus and geminy all three together haue for their ascension 90 degrees, which number agreeth with the quantity of 3. signs, and therfore is their ascension mean. Also I may 
A TABLE FOR THE ASCENSIONS of the twelve signs in the right Sphere.  Degrees of signs. Aries Taurus geminy Cancer lo Virgo   Deg. Min. Deg. Min. Deg. Min. Deg. Min. Deg. Min. Deg. Min. 1 0 55 28 52 58 51 91 5 123 14 153 3 2 1 50 29 49 59 54 92 11 124 16 154 0 3 2 45 30 47 60 57 93 16 125 18 154 57 4 3 40 31 45 62 0 94 22 126 20 155 54 5 4 35 32 43 63 3 95 27 127 21 156 50 6 5 30 33 41 64 7 96 32 128 23 157 47 7 6 26 34 39 65 10 97 37 129 24 158 44 8 7 21 35 38 66 14 98 43 130 25 159 40 9 8 16 36 36 67 18 99 48 131 26 160 36 10 9 11 37 35 68 21 100 53 132 27 161 32 11 10 7 38 34 69 26 101 59 133 28 162 48 12 11 2 39 33 70 30 103 3 134 28 163 24 13 11 57 40 33 71 34 104 8 135 28 164 20 14 12 53 41 32 72 38 105 12 136 28 165 16 15 13 49 42 32 73 43 106 17 137 28 166 11 16 14 44 43 32 74 48 107 22 138 28 167 7 17 15 40 44 32 75 52 108 26 139 27 168 3 18 16 36 45 32 76 57 109 30 140 27 168 58 19 17 32 46 32 78 2 110 34 141 26 169 53 20 18 28 47 33 79 7 111 39 142 25 170 49 21 19 24 48 34 80 12 112 42 143 24 171 44 22 20 20 49 35 81 17 113 46 144 22 172 39 23 21 16 50 36 82 23 114 50 145 21 17 34 24 22 13 51 37 83 28 115 53 146 19 174 30 25 23 10 52 39 84 33 116 57 147 17 175 25 26 24 6 53 40 85 38 118 0 148 15 176 20 27 25 3 54 42 86 44 119 3 149 13 177 15 28 26 0 55 44 87 49 120 6 150 11 178 10 29 26 57 56 46 88 55 121 9 151 8 179 5 30 27 94 57 49 90 0 122 11 152 6 180 0 
THE SECOND TABLE OF THE Ascensions of the twelve signs in the right Sphere.  Degrees of signs. Libra. Scorpius Sagitari. Capricor. Aquarius Pisces   Deg. Min. Deg. Min. Deg. Min. Deg. Min. Deg. Min. Deg. Min. 1 180 55 208 52 238 51 272 5 303 14 333 3 2 181 50 209 49 239 54 272 11 304 16 334 0 3 182 45 210 47 240 57 273 16 305 18 334 57 4 183 40 211 45 242 0 274 22 306 20 335 54 5 184 35 212 43 243 3 275 27 307 21 336 50 6 185 30 213 41 244 7 276 32 308 23 337 47 7 186 26 214 39 245 10 277 37 309 24 338 44 8 187 21 215 38 246 14 278 43 310 25 339 40 9 188 16 216 36 247 18 279 48 311 26 340 36 10 189 11 217 35 248 21 280 53 312 27 341 32 11 190 7 218 34 249 26 281 58 313 28 342 28 12 191 2 219 33 250 30 283 3 314 28 343 24 13 191 57 220 33 251 34 284 8 315 28 344 20 14 192 53 221 32 252 38 285 12 316 28 345 10 15 193 49 222 32 253 43 286 17 317 28 346 11 16 194 44 223 32 254 48 287 22 317 28 347 7 17 195 40 224 32 255 51 288 26 319 27 348 3 18 196 36 225 32 256 57 289 30 320 17 348 58 19 197 32 226 32 258 2 290 34 321 26 349 53 20 198 28 217 33 259 7 291 39 322 25 350 49 21 199 24 228 34 260 12 292 42 323 24 351 44 22 200 10 229 35 261 17 293 46 324 22 352 39 23 201 16 230 36 262 23 294 50 325 21 353 34 24 202 13 221 37 263 28 295 53 326 19 354 30 25 203 9 232 39 264 33 296 58 327 17 355 25 26 204 6 233 40 265 38 298 0 328 15 356 20 27 205 3 234 42 266 44 299 3 329 13 357 15 28 206 0 235 44 267 49 300 6 330 11 358 10 29 206 57 236 46 268 55 301 9 331 8 359 5 30 297 54 237 49 270 0 302 22 332 6 360 0 say, that the last degree of geminy, or any star in that degree, or in the last degree of Virgo, Sagittarius or Pisces, haue a mean Ascension, so that the same star haue no latitude: how be it in the end of geminy and Sagittarye, although they haue never so much latitude, yet is their ascension mean. which prerogative those two points haue, because the lines or circles of their longitudes do touch both the Poles of the zodiac and of the equinoctial, and so doth no other circled of longitude: wherefore all stars out of those places limited where so ever they be, they haue no mean ascension, but other right ascension, or else Crooked.  Scholar. 
Thus I perceive that the two tropic points haue a privilege above the two equinoctial points in the ascensions.  Master. 
It seemeth so in the right sphere, but in the obliqne sphere the equinoctial points haue the greater privilege: for always in all places where they do ascend, they keep their mean ascension, but so doth not the tropic points in any obliqne sphere. no neither any stars of their longitude, that is to say in their colour. for although two points in the sky, where their colour doth cut the equinoctial circled, haue a mean ascension, yet in those 2. places is there no star that hath been noted, as hereafter you shall better understand. But that you may in the mean season know what signs do ascend right, and which do ascend crokedlye in the right sphere, you shall mark this little table which I haue drawn out of the former great table, where you see that 4 signs agree still in their ascension, and the first 4 haue but 27 degrees and 54 minutes of the Equinoctial answering to each of their ascensions: the other 4 signs haue 29 degrees, 55 minutes for their ascension: and the last 4 haue 32 degrees and 11 minutes agreeing to their rising, which degrees and minutes added together, do make just 90 degrees that is exactly one quarter of the equinoctial 
A brief table for the right Sphere.  Ascension. The twelve signs. Partes of the equinoctial Partes of time     Deg. Min. Ho. Min. Crooked Aries Virgo Libra Pisces. 27 54 1 51 3/ 5 Crooked Taurus lo Scorpius Aquarius 29 55 1 59 2/ 3 right geminy Cancer Sagitarius Capricornus 32 11 2 8 14/ 15 The addition of those partes each to his own kind 90 0 6 0 and so are each ternary of those signs one just quarter of the zodiac.  Scholar. 
And in like case I perceive, the 6 hours of time that answereth to those whole quarters, is also the just quarter of the natural day, which amounteth by the addition of the three several times agreeing to those 3 several ascensions. And as I understand it, the quantity of time is gathered after the rate of 15 degrees ascendinge every hour, as you said before. so that every degree asketh 4 minutes of an hour: and 15 minutes of a degree in the equinoctial do rise in one minute of an hour: for this is always to bee remembered, that a minute is ever more the 60 part of that thing whereunto it is referred. But now ther cometh to my mind the saying of joannes de Sacro Bosco, which long hath troubled my mind, and I can not learn of any man howe to understand him well: for in mine opinion his words import an impossibility. he blameth this argument as evil: These two arkes are equal, and they begin to rise together, and continually ther riseth a greater portion of the one ark then of the other: ergo that ark will bee full risen soonest, whose greater portion did always rise. This argument seemeth invincible in mine opinion, and yet John de Sacro bo sco for improving of it allegeth an example, whereby as he seemeth to intend, the antecedent may be true, and the consequent false: and therefore the argument must needs be nought.  Master. 
Repeat you his example, that we may examine it:  Scholar. 
He willeth to take any quarter of the zodiac, compared with his like quarter of the equinoctial, and to begin with that quarter from the first point of Aries, to the latter end of geminy, always the greater portion riseth of the zodiac, and the lesser of the equinoctial, and yet those two quarters ascend fully together: and the like must you understand of the third quarter, from the beginning of Libra, to the end of Sagittarye. but contrary ways, in the quarter that lieth from the first parte of Cancer, to the last of Virgo, the portion of the Equin octiall in ryfynge, is still greater then the parte of the zodiac that riseth with it: and yet those both arkes do rise justly to gether at the end.  Master. 
Here is a great fallation by Amphibologye, as logicians do call it, so that in one sense it may be true, and in an other it is false. And first for declaration of John his meaning( as I think) mark as many partes of those 2 first quarters as you list, and still by the former table, as well as by turning the Sphere itself, it will appear manifestly, that the portion of the zodiac is ever greater then the match portion of the equinoctial.  Scholar. 
That is most true. for with 12 degrees of Aries there ascendeth of the equinoctial 11 degrees and two minutes only of the equinoctial, that is 59 minutes less: with 30 degrees of Aries there riseth but 27 degrees and 54 minutes, which is less by two degrees and syxe minutes: also in Taurus, 15 degrees hath for their ascension 42 degrees and 32 minutes, that is two degrees and 28 minutes to little: the last of Taurus ascendeth with 57 degrees and 49 minutes, which should be 60 if it were equal with the degrees of the zodiac. again the 16 degree of geminy answereth to the ascension of the 74 degree and 48 minute of the equinoctial, which in equality would be 76: and the 29 degree of geminy should haue by order of equality the 89 degree of the equinoctial,& hath but 88 degrees& 55 minutes, which is lesser by 5 minutes then equality requireth, and so doth it appear in all the rest, save in the very last degree of geminy, where both numbers appear even.  Mast. 
Then are the words of John desacro bosco true.  Scholar. 
This matter troubleth me to much: for of this am I assured, that if any two quantities be equal together, and a lesser portion of the first matched with a greater part of the second, then of necessity that parte that remaineth of the first quantity, must needs be greater then that that resteth of the second.  Master. 
That is true also: for if you abate unequal partes from 2 equal quantities, the portions that remain will be unequal, and that parte will bee least, from which the greater portion was abated.  Scholar. 
As that can not be false, so it seemeth to me, that seeing there doth ascend with the whole sign of Aries but 27 degrees, and 54 minutes, there must needs remain 62 de grees and 6 minutes of that quarter, and that is more then the 60 degrees which resteth of the like quarter of the zodiac. Now those 62 degrees and 6 minutes will ascend with the 60 degrees of the zodiac, so that then there doth not still ascend a lesser portion of the equinoctial: for as the first portion was lesser, so this second parte is greater.  Master. 
Your conjecture is good: and to approve it the better, you may confer some lesser partes of those 2 quarters together, as from the 20 degree of Taurus, to the 10 degree of geminy, the degrees between them are 20:& to know the ark of the equinoctial that ascendeth with those 20 degrees, subtracte the lesser from the greater, and the ascension of those 20 degrees will remain.  Scholar. 
The ascension of the 20 degree of Taurus is 47 degrees and 33 minutes: the ascension of the 10 degree of Geminiis 68 degrees, and 21 minutes. wherefore setting those numbers in convenient order, and making subtraction duly, ther resteth 20 degrees;& 48 minutes, so is this portion of the equinoctial the greater by 48 minutes.  Master. 
prove again from the 28 degree of Taurus, to the 28 degree of geminy: which difference is 30 degrees.  Scholar. 
With the 28 degree of Taurus there doth ascend 55 degrees, and 44 minutes: and with the 28 of geminy, 87 and 49. and by Subtraction the difference appeareth to bee 32 degrees, and 5 minutes. so is the ark of that equinoctial greater by two degrees and 5 minutes, then the match ark of the zodiac. And therefore are not John de Sacro bosco his words true.  Master. 
prove yet more before you condemn him. try the ark from the tenth degree of Taurus, to the 22 degree of the same sign, which ark includeth 12 degrees of the zodiac.  Schol. 
The 10 degree of Taurus, ascendeth with 37 degrees& 35 minutes of the equinoctial the 22 degree of the same sign hath for his ascension 49 degrees& 35 minutes, the difference between them by subtraction is found to be 12 degrees just: and so that ark of the equinoctial is equal with his match ark in the zodiac.  Master. 
Yet ones more prove the ark from the last degree of Aries to the second degree of geminy, which ark is 32 degrees.  Scholar. 
The last degree of Aries riseth with 27 degrees, and 54 minutes: and the 2 of geminy hath 59 degrees and 54 minutes in his ascension. between which 2 numbers, the distance is 32 degrees exactly, and so are those 2 arkes equal also, and neither of those 2 examples do make the ark of the equinoctial lesser then the match ark in the zodiac: so that they make against John de Sacro bosco.  Master. 
In deed as his words be placed in the Present time, they can not be true, but his meaning may be more favourably gathered, by turning the Present time into the Perfect time,& referring the name of ascension to the whole ark that is fully risen in that quarter, as I did in the explication of his words occasion you to make proof: wherefore take any parte of the first quarter, and account from the beginning of Aries: or likeways any part of the third quarter, and reckon from the beginning of Libra, and so shall you see always that the portion of the zodiac which is ascended, shall be greater then the parte of the equinoctial that is risen with it:& so shall it continue even to the very last degree of them both, and then at length doth both the quarters end their ascensions exactly together.  Scholar. 
As you say. now do I perceive it, so that the fault is rather in his words then in his meaning.  Master. 
Such mean matters must be winked at in other, but not followed. And now for the order of Ascension of the other 2 quarters which begin at Cancer& capricorn, you shall understand the like: but that the greater portion the ascendeth is referred to the Equinoctial circled& not to the zodiac▪  Scholar. 
So I understand by this former table that with the 28 degree of Cancer there ascendeth 120 degrees and 6 minutes of the equinoctial, which is two degrees and 6 minutes more then equality would yield: and with the 26 degree of Virgo, there riseth the 176 and 20 minutes of the equinoctial, which is also more then equallenes by 20 minutes: and so if I take any degree of any sign in that second quarter, or in the fourth quarter, beginning at Capricorn, I may lightly see by the table that the portion of the equinoctial in his ascension is greater then the match ark of the zodiac from the beginning of Aries to that degree. whereby it appeareth that al those 6 signs do ascend right, because a greater portion of the equinoctial ascendeth with thē.  Master. 
Then by the like reason, the other 6 signs Aries, Taurus, geminy, Libra, Scorpius and Sagittarius do ascend crookedly, because the lesser portion of the Equinoctial doth ascend with thē: after the sort of conference, which is contrary to the I said before, the 4 signs only do ascend right in the right spher: wherefore you must understand, that for to know the ascension of every sign, you must consider that sign alone, and the ark of the equinoctial that doth ascend with it, and so shall you see exactly the ascension of every sign severally. And here you shall understand, that all Astronomers commonly do call the Right ascension so largely, 
An other signification of right ascension.  that it extendeth to the ascension of all the signs in a Right sphere: and so they name the obliqne ascension the rising of all the signs in any obliqne Sphere, whereby it appeareth that they give the name of right and Crooked ascensions, according to the Horizontes or pofitions of the Sphere, and not after the quantities of time in their ascension. And this shall suffice at this time touching ascensions in the right Sphere: in which also the descensions or settinges under the horizon, are equal with the Ascensions, 
Of the descension of signs.  so that they need not to haue any peculiar declaration: but in the obliqne Spheres it is not so, but contrary ways. those signs that do ascend right, do descend crooked: and they that ascend crooked, do descend right: so that the descension of any sign in an obliqne sphere, is equal precisely to the ascension of the contrary sign.  scholar. 
You mean that the defcending of Aries is equal to the ascendinge of Libra, and the descendinge of Taurus is one in quantity of time with the ascension of Scorpius.  Master. 
So is it in dead. And in this great variety you shall mark one constant uniformity, that the ascension and descension of any sign in any crooked sphere joined by addition together, do make an equal sum of time with the ascension and descension of the same sign in a right sphere, in like sort joined together: but to the intent that you may understand all these things the better, and also know the just ascension of every sign in this our Climat where the elevation of the pole is 52 degrees, I haue drawn here a special table for that latitude. in which you shall use the like manner of entering, as you did in the other, so that 
A TABLE OF ASCENSION OF the signs in 52 degrees of Latitude.  Degrees of signs. Aries Taurus geminy Cancer lo Virgo   Deg. Min. Deg. Min. Deg. Min. Deg. Min. Deg. Min. Deg. Min. 0 0 0 12 48 29 42 56 11 94 6 137 0 1 0 24 13 16 30 24 57 17 95 30 138 37 2 0 48 13 45 31 7 58 24 96 54 139 54 3 1 13 14 14 31 50 59 31 98 18 141 20 4 1 37 14 43 32 34 60 39 99 42 142 47 5 2 2 15 12 33 18 61 48 101 7 144 13 6 2 16 15 42 34 3 62 58 102 32 145 40 7 2 51 16 13 34 49 64 9 103 57 147 6 8 3 15 16 43 35 36 65 20 105 22 148 32 9 3 40 17 14 36 24 66 32 106 47 149 58 10 4 5 17 45 37 12 67 45 108 12 151 24 11 4 30 18 16 38 1 68 59 109 38 152 50 12 4 55 18 48 38 51 70 13 111 4 154 16 13 5 20 19 20 39 42 71 28 112 30 155 42 14 5 45 19 52 40 34 72 44 113 56 157 8 15 6 10 20 25 41 26 74 0 115 23 158 39 16 6 35 20 59 42 19 75 17 116 49 160 0 17 7 1 21 34 43 13 76 34 118 15 161 26 18 7 26 22 8 44 8 77 52 119 42 162 52 19 7 52 22 43 45 3 79 11 121 8 164 18 20 8 18 23 18 45 59 80 30 122 35 165 43 21 8 44 23 54 46 56 81 50 124 2 167 9 22 9 11 24 31 47 54 83 10 125 28 168 35 23 9 37 25 8 48 53 84 31 126 55 170 1 24 10 4 25 45 49 53 85 51 128 22 171 27 25 10 31 26 23 50 54 87 12 129 48 172 52 26 10 58 27 2 51 56 88 34 131 15 174 18 27 11 25 27 41 52 59 89 57 132 41 175 44 28 11 53 28 21 54 2 91 20 134 8 177 9 29 12 20 29 1 55 6 92 43 135 34 178 35 30 12 48 29 42 56 11 94 6 137 0 180 0 Degrees of signs. Libra Scorpius Sagittari. Capricor. Aquarius Pisces   Deg. Min. Deg. Min. Deg. Min. Deg. Min. Deg. Min. Deg. Min. 0 181 0 223 0 265 54 303 49 330 18 347 12 1 181 25 224 26 267 17 304 54 330 59 347 40 2 182 51 125 52 268 40 305 58 331 39 348 7 3 184 16 227 19 270 3 307 1 332 19 348 35 4 185 42 228 45 271 26 308 4 332 58 349 2 5 187 8 230 12 272 48 309 6 333 37 349 29 6 188 33 231 38 274 9 310 7 334 15 349 56 7 189 59 233 5 275 29 311 7 334 52 350 23 8 191 25 234 32 276 50 312 6 335 29 350 49 9 192 51 235 58 278 10 313 4 336 6 351 16 10 194 17 237 25 279 30 314 1 336 42 351 42 11 195 42 238 52 280 49 314 57 337 17 352 8 12 197 8 240 18 282 8 315 52 337 52 352 34 13 198 34 241 45 203 20 316 47 338 26 352 59 14 200 0 243 11 284 43 317 41 339 1 353 25 15 201 26 244 37 286 9 318 34 339 35 353 50 16 202 52 246 4 287 16 319 26 340 8 354 15 17 204 18 247 30 288 32 320 18 340 40 354 40 18 205 44 248 56 289 47 321 9 341 12 355 5 19 207 10 250 22 291 1 321 59 341 44 355 30 20 208 36 251 48 292 15 322 48 342 15 355 55 21 210 2 253 13 293 28 323 36 342 46 356 20 22 211 28 254 38 294 40 324 24 343 17 356 45 23 212 54 256 3 295 51 325 11 343 47 357 9 24 214 20 257 28 297 2 325 57 344 18 357 34 25 215 47 258 53 298 12 326 42 344 48 357 58 26 217 13 260 18 299 21 327 26 345 17 358 23 27 218 40 261 42 300 29 328 10 345 46 358 47 28 220 6 263 6 301 36 328 53 346 15 359 12 29 221 33 264 30 302 43 329 36 346 44 359 36 30 223 0 265 54 303 49 330 18 347 12 360 0 although the numbers differ, yet the work differeth not in this table. the first column containeth the degrees of the signs, and the other columns do contain the degrees& minutes of the equinoctial under each sign, accordingly as they do answer to the Ascension of the degrees of the same signs. By this table may you see a great diversity in the Ascensions from those in the right Sphere: And yet this may you certainly observe: that every two signs being contrary to gether, the one lying against the other, as they haue far unlike ascensions, so yet if you add their both ascensions together, they will be equal to the ascensions of the same two signs in the Right sphere.  Scholar. 
Then in as much as the ascension of Aries is in this latitude 12 degrees and 48 minutes,& the ascension of Libra, 43 degrees just,( abating as I ought 108 degrees) and so they both by addition do make 55 degrees, and 48 minutes. And in the right sphere each of these signs hath for his ascension 27 degrees and 54 minutes( for the contrary signs there are equal in their ascension) wherefore by addition there will amount the same sum precisely that was gathered before: and so likewaies of Taurus and Scorpius: their ascensions joined together maketh 59 degrees and 48 minutes: but in the right sphere, those two ascensions maketh 59, 50. that is two minutes only difference in two signs, so is it but one minute in one sign, that is not to be regarded.  Master. 
Not greatly, and especially in an Introduction. But do you mark here the signs that ascend right, and them that ascend crooked?  scholar. 
Although I see a difference by this table from the other: I had thought that the more crooked Sphere had made the more crooked ascension only: but yet that they always had kept one name in general, and not haue changed it. but by your question only I am admonished of mine error: for I see that Libra( as it is easily viewed) doth ascend here right, and hath for his ascension 43 degrees, and in the right sphere it did ascend crookedly, and had but 27 degrees and 54 minutes for his ascention, and therefore may I doubt of all the rest, till I haue examined their ascensions better.  Master. 
To ease you of pain, lo here is a table of their just ascensions, which you may examine at leisure.  

A brief TABLE FOR 52. degrees of latitude.  Ascention The 12 signs. Parts of the Equin. Partes of time.     Degrees. Minutes. hours. Minutes. Crooked Aries, Pisces, 12 48 0 51 3/ 15 Crooked Taurus, Aquarius, 16 54 1 7 9/ 15 Crooked geminy, Capricornus 26 29 1 45 14/ 5 right Cancer, Sagittarius, 37 55 2 31 10/ 15 right lo, Scorpius, 42 54 2 51 9/ 15 right Virgo, Libra, 43 0 2 52 The addition of those partes 180 0 12 0  
By this table you may perceive what signs do rise crokedlye, and which do ascend right, and that there bee of each sort 6. so that from Cancer unto capricorn all the signs in direct order do ascend right, and from capricorn to Cancer, in natural order of the signs, all those 6 signs do rise crookedly. And this rule is general in all these north climates, that lie from 30 degrees of latitude( under which Memphis and Alcayre are and mount sinai: also the yste of Madera, and the parte of the west Indies, called Terra florida) unto 66 degrees and a half of latitude, in that Climate where iceland lieth and the north partes of Nor ways, and namely Halgoland, where Oht here difficult, that was the first discoverer of the north voyage toward Moscouia.  Scholar. 
That voyage I desire much to understand, and so do many other.  Master. 
An other time shall serve for it, for now we haue an other matter in hand.  Scholar. 
Then for this present matter: Is there any other variety of ascention between the equinoctial circled and the Latitude of 30 degrees? 
Varietes of Ascensions.   Master. 
Yea, much diversity: for( as you haue heard) under the equinoctial 8 signs do ascend crookedly, and but 4 right: but from the equinoctial unto 10 degrees of latitude, 6 signs ascend right,( geminy, Cancer, lo, Scorpius, Sagittarius, Capricornus) and other syxe crooked, that is Aries, Tarurus, Virgo, Libra, Aquarius& Pisces. And from 10 degrees unto 30 there are 8 signs that rise right, as geminy, Cancer, lo, Virgo, Libra, scorpion, Sagittarius, and Capricornus: and the other four, Aries, Taurus, Aqua rius and Pisces, rise crookedly. but to the intent that you may haue the better habilitie to judge of such varieties, I haue here set forth diuers tables for examples sake: and namely such, which import any variety of alteration, or help to the apt understanding of the same.  

A TABLE FOR THE LAtitude of. 1. degree.  Ascention The 12 signs. Parts of the Equin. Partes of time.     Degrees. Minutes. hours. Minutes. Crooked Aries, Pisces, 27 42 1 50 12/ 15 Crooked Taurus, Aquarius, 29 44 1 58 14/ 15 right geminy, Capricornus 32 8 2 8 8/ 15 right Cancer, Sagittarius, 32 16 2 9 2/ 25 right lo, Scorpius, 30 4 2 0 4/ 15 Crooked Virgo, Libra, 28 6 1 52 8/ 15 The sum of those partes 180 0 12 0  

A table for 10. degrees of latitude.  Ascention The 12 signs. Parts of the Equin. Partes of time.     Degrees Minutes. hours. Minutes. Crooked Aries, Pisees, 25 51 1 43 6/ 15 Crooked Taurus, Aquarius, 28 14 1 52 14/ 15 right geminy, Capricornus 31 31 2 6 1/ 15 right Cancer, Sagittarius, 32 53 2 11 8/ 15 right lo, Scorpius, 31 34 2 6 4/ 15 Crooked Virgo, Libra, 29 57 1 59 12/ 15 The sum of those partes 180 0 12 0  

A table for 11 degrees of latitude.  Ascention The 12 signs. Partes of the Equin. Partes of time.     Degrees. Minutes. hours. Minutes. Crooked Aries, Pisces, 25 38 1 42 8/ 15 Crooked Taurus, Aquarius, 28 4 1 52 1/ 15 right geminy, Capricornus 31 27 2 5 12/ 15 right Cancer, Sagittarius, 32 57 2 11 12/ 15 right lo, Scorpius, 31 44 2 6 14/ 15 right Virgo, Libra, 30 10 2 0 10/ 15 The sum of the partes. 180 0 12 0  

A table for 20. degrees of latitude.  Ascension The 12 signs. Partes of the Equin. Partes of time.     Degrees Minutes. hours. Minutes. Crooked Aries, Pisces, 23 39 1 34 9/ 15 Crooked Taurus, Aquarius, 26 27 1 45 12/ 15 right geminy, Capricornus 30 48 2 3 3/ 15 right Cancer, Sagitarius, 33 36 2 14 6/ 25 right lo, Scorpius, 33 21 2 13 6/ 15 right Virgo, Libra, 32 9 2 8 9/ 15 The sum of the partes. 180 0 12 0  

A table for 29. degrees of latitude.  Ascension The 12 signs. Parts of the Equin. Partes of time.     Degrees Minutes. hours. Minutes. Crooked Aries, Pisces, 21 25 1 25 10/ 25 Crooked Taurus, Aquarius, 24 37 1 38 7/ 15 right geminy, Capricornus 30 1 2 0 1/ 15 right Cancer, Sagittarius, 34 23 2 17 8/ 15 right lo, Scorpius, 35 11 2 20 12/ 15 right Virgo, Libra, 34 23 2 17 8/ 15 The sum of the partes 180 0 12 0  

A table for 30 degrees of latitude.  Ascension The 12 signs. Partes of the Equin. Partes of time.     Degrees. Minutes. hours. Minutes. Crooked Aries, Pisces, 21 9 1 24 9/ 15 Crooked Taurus, Aquarius, 24 23 1 37 8/ 15 Crooked geminy, Capricornus 29 56 1 59 12/ 25 right Cancer, Sagittarius, 34 28 2 17 13/ 15 right lo, Scorpius, 35 25 2 21 12/ 15 right Virgo, Libra, 34 39 2 18 9/ 15 The sum of the partes. 180 0 12 0  

A table for 50. degrees of latitude.  Ascension The 12 signs. Partes of the Equin. Partes of time.     Degrees. Minutes. hours. Minutes. Crooked Aries, Pisces, 13 52 0 55 7/ 15 Crooked Taurus, Aquarius, 17 55 1 11 10/ 15 Crooked geminy, Capricornus 27 0 1 48 right Cancer, Sagittarius, 37 24 2 29 〈◇〉 right lo, Scorpius, 41 53 2 47 ●/ 15 right Virgo, Libra, 41 56 2 47 11/ 15 The sum of the partes. 180 0 12 0  

A table for 60. degrees of latitude.  Ascension The 12 signs. Parts of the Equin. Partes of time.     Degrees Minutes. hours. Minutes. Crooked Aries, Pisces, 7 16 0 29 1/ 15 Crooked Taurus, Aquarius, 10 56 0 43 11/ 15 Crooked geminy, Capricornus 22 56 1 31 11/ 15 right Cancer, Sagittarius, 41 28 2 45 13/ 15 right lo, Scorpius, 48 52 3 15 7/ 15 right Virgo, Libra, 48 32 3 14 2/ 15 The sum of the partes 180 0 12 0  

A table for 66 degrees and ½ of latitude.  Ascension The 12 signs. Partes of the Equin. Partes of time.     Degrees. Minutes. hours. Minutes. Sudden Aries, Pisces, 0 0 0 0 Sudden Taurus, Aquarius, 0 0 0 0 Sudden geminy, Capricornus 0 0 0 0 right Cancer, Sagittarius, 64 22 4 17 7/ 15 right lo, Scorpius, 59 49 3 59 4/ 15 right Virgo, Libra, 55 49 3 43 4/ 15 The sum of the partes. 180 0 12 0  Scholar. 
Sir I thank you most heartily for these tables, for I haue not seen the like of them before: and their order is so easy, that I need no great help in the understanding of them: For as in the title of each of them is set the degree of the latitude of the Region for which the table is calculate, so in the first column is set the differences of the ascensions in name, and in the second column are the names of the signs, which haue those diuers Ascensions, each row containing two signs, whereby they differ from the right Sphere, for in it 4 signs agree in one quantity of ascension, whereas in all these obliqne spheres, only two signs do agree in likeness of ascension. And in each of them are there set in the third column, the degrees of Ascension, and minutes after them, which appertain to every sign: and in the fourthe column are the partes of time, agreeynge to those partes of the equinoctial circled: by which it may appear not only howe many degrees and minutes those signs occupy in their Ascension, but also howe many hours or minutes do answer to the same. And in each table is set the full quantity of half a day, and also of half the zodiac, which is the full sum by addition of all the other percelles over them: 
The first rule of obliqne Ascention.  whereby I perceive it to bee true, that each half of the equinoctial doth equally ascend with each half of the zodiac.  Master. 
beginning the halves of them both at the equinoctial points, in Aries and Libra, it is most true: but not so yf you begin at the tropic points, or in any other partes of them: for yf you begin at any of the northerly signs between Aries and Libra, and so reckon 6 signs together, those signs shall haue a right Ascension: for with them shall ascend a greater portion of the equinoctial. But if you do reckon syxe signs and begin that account between Libra and Aries, in the south parte of the zodiac, then do those syxe signs ascend crookedlye: for as much as the portion of the equinoctial that riseth with them, is less then half of it.  Scholar. 
For proof thereof I take the table of ten degrees of latitude, and I begin with Taurus, and so do I reckon syxe signs, Taurus, geminy, Cancer, lo, Virgo and Libra, unto which signs these syxe numbers answer as they be here set, accounting one number twice, Degrees Minutes. 20 14 31 31 32 53 31 34 29 57 29 57 184 6 that is first for Virgo, and then for Libra, and so the whole sum of partes of the equinoctial is 184 degrees and 6 minutes: that is 4 degrees and 6 minutes more then half: wherefore those signs do ascend right. And so I perceive it will be in the other like works, if I do begin with any sign in that north half of the zodiac, for seeing Aries hath the least of all other Ascensions, if I take any other sign, and omit him, I shall haue a greater noumbre then the half of the equinoctial circled. But now contrary ways if I begin with any of the south signs, and so reckon syxe continual signs, their Ascension you say will bee an Oblyque ascension, because their degrees will bee more in noumbre then the degrees of the equinoctial circled: for example I take my beginning at Sagittarius, and so reckon sorthe directelye syxe signs, that is Sagittarius, Capricornus, Aquarius, Pisces, Aries and Taurus. and for them I take the numbers of their Ascensions, and set them down as here you se: so that by addition they do make 172 degrees, and 34 minutes: that is less then the half circled by seven degrees, and 26 minutes. wherefore it must needs bee, that those signs do ascend crookedlye.  
Deg. Min. 32 53 31 31 28 14 25 51 25 51 28 14 172 34  Master. 
And so must it follow where so ever you begin after Libra in that south half of the zodiac: for so much as you omit the ascension of Libra, beeynge 29 degrees and 57 minutes, and in stead of it you take the ascension of Aries, which is but 25 degrees and 51 minutes.  Scholar. 
this reason doth appear manifest enough: and that not only in this table, but also in al the other, save that in the last table I see a strange dysagreemente from all the other. for in these syxe signs, Aries, Taurus, geminy, Capricornus, Aquarius& Pisces, there is set no numbers of degrees or minutes for their ascension, but only ciphers, which thing is strange to me, for thereby may it be conjectured, that those 6 signs haue none Ascension at all: and yet I am sure that the first three of them do ascend not only in that Climate, but also in all other Climates be north that latitude even to the north Pole.  Master. 
A little mistakinge doth disturb your mind much, but yf you do place the sphere in the Horizonte, in such sort, that the north Pole be 66 degrees and half above the Horizonte, and then turn the first degree of Aries, to the east Horizonte ready to ascend, and afterward yf you turn the Globe toward the west, but by the quantity of half one degree in the equinoctial, you shall perceive that all those six signs which lie from the winter tropic unto the summer tropic, that is to say, Capricornus, Aquarius, Pisces, Aries, Taurus, and geminy, will ascend suddenly in one moment all 6 at ones: so that for their ascension there can be assigned no degree of the equinoctial, neither any sensible parte of time, sith it is done in a moment of time. and therfore must I put no degree for their Ascension, neither yet any time. And because I thought no less but that this would seem some thing strange unto you, therefore haue I not touched any thing of the other Ascensions for these Climates that bee between the tropic of Cancer and the Pole, being adsured that they would seem to you much more strange, then this doth. but hereafter yf I perceive that you travail well in this first Introduction, I will instruct you more largely in all that shall bee needefulle for you: and in the mean season I coil prosecute the rules of these Ascensions in the Oblyque Spheres: as I did begin.  
wherefore you shall note, that although each half of the zodiac do agree in ascension with each half of the equinoctial, yet the partes of those halves, I mean the several signs, and their distinct portions do not so agree, but are either more or less.  Scholar. 

John de sacro Bosco his rules examined.  So I remember doth John de sacro Bosco affirm: for( saith he) in that half of the zodiac, which is between the beginning of Aries, and the end of Virgo, always the portion of the zodiac which riseth, is greater then the like half of the equinoctial: and yet those halves do rise together.  Master. 
This he speaketh of the obliqne sphere.  Scholar. 
So doth he in deed.  Master. 
propound you an example, that I may know howe you do understand it.  Scholar. 
I take an example out of the table of 50 degrees of latitude, and for the first five signs I set the quantities of their ascensions, as here is seen, which by Addition do make 138 degrees and four minutes. so doth there want of 150 degrees, which are the full degrees for five signs, 11 degrees and 56 minutes. that ark therefore of the equinoctial is lesser then the match ark of the zodiac: but now there resteth in that half of the equinoctial 41 degrees and 56 minutes, which is the just ascension of Virgo, in that latitude. and so those both halves do ascend jointly together.  Master. 
prove the like work in the table of 10 degrees of latitude.  Scholar. 
For the first 5 signs Aries, Taurus geminy, Cancer and lo, I set their ascensions thus. And by addition I finde that their whole sum for all that arkes ascension is 150 degrees and three minutes. that is three minutes more then the degrees of five signs, which is 5 times 30. And so is this example against the rule, for here the greater portion is of the equinoctial.  Master. 
prove yet again in the table of one degree of latitude.  Scholar. 
The ascensions of the first 5 signs in that latitude, are these: and make in one total sum, 151 degrees, and 54 minutes: that is 1 degree, and 54 minutes more then the like ark of the 5 signs in the zodiac, which containeth but only 150 degrees. And so is this example also against the rule.  Master. 
So you haue two examples contrary to that rule.  Scholar. 
It can not be denied.  Master. 
Then is that no certain rule.  Scholar. 
It seemeth so.  Master. 
In deed it is true only above 13 degrees of latitude. for in all climates and parallels under 13 degrees of latitude, the equinoctial maketh greatest number of degrees in his ark. so that John de sacro Bosco his words may not be accounted true generally( as they sound) but particularly between 13 degrees of latitude, and 66 and an half: and so is it to be said of diuers other of his rules.  Scholar. 
Is there the like diversity beyond 66 degrees and a half northward?  Master. 
There is more diversity, but such and so strange as I will not at this time trouble your head withall, but will appoint a more convenient place for it.  Scholar. 
Then I beseeke you to prosecute the rest of John de sacro Bosco his rules, touching ascensions.  Master. 
repeat you the rules.  Scholar. 
His next rule is: that in the other half of the zodiac, from the beginning of Libra, to the end of Pisces evermore there riseth a greater parte of the Equinoctial then of the zodiac, and yet both those halves do rise fully together.  Master. 
prove it by some examples.  Scholar. 
In the latitude of 30 degrees I take Libra only, and finde against it 34 degrees and 39 minutes: so is there 4 degrees and 39 minutes more of the equinoctial then of the zodiac agreablye to the rule. Also in the table of 60 degrees with Libra, there doth ascend in the equinoctial 48 degrees and 32 minutes. that is to say 18 degrees and 32 minutes more then the 30 degrees of Libra.  Master. 
assay the like in the latitudes of one degree, and of 10 degrees.  Scholar. 
In the latitude of 10 degrees, the sign of Libra hath for his ascension 29 degrees, and 57 minutes of the equinoctial, that is 3 minutes less then the degrees of the zodiac, and so is that contrary to the said rule.  Master. 
now prove the other.  Scholar. 
In that parallel where the Pole is but one degree high, the sign of Libra ascendeth with 28 degrees and 6 minutes of the equinoctial, so is that ark of the equinoctial lesser then the degrees of the said sign of Libra, by 1. degree and 65 minutes, and yet by the rule it should be greater. wherefore I may perceive, that this rule doth not serve for all Latitudes, but for certain of them. And as I think, not for any above 10 degrees, although( as you said) the other exception did extend to 13 degrees of latitude.  Master. 
What causeth you to think so?  Scholar. 
The table calculate by you for 11 degrees of latitude, where I see 30 degrees, and 10 minutes of the equinoctial, assigned for the ascension of the sign of Libra, and there is the portion of the equinoctial greater by 10 minutes then the portion of the zodiac.  Master. 
In deed for whole signs this exception extendeth not above 10 degrees of latitude, and no more doth the other former exception, but yet in partes of signs it extendeth in them both to 13 degrees, as hereafter you shall perceive more at large. but now go forth to the next rule.  Scholar. 
The fourthe rule is this: that those arkes which succeed after Aries unto the end of Virgo in the obliqne sphere, 
The fourth rule.  do abate their ascensions in comparison to the ascensions that they haue in the Right sphere: namely seeing less doth rise of the equinoctial.  

A TABLE OF ASCENSIONS showinge all diversities of them, unto the Polare circled, peculiar for every several sign.  Degrees. of latitude. Aries Pisces Taurus Aquarius geminy Capricor Cancer Sagittari. lo Scorpius. Virgo Libra   Deg. Min. Deg. Min. Deg. Min. Deg. Min. Deg. Min. Deg. Min. 0 27 54 29 54 32 12 32 12 29 54 27 54 1 27 42 29 44 32 8 32 16 30 4 28 6 2 27 30 29 34 32 4 32 20 30 14 28 18 3 27 17 29 25 32 0 32 24 30 23 28 31 5 26 53 29 4 31 52 32 32 30 44 28 55 8 26 16 28 34 31 40 32 44 31 14 29 32 10 25 51 28 14 31 31 32 53 31 34 29 57 11 25 38 28 4 31 27 32 57 31 44 30 10 15 24 46 27 23 31 10 33 14 32 25 31 2 20 23 39 26 27 30 48 33 36 33 21 32 9 25 22 27 25 27 30 24 34 0 34 21 33 21 30 21 9 24 23 29 56 34 28 35 25 34 39 35 19 43 23 9 29 24 35 0 36 39 36 5 40 18 4 21 45 28 47 35 37 38 3 37 44 45 16 10 20 3 28 1 36 23 39 45 39 38 50 13 52 17 55 27 0 37 24 41 53 41 56 55 11 1 15 5 25 31 38 53 44 43 44 47 60 7 16 10 56 22 56 41 28 48 52 48 32 65 2 4 3 44 15 20 49 2 56 5 53 45 66 ½ 0 0 0 0 0 0 64 22 59 49 55 49  Master. 
For trial of this rule I haue set forth here a table containing all the diversities( though not all the several degrees of latitude) that happen in any Climate under 67 degrees of latitude, that is unto the Polare circled. So that by this table you may examine all the rules both of John de Sacro Bosco, and also of others. now therefore examine those arkes that follow Aries, and so abate their ascensions, as your rule saythe, from Aries, unto the end of Virgo.  Scholar. 
first for Aries itself: I see that it abateth in this table from 27 degrees and 54 minutes unto nothing. And Taurus abateth also from 29 degrees and 54 minutes unto nothing. likewise geminy abateth from 32 degrees and 12 minutes unto nothing. But contrary ways, Cancer, lo, and Virgo, do not abate, but increase the quantities of their Ascensions. so that in the three first signs only( that is Aries, Taurus and geminy) that rule is true, and in the other three signs, Cancer, lo and Virgo, it appeareth utterly to be false.  Master. 
Yet in one manner of consideration those words may be true as he hath spoken them, though not so largely as the words do sound: for it appeareth that your author doth account the beginning of those arkes( whereof he speaketh) not from diuers and several points, but from one common beginning, which is the first degree of Aries, and in that sense his rule is true. for proof whereof here is two other tables set forth, in which is declared the quantities of the Ascensions of the twelve signs, but not in such sort as it was in the table next before, for there every ark of the several signs did take his beginning at the first degree of the same sign. but in these two tables the ark of ascension is accounted from the first degree of Aries, as from the common beginning, and eandeth at the last degree of every several sign. And now by this first table if you examine the former rule you shal find it to be true 
A TABLE FOR THE DIVERSITIES of Ascensions for the first 6 signs from the equinoctial to the Polare circled, accounting the beginning of every ark, from the first degree of Aries.  Theleuation of the Pole. Aries Taurus geminy Cancer lo Virgo   Deg. Mi. Deg. Min. Deg. Min. Deg. Min. Deg. Min. Deg. Min. 0 27 54 57 48 90 0 122 12 152 6 180 0 1 27 42 57 26 89 34 121 50 151 54 180 0 2 27 30 57 4 89 8 121 28 151 42 180 0 3 27 17 56 42 88 42 121 6 151 29 180 0 4 27 5 56 20 88 15 120 44 151 17 180 0 5 26 53 55 57 87 49 120 21 151 5 180 0 8 26 16 54 50 86 30 119 14 150 28 180 0 10 25 51 54 5 85 36 118 29 150 3 180 0 11 25 38 53 42 85 9 118 6 149 50 180 0 15 24 46 52 9 83 19 116 33 148 58 180 0 20 23 39 50 6 80 54 114 30 147 51 180 0 25 22 27 47 54 78 18 112 18 145 39 180 0 30 21 9 45 32 75 28 109 56 145 21 180 0 35 19 43 42 52 72 16 107 16 143 55 180 0 40 18 4 39 49 68 36 104 13 142 16 180 0 45 16 10 36 13 64 14 100 37 140 22 180 0 50 13 52 31 47 58 47 96 11 138 4 180 0 55 11 1 26 6 51 37 90 30 135 13 180 0 60 7 16 18 12 41 8 82 36 131 28 180 0 65 2 4 5 48 21 8 70 10 126 15 180 0 66 ½ 0 0 0 0 0 0 64 22 124 11 180 0  Scholar. 
I perceive that the first line of numbers under the signs, against the cipher 0, doth represent the quantities of the Ascensions in the right sphere, and all the other lines do declare the special quantities of several ascensions 
A TABLE OF THE DIVERSITIES of Ascensions for the 6 southerlye signs, accounting the beginning of those Ascensions, from Aries first degree.  Degrees of latitude. Libra Scorpius. Sagittari. Capricor Aquarius Pisces   Deg. Mi. Deg. Min. Deg. Min. Deg. Min. Deg. Min. Deg. Min. 0 207 54 237 48 270 0 302 12 332 6 360 0 1 208 6 238 10 270 26 302 34 332 18 360 0 2 208 18 238 32 270 52 302 56 332 30 360 0 3 208 31 238 54 271 18 303 18 332 43 360 0 4 208 43 239 16 271 45 303 40 332 55 360 0 5 208 55 239 39 272 11 304 3●… 333 7 360 0 8 209 32 240 46 273 30 305 10 333 44 360 0 10 209 57 241 31 274 24 305 55 334 9 360 0 11 210 10 241 54 274 51 306 18 334 22 360 0 15 211 2 243 27 276 41 307 51 335 14 360 0 20 212 9 245 30 279 6 309 54 336 21 360 0 25 213 21 247 42 281 42 312 6 337 33 360 0 30 214 39 250 4 284 32 314 28 338 51 360 0 35 216 5 252 44 287 44 317 8 340 17 360 0 40 217 44 255 47 291 24 320 11 341 56 360 0 45 219 38 259 23 295 46 323 47 343 50 360 0 50 221 56 263 49 301 13 328 13 346 8 360 0 55 224 47 269 30 308 23 333 54 348 59 360 0 60 228 32 277 24 318 52 341 48 352 44 360 0 65 233 45 289 50 338 52 354 12 357 56 360 0 66 ½ 235 48 295 36 360 0 0 0 0 0 0 0 in each of those distinct latitudes, which be noted in the first column in both tables. Therfore now I may perceive according to the former rule, that the greatest numbre of any down right column is the highest numbre in the head of the same column, so that it may truly bee said( as appeareth in this first table) that in each obliqne sphere the ascensions of the arkes from Aries unto the and of Virgo, do abate still and wax less and less, in respect to their ascensions that they haue in the Right sphere.  Master. 

three signifiations of Ascension.  Thus you see, howe there may be accounted diuers forms of ascensions: first( as I said at the beginning of that definition) it may signify that degree certenlye of the equinoctial, which doth ascend with any sign or parte thereof: as for example. in the latitude of 50 degrees, the last degree of Aries hath for his ascension the 13 degree and 52 minute of the equinoctial, as by the first of these two tables it doth appear: and in the same table it appeareth, that the last degree of Taurus hath for his ascension in the same latitude the 31 degree and 47 minute of the equinoctial. And in the second signification, the ascension of Aries whole sign is that whole ark of 13 degrees and 52 minutes, and so the whole ark from the beginning of Aries, to the end of Taurus, hath for his ascension that whole ark of 31 degrees, and 47 minutes of the equinoctial. And in this signification doth John de sacro Bosco use the name of Ascension, and in this sense his rules be true: according to which sense I haue drawn to you certain tables: the first for the ascensions of the twelve signs in the right Sphere: the second, for the ascension of the signs in 52 degrees of latitude: the third and fourthe are these two tables last before, which for diuers latitudes do declare the quantities of the Ascensions of al arkes of whole signs accounted from the beginning of Aries. The thyrde signification of ascensions is the quantity of that ark of the equinoctial which ascendeth with any certain ark of the zodiac: as for example. that ark of the equinoctial that ascendeth with any sign severally taken, is called the ascension of that sign. So haue you for every sign certain several arkes of ascension assigned, and set forth here in diuers tables, according to diuers elevations of the Pole. And in this signification must it be understand, when it is said that any sign hath a Right ascension or an obliqne ascension, for if the ark of the equinoctial that riseth with that sign, bee greater then 30 degrees, 
A right ascension.  then hath that sign a right ascension: and if the ark of the equinoctial be lesser then 30 degrees, then is that ascension called an obliqne ascension: 
An obliqne ascension. A mean ascension.  but if the said ark of the equinoctial be just 30 degrees, then is it a mean or equal ascension.  Scholar. 
now do I better understand the use of these names then I did before: and also I perceive howe the names of greater and lesser portion are to be referred, not of each greater to each lesser, for so the ascension of Taurus might be accounted greater then the ascention of Aries, and lesser then the ascention of geminy, in all climates with out the Polare circled. And so one ascension might be both greater and lesser, and therefore both right and crooked which is an absurdity.  Master. 
Thus hath order taught you, that whereof you were in doubt and manifestly approved that that seemed very obscure. Now therfore return to your author again. And repeat his other rules as he doth teach them.  Scholar. 

The fifte rule.  His fifte rule is this: The arkes which follow Libra, unto the cande of Pisces, in an obliqne sphere, do increase their ascensions above the ascensions that they haue in the Right sphere in as much as the portion of the equinoctial is augmented. And the increase of those ascensions is agreeable in rate to the decrease of those other ascensions which succeed from Aries to Libra.  Master. 
This rule must be understand of ascensions in the second signification: and that may you try by the later of those two tables which I gave you last.  Scholar. 
It appeareth so in dead. for Libra increaseth from 207 degrees and 54 minutes, unto 235 degrees& 48 minutes. And scorpion from 237 degrees& 48 minutes, unto 295 degrees and 36 minutes. likwaies Sagittarius from 270 degrees unto 360 degrees. So doth it appear, that Libra doth increase between the equinoctial and the Polare circled, 27 degrees, and 54 minutes. And scorpion increaseth 57 degrees and 50 minutes. Also Sagittarius augmenteth by 90 degrees. And now contrary ways, Aries doth a bait from 27 degrees and 54 minutes to nothing. Taurus diminisheth from 57 degrees and 48 minutes unto nothing also. And geminy abateth from 90 to 0: so doth these three in decrease agree with the other in increase exactly.  Master. 
And so may you judge of the other three couples. And therefore saith your author, 
The sixte rule.  that hereby it is manifest, that two equal arkes lying one against the other, and in an obliqne sphere, haue their ascensions ioyntlye taken together equal with the Ascensions of the same arkes in a right Sphere, ioyntlye taken also: for although those arkes bee unequal together, yet as much as the one abateth on the one side, so much the other increaseth on the other side, and so both arkes in the right sphere are equal to both those arkes in any obliqne sphere.  Scholar. 
But I pray you, in what signification of ascension is that rule to be understand?  Master. 
In any of those two which be referred to arkes: for the first can haue no place here, because it signifeth the ascension of one point only, and not of any ark as the other two do, and as this rule doth import.  Scholar. 
Then may I prove by examples in both sorts of tables. And first to begin with those tables that account the whole arkes from the beginning of Aries, I find the ascension of Aries in the head of the table, that is in the right sphere, to be 27 degrees& 54 minutes,& the ascension of Libra( which is against it) 207 degrees& 54 minutes. which both joined together, make 235 degrees& 48 minutes. Now to prove the like in an obliqne Sphere, I take the latitude of 40 degrees. and there I finde for Aries his ascension is degrees and 4 minutes: and for Libra I finde in the second table 217 degrees and 44 minutes: which both being added together, do make 235 degrees and 48 minutes. that is precisely equal with the former ascensions in the right sphere. Also in the eletration of 60 degrees I try the like, where Aries hath 7 degrees and 16 minutes, and Libra hath 228 degrees and 32 minutes, which by addition amount to the same sum as before.  Master. 
Attempt the like in the other tables.  Scholar. 
I take the ark of Aries ascension as before 27 degrees and 54 minutes: and the ascension of Libra( accomptyng only the ark of it from his own beginning) in like sort 27 degrees and 54 minutes. so that both joined together, make 55 degrees and 48 minutes. Then in the latitude of 55 degrees, I finde for Aries 11 degrees and one mynute: and for Libra, 44 degrees and 47 minutes. and by addition I find that they make the same number as before.  Master. 
Make proof in some other ark.  Scholar. 
I take first the ark from the beginning of lo, to the end of the same sign, and find it to bee 29 degrees and 54 minutes in the right sphere: and so for the Ascension of the sign of Aquarius, being equal to it, and against it in the zodiac, I finde the like noumbre, which make by addition 59 degrees and 48 minutes. Then in the latitude of 30 degrees I try the like, and finde for lo 35 degrees and 25 minutes: and for Aquarius there doth rise 24 degrees and 23 minutes: which make also together the same sum of 59 degrees and 48 minutes. So in both those significations, whether I account several arkes from several beginnings, on general arks from one general beginning, the rule is found true. Now resteth but one rule more of ascensions in this author to be discussed, and that is this: 
The 7 rule  that in an obliqne sphere echez arkes of the zodiac being equal and equally distant from any one of the equinoctial points, shall haue equal ascensions.  Master. 
This rule is partly a agreeable with the last rule, and partly several, in as much as every contrary ark is like distant from the one equinoctial point, as the first ark is from the other equinoctial point. this rule doth agree( after a sort though not properly) with the other last before: but considering that Aries and Pisces as whole signs haue like arkes, and are equally dystaunt from one equinoctial point, though in back order: for the end of Aries is just equal in distance from the precise Equinoctioll point, as the beginning of Pisces is from the same. And in this point these signs haue this seventh rule as a special rule for them and their Ascensions. likeways Taurus compared with Aquarius, geminy with capricorn, Cancer with Sagittarius, lo with Scorpius, and Virgo with Libra, as this figure doth  diagram of the zodiac. show exactly, although in the same I haue marked also the contrary signs that it might be a common figure for both those rules, so that every several sign hath 2 matches, with which it may be conferred, one of them right against him. and that comparison is in the 6 rule: and the other less distant,& ther conference belongeth to this 7 rule.  Scholar. 
As this figure doth teach me what signs may be conferred together, so the tables before written do declare the quantities of their ascensions in those several latitudes: and the true meaning of both those rules, as well as of other, touching ascensions.  Master. 
But this must you farther know, that those rules do speak generally of any two arkes, whether they bee greater or lesser then a sign, and do not mean of signs only.  Scholar. 
That must needs follow orderly: for if Aries bee equal in ascension with Pisces, and Taurus equal in rising with Aquarius, then jointly Aries and Taurus must needs be of one quantity in ascension with Aquarius and Pisces, by composition of proportions, as is taught in geometry and arithmetic also.  Master. 
Lykewaise( by resolution of propositions) if al Aries be like in ascension with all Pisces, then the first degree of Aries shall ascend equally with the last degree of Pisces: and the 20 degree of Aries, with the 10 degree of Pisces:& in like manner of each other degree equally distant from the equinoctial points: and so likeways of every minute: for these rules of equality or inequality of Ascensions of arkes, do serve as well for the arkes of degrees and minutes, as for the arkes of whole signs, or of greater quantities. Also this rule is general, that all arkes that ascend rightly, do descend crookedly, be they great or small: and contrary ways, what ark so ever ascendeth crookedlye, doth descend right: whereby it cometh to pass, that always the one sign counteruailyng with his contrary, there is evermore one half of the zodiac above the Horizonte, as well as there is one half of the equinoctial above the same. so that when so ever any degree of the zodiac doth set in the west, the contrary degree doth rise in the east. Of this it followeth, that in the longeste day in the year there doth rise but syxe signs, and in the shortest day there riseth as many signs.  Scholar. 
Thereof it may seem to come to pass, that in ancient time the day and the night were evermore diuiuided into 12 equal parts,( how long or how short so ever they were) and those partes were called unequal hours, of which yet many men do writ, 
hours unequal.  and do call them hours of the Planets: but as I judge by the order of the ascensions, every sign hath not equal Ascension, nor equal time in rising,& therfore may those hours be well called unequal, which depend of the motion of the zodiac, being in itself unequal in his Ascension.  Master. 
It is thought of some men to be a more apt reason to call those hours unequal, because not only the summer hours are unequal to the winter hours, but also the day hours unequal to the night hours.  Scholar. 

natural hours.  John de sacro Bosco doth call them natural hours, and defineth them to be the measure of the time, in which half a sign doth ascend.  Master. 
As the 6 signs that rise in the day or in the night keep not one uniform equality in their rising, so doth the Ascensions of the half signs differ more vnequallye: and by that means the hours of the day can not be equal together, neither yet the hours of the night may be called equal together: wherefore other you must not allow that definition, or else you must not parte the day and the night into equal partes.  Scholar. 
I know not what to say to this, for neither can I defend that definition, neither yet can I improve that partition.  Master. 
Those hours haue been the occasion of much contention, and therfore were they wittilye rejected out of the daily use, wherein they were ones common, and were left only to learned men, 
equal houres called Equinoctial hours.  for learned uses, and in their stead other hours more certain and equal were divised, which do divide the natural day into 24 equal partes, and these keep one just quantity, how so ever the artificial day do vary his quantity.  Scholar. 
This I know well: but yet touching the first hours, called the Planet hours, I would gladly understand some example for their exact diversity in some one day.  Master. 
You shall haue anon one general table for many dayes, namely for every sixth day in the year nigh hand, and that table shall suffice for the whole year: and yt shall be calculate according to that exact form of distinction of hours, by half signs of the zodiac: but in the mean season, because you shall not be ignorant of the vulgar form of unequal hours, I haue here set forth an ordrelye partition of them, according to the length of every day or night in the year, by increase from 12 minutes to 12 minutes, for each day or night, from the shortest day, or night of 1. minute of length, unto the longest day or night of 24 hours.  Scholar. 
But what if the longest day be not so long, as it is not with us in england?  Master. 
The table doth serve for all places where the dayes be of shorter length: as by the overmost title and that first column on the left hand you may perceive.  Scholar. 
I was to negligent, that I did not consider that, for as it may serve for that day in the year which is but 16 hours long,( though the longest day bee longer) so may it serve for that place where the longest day is but 16 hours in quantity.  Master. 
Yea and for the middle of the earth under the Equinoctial, where the longest day is but 12 hours, so that it serveth from the equinoctial circled, unto the Polare circled, and for all Climates that be between them, as by the hours in the first column you may perceive. 
The use of the table.  So that if you will know the quantity of any hour unequal, or hour of the planets, after this form: first you must know the 
A TABLE FOR THE HOVRES OF planets after the common form.  Minutes. 0 12 24 36 48 Houres Hour. Minu. Hour. Minu. Hour. Minu. Hour. Minu. Hour. Minu. 0 0 0 0 1 0 2 0 3 0 4 1 0 5 0 6 0 7 0 8 0 9 2 0 10 0 11 0 12 0 13 0 14 3 0 15 0 16 0 17 0 18 0 19 4 0 20 0 21 0 22 0 23 0 24 5 0 25 0 26 0 27 0 28 0 29 6 0 30 0 31 0 32 0 33 0 34 7 0 35 0 36 0 37 0 38 0 39 8 0 40 0 41 0 42 0 43 0 44 9 0 45 0 46 0 47 0 48 0 49 10 0 50 0 51 0 52 0 53 0 54 11 0 55 0 56 0 57 0 58 0 59 12 1 0 1 1 1 2 1 3 1 4 13 1 5 1 6 1 7 1 8 1 9 14 1 10 1 11 1 12 1 13 1 14 15 1 15 1 16 1 17 1 18 1 19 16 1 20 1 21 1 22 1 23 1 24 17 1 25 1 26 1 27 1 28 1 29 18 1 30 1 31 1 32 1 33 1 34 19 1 35 1 36 1 37 1 38 1 39 20 1 40 1 41 1 42 1 43 1 44 21 1 45 1 46 1 47 1 48 1 49 22 1 50 1 51 1 52 1 53 1 54 23 1 55 1 56 1 57 1 58 1 59 24 2 0                 just quantity of the day artificial, from son rising to son setting, and thereby also the quantity of the night: then shall you seek the houres of their length in the first column, under the title of hours: and if the day or night haue any minutes above those even hours, you shall seek them in the highestrange of numbers, where they bee set from 12 to 12, and take that number of minutes that is next in quantity to your minutes in the day propounded: and in the common angle, against your hours and under your minutes, you shall finde the just quantity of the minutes that make an hour unequal, for that day or night: but that must you understand severally.  Scholar. 
I were to gross headded if I would make a doubt thereof. And because I will declare unto you how I understand the use of it, I will by an example or two make it appear. When the artificial day is 14 hours long, and 20 minutes, and the night then is 9 hours long and 40 minutes of necessity: I would know the just quantity of the hours unequal. first therefore, in the first colomne I seek out the number of the hours, which is 14, then in the highest range of numbers I seek the odd minutes, being 20, and because I finde no such number there, I take the next number which is 24, and by those 2 numbers in their common angle against 14 toward the right hand, directly under the 24 minutes, I finde 1, 12, whereby I understand, that each unequal hour is longer then the equal hour by 12 minutes that day. and for the night I finde against 9 and under the number of 36( which is next unto 40) the just quantity of each vnequalle hour of the same night, to bee 0, 48, that is but 48 minutes: and so is the unequal hour of the night lesser by twelve minutes, then is the equal hour. And so both those hours joined together, do make two hours, equal to two equinoctial or equal hours. for so much as the one is to little, the other is to great. again for an other trial, I take the artificial day to bee 8 hours and 36 minutes long, and therfore to know the quantity of an unequal hour, I seek against 8, and vndernethe 36, where I find 0, 43, which giveth me to understand that the unequal hour that day is only 43 minutes in quantity,& the night then being 15 hours long and 24 minutes, yieldeth his unequal hours of 1 hour and 17 minutes long: whereby it is seen also, that so much is supplied by the one hour as was wanting in the other. so that evermore one unequal hour of the day joined with an unequal hour of the night, will make two hours equal to two equinoctial hours.  Scholar. 

hours equal, equinoctial, vulgar and natural.  You mean those common hours which we use vulgarlye, which are called also of some men natural hours, taking that name of the natural day, which they divide into 24 equal partes,( though other men ascribe that name to unequal hours) and so of their common use ar they name vulgar, like as they are called equinoctial hours, because( as I haue learned) they depend of the revolution of the equinoctial: and therefore keep they one constant quantity, each being equal with other.  Master. 
You remember it well. And as these are taken of the motion of the equinoctial, and are nothing else but the space or measure of time wherein 15 degrees of the equinoctial do pass the meridiane line, 
unequal hours.  so again it seemeth to the wisest sort of men, that the unequal hours ought to bee gathered by the motion of the zodiac, whose several form of ascension for every half sign, doth make a several and distinct quantity of unequal hours, and haue no fewer sorts of differences, then there be distinct and several degrees or points, at which that ark of 15 degrees may begin his ascension, 
The declaration of the table.  as partly in this table following it doth appear: where you may see in the first column on the left hand, and in the last on the right hand, the degrees of the signs set: not every one severally, but only from 6 degrees to 6 degrees, which are so mennye as may seem to suffice for a convenient distinction of the several diversities in such hours, namely in that latitude of 52 degrees, for which it is calculate. And next unto those degrees in the second column, and in the last save one, are set the names of the 12 signs in their convenient order, that is to say, in the one parte the 6 signs which be called north signs, as Aries, Taurus, geminy, Cancer, lo, and Virgo: and in the other are set the 6 south signs, Libra, scorpion, Sagittarius, Capricornus, Aquarius,& Pisces. And against those signs and degrees ar set the quantities of every hour in the day for that time, when the son is in any such degree of those signs. And for the better knowledge of the hours, their names and numbers are set forth in the head of the table: where also is set a distinction by diversity of the day and night accordingly as the son is then in the south signs or in the north signs.  Scholar. 
I do perceive it to bee reasonable, that the first hour of the day must be accounted that hour, in whose beginning the son doth rise: so that every day the first hour is begun with the ascension of that degree of any sign wherein the son is. And the first hour of the night is begun with the ascension of that degree, which is opposite or contrary to the place of the son: which place is commonly called in latin Nadir Solis, although in deed the one word is an arabic word, and not latin. And after that first hour as the other hours of necessity do follow in order of number, so their distinction in quantity doth follow in this table: and the difference of them is agree able to the diversity of the ascension of each half sign of the zodiac, as they do follow in order. 
example.  So that to come to an example, for declaration that I do understand that table. yf I would know the quantity of the unequal hours, when the son is in Aries and in his first degree, I must entre the first parte of the table, where I finde on the left hand the signs and their degrees: wherefore against Aries and the cipher o, which betokeneth the very beginning of the sign, I note all the hours as they follow in order: whereby I perceive that the first hour of the day is but 25 minutes of an equal hour in length: the second hour 
A TABLE FOR THE DISTINCTION OF THE VNEQVALL hours, calculate for the latitude of 52 degrees.  
hours of the day, for the north signs: and of the night, for the south signs.  signs 1 2 3 4 5 6 7 8 9 10 11 12 Hours 1 2 3 4 5 6 7 8 9 10. 11 12   H. M. H. M. H. M. H. M. H. M. H. M. H. M. H. M. H. M. H. M. H. M. H. M. 0 ♈ 0 25 0 27 0 30 0 37 0 47 0 59 1 11 1 20 1 25 1 26 1 27 1 25 6 0 25 0 28 0 33 0 41 0 52 1 4 1 16 1 23 1 26 1 27 1 26 1 26 12   0 26 0 30 0 36 0 45 0 57 1 9 1 19 1 24 1 26 1 26 1 26 1 26 18 0 27 0 32 0 39 0 49 1 2 1 13 1 22 1 26 1 27 1 26 1 26 1 26 24 ♉ 0 29 0 34 0 43 0 54 1 7 1 17 1 24 1 26 1 26 1 26 1 26 1 26 30 0 30 0 37 0 47 0 59 1 12 1 20 1 25 1 26 1 27 1 25 1 26 1 26 6   0 33 0 41 0 52 1 4 1 16 1 23 1 26 1 27 1 26 1 26 1 26 1 26 12 0 36 0 45 0 57 1 9 1 19 1 24 1 26 1 26 1 26 1 26 1 26 1 27 18   0 39 0 49 1 2 1 13 1 22 1 26 1 27 1 26 1 26 1 26 1 26 1 26 24 0 43 0 54 1 7 1 17 1 24 1 26 1 26 1 26 1 26 1 26 1 27 1 26 0 ♊ 0 47 0 59 1 11 1 20 1 25 1 26 1 27 1 25 1 26 1 26 1 26 1 29 6 0 52 1 4 1 16 1 23 1 26 1 27 1 26 1 26 1 26 1 26 1 26 1 24 12   0 57 1 9 1 19 1 24 1 26 1 26 1 26 1 26 1 26 1 27 1 26 1 22 18 1 2 1 13 1 22 1 26 1 27 1 26 1 26 1 26 1 26 1 26 1 24 1 19 24 ♋ 1 7 1 17 1 24 1 26 1 26 1 26 1 26 1 26 1 27 1 26 1 27 1 15 30 1 11 1 20 1 25 1 26 1 27 1 25 1 26 1 26 1 26 1 25 1 21 1 19 6   1 16 1 23 1 26 1 27 1 26 1 26 1 26 1 26 1 26 1 24 1 17 1 7 12 1 19 1 24 1 26 1 26 1 26 1 26 1 26 1 27 1 16 1 22 1 13 1 2 18   1 22 1 26 1 27 1 26 1 26 1 26 1 26 1 26 1 24 1 19 1 9 0 57 24 1 24 1 26 1 26 1 26 1 26 1 26 1 27 1 26 1 27 1 15 1 4 0 52 0 ♌ 1 25 1 26 1 27 1 25 1 26 1 26 1 26 1 25 1 21 1 11 0 59 0 47 6 1 26 1 27 1 26 1 26 1 26 1 26 1 26 1 24 1 17 1 7 0 54 0 47 12   1 26 1 26 1 26 1 26 1 26 1 27 1 26 1 22 1 13 1 2 0 49 0 39 18 1 27 1 26 1 26 1 26 1 26 1 26 1 24 1 19 1 9 0 57 0 45 0 36 24 ♍ 1 26 1 26 1 26 1 26 1 27 1 26 1 27 1 15 1 4 0 52 0 42 0 33 0 1 27 1 25 1 26 1 26 1 26 1 25 1 21 1 11 0 59 0 47 0 37 0 30 6   1 26 1 26 1 26 1 26 1 26 1 24 1 17 1 7 0 54 0 47 0 34 0 33 12 1 26 1 26 1 26 1 27 1 26 1 22 1 13 1 2 0 49 0 39 0 32 0 27 18   1 26 1 26 1 26 1 26 1 24 1 19 1 9 0 57 0 45 0 36 0 34 0 26 24 1 26 1 26 1 27 1 26 1 27 1 15 1 4 0 52 0 41 0 33 0 28 0 25 30   1 26 1 26 1 26 1 25 1 21 1 22 1 59 0 47 0 37 0 30 0 27 0 25     H. M. H. M. H. M. H. M. H. M. H. M. H. M. H. M. H. M. H. M. H. M. H. M.  

hours of the night, for the north signs: and of the day, for the scuthe signs.  7 8 9 10 11 12 signs 1 2 3 4 5 6 1 2 3 4 5 6 7 8 9 10. 11 12 Houres H. M. H. M. H. M. H. M. H. M. H. M. H. M. H. M. H. M. H. M. H. M. H. M.   1 26 1 26 1 26 1 25 1 21 1 11 0 59 0 47 0 37 0 30 0 27 0 25 ♎ 0 1 26 1 26 1 26 1 24 1 17 1 7 0 54 0 47 0 34 0 33 0 26 0 24 6 1 26 1 27 1 26 1 22 1 13 1 2 0 49 0 39 0 32 0 27 0 25 0 25   12 1 26 1 26 1 24 1 19 1 9 0 57 0 45 0 36 0 34 0 26 0 25 0 25 18 1 27 1 26 1 27 1 15 1 4 0 52 0 41 0 33 0 28 0 25 0 24 0 26 ♏ 24 1 26 1 25 1 21 1 11 0 59 0 47 0 37 0 30 0 27 0 25 0 25 0 27 0 1 26 1 24 1 17 1 7 0 54 0 47 0 34 0 33 0 26 0 24 0 25 0 28   6 1 26 1 22 1 13 1 2 0 49 0 39 0 32 0 27 0 25 0 25 0 26 0 30 12 1 24 1 19 1 9 0 57 0 45 0 36 0 34 0 26 0 25 0 25 0 27 0 32   18 1 27 1 15 1 4 0 52 0 41 0 33 0 28 0 25 0 24 0 26 0 29 0 34 24 1 21 1 11 0 59 0 47 0 37 0 30 0 27 0 25 0 25 0 27 0 30 0 37 ♐ 0 1 17 1 7 0 54 0 47 0 34 0 33 0 26 0 24 0 25 0 28 0 33 0 41 6 1 13 1 2 0 49 0 39 0 32 0 27 0 25 0 25 0 26 0 30 0 36 0 45   12 1 9 0 57 0 45 0 36 0 34 0 26 0 25 0 25 0 27 0 32 0 39 0 49 18 1 4 0 52 0 41 0 33 0 28 0 25 0 24 0 26 0 29 0 34 0 43 0 54 ♑ 4 0 59 0 47 0 37 0 30 0 27 0 25 0 25 0 27 0 30 0 37 0 47 0 59 0 0 54 0 47 0 34 0 33 0 26 0 24 0 25 0 28 0 33 0 41 0 52 1 4   6 0 49 0 39 0 32 0 27 0 25 0 25 0 26 0 30 0 36 0 45 0 57 1 9 12 0 45 0 36 0 34 0 26 0 25 0 25 0 27 0 32 0 39 0 49 1 2 1 13   18 0 41 0 33 0 28 0 25 0 24 0 26 0 29 0 34 0 43 0 54 1 7 1 17 24 0 37 0 30 0 27 0 25 0 25 0 27 0 30 0 37 0 47 0 59 1 11 1 20 ♒ 0 0 34 0 33 0 26 0 24 0 25 0 28 0 33 0 41 0 52 1 4 1 16 1 23 6 0 32 0 27 0 25 0 25 0 26 0 30 0 36 0 45 0 57 1 9 1 19 1 24   12 0 34 0 26 0 25 0 25 0 27 0 32 0 39 0 49 1 2 1 13 1 22 1 26 18 0 28 0 25 0 24 0 26 0 29 0 34 0 43 0 54 1 7 1 17 1 24 1 26 ♓ 24 0 27 0 26 0 25 0 27 0 30 0 37 0 47 0 59 1 11 1 20 1 25 1 26 0 0 26 0 24 0 25 0 28 0 33 0 41 0 52 1 4 1 16 1 23 1 26 1 27   6 0 25 0 25 0 26 0 30 0 36 0 45 0 57 1 9 1 19 1 24 1 26 1 26 12 0 25 0 25 0 27 0 32 0 39 0 49 1 2 1 13 1 22 1 26 1 27 1 26   18 0 24 0 26 0 29 0 34 0 43 0 54 1 7 1 17 1 24 1 26 1 26 1 26 24 0 25 0 27 0 30 0 37 0 47 0 59 1 11 1 20 1 25 1 26 1 27 1 25   30 H. M. H. M. H. M. H. M. H. M. H. M. H. M. H. M. H. M. H. M. H. M. H. M.   is 27 minutes long: the third hour 30 minutes, that is half an equal hour just: and in the same line going forward, the 12 and last hour of the day is 1 hour and 25 minutes in length. Then for the night the hours appear in the other parte of the table, where the first hour doth contain one equal or common hour, and 26 minutes: the second hour and the third be of like quantity, and so do they afterward decrease until the last hour of the night. An other example: 
example.  when the son is in the 10 degree of Cancer, because I can not finde that degree in the table, I take the degree next unto it, which is the 12 degree, and proceeding with it, I finde the first unequal hour to contain 1. equal hour, and 19 minutes: and the second unequal hour hath in it 1. equal hour and 24 minutes. now for the night I look in the second parte of the table, and finde the first unequal hour to bee but 49 minutes in length, and the second but 39 minutes. and so in order following. This must I do when the son is in any of the north signs, but if the son be in any of the south signs, thē must we account the day hours in the second part of the table,& the hours of the night must be sought in the first parte of the table: in all other points I perceive there is small difference.  Master. 

an order for proportion.  Yet by the way this may you note, that if you would desire more precisely to know the just quantity of the hours, for any such degree of the signs as is not expressed in your table, you shall work by the rule of proportion, to know the more exact quantity of the unequal hours. as for example: In the former work where you supposed the son to be in the 10 degree of Cancer, because that degree is not found in the table, you must work by proportion to know it,& that in this form: first consider the hours against the next numbre of degrees, as well beneath your degree as also above the same,& mark the difference between them two, which difference shall always be the second number in the Golden rule: and the first noumbre of that work shall always be 6 degrees, because that is the ordinary excess in this table of each two numbers next together: Now for the third number, you shall set the excess of your degrees proponed, above the lesser degrees in that table, next beneath your said number, which in this example is 4, for so much is between 6& 10. And the difference in hours in the table is but 3 minutes: for against the 6 degree of Cancer, ther is but one hour and 16 minutes: and against the 12 degree is set one hour and 19 minutes. Therefore thus do I set those numbers according to the golden rule, saying: If 6 degrees give three minutes, then 4 degrees must yield two minutes. those two must bee added to the lesser number, and so doth there rise one hour and 18 minutes for the exact quantity of the first unequal hour, the son beeynge in the tenth degree of Cancer.  Scholar. 
I pray you let me prove the same for the second hour of the night, where against the 6 degree I find o hour and 47 minutes: and against the 12 degree I see o hour, and 39 minutes, here the excess is 8 minutes: then set I the figures thus in the golden rule, and say: If 6 yield 8, then shall 4 give 5 l⅓: if I add these unto the lesser number of time, which is 39 minutes,  Master. 
You are to far deceived, and therefore I interrupt your words, for all things are to bee governed by reason. So that if the hours do increase in quantity, then is it reasonable to add the parte proportionable to the lesser number of time, as it was in the former example: but in this example you see the time doth not increase, but decrease,( seeing the time against 6 degrees is greater then the time against 12 degrees) and therefore by good reason the parte proportionable is to be abated from the greater, and not to be added to the lesser.  Schol. 
So is it reasonable: therfore must I take that 5 l⅓ from 47,& then resteth 41 2/ 3, which is the precise quantity of that unequal hour. And now I thank you, I am fully instructed touching that matter: so that for any unequal hour according to the place of the son in this latter table, and after the length of the day in the first table, I can finde out the quantity of each vnequalle hour: but these two forms do not make exactly one quantity of hours unequal.  Master. 
As in that you shall haue more exacter declaration hereafter. And for this present time I will say no more but that each of both ways hath good uses. And the first form which seemeth most plain and least artificial, hath comprobation of many men, and namely of Ptolemye in the ninth chapter of his second book of Almagestes. but omitting for a time that that remaineth touching hours, I will now speak somewhat of the quantities of daies, in which matter you shall call to mind, 
Daies artificial and natural.  that the natural day is not one with the artificial day: for the first is commonly accounted from son rising one day, to son rising the next day. but the second, that is the artificial day, is reckoned only from son rising, to son setting: so that there is no night accounted in the artificial day, as there is in the natural day.  Scholar. 
This I perceive well enough: and farther also, that the natural daies are ever 24 hours long, in all our known countries, but the artificial daies do increase and de crease diuerfely. And as I desire to know the causes therof, so I do marvel how it cometh to pass, that in any country or climat the natural daies should differ.  Master. 
To the intent that we may proceed orderly, we will begin with the one fort of daies, and so come to the talk of the other. And first as concerning natural dayes, I said that they were commonly accounted from son rising to son setting: which description being true, what shal we say of those north and south countries, where the son continueth above the horizon in some places three weekes, in other 6 weeks, and so increasing till it extend to half a year. in al which places if we call the natural day the space from son rising to son rising again, then can not the natural day be of one quantity to all nations, and so should those daies natural differ in nature, which were against nature utter lie: and therefore did I use that word commonly in the former description: but if I shall define the natural day exactly, I must call it that just time in which the eight Sphere or firmament doth exactly accomplish his course, 
The natural day.  which time of natural day is the common meafure of all other times: and this time is always equal in all places, howe be it according to the former description, yf the returning of the son bee accounted from any one parte of the Meridiane line, to the same parte of the said line, then may that description well extend to all partes of the world: for although some nations haue the son in sight half a year together, yet doth the son return to their meridiane line toward the south, at the and of 24 hours within a little, and in all places likeways where the day it not full 24 hours, the son doth return to their horizon, at the and of 24 hours nigh hand.  Scholar. 
I hear you speak in both these declarations, with a doubtful limitation of the 24 hours, as though that time were not the precise or just measure of the natural day.  Master. 
So shall it appear unto you, yf you consider that the son doth every day run one degree almost toward the east, according to the succession of the signs, as before is mentioned: for if this day the son be in the first degree of Libra justly at noon, then to morrow at noon he will bee in the second degree: and so the third day hence in the third degree: and by the same reason at the months end, will the son haue passed Libra clearly, and bee in the beginning of the next sign, which is Scorpius: and therefore must he be slacker in coming to the Meridian line, by so much time as serveth for the rising of all the sign of Libra in a right sphere.  Scholar. 
That time must be an hour and 52 minutes. for( as I remember) the partes of the equinoctial which do serve for the ascension of Libra, are 27 degrees and 54 minutes.  Master. 
As that is true, so mark what is the difference now for every day of that month, 
The first cause of diversity in natural dayes.  and then shall you perceive the difference of the natural dayes, as much as dependeth of that cause.  Scholar. 
For the first degree of Libra, the quantity of his ascention is 55 minutes of the equinoctial, which maketh in time of an hour 3 minutes and ⅔, and so may I see for diuers degrees at the beginning of Libra, by the table of the astensions in the Right sphere: but toward the end of the same sign, I see 57 minutes agreeyng to the ascension of one degree, which maketh some difference in time also, though it bee small.  Master. 
mark now about the middle of Scorpius, how each degree of the zodiac hath one degree of the equinoctial agreeynge to his ascension, which maketh in time 4 minutes of an hour: and about the middle of Sagittarius one degree of the zodiac hath answerable to him 64 or 65 minutes of the equinoctial. and so in other diuers degrees of signs shall you find diuers quantities of their ascensions, whereby it must needs appear, that if the son did move forward in the zodiac every day one degree justly, that the son should be 4 minutes after the 24 hours slacker then he was the day before in touching the meridiane line, if there were not an other cause of diversity by the sundry quantities of the ascensions.  Scholar. 
This cause is manifest. And because I see for some degrees of the zodiac but only 55 minutes of the equinoctial, which maketh in time 3 minutes and ⅔: and for other degrees 65 minutes, which is 4 minutes and 1/ 3;: so doth it appear that the greatest difference is but 2/ 3 partes of a minute: which is a small matter.  Master. 
Yet this small matter will cause much matter in astronomical computations, though there were no more difference of diversity in natural dayes but this only: but yet are there two other causes in all obliqne spheres, and but one in the Right sphere. The second common cause in both spheres, is the eccentricitye of the son. 
The second cause of vn equal daies natural.   Scholar. 
What mean you thereby? for I do not understand that eccentricitye.  Master. 
It is a matter not agreeable for this treatise, but that by occasion I am moved to name it as a concurrente cause touching inequalitye of natural dayes: yet somewhat to say of it as may suffice for this present, by example you shall understand both what eccentricitye is, and also howe it may cause diversity in natural dayes: for declaration  Geometric diagram. whereof here in this figure you see two circles a greater and a lesser: the greater doth betoken the eight sphere or firmament, and the lesser doth represent the eccentrike circled of the sphere of the son.  
These 2 circles as you see, are eccentrike, for that they haue not one common centre, sith the centre of the greater circled is by A, and the centre of the lesser circled is by B. the distance between A and B is the quantity of their eccentricitye. now may you see that each circled is divided into 4 quarters: and likewise you may se, that the higher half of the lesser circled doth not fully answer to half the greater circled: and again the nether half of the lesser circled doth occupy more then the half of the greater circled. whereby it must needs bee evident to all men, that when the son moveth in the higher part of his eccentrike circled, he doth move slowlyer then he doth in the nether parte of the same eccentrike: I mean in comparison to the zodiac of the eight sphere: and thereby must it appear that the son doth not every day move like number of minutes in the zodiac: and you may easily conjecture hereby, that this is an other cause of diversity in the quantity of the natural dayes. 
The third cause of diversity of daies natural.  A thyrde diversity is that which is peculiar to every several climate, and not common to any two on one side of the equinoctial, and that is the obliquity of the Horizonte, yf the day shall bee accounted from son rising to son rising again: but this variety is so great and so diuers, that it is in manner infinite: and therfore do Astronomers reject the order of account of daies, and reckon the day from noon to none, which account serveth generally for all the partes of the world, as if all Climates had one horizon: for as in the right sphere both the Poles do touch the horizon, so the meridianes of every climate and of all regions do pass by both the Poles of the world: and therefore all ascensions accounted unto that meridiane line, must bee esteemed as right ascensions, I mean ascensions like unto them that be in the right sphere.  Scholar. 
now do I perceive, that although there may be assigned three causes of variety in the natural dayes, yet one of them which is gathered by the obliquity of the horizonte in not regarded of Astronomers, sith they do account the beginning of the day from the noon steede, and the son being in the meridiane line. The second cause by the eccentricitie of the son I may conjecture to appertain to a more higher speculation, then this treatise doth admit: but yet may be somewhat understand even now by a small explication. The third cause which dependeth of the diversity of the ascensions by obliquitye of the Horizonte, is peculiar to this treatise, and may be gathered out of the tables of ascensions which serve for the right sphere: of all which varieties at a time of more convenient leisure, I will make for mine exercise a table at large. but in the mean season I pray you, proceed as you haue begun.  Master. 
Touching the diversities of natural dayes this may suffice: and for a common and mean quantity you may assign 24 hours and 4 minutes, because that is the common nombre: for although many be greater, yet many other bee lesser. and this number is most nighest the mean. 
The diversity of the artificial daies.  now touching artificial daies you shall finde no fewer diversities: wherein although all the former three causes be concurrent, yet the principal cause is the obliquity of the horizon. And although I haue twice before made mention of those daies, yet doth there rest more to be said of them. for in both places before I did briefly touch the causes of diversity of such Artificialle daies in diuers climates, and in the table of the distinction of climates, I did set forth the quantity of the longest day in each of them: and now will I show you somewhat of the reason of their inequality in any one climate. first therfore to begin withal, you know that before the son in his natural course can pass the full of one degree, he is carried by the violence of the Starrye sky round about the earth. so that in going between the first degree of capricorn, and the first of Cancer, he doth consume half a year, and therefore maketh above is 2 revolutions like spirall circles, which are diuerslye partend by the horizon, according to the diversities of the elevation of the Pole. As in the right sphere they are all partend by the horizon into two equal partes: so in every bowing Sphere, they are unequally divided by the horizon, so that where the north pole is elevate above the horizon, there those circles of the sons revolutions which be from the equinoctial northward, haue the greater portion above the horizon, and the lesser parte under the same: and contrary ways those circles( or spires if you like better so to call them) which be from the equinoctial to the tropic of capricorn, and serve for explication of the sons motion, they haue their greater portion under the horizon, and the lesser portion above the same. And comparing each one of these to other, that circled which is farthest toward the south, is most parte under the horizon of any other. and every one of them the more it departeth from the south and draweth toward the north, the greater is his portion that is above the horizonte, and the lesser is that other portion which is under the same. wherefore the middlemost bound of those two extremes, is just half under, and half above the Horizonte: and therfore the son being in it, doth make his abode just like time above the earth, as he doth under it, and thereby the daies and nights are equal: but from thence toward Cancer, the day doth still increase above the night: and from thence toward capricorn, the day doth still abate shorter then the night: which thing will easily appear to the sight, both by these  Geometric diagram. figures here drawn, and also by the diuers positions of the material Sphere or globe. And still the higher that the Pole is elevate above the horizon, the greater parte of the northerly circles is above the horizon, and the lesser parte of them under the Horizonte. And contrary ways of the southerlye circles, the greater portions of them are under the horizon, and the lesser portions above it. now is it easily perceived, that seeing the son doth keep his daily course in one of those circles, then accorginglye as that circled in which the son doth move, is partend by the horizonte, so is the partition of the 24 hours into day and night agreeablye: so that if the circled of the sons course be more under the horizon then above it, then shall the night be longer then the day: and if the greater parte of the sons circled be above the horizon, then the day shal exceed the night, in like proportion as the partes of the circles are in comparison together.  Scholar. 
These diuers circles( I perceive) are not in the sphere of the son, but are accounted in the eight sphere between the two tropics, so that every day by the revolution of the Firmament, the son is carried from east to west round about the earth, and by this violent motion doth describe a spirall circled( as you call it) and not an exact circled: but yet may it serve in this case, as if it were a just circled: the difference is so little of the space between the spirall lines in comparison to their compass, which by the table of declination before expressed, I guess to bee in proportion scarce 1/ 1000, which is no part notable in this case. And this farther I note: that two circles on contrary partes of the equinoctial equally distant from it, are partend by the horizon after one rate, and into like portions: but yet in such difference, that the parte of the one circled above ground, is equal to the parte of the other that is under ground: and so contrary ways. whereby it followeth, that the day of the one is equal to the night of the other, and so contrary ways also. Again seeing that the son doth descend from Cancer unto capricorn, by the same circles of revolution, by which he did ascend from capricorn unto Cancer, it must needs follow that every two dayes in the year equally distant from the longest day, or from the shortest, are equal in their artificial day, and in their night. These general things I may easily gather: but howe I may know justly the quantity of every artificial day from other, and the precise time of the son rising and setting, I can not so easily gather. wherefore if it please you in those two points I desire your instruction.  Master. 
although for this treatise the aptest form be by the use of the sphere and the due placing of it, yet it is hard to place the sphere so well, and to use it so aptly, that it might declare a just preciseness. and therfore after that I haue taught you the use of the Sphere for that point, I will also by supputation give you a table sufficient to declare both unto you for all partes under our parallel, and somewhat more. first for the use of the globe, you must set it according to the latitude of the Region that you desire to know the daies in, and then mark the degree of any sign that the son is in that day, whose quantity you desire to know: set that degree just in the horizonte toward the east, and mark what degree of the equinoctial is in the horizonte at the same time: then turn the sphere westward till the degree of the son be just in the Horizonte again in the west parte, and mark then what degree of the equinoctial doth light on the horizon in the east parte, accounting truly howe many degrees bee betwixt those two degrees which you haue marked, and that ark of the equinoctial, is called the ark of that day: which you may easily turn into hours, accounting is degrees to an hour, and for every degree less then 15 accounting 4 minutes of an hour.  Scholar. 
This were easy enough to do, if I use the help of the table that I see in some books, which teacheth easily howe to turn degrees of the equinoctial into partes of time, as here in Orontius work it is set forth. but I did abbrydge it for myself as here appeareth: and because the table was not extended above 60 degrees by Orontius, 
A TABLE FOR CONVERTINGE degrees of the equinoctial into partes of time.  The ark of the Equino. Partes of time. Degree Houres minutes. 1 0 4 2 0 8 3 0 12 4 0 16 5 0 20 6 0 24 7 0 28 8 0 32 9 0 36 10 0 40 11 0 44 12 0 48 13 0 52 14 0 56 15 1 0 20 1 20 25 1 40 30 2 0 35 2 20 40 2 40 45 3 0 50 3 20 55 3 40 60 4 0 65 4 20 70 4 40 30 2 0 35 2 20 40 2 40 45 3 0 50 3 20 55 3 40 60 4 0 65 4 20 70 4 40 75 5 0 80 5. 20 85 5 40 90 6 0 95 6 20 100 6 40 105 7 0 110 7 20 115 7 40 120 8 0 125 8 20 130 8 40 135 9 0 140 9 20 145 9 40 150 10 0 155 10 20 160 10 40 165 11 0 170 11 20 175 11 40 180 12 0 185 12 20 190 12 40 195 13 0 200 13 20 205 13 40 210 14 0 215 14 20 220 14 40 225 15 0 230 15 20 235 15 40 240 16 0 245 16 20 250 16 40 255 17 0 260 17 20 265 17 40 270 18 0 275 18 20 280 18 40 285 19 0 290 19 20 295 19 40 300 20 0 305 20 20 315 21 40 330 22 0 340 22 40 350 23 20 360 24 0 I did for mine own ease make out the rest in this for me.  Mast. 
This is a table of to much ease, and therfore doth rather teach negligence, then any thing else. for him that listeth to exercise his wit in readiness of account, it is an easy matter to turn degrees into hours without any tables, and therefore such tables might well bespared,& yet many books are full of them: but if you listed, you might haue abridged it more from 15 upward, taking only even 15 still. as thus. 15, 30, 45, 60, 75, &c. so seemeth all the rest superfluous, except your number of degrees in the day ark, happen just agreeable with some one of those in the table: but now to procede, give one example for declaration of your understanding herein.  Scholar. 
Then to begin I set the globe to the elevation of 52 degrees, 
example.  and considre the place of the son the 14 day of august, and finde it to be by the Ephemerides, in the first beginning of Virgo, therefore do I set the beginning of Virgo in the very horizon, and then do I see with it the 137 degree of the equinoctial in the same horizon, which I do mark: afterward I turn the sphere till the place of the son be in the horizon on the west part, and then in the east parte I mark the degree of the equinoctial, which is 347 degrees. now abatinge 137 out of 347, there resteth the whole day ark, which is 210 degrees, which make 14 hours, as by the former table is easily seen. wherefore I conclude that the 14 day of August, the son shineth 14 hours, and then must the night be but even 10 hours, sith both times make just 24 hours: but yet I see not howe to know the hours of the son rising, and setting.  Master. 
I am sure you think that the noon is the middle of the day, and that the son shineth like space before noon and after noon.  Scholar. 
That is most certain.  Master. 
Then partinge the whole time of the son shining, or of the artificial day into 2 equal parts, the one half doth limit the hour after none at which the son doth set.  Scholar. 
That is in this example 7, and so must it needs be. And now I see by the same reason, the son must rise 7 hours before noon, that is at 5 of the clock in the morning.  Master. 
So is it. And for that end that you may haue a general rule therein, evermore abate half the quantity of the day from 12 hours, and then will the remainder declare the just hour and minute of the son rising.  Scholar. 
Then by your favour I will prove ones again: 
example.  wherefore I take the 16 day of January, the son being in the 3 degree of lo, which degree I set in the east parte of the horizonte, and then doth there appear in the same Horizonte the 98 and almost 1/ 3 degree of the equinoctial: then turning the degree of the son to the west part of the horizonte, I finde in the east parte the 332 and 1/ 3 almost of the equinoctial: then subtrayinge the lesser from the greater, there resteth 234: which I turn into partes of time, and it doth yield 15 hours and 36 minutes. which is the just length of that artificial day. and of it the one half is 7 hours and 48 minutes: whereby I know that at 48 minutes, after 7 of the clock at night, the son setteth on that 16 day of july: and then abating so much from 12, there resteth 4 hours and 12 minutes: so that the son rising appeareth to be twelve minutes after 4. of the clock in the morning. And now I think myself cunning enough in all this matter.  Master. 
Yet for more ease: after that you haue noted the degree of the equinoctial that doth rise with the place of the son, you may mark the degree that riseth with the contrary point against the son: and abate then the first out of the second, and so accomplish your work, as you did before. for it is all one thing, but that you need not to look in contrary sides of your sphere for your work. And this shall you note farther: that if the first ascension of the place of the son be greater then the second ascension of the Nadir of the son, you shal put to the second ascension, 360 degrees, 
A cautel. & then abate as you are taught before. As for example: the first day of February the son is by the Ephemerides in the 22 degree 
example.  of February the son is by the Ephemerides in the 22 degree 
example.  of Aquarius, that degree I find in the zodiac of my spher, and I set it just in the east parte of the Horizonte, and ther may I se that the 343⅓ degree of the equinoctial doth ascend at the same instant in the horizon also: which I must account for the true ascention of that degree of Aquarius. Then turn I to the 22 degree of lo, being the Nadir of the son, and with it when it is set in the Horizonte, I mark the 125⅓ degree of the equinoctial to ascend. now when I would subtracte 343⅓ out of 125⅓, it will not be: and therfore I put unto the lesser number 360, and so it amounteth to 485¾, and then from it I abate 343⅓, and there remaineth 142 5/ 12: which if you change into partes of time, do make 9 hours and 30 minutes: and that is the quantity of the first day of february.  Scholar. 
The half of that is 4 hours, and 45 minutes, whereby I know, that at the 45 minute that is ¾ of an hour after 4 of the clock the son setteth: and riseth in the morning 15 minutes, that is ¼ of an hour after 7 of the clock. But why do you add those 360 degrees?  Master. 
seeing wee intend to abate the first ascension out of the second, to thintente that their distance may bee known, seeing the whole compass of the circled is but 360, from which if you abate the first ascension being the greatest number, then will there remain the distance between that ascention& the end of the equinoctial: unto which difference you must add so many degrees as the second ascention requireth, as both reason& practise will declare unto any man.  Scholar. 
It is reasonable. Therfore now it may please you to declare the same work by exactness of tables.  Master. 

The declaration of the tables.  because you shall not be driven to seek in the Ephemerides for the place of the Son, but that one table may serve for it, as well as for the quantities of daies and other conclusions clusions also, I will make the tables common for sundry uses, whose partes I will first declare, and after that will express the uses of them also.  

THE TABLES OF QUANTITIES of dayes artificial, and nights, for all england.  signs for the day. elevation of the Pole, or latitudes of Regions. signs for the night. daies of moneths degrees of signs. daies of moneths degrees of signs. 51 52 53 54 55 degrees of signs. daies of moneths degrees of signs. daies of moneths.   10 ♈ 0   13 ♍ 30 12 0 12 0 12 0 12 0 12 0 0 ♎ 13   30   10     11   1   12   29 12 4 12 4 12 4 12 4 12 4 1   14   29   9     12   2   11   28 12 8 12 8 12 8 12 9 12 9 2   15   28   8   march. 13   3   10   27 12 12 12 12 12 12 12 14 12 14 3   16 september. 27   7     14   4   9   26 12 16 12 16 12 16 12 18 12 18 4   17   26   6     15   5   8   25 12 20 12 20 12 21 12 22 12 23 5   18   25   5     16   6   7   24 12 24 12 24 12 26 12 26 12 28 6   19   24   4     17   7   6   23 12 28 12 28 12 30 12 30 12 32 7   20   23   3     18   8   5   22 12 32 12 32 12 34 12 35 12 36 8   21   22   2 march.   19   9   4   21 12 36 12 36 12 38 12 40 12 40 9   22   21   1     20   10   3   20 12 40 12 40 12 42 12 44 12 44 10   23   20   29     21   11 september. 2   19 12 44 12 44 12 46 12 48 12 49 11   24   19   28     22   12   1   18 12 48 12 48 12 50 12 52 12 54 12   25   18   27     23   13   31   17 12 52 12 54 12 54 12 56 12 58 13   26   17   26     24   14   30   16 12 54 12 58 12 59 13 1 13 3 14   27   16   35     25   15   29   15 12 58 12 2 13 4 13 6 13 8 15   28   15   24     26   16   28   14 13 2 13 6 13 8 13 10 13 12 16   29   14   23     27   17   26   13 13 6 13 10 13 12 13 14 13 17 17   30   13   22     28   18   25   12 13 10 13 14 13 16 13 18 13 22 18   1 OCTOBRE. 12   21     29   19   24   11 13 14 13 18 13 20 13 22 13 26 19   2   11   20     31   21   22   9 13 22 13 26 13 28 13 32 13 36 21   4   9   18     1   22   21   8 13 26 13 30 13 32 13 36 13 40 22   5   8   17     2   23   20   7 13 30 13 34 13 36 13 40 13 44 23   6   7   16   APRIEL. 3   24   19   6 13 34 13 38 13 40 13 44 13 48 24   7   6   15     4   25 august. 18   5 13 38 13 42 13 44 13 48 13 52 25   8   5   14     5   26   17   4 13 42 13 46 13 49 13 53 13 57 26   9   4   13 FEBRVARYE.   6   27   16   3 13 46 13 50 13 54 13 58 14 2 27   10   3   12     7   28   15   2 13 50 13 52 13 58 14 2 14 6 28   11   2   11     9   29   14   1 13 52 13 56 14 2 14 6 14 11 29   12   1 ♓ 10     10   30   13   0 13 56 14 0 14 6 14 10 14 16 30   13   0   9                   H. M. H. M. H. M. H. M. H. M.                  

The second parte of the table.  signs for the day. elevation of the Pole, or Latitude of Regions. signs for the night daies of moneths degrees of signs. daies of moneths degrees of signs. 51 52 53 54 55 degr. of signs daies of moneths degr. of signs. dayes of moneths APRIEL. 10 ♉ 0   13   30 13 56 14 0 14 6 14 10 14 16 0 ♏ 13   30   9     11   1   12   29 14 0 14 4 14 10 14 14 14 20 1   14   29   8     12   2   11   28 14 4 14 8 14 14 14 18 14 24 2   15   28   7     13   3   10   27 14 8 14 12 14 18 14 22 14 28 3   16   27   6     14   4   9   26 14 12 14 16 14 22 14 26 14 32 4   17   26   5     15   5   8   25 14 14 14 20 14 26 14 30 14 37 5   18   25   4 FEBRVARY.   16   6   7   24 14 18 14 24 14 30 14 34 14 42 6   19 OCTOBRE. 24   3     17   7   6   23 14 22 14 28 14 33 14 38 14 46 7   20   23   2     18   8   5   22 14 26 14 32 14 36 14 43 14 50 8   21   22   1     19   9   4   21 14 30 14 34 24 40 14 48 14 54 9   22   21   31     20   10 august. 3   20 14 34 14 38 24 44 14 52 14 58 10   23   20   30     21   11   2   19 14 36 14 42 14 48 14 56 15 2 11   24   19   29     22   12   1   18 14 40 14 46 14 52 14 0 15 6 12   25   18   28     23   13   31   17 14 44 14 50 14 56 15 3 15 10 13   26   17   27     24   14   30   16 14 46 14 54 15 0 15 6 15 14 14   27   16   26     25   15   29   15 14 50 14 56 15 4 15 10 15 18 15   28   15   25     26   16   27   14 14 54 15 0 15 8 15 14 15 22 16   29   14   24     27   17   26   13 14 56 15 4 15 11 15 18 15 26 17   30   13   23     28   18   25   12 15 0 15 8 15 14 15 22 15 30 18   31   12   22     29   19   24   11 15 4 15 10 15 17 15 26 15 34 19   1   11   21     30   20   23   10 15 6 15 14 15 20 15 30 15 38 20   2   10   20   may. 1   21   22   9 15 10 15 18 15 24 15 34 15 42 21   3 NOVEMBRE. 9   19     2   22   21   8 15 12 15 20 15 28 15 37 15 45 22   4   8   18     3   23   20   7 15 16 15 24 15 32 15 40 15 48 23   5   7   17     4   24   19   6 15 18 15 28 15 36 15 44 15 52 24   6   6   16     6   25   18   5 15 22 15 30 15 39 15 47 15 56 25   7   5   15     7   26   17   4 15 24 15 34 15 41 15 50 16 0 26   8   4   14     8   27   16   3 15 28 15 36 15 44 15 54 16 4 27   9   3   13     9   28   15   2 15 30 15 40 15 47 15 57 16 7 28   10   2   12     10   29 IVLYE. 14 ♌ 1 15 34 15 42 15 50 16 0 16 10 29   11   1 ♒ 11     11   30   13   0 15 36 15 44 15 54 16 4 16 14 30   12   0   10 IANVARYE.                 H. M. H. M. H. M. H. M. H. M.                  

The thyrde parte of the table.  signs for the day. elevation of the Pole, or latitude of Regions. signs for the night. daies of moneths degrees of signs. daies of moneths degrees of signs. 51 52 53 54 55 degrees of signs daies of moneths degrees of signs. daies of moneths   11 ♊ 0   13   30 15 36 15 44 15 54 16 4 16 14 0 ♐ 12   30   10     12   1   12   29 15 38 15 46 15 56 16 6 16 17 1   13   29   9     13   2   11   28 15 41 15 49 15 59 16 9 16 20 2   14   28   8   may. 14   3   10   27 15 44 15 52 16 2 16 12 16 24 3   15 NOVEMBRE. 27   7     15   4   9   26 15 46 15 54 16 4 16 14 16 26 4   16   26   6     16   5 IVLY. 8   25 15 49 15 57 16 7 16 17 16 29 5   17   25   5     17   6   7   24 15 52 16 0 16 10 16 20 16 32 6   18   24   4     18   7   5   23 15 54 16 2 16 12 16 22 16 34 7   19   23   3     19   8   4   22 15 56 16 5 16 15 16 25 16 37 8   20   22   2 IANVARYE.   20   9   3   21 15 58 16 8 16 18 16 28 16 40 9   21   21   1     21   10   2   20 16 0 16 10 16 20 16 30 16 42 10   22   20   31     22   11   1   19 16 2 16 12 16 22 16 32 16 44 11   22   19   30     23   12   30   18 16 4 16 14 16 24 16 34 16 46 12   23   18   29     24   13   29   17 16 5 16 15 16 26 16 36 16 48 13   24   17   28     25   14   28   16 16 6 16 16 16 28 16 38 16 50 14   25   16   27     26   15   27   15 16 8 16 18 16 30 16 40 16 52 15   26   15   26     28   16   26   14 16 9 16 19 16 31 16 42 18 54 16   27   14   35     29   17   25   13 16 10 16 20 16 32 16 44 16 56 17   28   13   24     30   18   24   12 16 12 16 22 16 34 16 46 16 58 18   29   12   23     31   19   23   11 16 13 16 23 16 35 16 47 16 59 19   30   11   22   june. 1   20   22   10 16 14 16 24 16 36 16 48 17 0 20   1   10   21     2   21   21   9 16 15 16 25 16 38 16 50 17 2 21   2 december. 9   20     3   22   20   8 16 16 16 26 16 38 16 51 17 3 22   3   8   19     4   23   19   7 16 17 16 27 16 39 16 52 17 4 23   4   7   18     5   24   18   6 16 18 16 28 16 40 16 52 17 4 24   5   6   17     6   25   17   5 16 19 16 28 16 40 16 53 17 5 25   6   5   16     7   26 june. 15   4 16 20 16 29 16 41 16 54 17 5 26   7   4   15     8   27   14   3 16 20 16 30 16 42 16 54 17 6 27   8   3   14     9   28   13   2 16 20 16 30 16 42 16 54 17 7 28   9   2   13     10   29   12 ♌ 1 16 20 16 30 16 43 16 54 17 8 29   10   1 ♑ 12 december.   11   30   11   0 16 20 10 30 16 44 16 54 17 8 30   11   0   11                   H. M. H. M. H. M. H. M. H. M.                  
in the first column are set the daies of the monthes, and in the second the degrees of the signs in the zodiac, in which the son is that day: so likewaies the third and fourth column do serve for the like matter, seeing twice in the year the daies are equal. And because at other 2 times in the year the nights ar equal to those daies, therfore on the right hand of the table are ther 2 columns of moneths, and other two columns of signs agreeable thereto, in which those nights are equal with the daies of the months on the left hand, and therfore ar the title set over the signs& moneths on the left hand, signs for the day: and on the right hand signs for the night: that is to say, that if the month and sign for which you seek, be on the left side of the table, then do the numbers under the elevation of the Pole declare the quantity of the day: but if the months& signs be on the right side, then is that quantity the length of the night. and over the 5 middle pillars, you se the title to be the elevation of the Pole, or latitude of regions; which are there but only 5 expressly set, namely 51, 52, 53, 54,& 55: which may serve for all England, from the south sea unto Scotland. And so may it do for diverse of the north partes of Europe and Asia. now for the use of them, this is the order. When so ever you would know the quantity of the day artificial and of his night, seek out the day in the columns on the right hand, or on the left hand as it will chance, and by it in the next column you may see the place of the Son in the zodiac: then going right forth toward the middle of your table till you come directly under the column that serveth for your Region in latitude, there shall you find 2 numbers: the first be tokening hours, and the second minutes of hours, which declare the just quantity of the day for the moneths on the left hand: or else if the month that you seek for be on the right hand, then do those numbers of hours and minutes betoken the quantity of the night.  Scholar. 
I perceive it well, and I se by reason it must needs be so: as for examples sake. the 24 day of august I desire to know the length of the day and the place of the son in the zodiac: wherefore finding the said 24 day in the first table of those three right against it, I may see the place of the son, which is then the 11 degree of Virgo: and from thence proceeding forth right toward the middle of the table, I finde under the number of 52 degrees of latitude 13 hours and 18 minutes: whereby I perceive that the artificial day from son rising to son setting, is so long with us: and the night is the rest of 24 hours, that is 10 hours and 42 minutes. And the like quantities of day and night must needs be the 29 day of march, when the son is in the 19 degree of Aries. But on the 20 day of February, the son being in the 11 degree of Pisces, that 13 hours and 18 minutes is the quantity of the night, and the day then is but 10 hours and 42 minutes in length: and so likewaies the second day of Octobre, when the son is in the 19 degree of Libra.  Master. 
This is sufficient: for as you haue done in this so may you do in all other like. yet for the more certainty I will prove you with one question more: For London which is supposed to be 51 degrees and 24 minutes in latitude, I would know the quantity of the day Artificialle when the son is in the 28 degree of scorpion.  Scholar. 
I finde that sign of scorpion in the second table on the right hand, and the 10 day of Nouembre answering unto it. And because 24 minutes are less then half a degree, I do seek the quantity of the day under 51 degrees rather then under 52, and so finde I 15 hours and 30 minutes: which in this case is the quantity of the night, as the title declareth that is over those signs: therfore the length of the day is 8 hours and 30 minutes.  Ma. 

A cautel for the part proportioble.  You haue done well. But yet for an exacter preciseness, you may take the part proportionable for the odd minutes of the elevation, as thus. for the latitude of 51 degrees, the day is 8 hours and 30 minutes: and for 52 degrees, it were 8 hours and 20 minutes: so are there 10 minutes difference between those two elevations. Then say by the Golden rule: If 60 minutes give 10, what shall 24 minutes give? and it will appear to bee 4 minutes. Those 4 minutes must I abate from the greater noumbre in this example( and in all this work where the numbers decrease) and it will yield 8 hours& 26 minutes: where as yf you did finde the numbers to increase, then should you add those partes porportionable unto the lesser number, as by proof you may try, for that day when the son is in the second degree of lo.  Scholar. 
That is( by the second table) the 15 day of july, and then is the day in length 15 hours and 30 minutes, in the latitude of 51 degrees: but in the latitude of 52 degrees, it is 15 hours and 40 minutes, so it increaseth 10 minutes: and therfore must I add the parte proportionable( which is 4 minutes as before) unto 30. and so haue I the true quantity 34 minutes above 15 hours. And now I think I am perfect enough for all places between 51 degrees of latitude and 55: but for other places I know no such way.  Master. 
It were to long a work to set out all diversities of elevations, and scarce agreeable for this treatise, where these things are but incidente, and not principal matters. but at other times in more convenient place it shall be done if I may understand this my labour to be profitably employed. And thē also will I make explication of dyvers other matters, which you did in your table at the beginning of this treatise propound, although at this time I think many of them little appertaining to this book. But yet before I end this treatise, I must speak somewhat of two or three matters more: 
Constellations.  And first of the chief Constellations and figures in the Starry sky. For a ground you shall note, that the stars are not only in multitude infinite, but many of them also so small, that scarce any mans eye can discern them. wherefore to avoid confusion, and to grow to a certainty, the ancient Astronomers did note only 1022 stars, whereof the most parte they did assign to certain limits, enclosing them in figures of men, beasts, or other forms, and accordingly gave them names, partly that they might the more easily bee remembered, partly for remembrance of some worthy fact, and partly also for some notable signification of the stars comprehended in each of them. All which matters I will nowe-ouerpasse, till a more convenient place, and will repeat only their names and places generally, distincting them according to the accustomend manner, into three sorts: whereof the one sort are called northerly constellations, the other sort Southerly constellations, and the third sort are the twelve signs, which pass in the middle between south and north: for here in this place I mean not to refer south and north to the Poles of the equinoctial, but as all learned men before me haue done, to the poles of the zodiac. And so may the zodiac be accounted exactly in the middle. But now to begin as Ptolemye doth, 
The north constellations  with the northerly constellations: The most northerly constellation is the lesser bear, called Vrsa minor, and Cynosura, 
1 Vrsa miner  and containeth in it 7 stars. This is the chief mark whereby mariners govern their course in saylinge by night, and namely by 2 stars in it, which many do call the shaft, and other do name the Guardas, after the Spanish tongue. Nigh unto it is the greater bear, called Vrsa maior, containing 27 stars, 
2 Vrsa maior  whereof 7 are most notable, and are in latin name Plaustrum, and in english Charles wain, which serveth also well in sailynge: and many of the old Greekes observed it only in their navigation, 
3 Dragon. 4 Cepheus. 5 Bootes.  as the Sydonians and all the phoenicians marked the lesser bear. A bout these 2 bears is there a long trace of 31 stars, commonly called the Dragon. Then followeth Cepheus, which consisteth of 11 stars.  
Bootes also is in the same coast, whom Proclus and others do name Arctophylax. and it hath 22 stars, beside one very bright star called Arcturus, 
6 The north crown. 7 Hercules.  which standeth between Bootes legs. By Arctophylax right hand, is the north crown, called also Ariadnes crown, and hath in it 8 stars. Then followeth Hercules, whom the greekes do call Engonasin, as it were the Kneeler, because of his gesture: and it containeth 28 stars. By his left hand, is there an other constellation, 
8 Lyra.  which is called the harp, in latin Lyra and Fidicula. and also vulture cadens, that is the falling gripe, 
9 The Swan.  it comprehendeth 10 stars. By it is the swan; name Cygnus, and avis generally, as the Greekes call it Ornis, which some men of to much ouersyght do translate, 
10 Cassiopeia. 11 Perseus.  Gallina a Hen: it consisteth of 17 stars. After it doth Ptolomye reckon Cassiopeia, which is by Cepheus, and hath 13 stars. next unto hir is Perseus, with Medusas head, and it includeth 26 stars. Then followeth Erichthonius, 
12 The Carter  with the goat and the 2 kids. this constellation is also name Auriga the Cartar: and containeth 14 stars with one in his right foot, which is common to Taurus also. An other constellation is there which joineth head to head with Hercules, 
13 Serpentarius 14 The serpent  and is called of the Greekes, Ophiuchus, and of the latins Serpentarius, that is the man with the serpent, or Serpent bearer: and it hath 24 stars. beside the Serpent, which containeth 18 stars in himself, and is name of latins Anguis, and of greekes Ophis. Then is there an other small constellation of 5 stars, 
15 The Dart.  a little south of the tens head, and it is name the dart, Sagitta or Telum in latin, and in greek Oistos. 
16 The eagle.  By it toward the south, is the eagle, includynge 9 stars: he is called not only Aquila in latin, but also vulture volans, and in greek Aetos. under it toward the south is a constellation hard adjoining name Antinous in all tongues, 
17 Antinous. 18 The dolphin 19 The fore-horse.  and hath but 6 stars. A little from it is the Dolphine, which hath in it 10 stars.  
Then followeth the fore-horse, noted with 4 dark stars, and hard by him is the Flying horse, name Pegasus: 
The Flying Horse.  and doth consist of 20 stars. unto him joineth Andromeda, so that hyr head lieth on the navel of Pegasus, 
21 Andromeda  and one star is common to them both. This constellation doth contain 23 stars.  
By hir left foot is ther a small constellation of 4 stars, 
22 The triangle  which is commonly called the Triangle, and in latin Triangulus, but the greekes name it after one of their letters Delta and Deltoton. And thus haue I briefly reckoned all the northely constellations, except Berenices hear, of which I will speak last of all other. And therefore now next in due order must the 12 signs follow: amongst which Aries occupieth the first place, 
1 Aries.  and containeth 13 stars. Then Taurus which is adorned with 33 stars, 
2 Taurus. Water stars  whereof 5 be in his forehead and face, and are called of the Greekes Hyades, and of the latins Succule: amongst which, one is more notable then all the rest, and is called Oculus Tauri, the bulls eye: but the Greekes call it Lampadias, and the latins Palilicium: the Arabitians Aldebaran. Other 6 stars( as Proclus numbereth them, though other account them 7) ar in the back of this sign, and be called Vergiliae in Latin, and in greek Pleiades, and also Atlantides: they are name in english the brood hen, 
The seven stars.  and the seven stars, yet they cluster so nigh together, that it is hard to number them truly. and therfore many do disagree in reckoning them. 
3 geminy.   
After Taurus, geminy do follow, which comprehend 18 stars: of which two bear name as most famous, and they are in their heads: the foremost is name Appollos head, and the next is called Hercules head, because those two twins were so name of some men, yet other do call them Castor and Pollux. Before their formoste foot is there one fair star( beside the 18, 
Propus. 4 Cancer Crybbe, Asses. 5 lo. ) which therfore is name in greek Propus. After geminy foloweth Cancer containing 8 stars, beside a cloudy tract which is name the Manger or Crybbe. 
Asses. 5 lo.  Other two stars are called the Asses which seem to stand at the Crybbe. Then the Lion is next, as a princely sign, in whom are 27 stars, but two of them more notable then the rest: the one is in the tail, and therefore is called Cauda Leonis, the other in the breast and is called the Basilyske or Kyngely star, and also the Lions heart, Cor Leonis in Latin, and Basiliscos in greek. next after lo, 
6 Virgo.  cometh Virgo, garnished with 26 stars, but one especially glystereth above the rest, and is called Spica Virginis, the Virgins spike.  
A lesser star there is also, which yet is notably marked, and called Protrigetes, Praeuindemiator.  
After Virgo cometh Libra, 
7 Libra.  the sign of Iustice and equity: but it is the least sign in quantity of all other in the zodiac, for it occupieth scarce half a sign in length, and no marvel, sith that cruel Scorpius doth invade so great a portion, and presseth all that sign out right. yet hath it 8 stars, but not one out of the Scorpions claws. 
8 Scorpius.   
Then Scorpius with his hooked tail, and with his claws doth reach so far, that two full signs he taketh in length and 30 degrees almost in breadth, yet hath he but 21 stars beside those which bee in his claws, and are common to them& to Libra: amongst all which the principal is that, which is called the Scorpions heart, and is name of the Greekes Antares, 
9 Sagittarius  and of Arabitians, Calb alatrab.  
After him ensueth one of the centaurs like an archer on horse back, with many fair stars, though they bee not of the greatest: he hath in all 31. this sign is called Sagittarius in latin, 
10 Capricorn.  and in greek Toxotes. Capricorn then followeth with his monstrous shape, neither fysh nor flesh, but mixed of both: a winterly sign and no ways pleasant, but that he giveth hope of the comfort of the spring, because in it the son beginneth to return to us again. he hath in him 29 stars of mean quantity.  
Aquarius so fast doth follow him at hand, 
11 Aquarius.  that he reacheth almost as forwardlye as capricorn, within less then 8 degrees: this sign hath in him 22 stars peculiar to himself, although Proclus name 4 of them in his right arm, to be the Water pot. 
The water pot.  But beside these 22 stars, there are other 19, which in their dyvers and crooked position do make a form of a river, and are called the Water which Aquarye sheddeth. With these 19 stars Ptolemye doth account one more, 
The waver  which is a beautiful star of the bryghtest sort, and is in the mouth of the south fish, so that it is common to them both. this star is called of Arabitians Fomahant: so that in all there are reckoned in this sign, 42 stars.  
last of the 12 signs cometh the fishes, 
12 Pisces.  tied by the tails with a common line: 
The line.  the formoste fish hath but 9 stars, and his line hath 10. the latter fish hath 11 stars, and his line hath but 5. and where those two lines are knit together, there is one star more, which is called the knot, that is in greek name Syndesmos: so that all the stars together, of this sign, are 34.  
Whether Proclus did mistake any thing in this sign, I wish other to judge, because I intended here not to entreat at large, and much less to scan other mennes writings. And thus will I end the 12 signs of the zodiac.  

1 The Whale  now to diuerte unto the south signs: first appeareth the great Whale, containing 22 stars, whereof three bee most noted: the first in the nether chappe, which is in latin called Mandibula ceti, and in arabic Menkar. the second is called the Whales belly, in arabic Baten kaitos, and in latin venture Ceti. the third is the Whales tail, name Cauda ceti in latin, and in arabic Deneb kaitos. next followeth Orion, the Stormy sign, 
2 Orion.  and hath diuers stars to the number of 38: but the most notable are 6. the first is in his right shoulder, and is called by the Arabitians Bed Algeuze. The second is in the left shoulder and is name Bellatrix. Other three stand as bullions set in his girdle, and are called of many engly she men the Golden yard. Then is there in his left foot, a great star of the brightest sort, which is name of Arabitians Algebar, and Rigel Algeuze. Beside these six there are other stars more notable for their form then for their quantities. as the two stars which betoken his club in his right hand, and 9 stars by his left hand, which represent a Lions skin: and other three do limit his sword, lying cross his back under his girdle.  
between Orion and the Whale is there a great tract of stars, which represent the form of a river: and therefore are they called the river. 
3 The river  which some more peculiarly name Eridanus, and other Nilus. Proclus calleth it Orions river, because it beginneth at his left foot and hath one star common with his foot, but beside that it hath 34 stars: whereof the last is one of the greatest light.  
By the beginning of this river, under the feet of Orion is there a constellation of 12 stars, 
4 The Hare.  name the Hare. And after it toward the east is the greater dog, 
5 The great dog. ( of whom the Caniculare daies bear name) and is called of the greeks Sirius, and of the latins Canis, having 18 stars, but one especially in brightness more notable then any of the rest, and that is in his mouth, 
6 The lesser dog.  and is called peculiarlye Sirius and Canis, by the name of the whole sign, and of the Arabians Alhabor. north almost from this dog is ther a constellation of 2 only stars name Canicula, the lesser dog: and in greek protion, the fore dog, whom Tully therfore calleth Antecanis, and other name him Precanis. At the tail of the greater dog is the famous ship Argo, 
7 Argo the ship.  which comprehendeth 45 stars, whereof 8 bee beautiful but one in especial which is in the foot of the roother& is called Canopus,& of the Arabitians Suhel. This star is not seen in England, France, Germany nor Italy,& scarcely in the most southerly partes of spain. And here by the way I will note a place in Proclus very much corrupted, which now I will only correct as I think good: and an other time will entreat more largely of it and of other mo. the words in greek are these.  
{αβγδ} 
{αβγδ} in all the greek books.  {αβγδ}.  

Non cernitur. transtulit latinus interpres, greaci codicis errorem imitatus.  Stella vero illa splendida quea in imo Argus gubernaculo sita est, Canopus dicitur. ea in Rhodo vix conspicitur, aut certè ab editis locis. In Alexandria vero prorsus* conspicua est, utpote ferè quarta signi portione supra Horizontem euecta.  
The bright star in the foot of the roother of Argus is called Canopus, which in the Rodes can scantely be seen, except it be from high places: but in Alexandria it may well be seen, for it doth rise there nigh a quarter of a sign above the horizon.  Scholar. 
This is contrary to the common translation.  Master. 
And that common translation is as contrary to common sense, but therof an other time shall we talk, when I mind to teach you the exact order of ascension for all these constellations, and of their chief stars also. And now to proceed as we began. 
8 The Serpent of the south.  next after this ship ther followeth the great Serpent which is called of the greekes and latins Hydra. it containeth 25 stars, and stretcheth in great length by the space of 3 whole signs. one star there is in it bryghter then the rest, and that is name by the Arabians, Alphard.  
On this Hydre there resteth other 2 small constellations, the one name the cup, and the other the raven. 
9 The cup   
The cup includeth seven stars all of one bigness. This cup standeth on the Hydres back, almost in the middle of him.  

10 The raven.  The raven standeth on the same Hydre, more nearer toward the point of his tail: and it is formed of 7 stars also, of which that which is in his left wing, is called in arabic, Algorab. 
11 The centaur.   
under the tail of this Hydre and those two other small constellations, there standeth the centaur Chiron, like a light horseman with his chasinge staff: 
The Centaurs spear  he hath in him 37 stars, whereof 4 be in the garnish or pensile of his spear, and them doth Proclus reckon as a peculiar constellation. and nameth it in greek Thyrsolochus. And Ptolemy doth reckon those stars naming them to be in that spear: wherefore I muse howe Stofler seemed so ignorant herein, to deny that Ptolemye doth make any mention of that spear, and himself deviseth out of Ptolemye 6 wrong stars for that purpose: it appeareth he was deceived by the old translation, where Clypeus is translated for Hasta: that is, shield for spear. which wrong translation Schoner, Copernicus, and Erasmus Rheinhold do follow, and dyvers other learned men, but against reason.  Scholar. 
I think it( as many things else be) is received by credite of authority, without disquisition of reason, which blindeth many wittye men oftentimes.  Master. 
Yet is their fault the more pardonable, if they acknowledge their error when they be friendly admonished: but this is beside our purpose at this time, therefore to return: This centaur with his right hand doth hold a wolf, 
12 The wolf.  which is a several constellation made of 19 stars, although Hyginus and others do reckon fewer in him, as they do vntrulye in many other. under that beast toward the south, hard under the Scorpions tail, standeth the Altar, 
13 The Altar.  made of 7 stars, of the meanest light: but it is not seen in england above the horizon. By this Altar eastward between the two former feet of Sagittarye, there is the crown of the south, 
14 The south crown.  formed of 13 small stars: Proclus and Theon do call it also Vraniscus, as many later writers in their time did name it: but Theon doth farther affirm that it hath 19 stars: which must seem to bee an error, rather in the book then in the author: wherein observation can not help us in england, sith it riseth not above our horizon, but only toucheth it.  
After it followeth the south fish, containynge 12 stars: 
The south fish.  whereof one only is of the greatest light, and that is it which standeth also for the end of the water that runneth from Aquarius. This fish lieth between the constellations of capricorn and Aquarye, so that it is partly under them both.  
These bee the Constellations most commonly noted amongst ancient writers: howbeit one more there is name to lie between the Lions tail and Vrsa maior, which is called Berenices hear, some call it in latin Trica, 
16 Berenices hear.  and other Berenicis crines. Conon that famous astronomer did first name it, and Callimachus did de●… re it, and therefore doth Proclus ascribe the first noting of them unto Callimachus. The stars in it are 7, as Hyginus and Bassus do account them: but they are very dark, and therefore Ptolemye doth number only three of them, as the bounds of that form. beside these 50 constellations, there bee a great number of stars, which be not assigned to any figure, but lie dispersedly about those other constellations, whereof 61 are in the north parte of the sky, and annexed with the northerly signs: and other 19 in the south part of the zodiac, unto which if you add 337 which be in the north constellations, and 316 in the south constellations, with 292 in the zodiac, so haue you in all 1025 stars which be noted by Astronomers, but in Ptolemyes account there appear but 1022, because he doth not account any star of Berenices hear, but called it the Traces of hear. These stars be not of one quantity, but some much brighter then other, and therefore are they distinct into diuers measures of light, and namely 8, which are called the first greatness, the second, the third, the fourthe, the fift an the sixth, under which they are that be called Cloudy stars: and a lesser fort yet name dark stars: of all which, and the measure of their quantity, I will at an other time speak more fully, for this place and time agreeth evil with the matter, and that much worse, then at the beginning it seemed to do.  Scholar. 
There remain yet many titles untouched of them which I gathered.  Master. 
And many of them smally agreeable for this treatise, but do more aptly appertain to Cosmography, and therefore ought to be reserved for that work: save that some of them are peculiar for the Theorike of planets, and yet will I lightly touch them in few words, for so much as may seem to help to this treatise.  Scholar. 

Howe the number of spheres is known.  I remember at the beginning you promised to show a cause why you name but 8 spheres, where as other men do account more: and also how it may appear, that there are so many, for the eyes can see but one only, which is the firmament.  Master. 
yourself said, you had marked( as many mariners, 
The moon  yea and all men do almost) that the moon doth every day run eastward notably, so that in a week shee passeth a quarter of the sky in that course, and in 15 daies she runneth half the compass of the sky, and so in a month she returneth to the son again, having passed all the circuit of heaven. so of the son you haue understand that in a year he trauerseth over all the length of the zodiac, 
The son.  contrary to the course of the Firmament, whereby it must needs appear unto you, that seeing the son and the moon haue courses distinct from the Fixed stars, they must needs haue distinct spheres also, wherein they do move, and accomplish their courses.  Scholar. 
I remember I haue heard it often repeated as a principle in nature, that one simple body can haue but one simple motion. and therfore where diuers motions bee, it must needs follow that there are diuers bodies as their workers, which you in this talk do call spheres.  Master. 
As you may think that their spheres are distinct from the Firmament by reason of their several motions, so are they distinct a sunder by the same reason.  Scholar. 
It is most certain.  Master. 
Then if by good observation it haue been proved, that there be 5 other stars which haue their motions all distinct from the Starry sky, and each of them from their fellowes, it will appear reasonable that every one of them hath a several sphere peculiar for himself, and for his private motion.  Scholar. 
It will follow of necessity.  Master. 
Then I will begin with yourself for one of them, which I am sure you can not but mark, as all men, yea the very ploughmen do. And that is Venus, which I dare say, 
Venus.  you haue marked in the evening to set after the son,& then is she name the evening star,& yet doth she not at al times shine like space after son setting, but some times more& sometime less. And if you mark hir well, then shall you perceive, that the first night that she appeareth, shee shineth less time then she doth the second night, and so increaseth the time of hir shyninge for a space, and then doth shee abate again by little and little, till she join with the son, and then appeareth no more at evening, but shortly after will she show in the morning before the son rising, and increase the time of hir shining by little and little, till she comme to the farthest of hir distance from the son, and then will she abate again in like manner, till she come within the beams of the son, and lose hir appearynge for a time.  Scholar. 
This is most certain and known of all men vulgarly, although few men do considre the cause therof: but now I do remember, what you taught me of the ascensions poetical( as they be name) and namely of that which you thought meter to bee called apparition, whose contrary you called Occultation: so that when Venus doth shine at evening after son setting, she doth rise as some term it, with a sonnely rising: and when shee is hidden again, she is set with a sonnely setting. but that you judge Apparition and Occultation more apt terms.  Master. 
You do not guess much amiss. And to the intent that you may considre this matter the better, I think it good that you do mark hyr motion the more diligently hereafter: as in this present month of september, at the beginning of the month she was about 36 degrees behind the son, and so should she shine almost 2 hours and a half after the son, as it might appear by the degrees of distance. but considering the obliquity of the zodiac, and the latitude of Venus at that time, she didde scarce shine three quarters of an hour after the son.  Scholar. 
This talk is to obscure for me yet.  Master. 
I know it right well. but yet I thought good to admonish you in that matter, least at any time you should finde the doubt, when you shall haue no opportunity to ask council therein: but now to proceed. before the and of the same month of september, the said Planete will be clean hid with the son beams: for within 2 dayes after( I mean the second day of Octobre) she doth join with the son by coniunction. And from that day forward the son doth outgo hir so fast, that by the 13 day of Octobre, she will be out of his beams again, and rise almost an hour and a quarter before the son. and at the end of Nouembre, she will be 46 degrees behind the son, in order of the signs, and yet shall she rise 4 hours and more before the son, where as the number of degrees are equal to little more then three hours. but the obliquity of the horizon, doth make all the diversity in this, except a mean trifle by the latitude of Venus. And thus may you mark Venus in all that month, and in december also unto the end of the year: but then doth she abate her distance again, whereby it is easy to understand that she hath a several motion from the son, and a several sphere also.  Scholar. 
In Venus it doth appear now easy enough to considre, as well as in the son and moon: but is it as easy in the other four planets?  Master. 
Yea in deed, for three of them which bee most highest, if you list to learn to know them, and to mark their courses: but Mercury is not so well marked, because he doth always keep his course nigh about the son, 
Mercury.  and therfore his observation requireth great diligence, and his courses appear most strange, yet both he and Venus do accomplish their course in a year with the son: 
Saturne.  but Saturne is so slack a mover, that you shall not well perceive his motion under 4 moneths. in which time he doth move about 4 degrees: so that if you mark his place at any time, and within 4 monthes after that time yf you do mark him again, you shall perceive that he is gone 4 degrees eastward, which you may mark by the fixed stars about that place: but if you do after a whole year mark his place, then shall you perceive well and manifestly, that he is gone eastward 12 degrees, and somewhat more: as for example. The first day of september, the last year 1555, Saturne was in the 12 degree of Aries, and this year of 1556 we see him to be in the 26 degree of the same sign, whereby it doth appear, that he hath moved 14 degrees eastward in that year space. And if you will haue farther proof: In the year of our lord 1549, the last day of Nouembre, Saturne was seen in the 26 degree of capricorn, and this year of 1556 the first of september, the same star was in the 26 degree of Aries: whereby it may bee known that he hath moved three whole signs( which is a quarter of the zodiac) in 7 year space. And so in less then 30 yeares, he doth go about the whole zodiac.  
jupiter hath a swyfter course, for he passeth the circuit of heaven in less then 12 yeares. 
jupiter.  so doth he every year run over one sign, and every two moneths he passeth 5 degrees.  
Mars is yet swyfter in course then he, and compasseth all the zodiac in 2 year, 
Mars.  and every month passeth half a sign. whereby for this point, he is more easy to be marked, then any of the other. but yet are his motions difficult to mark in other points: but this may suffice for trial that he moveth eastward, as all the other planets do: and therfore must he be judged, as all the other also ought to haue several spheres in which they move. And although their spheres can not bee seen, yet in as much as their stars may be so well perceived, it must needs follow, that they haue spheres also: except we should come to that absurdity to say, that they move in the air as birds do, or as fishes in the water: which were to much repugnant to any one orderly motion, and much more disagreyng to so many diuers motions as are in the planets, but namely in Mars and Mercury. And to the intent that you may know them the better, it shall bee good that you learn their true places by the Ephemerides, and accustom yourself to look for them, and to mark their bigness and colours how they differ from other stars. which is spoken by way of exhortation only, and not propouned as any piece of this book, but an other time I will instruct you better therein.  Scholar. 
But in the mean time, howe shall I know whether there be any more spheres or no?  Master. 
There is thought to be in the 8 sphere or Firmament, two other motions, 
Of the nith and tenth sphere.  which be disagreeable from all other movings before mentioned, and therfore many think that they must of necessity confess 2 other spheres from which those motions must proceed peculiarly.  Scholar. 
What motions are those, and howe are they known?  Master. 
first there is one notable observation by conference of learned men in diverse ages, concerning the equinoctial points, and like ways concerning those tropical points, that the son toucheth twice every year: for about the incarnation of Christ, the equinoctial point or instant happened about the 25 day of march, and now it is about the tenth of the same month, which disagreemente doth rise partly by the miss order in the leap yeares, but most principally clothe the anticipation of the equinoctial terms. For although the son do at the yeares end return to the same point in the Starrye sky where he was at the beginning of the same year, yet is he not exactly so nigh unto the equinoctial point as he was before, but doth over run it every year, and thereby in continuance of time it cometh to pass, that men may sensibly perceive that the stars are run eastward from that equinoctial point.  Scholar. 
This seemeth something obscure, except you can declare it more plainly.  Master. 
Do you not considre between the son and the moon, that when she doth join with him by coniunction and then ouerpasseth him by her swift motion, that when she returneth again to the same place where she did leave the son, she doth not finde him there, but she must over go that place, before shee can overtake the son again, by reason that the son did move forward after the moon in the same course, though much more slowly: So likewaies when the son departeth from any star in the sky, in the very instant of the equinoctial equality, and in the very point of the intersection of the equinoctial and the ecliptic line, where of necessity that equality must happen: if the son returning after a year unto that equinoctial point, do not finde the star there precisely, which he left there, but that he must over run that point, before he can come again to the said star, may not we yea and must not we say, that that star is moved forward in his course eastward, as all the planets do move? Howe bee it the quantity is so little, that it is not perceived by sight alone, neither yet by instruments, in less then an hundreth year, so that no one man is able to mark any great diversity in his own age, but must be fain to confer with other men that hath made observations long before and written them: so did Ptolemye confer his observations, with Hipparchus observations, and found that from Hipparchus time unto his own age, the Fixed stars were moved forward from the equinoctial point, two degrees, and 40 minutes: whereby he did conjecture, that they moved every hundreth year one degree, sith the time between their 2 observations was 265 year: and after the like rate was the same motion found by conference of the observations of Timochares& Hipparchus. what other men say for more preciseness herein sith their time, I will in the The orikes declare unto you: but all agree herein, that the stars do move uniformly with all their sphere eastward as the planets do. wherefore many assign that motion as peculiar to the eight sphere, and the daily motion from east to west they appoint to the ninth sphere. Other men perceauinge that the stars do also ascend northward, and descend again southward, do assign a certain motion, which is name by them Motus trepidationis, and they note it to bee peculiar for the eight sphere, and the other motion last name before, they account to be proper to the ninth sphere, and then of necessity it followeth, that a ten the sphere( as they say) must be assigned for the daily motion.  Scholar. 
If it be true that there be such varieties of motions, then it seemeth reasonable to assign so many spheres as there be motions several.  Master. 
Although you think so now, you may be persuaded peradventure to think the contrary hereafter, as most wise men in that arte do.  Scholar. 
But in the mean season what shall I think?  Master. 
think well on that that you haue learned, and labour to be expert in all that, by often conference of your learning, with the practise of the globe, and so shall you be apt to bee instructed in all the rest the more easily. for it will require a wit somewhat ready, and practised in these former matters.  Scholar. 
I will then prepare me a Sphere( without which I see I can do little good herein) and so will I practise these former lessons, that I trust to be as ready in them, as any auditor in framynge of account.  Master. 
By that means shall all other things in this arte appear easy unto you, which now might seem untimely put forth, if I should offer to teach them, as the motions of the son, moon, and other planets, with their eccentrikes, equantes, differences and Epicycles.  Scholar. 
In deed I think this to hard yet, but of the progression, retrogradation, and station of the planets, and also of the eclipses of the son and moon, I know that John de sacro Bosco did writ somewhat, and so might you briefly now do.  Master. 
His words are short and therefore obscure, and so should my words be. beside that, it is a disordrely form to put the cart before the horse: I mean to writ of the passions of the Planets, before I haue sufficiently taught the full order of their motion. Therefore I will say in few words, that the reasons of the passions can not bee taught aptly, before the Theorikes of their motions. but for contentation of your mind, I may define after a sort the eclipses of both the son and moon: whereof the first is but an appearaunte and a countrefete Eclipse: 
The Eclipse of the son.  and is no want nor loss of the light in the son itself, but is an impedimente, that his light doth not or can not extend unto us, by reason that the moon doth run beetwene him and our sight. And this Eclipse as it hideth the son from us for a time, so in some partes of the earth at the self same instant he is not any whit eclipsed, but shineth clearly and wholly. And therfore is that eclipse called no general eclipse, which should extend to all the world, namely for that hemispherye, but is particular for some one climate, and yet not universal to all that climate. 
The Eclipse of the moon.  but contrary ways the eclipse of the moon is a true eclipse in deed: for there is no thing that runneth between our sight and her, and so hideth from us her light, but she loseth her light certainly. As if a glass that standeth in the son, do receive the light of the son, and do cast beams( as wee may see) from him, till some cloud or some other dark body pass between the son and it, and then it loseth his light clearly, and hath no light but his own brightness, which can cast no beams, neither deserve any name of light, in comparison to the light that it had of the son: So the moon keeping hyr course till shee bee at the full, that is to say, in the contrary point of the zodiac to the son, and that then she bee without all latitude, and run right under the ecliptic line in the zodiac, then doth shee light directly in the shadow of the earth, and therefore can not receive the light of the son, but loseth it for the time, howe bee it not always a like. for sometime shee cometh wholly without the shadow of the earth, and then is shee wholly eclipsed: at other times shee cometh but partly into the shadow, and that some times in the over parte, and sometime in the nether parte, whereby shee is eclipsed partly, and not vniuersallye: for if the mone pass by the north or over part of the shadow, and touch it with any parte of herself, then is that parte eclipsed of necessity, which is the south part of the moon or the nether part of her. And again if the mone do touch the nether parte of the shadow which is next to the Horizonte, then is the higher or northerly parte of the moon eclipsed. To tell you now of the ecliptical points, which be commonly called the head and the tail of the Dragon, it were very untimely, and hard for you briefly to conceive, and therefore I do willingly omit them.  Scholar. 
Yet this I perceive by you, that the son is not darkened in himself, but is hid by the moon from us, which happeneth diuerslye: for sometime all the son is hid, and sometime the higher part only, and at other times, the nether parte only of all which forms, I may see examples on every common Almanach after a gross fort: but this Figure doth  Astronomical diagram. more aptly express the cause thereof: where the moon doth appear to be between any one Region and the son, and therefore hideth the Son from the inhabitants of that place: but in other Regions there appeareth no such let of the moon, but that they may fully see the son. And other Nations between them, see parte, and lose other parte.  
And this I perceive may bee considered dyuerselye, in as much as any bee nigher to them that see the whole son, or nigher to those that see his Eclipse.  Master. 
There is in that nighnes double consideration: one is of distance between east and west, and that other is of distance between south and north. for when any nation doth perceive the higher cantle of the son enclipsed, then they that dwell more northerly,( under the same meridian) do lose more of the son, and judge that eclipse the greater: and contrary ways they that dwell directly toward the south, the farther south they dwell, the lesser doth the part eclipsed appear to them to be, till at length unto them that dwell more south there appeareth no eclipse at all. The second consideration betwixt east and west, doth cause only diversity in time of the Eclipse, but not in form:& that is common also for the eclipse of the moon, but so is not the first consideration, but serveth for the sons eclipse only.  Scholar. 
As for the eclipse of the mone, I think the former figures which you did show me, do comprehend all varieties of forms sufficiently, which be these two, for the  Astronomical diagram of the eclipses of the moon. other two do represent those false forms, that do follow of certain false figures of the earth: and therfore do not serve here in place of true doctrine.  Master. 
This may you now also considre, that although the eclipse of the son is not general to all nations, because it is not a true eclipse or want of light, but only an appearaunte eclipse, yet the eclipse of the moon is a very Eclipse in deed, that is to say, a want of light in herself,& therfore who so ever doth see her, doth see also hir eclipse exactly as it is: and it appeareth vniformlye to them all, though at that time the moon be not, nor can not bee above the horizonte to all people: and therefore unto them that haue the moon under their horizon, it is accounted none eclipse. And that is the cause why many eclipses of the son and moon also are not noted in the common Ephemerides and Almanachs, because they appear in such time as the Planet eclipsed, is under the horizon of that region for which the Almanach or Ephemerides is written. farther more this is to be considered as a very truth and most unfallible, that the eclipse of the son can never happen but at the very change of the moon, for at other times shee is so far in order of hir course from the son, that shee can not hide any parte of him from any nation in earth. And for the eclipse of the moon, the time of opposition or full moon doth serve only. for the shadow of the earth which alway runeth toward the Nadir of the son directly, can not touch the moon, except she be very nigh unto the same place. And that is the cause why the eclipse of the son which happened at the death of Christ, may not be accounted a natural eclipse, for so much as it happened in the time of the full moon, when it is not possible by natures order, that any such eclipse should happen. And therfore did Dionyse the Areopagite being in Alexandria, and Apollophanes his companion, not only wonder at this strange and unnatural eclipse, but concluded that it could not happen without some marvelous cause, and a wonderful immutation of natures works.  Scholar. 
So doth our author of the sphere note it, affirming that Dionyse did say then: Other doth the God of nature suffer now, or else the whole frame of the world shall now be dissolved.  Master. 
With this good clause did he end his book, and so will we with the same end close up our talk. learning this good use in this natural arte, that it leadeth men wonderfully to the knowledge of God, and his high mysteries. as not only by example of these two philosophers here it doth appear, but by the testimonies of the scriptures in sundry places.  Scholar. 
This was that Dionyse, whom saint paul did convert afterward at Athenes, and rather much because he had in remembrance that miraculous Eclipse.  Master. 
So may wee gather many arguments by like matters against infidels and false Christians also: but that fruit will I reserve for an other place: and for this present will only say, that there was never any good Astronomer, that denied the majesty and providence of God, though many other denied both: but now farewell for a time: I am driven to omit teaching of Astrononye, and must of force go learn some lawe.  Scholar. 
The god that is author of true astronomy, and made all the heauens for men to behold, keep you in health and clear from all trouble, that you may, as you mind, accomplish your works, and finish well and speedily, the fruits of your study.  Master. 
Amen, and Amen.   

The titles of the fourthe Treatise.  

What occasions moved men first to judge the form of the world to be round, and namely three principal reasons thereof.  
That the heauens are round inform contrary to the error of Lactantius Firmianus, which thought it to bee flat, and his opinion confuted by diuers reasons, namely by the view of the stars, by aptness of moving, by reason of capacytie, and avoiding of emptiness.  
That the Firmament doth move, though Lactantius thought the contrary: and howe it may be proved, especially by the Milkye way. And that the stars do not move as birds in the air; or as fishes in the water.  
That the heauens are not cornered, neither of many angles.  
That all things show greater then they be, through vapours, and therfore the stars with the son and moon do appear greatest nigh unto the horizon.  
diverse opinions of the form of the earth: some thinking it to be of Cubike form, other judging it Rygge formed, other affirming it to be plain, other deeminge it hollow as a dish, and other esteemynge it long and round, like a pillar or roller: all which being sufficiently confuted, it is full proved, that the earth is justly round in shape.  
Then follow diverse reasons, approving the water to be round, and a declaration with proof why the water doth not, neither can not ouerronne the whole face of the earth.  
That the earth and water together do make but one round Globe, and haue therefore one common centre.  
That the earth is but as a prick in comparison to the sky, which is approved by four dyvers arguments.  
The distance of every sphere from the centre of the earth, with an order to try the quantities of the son and moon &c. in comparison to the earth.  
That the earth is in the middle of the world, and the contrary opinions repeated and confuted by sundry proofs.  
That the earth doth not move from the centre of the world.  
A brief rehearsal of the parallel circles, with an instruction howe to finde the distance of the tropics, and the greatest declination of the son, and of every degree of the zodiac from the equinoctial circled.  
That the arctic and Antarctike circles are not permanente, but mutable, according to the change of the regions, and so their quantities varieth, and their distance altereth, in respect to tother parallels: and their order changeth diversly.  
The Zones being immutable, ought not to be distinct by the arctic and Antarctike circles which are mutable, but rather by the Polare circles which persevere still, and keep their quantities, their distance and their order uniformly.  
That there ar no Zones vninhabitable other for heat or could, but may be and are also inhabited, as it is well known.  
The zodiac is name of the twelve signs, which signs are taken in diuers significations. and howe any star or Planete is name to bee in any sign. also what is the longitude, latitude and declination of any stars or planets.  
The colours, what they be, and howe many in number, and whereof they take their name.  
The Horizonte celestial and terrestrial, howe they be distinct: where Proclus sentence is reprehended, and three several tables set forth for distinction of hours, according to distance of miles from east to west, and that for diverse climates.  
The order and number of the Climates, with the elevation of the Pole and the quantities of the longest day in each of them.  
Of ascention astronomical and poetical, and how every one of them is distinct. with certain rules of ascention astronomical, and tables for the same, both in the right sphere, and also in diuers obliqne spheres. with an examination of the rules of John de sacro Bosco.  
The distinction of hours into hours equal, and hours unequal: and that hours unequal be considered in two diuers sorts, with tables set forth for each sort, concerning their quantities.  
Of daies artificial and natural. and what are the causes of diversity in each of them, with tables for the quantities of the same: and a declaration of the son rising and setting.  
The names of the constellations, with the number of their stars.  
A brief declaration of the motions of the planets, and consequently a reasonable proof for the number of their spheres. And farther what occasion there was, that men should imagine the ninthe and tenth sphere to be, Where as there can none be seen above the eight sphere.  
A short explication of the eclipses of the son and the moon.    


Though faults oft times do much abound,  
When men do least such chance suspect:  
Yet good redress may soon be found,  
If faults bee spied and full detect.  
But who that will in work proceed,  
And seek not first the faults tamend,  
I promise him small gain in deed,  
though truth to seek he do pretend:  
Therefore amend if thou wilt speed  
These faults, ere thou on me do read.   
The first number signifieth the page., the second the line of the page..  
9.28, sphere which is. 10.12, eight sphere. 10.29, proof of my words and in the mean season to procede as I began: you must. 17.17, doth. 18.1, the semicircle. 18.15, {αβγδ}. 21.7, {αβγδ}. 23.10. {αβγδ}. 24, in the figure H, must be set by the middle line against G. 25.26, {αβγδ}. 27.8, {αβγδ}. 29.17, moveth or runneth. 30.7, {αβγδ}. 32.22, there 2 circles. 33.22, drawn. 34.21. declareth. 36.18, and through. 41.17, they do. 56.12, to the colours. 57.35, their forms. 63.34, by their qualities. 68.17, call the latitude. 80.22, round about. 89.35, accordingly. 97.20, at home. 103, in the margin, lib. 3, c. 24.106.11, although. 106.33, heaven. 111.6, most apt of all other. 114.31, the rygge. 114.32. the one. 116. in the margin, the reproof. 117.21, instant. 121.19, the fifte parte. 121.20. the fifte parte. 124, in the margin is the line wrong set. 136.18, that is by D. 136.24, that is by B. 145, and 146, the four figures are not well placed in order, for the first should be the third, the second should be first, and the third ought to bee second. 147, set D vpon the greatest shadow, and E vpon the myddlemost. 153.11, 33 minutes. 171.4, foully. 172.8, {αβγδ}. 177.9, Arcturus is in libra &c. above 31 degrees. 180.35, And H& L the 2. extreme points on the earth, unto which &c. 186.23. stand. 189.5, at an other time. 192, in the figure of the climates, B and D should stand lower against the double line, which is the equinoctial. 194.23. considre. 207, the line in the example is wrong placed. 212.1, differeth not in this table the first. 212.16, 180 degrees. 233.16, of proportions. 245.22, the day is not. 248.20, reject that order. 248.33, is not regarded. 260.10, the titles set. 266.12, protrygetes. 270.3. right wing. 272.1. fifte and the.   

Imprinted at London by Reginalde wolf, Anno Domini, 1556.