these diuisions from th'equinoctiall by the diuisions of the Polary Circle vnto A Arkes or portions of Circles you shal haue the frame preparid in whiche you shall in the same maner that you did for England place such portion of the world as it can aptly receiue Spo. But may I not describe here the paralleles climates taking thē out of the table in the second boke as Ptolomaeus doth in his Geographie Phi. Yes verely it shall adorne the mappe not omitting the principall windes seruing for that part of th' earth nor yet th'inhabitāts called for the diuersitie of shadows Periscij Heteroscij Amphiscij but nowe beholde the frame of whose composition we haue made so manye wordes Spou. This mappe doth liuely expresse your meaning so that ther is none I suppose so ignorāt or dul but that without great difficultie he may practise the like ther fore I require you procede in the descriptiō of à Card for halfe the face of th' Earth whiche as I coniecture wyll conueniently serue for our Hemisphere Philo. Not for our Hemispere onely but also for any one halfe portion of th' earth as well seruing th' vse of thē that dwell vnder vs directly called therfore Antipodes as also any other But I will leaue to speake of th' vse of it because of it self it is manifest wil make plain vn to you the cōposition artificial praeparatiō of it First with your cōpase describe à Circle as great as your carde shal be withī which draw an other Circle à finger bredth distant iust to this also an other Then part these Cir cles in the middes with à right lyne th'endes of which ar A. C. crosse this lyne in the middes with an other ryghte line B. D. So is your Circle parted into 4. equal portions Then deuide euery portion in the cōpasse of the circle into 90. partes in this maner First into 3. then euery of thē againe into 3. after into 2. laste into 5. After write in them 5. 10. 15. 20. 25. 30. c frō B. C. vnto D A. so is the whole cōpasse of your card parted into 360. portions Spoud Unto what vse serueth the crosse lines drawen thorow the face of the Mappe Philo. The line A. C. repraesenteth the meridiane as the line B. D. The halfe Aequinoctiall circle Also A. C. repraesenteth the Poles of the world the plages or partes of the same north south as B. signifieth the weast D. th' East Spou. I perceiue your minde therfore procede Phi. Thē applie the ruler to the digr of the circle of A. B. C. note th'intersections of the ruler in th'Aequinoctiall in like maner do in th' other halfe Circle A. D. C. this ended you shall describe from A. vnto C. Paralleles or halfe circles by these diuisions in th'Equinoctiall then write on them from B. to D. 10 ▪ 20. 30. 40. c. Also you shall apply the ruler to the circle diuiding the Meridiane line A. C. as you did th'equinoctial B. D. describe in th'interfectiōs in like maner halfe circles which shall serue for Paralleles of Latitude Then accompte in the circle from B. toward A. xxiij digr 28. min. describe an arcke which shall repraesent the halfe tropick of Cancer also frō A. toward B. accōpte xxiij digr 28. min. draw with your compasse another arcke which shall signifie the halfe Articke or polary circle in like maner do with the tropike of Capricorne th'Antarticke circle After place the halfe part of th' earth in the mappe thus praepared describe the Climates Paralleles inhabitaūts winds with theyr proper names the mappe shal be perfaitlye finished as for example you maye beholde the frame of the Hemisphere of th' Earth before placed Spou. This carde should seme to giue à great light knowledge vnto Nauigation And if I do praepare me an other Mappe for th' other Hemisphere I shall in these two cōpraehende conteine th' vniuersall Earth Phil. Trew it is but as touching the light it bringeth to Nauigation we will make mētion of at our next meting now I will shewe you how in one carde or Mappe you may describe all th' earth in such wise as shal be most perfait in that forme figure whiche shal be right pleasant Spou. I pray you then begin I shall giue diligence Phi. First describe on some plaine place an halfe circle A. B. C. vpō the center D. so great as thou wilte haue the carde after deuide the right lyne A. D. into 90 portions equally Then place th' one ende of your compasse in A. stretching forth th' other ende vn to 86. degr xv min. xx secondes in the line A. D. so with your Compasse draw an arke frō D. vnto the halfe circle A. B. C. whiche shall crosse it in B for by this way th'arke A. B. being extended right forth shal be as long as the right line A. D. Then you shal diuide this arke A. B. into 90. equal partes After with your compasse take the quātitie of th'arke A. B. and placing th' one ende in B. take the lyke quātitie in the half circle towardes C. whiche in like maner you shal diuide into 90. portiōs so th'arke A. B E shal be parted into 180. parts Again with thy compasse take the lengthe of the line A. D. th' one ende beynge placed in A. take the lyke proportion from A. to F. so that A. F. shal be equall to the line A. D. Then diuide the line A. F. into 90. partes equally as you did A. D. after placing th' one fote of thy cōpasse in the Cēter D. thou shalt draw arkes in euery of the diuisiōs or els euery fift or x. diuision onlye note the hiest Arke nexte with G. H. then enter into the table folowing find out how many degrees in lōgitude answereth to 80. degrees of latitude north frō th'equinoctiall which in the table are 140. degrees 40 minutes that number you shal accompt in the half circle from A vnto E. applying your ruler vnto th' end of this nōber vnto the cēter D. drawà short line whiche shal extēd vnto H. again enter into your table with 70. degrees of Latitude you shall finde 138. degrees 23. minutes which I accompt from A toward E as before applying my ruler to the shorte line the degrees in Longitude with my pen I draw an other shorte line In like maner I do with th' other paralleles of Latitude 60. 50. 40. 30. 20. 10. Spou. So that by entringe into the table accompting the degrees in Longitude frō A. towardes E drawing short lines one at th' end of an other ther ariseth as it wer a portion of a circle frō D to B. if I could in like maner find the proportiō of th'equinoctiall vnto the South paralleles whiche in like nōbre are 90. thē the whole forme wolde repraesent
the pole arctike and antarctick in their Horizont Spoud Do you not call the two pointes or endes of the axe tree the fornamed poles Philo. It is so and for firmer printing it in memory beholde here the type of them that haue a right sphere As A. D. C. representeth bothe the axe tree and the right Horizont and A. C. the two poles Yea and B. D. the half parte of th' equinoctiall Spoud So that a maÌ„ inhabiting vnder B. D. which is th' equinoctial do perceiue both A. whiche is the North pole and C. whiche is the South leuell with th' earth and his verticall point in the for said Aequinoctial Philo. You do well perceyue it Spoud Then it foloweth that where ether of the poles is eleuated aboue th' earth they dwell not vnder the aequinoctial and so haue a croked an oblique sphere Philo. And that doe this figure perfitly proue Here C. E. is the halfe of the axe tree aboue th' earth B. E. is the halfe of th' equinoctial C. the one pole aboue th' earth Whiche maketh the halfe sphere A. B. C. D. to be oblique and croked according to my first meaniÌ„g Spou. I vnderstaÌ„d this perfitly Philo. Then is it expedieÌ„t for you to coÌ„sider that this sphere doeth in it conteine many Circles Spoud Your wordes bringe me in à doubt For I perceiue that à circle à sphere are both rounde haue like Centers Diameters Phil. They haue no lesse yet they do as greatlye differ as the worlde th' earth of which we made mention as this definition of Euclid do manifest plainly 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 which Scheubel excelleÌ„tly after his maner traÌ„slateth Circulus est figura plana vna linea compraehensa quae circumferentia appellatur ad quam ab vno quodam puncto eorum quae intra figuram sunt posita omnes cadeÌ„tes rectae lineae inter se sunt aequales And is thus much to say with vs. A Circle is à plaine and flat figure comprehended within one line which is called à circumference vnto whiche if lines be drawne from the Center or poynt of the circle vnto the circumference they beinge conteined within the same are found to be equall one to an other As in this example A. is the center of the Circle B. C. D. E. the Circumferent line c. Spou. By these wordes I finde à two foulde difference betwixt à sphere à circle First that à circle is à playne flat figure à sphere of rouÌ„de fourme like vnto à Ball. And then that à Circle is coÌ„praehended within one line a sphere within one plat fourme â–ª But now I pray you declare such Circles as are imagined to be in the sphere of the worlde most necessary for an introduction Phil. In This sphere chiefly x. Circles are imagined Of whiche 6. be great 4. be small whiche in order I will set out And therfore answer me Haue you not read among your authours of the HorizoÌ„t circle we will beginne with that firste because necessitie inforseth suche order Spou. Yes sir Proclus defineth it in this sorte 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Horizon est circulus qui diuidit nobis mundi partem quae videtur ab ea quae non apparet qui ita in duas partes aequales â—…otum discindit mundi globum vt eius dimidia pars altera supra terraÌ„ extet dimidia altera sub terra sit Which sounded in our language in this maner The Horizont is à Circle which deuideth parteth that part of the world which we see from that which do not appereâ—… which par teth the worlde in two equall partes in suche facion as th' one halfe is euer aboue th' earth th' other alway vnder Phil. Th' use of this Circle is right excellent for by it we finde out the rysing goyng downe of euery Planet Starre In this Horizont the daye nyghte haue also theyr beginning ende Spou. So that this Horizont is â lyne imagined to go rounde about by the face of th' earth parting the heauens in two partes and is saide of 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 whiche signifieth to decerne or ende But standing on an hie Mountaine steple or suche lyke thing shal I se but halfe the heaueÌ„s Philo. Yes verely you shall see more then an Hemisphere for so call they the halfe sphere as also beynge in à valley and lowe place you shall not see youre Hemisphere totally And althoughe you may obiecte that this Horizont deuideth not the heauen in two equal portioÌ„s yet it is proueth nothinge for th' Astrologians alowe no suche Horizont Spoud And is this Horizont à fixed Circle or not Philo. It is fixed and without motion Spou It should seme contrary For I beynge at London haue one Horizont and goyng to Andwerpe haue an other and so at Colein an other and at Heydelberge another c. Philo. I confesse no lesse but that proueth nothinge that the horizont moueth for loke into what errour you shoulde fall you muste graunte if the horizont moue that with the turning of the heauens your horizont Circle must come ouer your verticall poiÌ„t once in 24. houres Spoud Nay I will not graunt suche absurditie in any case wherfore I see that it is my chauÌ„gyng that maketh me to haue à newe horizont and not the horizont to moue with me Phil. You hit the naile on the head as the saying is Nowe your authour deuideth the horizont lyke to the sphere that is into à ryght horizont and into â croked or oblique Spoud What be they that haue a right horizont Phil. They haue a right horizont whan as this circle crosseth th' equinoctiall rightely in two partes and they haue a croked horizont whan eyther of the Poles is aboue th' Earth and th' other vnder suche is oure Horizont whiche inhabit Europe But for the better vnderstanding I haue made here a figure in whiche C. A. and E. is th' equinoctiall And because B. A. D. crosseth it rightely It is the right Horizont Also B. D. are the two Poles of the worlde because B. is eleuated aboue th' earth it maketh F. A. G. to be th' obliquè Horizont as these ij pictures here placed do shewe This Picture sheweth the fourme of a right Horizont This Figure represent a croked or oblique Horizont Spoud Seyng that the Horizont semeth onely necessary for to know the true risinge goynge downe of the Sonne Mone Planetes fixed sterres it can not any thynge helpe for to knowe whan anye of them are at the hiest aboue the Horizont for that daye in whiche place whan as the Sonne coÌ„meth it is midday For I perceiue euery Planet Starre to ascende by litle litle aboue th' earth vntyll they be at the hiest then in lyke maner do continuallye descende vntill they come to the Horizont in the West Phil. For this
you drawing from the center to the circumference a straight line shal haue your own desire Other willing to exchew the tediousnes of time in obseruation do prouide a Plate of Meatall well pullished or some thick planke smothe and plained in whiche is drawne à circle as in th' other aforsaid with a Wyer or like thynge set vp right in the center and do diligently before none obserue whan the shadow of the Wier in length is equall with the circumference and at th' end of it make à prick In like sorte after noone whan as the shadowe commeth vnto the circumference and make there also à prick thē with the compasse deuide the space betwixte these two prickes in the middes and make there à note or pricke after draw à right line from the center to that middle pricke and it shall alwaye shewe the whan as the sonne is in the meridian or middaye line for that eleuation of the Pole as in this example A. Is the Center B. E. C. F. the Circle drawne in the planke or plate of metall A. D. the Gnomon or thing which geueth the shadowe AE the shadowe before Noone A. F. the shadow after none nowe deuidinge the space E. F. in the middes whiche is C. and drawne à righte line from A. beinge the Center vnto C. and that is the true Meridian line Spoudeus This way semeth muche easier and facile then the other Philo. Yea and it is also as certaine as th' other and it was inuented as I suppose of Iohannes de monte regio or Vitruuius But Uernerus vseth no other way to find oute thys Line then onelye a Diall hauinge à perfaite nedle placinge it on some plaine and smothe place whan the nedle standeth stedfastlye in the righte Line wythin the Diall it dothe as it were poynte directlye North and South Spoud This waye in my iudgement doeth excell all the rest both for the easines therof also which you can not do by th' other that you maye by it finde the Meridiane or middaye Line at all tymes bothe daye nyght houre Phil. You may so but the neadle doeth sometime erre from right north south as hathe bene obserued I will shew you in the treatise of Nauigation Yea how you shall also correct your neadle but I also haue inuented two waies the first is I make a plaine roūde plate in the mids of which I fix à ruler hauing two sightes to loke thorow then whē the sonne risith halfe aboue the Horizont half vnder I placing my Instrument flat on th' earth do direct the ruler vnto the same so that I may see him thorow the sightes then my ruler not moued I drawe with à Chalke or like thing à right lyne frō the Center vnto the Sōne whan the Sōne goeth down I do in like maner drawe an other Line then I drawe à right Line from the Line of his rising vnto the Line of his goynge downe diuide this Line in the middes after I drawe a right Line from the Center vnto the middes of the ouerwart Line thē I fixe in the Center an vpright wier the shadow of whiche at all times shall shewe when as the Sonne is in the Meridiane Line in that habitation but or we further procede I wyll giue you hereof an example in which I do make A. for the Center then putting vpon it à wyer or pricke I do fasten the ruler ther on this beyng done I place my instrumēt flat applie the ruler with his sightes G. F. vnto the Sōne drawe there à Line A. D. in like sorte whan he is goyng downe make an other Line A. C. then I draw à right Line from C. vnto D. which I diuide in the middes E. crosse it with à Line A. B. which is the Line at midday But in place where I cannot haue this or other like instrmēt whē as I se the sōne to draw very nere the south I pricke vpright in the groūde à knife or such like thīg markīg diligētly how lōg the shadow doth decrease whā as I perceaue it decreaseth no more but rather waxe longe againe I drawe à line from my knife to the shadow which serueth for the Meridian line Spoud I thancke you sir for this your gentlenesse in beating these things into my grose and dulhed And I wil put them all in practise whan conuenient time shal serue but in the night I mīding to take the true height of anye Planet or fixed sterre in the nonestead lyne what ordre shall I obserue for then there is no shadowe which will do pleasure Philo. Therfore wyth some Quadrāt Astrolabe or Ptolomaeus ruler the fation of whiche I do here place and the makinge you shall finde amonge th' other Instrumentes and marke what hys It is made of 3. peaces beyng 4. square As in the Picture where A. F. is the first peace or rule A. D. The seconde G. D. the third rule E. The Foote of the staffe C. F. The Plumrule C. B. The ioyntes in which the second third Rulers are moued K. L. The sighte holes I. The Sonne H. The Zenit or ver ticall pointe M. N. The Noonestead Lyne altitude is then you may staye a season after à while obserue his hight again and so from time to time vntill he increase no hier which is a perfect token that then he is in the Meridian line The same you maye do also with the sonne And for that nightlye trauell hearein semeth somwhat combrous and painfull behold here is a Table of the sonnes height for euery degree of the signes in the Zodiake his greatest declination being 23. degrees 28. minutes and th' eleuation of the Pole arctike aboue the Horizont 52. degrees 10. minutes As concerning the vse of the Table I wil speke nothing but will reserue it for his due place only admonishing you at this present that first you finde out the place of the Zodiake in signes and degrees by some Ephemerides or out of my tables in the Gazophilaciō Astronomicum then loke in the ouerpart of the Table and if that signe be there mensioned descend downward in the first columne finde out also the degre and directly against it shalt thou haue the sonnes Meridian altitude But and the signe be found in the lower part of the Table then you shall serch out his degre in the last column and against it toward the left hand you shal in like maner finde the Altitude answering hereto Spoud I praye you geue me example hereof or you do take in hande any other matters Philo. The thing is so easy as it nede no farther working ▪ yet I will not refuse in so litle a request to satisfye your desire I find the sonne the first day of the new yere 1558 in the signe of the Goate xx degrees the. 37. minutes A TABLE OF THE SONNES MERIDIANE Altitude aboue the Horizont Calculated for
I do not so muche fansye Ptolomaeus in lōgitudes latitudes for he was not able being so mighty à Prince to trauell into those countris that to à priuate person for the greate distaunce à sunder was impossible And therfore receiuinge as he confesseth obseruations at other mens handes dyd in many sundry places swarue from the trueth Ph. And that was not to be imputed vnto Ptolomaeus as à crime seyng the errour ensued by other mens obseruations But for this cause I haue made my fifthe Booke in the whiche I haue folowed Ptolomaeus in certaine pointes touchinge his natiue Countrey places to them adiacent In th' other I haue vsed later writers trauelles not omitting my owne as you shall euidētly perceaue Spoudeus I pray you giue me an example of these thinges spoken Phil. Here minding to describe the plat forme of Englande I draw as you se à right line in the middes of the Mappe And because I finde in my fift boke that it is frō the Weast part of the same to th' East 11. digres I diuide this streght line beynge the Meridian Line for the middes of this Regiō into xj equall partes or portions Then do I searche how much the Pole Arctik is eleuated aboue th'Aequinoctiall in the furdest north part of Englande finde it 61. for vnder the name of Englande I comprehend the whole Ilande cōteyning also Schotlande Irelande Therfore I enter into the Table goyng before finde answering to 61. digr 29. minutes 5. secondes 19. thirdes Which space I take with my cōpasse in one of the diuisiōs of Lōgitude that I made in the meridian line so my compasse not opened wider I begin at the Meridian Line in the higher part of the Card make on either side 5. pricks that is to sai v. on the left hād v. on the right hād in like ma ner I find the south part to differ frō th'equinoctial lj di wherfore entring into the Table I find answering to lj dig 37. min. 45. seco 33. thir And with my cōpasse I take the like portion in one of the diuisions of the Meridian line then with my compasse I diuide the lower parte of the Table as I did the hier Then draw I right Lines from the Prickes in the hier part of the Table vnto the prickes in the lower part wright at th'endes of them the Digrees of Lōgitude as also in the diuisiōs of the Meridiam line I wright the digrees of latitude Thē seke I in the fifth boke for the notable Cities Townes Villages suche like place them in this card according to their true Longitude Latitude as in the card of Englād following you may well perceiue Spoudeus Nowe I perceiue by the makinge and describyng of this onely Mappe that the whole worke doeth chieflye depende vppon the Meridian Line appointing by them the longitudes of Regiōs by Paralleles of Climates whose vse in à Carde is to limite the Latitude frō th'Equinoctiall So that obseruing this order of you prescribed I may in like sorte at my pleasure drawe à Carde for Spaine Fraunce Germany Italye Graece or any perticuler regiō yea in à warme pleasaunt house without any perill of the raging Seas danger of enemies losse of time spending of substaunce werines of body or anguishe of minde Oh how precious â Iewell is this it may rightly be called à Cosmographicall Glasse in which we may beholde the diuersitie of countries natures of people innumerable formes of Beastes Foules Fishes Trees Frutes Stremes Meatalles Phi. You shall haue iust ccasiō to affirme whan as you vnderstande the whole cōmoditie of the same But I will shewe you to describe iij. or iiij Regiōs in one Mappe yea or so manye as are cōteined in th'eyght portion of th' Earth And therefore I call it à Carde conteining th'eyght part of th' Earth whose compasse in what quātitie you please the greater the better note it with A. B. C for the easier vnderstanding vn till you are exercised herein Then deuide the compasse of this Circle in iij equale partes marke the pointes of the diuision with A. B. C. After place th' one ende of the cōpasse in A. stretche out th' other ende vnto B. or C. with thy compasse draw an arcke or portion of à Circle from B. to C. Then set th' one ende of the compasse in B. draw the like arcke frō A. vnto C. After place the one ende of thy cōpasse in C describe the like arck frō B. to A. And here note that A. doth signifie the North or south Pole And th'arke B. C. the quadrant or iiij part of th'Equinoctial Circle This arke B. C. you shall di uide equallye in the middes at that pointe place D. Then draw à right line from A. vnto D. this shall repraesent the meridiane line for the middes of this carde This line shall you diuide into 90. partes euery one shall repraesent à digree or into 18. portions euery one shall answere vnto v. digr Or if the Mappe be small into 9. portions euery suche diuision shall signifie 10. digrees Then placing th' one ende of your compasse in A. extende or stretch out th' other vnto euery of these diuisions drawe arkes or portions of circles from th'arck A. B. vnto th'arck A. C. These ended you shall write in euery diuision from B. to C. th'equinoctiall vnto A. the Pole Arctik 1. 2. 3. 4. 5. or 5. 10. 15. 20 or 10. 20. 30. according to the diuision of the meridiane line After you shall accompt in this diuision 23. digrees 28. minutes from the quinoctiall which is the sonnes greatest declination and draw ther à double arke whiche shall serue for the Tropicke of Cancer or Capricorne noted with E L in like manner accompt 23. degrees 28. minutes from the North or South pole in that space draw in like sort à double arke which shal be in stead of the polary circle either Arctike or Antarctike set th'endes of it I K. and so are all the paralleles of latitude answering your mappe perfaitly finished Spou. I vnderstand the protracture of them very wel But shall there be but one Meridiane line for all thys Mappe Phil. Yes verely ther shal be so many as there are paralleles of latitude whose nombre as I saide was 90. Spou. Now I perceiue the reasō of this artificial working for like as the circuite of the heauens is distributed into 360. parts so in like maner the compasse of th' earth is also into 360 portions deuided both toward the Poles also from West to East Therfore I pray you shew me the waye howè to draw these meridiane lines Philo. You shal deuide the arke B D Cinto 90. or 18. or els 9. portions equally as I did the latitude from A vnto D. In like sort you shall deuide the polary Circle I K. then drawinge in
and Mone be aboue the other Planetes as wel as in that order you haue rehersed them Philo. This serueth not for our purpose but it is excellently proued of Ptolomaeus Alphraganus Tebitius Archimedes and other with suche inuinsible reasons as can not be denied But me thinke the pleasaunt Poet Ouidius maketh a good reason to proue the Sonne to haue his sphere in lyke order as is aforesayde whan as he speaketh vnder the parson of Phebus vnto yonge Phaëton entring into his Chariot in this maner Altius egressus caelestia signa cremabis Inferius terras medio tutissimus ibis In our english tunge the meaning of these versis is thus Directe thy Chariot in a meane clymbe thou not to bye Lest thou dost burne the heauēly Signes set in the sterry skye Or descending to lowe th' earth of heat shall fele the flame But kepe the meane y ◠shalt be fre frō feare eke frō blame Spoud The cause is so manifest that it nede no lenger declaration So that I suppose theis excellēt wryters aforesaid haue found out the true order of the spheres as you haue repeted them And that Crates with his company haue no lesse erred placing the luminaries aboue the eyght heauen then Albetragnius whiche supposeth Venus and Democritus whiche affirmeth Mercurye to be higher then the Sonne Philo. Yea and Plato whiche otherwyse is a graue Philosopher did no lesse erre then the other imagining the luminaries to haue their course vnder all the other Planetes Spoud Well let them passe and now to the nomber of the heauens whiche you affirme to be x. Philoni You haue ryghtly spoken Spoud I remember among other thinges that I haue redde in Diodorus howe that the Aegiptians supposed there were but eyght heauens and that by this perswasion They gaue to the seuen Planetes vij heauens And bycause they perceiued that heauen whiche you call the firmamēt to cary the fixed sterres in it and to kepe one vniforme order and distaunce in rysing none steed and going downe to circuit th' earth also in 24. houres and finally to cary the heauens of the Planetes by his swiftnes about th' earth with him contrary to their naturall motion they supposed of whose mynde I also am that there ware but eight heauens And that which you call the eight heauen they name primum mobile Philo. You may not to rashely adicte your selfe to any of their opinions before you are certaine they are eyther trew or els receiued as moste probable For by the lyke reason I can compell you to confesse there are ix heauens as Ptolomaeus affirmeth But for shortnes of time and that it sumwhat swaruith from our purpose I wyll omytte it and leane to th' authoritie of the famous king and graue Philosopher Alphonsus whose name by his trauell is made immortall Spoud Thus I perceiue your saiynge to be verified when you excused the olde writers that tyme bryng all thinges to their perfection But I haue redde also of an heauen whiche in greke is named 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Empyreū Philo. It is so named of the wonderful brightnes and beautie But because it is imoble and without any mouīg I exclude it out from the nūber of the mouable heauēs and that as not seruing to our purpose And thus you haue learned what the worlde is and also the heauenly region But for the redier conceiuing of that whiche is now spoken behold the figure insuing Spou. Wil it please you now to procede with th' elemētarye region which you declared to be th' other parte of the world Philo. Before we shall take this part in hande for the easier auoyding often repetitiō of one thing I wyll giue you some introduction into the celestiall sphere touching such circles as must of necessitie serue in this arte Spou. And that fault haue troubled yea right excellent authors for they obseruīg no methode were cōpelled to repete one thing diuers and sondry times But because you made mention of a sphere maye it please you to make definition of it Philo. All suche as haue wryten hereof do accorde in one as Theodosius Proclus Euclyde Orontius Iohn Halifax our worthy countryman called also Iohn de sacrobosco c. But as well for th' authoritie as also elegancie I wyll repete vnto you Theodosius definition who sayth in this wyse 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Sphaera est figura solida cōprehēsa vnâ superficie ad quā ab vno eorū pūctorū quae ītra figurā sūt oēs rectae lineae ductae sut inter se aequales A sphere is a sound body conteined within one platte forme and bounde vnto whiche all right lynes drawen from the Center they being cōteyned within the figure are founde aequal amōg thē selues To the vnderstanding of whiche definitiō is requisite to knowe both what the center axe tree and diameter of a sphere is Spoud Now I perceiue the reading of the pathway doth not a lytle helpe me in vnderstanding this definitiō of Theodosius as also suche wordes whiche are vsuall in Geometry But what is this axe tree of the sphere for I vnderstand that by a center is nothing mēte but a prick in the myddes of any circumference Philo. Theodosius calleth the axe tree a certain right line drawen by the center both endes of it ending in the plat forme of the said sphere the sphere being turned about it and yet this axe tree to remaine fixid without motion As in exāple Here you se A. B. C. to represent the halfe sphere the axe tree also drawen through it is A. D. C. whiche being fixid the halfe spheare turnynge round about maketh a parfait roūd body As this figure here placed maketh true mention Spoud I pray you what difference is there betwixt the diameter of a spheare and the axe tree Philo. I wil showe you omitting th' auctors names for briefnes A diameter of a sphere or globe is any lyne drawen thorowe the same goyng by the center of the sphere or globe And so there may be yea and you wyll xx diameters or as many as you please in a sphere but there can be but one axe tree on whiche the sphere or globe is reuoluid And this axe tree is voyde of all motion Spoud I wil and it please you make a profe wherby you shal perceiue if I rightly vnderstād your meaning Philo. do you so Spou. Here I wyl make a sphere in whiche I drawe right lines frō the one part of the circūferēce by the cēter so to th' other Such right lines or diameters are AD CF BE but I do imagine only A. D. to be the axe tree and imoble Philo. Very wel wrought Now procede we forth You must also consider that the sphere is deuided into a right sphere and into an oblique or crokyd sphere they only haue a right sphere which dwell vnder th' equinoctiall and haue both