THE SCHOOL OF SKILL: Containing two Books: The first, of the Sphere, of heaven, of the Stars, of their Orbs, and of the Earth, etc. The second, of the Spherical Elements, of the celestial Circles, and of their uses, etc. Orderly set forth according to Art, with apt Figures and proportions in their proper places, by Tho. Hill. AT LONDON. Printed by T. judson, for W. jaggard. 1599 To the Reader. divers have written of sundry matters in former Ages, to the intent to benefit these our later times, wherein a man can name no kind of Art or Science, liberal or mechanical, but there are as rare wits to be found as ever lived since learning flourished. The reason is good that it should be so. For first, we have come to our hands, use and judgement, whatsoever either autique or modern Authors have left behind. Secondly, the government (God be blessed) hath a long time (now these 40. years) been so peaceable, that Students had never more liberty to look into learning of any profession, for the enlarging of their understanding. Lastly, the means otherwise, aswell out of the universities, as in them, have been and are so many and so good, to attain to all knowledge, that I dare be bold to say, England may compare with any Nation for number of learned men, and for variety in professions. Of late a man of good merit, named Tho. Hill, painful with his pen whiles he lived, (as the world can witness, being possessed of sundry his works in Print) now deceased, left this Treatise Mathematical, entitled The Rudiments of the Sphere: which being found by judgement of the learned in the like profession, worthy the publishing, I have, not only for the memory of the Author, but also for the profit of alwel affected Students, undertaken to set forth. Wherein whosoever bestoweth time & labour to read, with a temperate and sober spirit, I doubt not but they shall be satisfied in all such points, as this Mathematician pretendeth to handle. His style is not to be plausible, considering the subject or matter whereof he discourseth, doth restrain him, both to terms of Art, and phrases consonant. But for his order and facility (such as a profession of this nature will bear) better to be conceived, than some (none dispraised) that have written of the like argument. It is not unlike, but he would (if God had spared him longer life) have held on as he began, to set forth for the common good of his and our Country divers necessary works. This seeming his last, and whereof there is use both on Sea and Land, printed according to his own copy, and the Figures answer able to the patterns as they were draune by pen, now newly stepped into the world, receive & read friendly, find no fault; but accept the good mind of the deceased man, and thank them by whose means this book, which otherwise night have been lost, is set on foot, and come abroad. April. 8. 1599 Yours W. I. THE FIRST PART OF THE RUDIMENTS OF THE SPHERE OF HEAVEN, of the Stars, of the Orbs of the Stars, and the EARTH. seeing this little Book of the Sphere doth entreat of that part of Astronomy, which showeth the divers motions of the Celestial Orbs and stars, the magnitudes and distances of their bodies from the Earth, with all the diversities and nearness of appearances in the Planets, and fixed stars: therefore doth the Author write of the Principles of the same, in this Treatise of the Sphere, to the great commodity of many young Students in the Art. For this containeth only the entreating of the Sphere: that is, of a perfect and very round body, containing divers Circles, which the learned do also call a Material Sphere: of the Celestial appearances that it describeth in the Instrument, named of them the Material Sphere. Now this teacheth five definitions of the same: two of the Sphere, one of the Centre, one of the Exe tree, and one of the Poles of the World. 1. What a Sphere is. EUCLID in his eleventh Book, thus defineth a Sphere. A Sphere (which in Latin is a Globe) saith he, is a sound Figure, made by the turning of a half Circle, the Diameter of which half Circle continuing so long steady, until it be brought again unto the place, where that Figure began to be drawn. Or thus: A Sphere is such a round and sound body, which is described by the drawing about of the half Circle. Theodosius teacheth another definition of the same: That the Sphere is a certain massy Body, or sound Figure, enclosed with an upper face or platform, in whose middle is a Prick, from which all lines drawn from the Circumference or platform are equally distant one from the other: and this Prick, of him named the Centre of the Sphere; and like of the Globe. The half Sphere is contained in the half of the Globe, and greatest Circle of the Sphere. The Exetrée of the Sphere is a right line, about which the Sphere fixed, doth the half Circle drawn about describe. There are also two manner of Orbs, as the soiled Orb, and hollow Orb: the Solyde is named the Globe or Sphere, which only containeth one round upper face, and the same embossed hollow outward: but the hollow Orb differeth, in that the same hath two upper faces, the one embossed outward, and the other hollow within. Also the Orbs of all the fixed stars, and Planets, are like hollow, and not Solyde. To the Sphere belong these differences, A Prick, a Line, Dyametre, Parallels, an upper face, a Centre, Exetrée, and Poles. A Prick or note is of no bigness, but the beginning of Magnitudes, which in the order of nature goeth before them, and not made as a part: in that a Line is not made of Pricks, nor Pricks are the parts of a Line. For if an infinite number of Pricks were heaped and joined together, yet would those never make a Line: so that a Line is caused, through the drawing of a Prick into length. A Line, is a length without breadth and deepness, and ended with two pricks, which cannot be comprehended, but by Imagination. A Dyametre, is any right line drawn by the Centre of a Circle, and middle of a Figure: whether the same be plain, Solyde, round, or cornered: whose ends reach and come from side to side of the Circle about, and divideth the Circle into two equal parts or just halves. The Parallels are two right Lines equally drawn, which extended on any Platform unto an infinite length, do always keep one like distance, and neither draw nearer, nor touch together. An upper face, is a length and breadth without deepness, made by the drawing of a Line into breadth: Of which, the plain upper face is that, which is expressed with those strait Lines which it hath: that neither the middle riseth up, or is raised at the ends, nor the same falleth within. The Spherical upper face is distinguished, into an embossed and hollow upper face. The embossed, is the outward compass about of the Sphere, or bodies round: but the hollow upper face, is the inward compass about in the hollow Orb, or the bodies hollow. A Centre, is the middle Prick in a Circle, from which all right Lines drawn unto the compass about the same, are equal between the one and the other. Also a Centre of the Sphere, is a middle Prick in the Sphere, from which all right lines drawn unto the embossed upper face, we agree in length. The Exe tree, is a right line drawn by the Centre of ●e Sphere, and with both his ends piercing unto the ●des of the embossed upper face, about which the Sphere 〈◊〉 turned. The Poles, are the very ends of the Exetrée, appeaing on each side, about which heaven is turned. Also the ●oles of the turning, are named the ends and tops, and named besides the ending points of the Exe-tree, drawn by the Centre of the Sphere: about which the Shere and Circles of the Sphere are turned. The Poles of the Sphere, and Circles described in the Sphere, are points consisting in the upper face of the Sphere, from which all right lines drawn unto the compass of the Circles are equal. Although every greater Circle in the Sphere of the world hath his Poles, yet is oftener mention made of the Poles of the world, or Equinoctial of the Zodiac, and Horyzont. The Poles of the world or Equinoctial, are the two extreme points and both end of the Exe tree of the world, about which the Sphere is turned. The one of the Poles, which elevated showeth to us dwelling into the North, and turneth always about in our sight, is named the boreal and North Pole, of the little Bear near to it: which Pole is continually seen and known by the two stars near to it; of which the one is notable and clear, of the third bigness, standing at the end or top of the tail of the little Bear, distant from the very Pole 4. degrees, and 9 minutes. But the other dimmer, of the fourth bigness, not far distant from the other star afore, is come nearer, and doth scarcely differ now 50. minutes from the place of the true and very Pole. If any will know the Pole of the world or Pole star, let him turn his face toward the North, the sky then being clear; leaving the East on the right side, and west on the left side, and he shall see in the little Bear seven stars, placed like to the form of the stars of the great Bear, which are brighter. Of these stars three do fashion the tail, and that which is in the top of the tail, is named the Pole star, which declineth in our time from the Equatour 85 degrees, and 5●▪ minutes. So that being no further off by this declination from 90 degrees, the distance of it from the very Pole shall remain and be 4. degrees, and 7. minutes: and this star also in process of time shall be joined with the Pole. The other Pole, which through the swelling of the earth, is continually hid to us of the North, is named the Meridional or South Pole, right against as it were the North Pole. Being evermore so low depressed, as the North Pole raised, in any country to the North, above the Horizont. The Poles of the Zodiac, are continually so far distant from the Poles of the world, as is the greatest declination of the Sun, which in our time is found and noted by observations to be of 23. degrees, 28. minutes, and 30. seconds. But the Boreal or North Pole of the Zodiac, distant from the two dim stars, in the triangle of the Dragon (being stars of the sixth bigness) which a right line by imagination drawn from the third star in the tail of the little Bear, unto that constellation named Lyra, expresseth the same, that it is but a little further distance than two degrees. The Poles of the Horizont, are the two extreme points or ends of the right line, drawn out of the Centre of the Earth, by the top over our head, unto the opposite places of the Dyametre of the Merydyan: of which the one, directly over our head, named the vertical point, and of the Arabians Zenith, the other right against, named of them Nadir. And the Poles of each of the greater Circles, do differ from their Circles 90. degrees, or a quarter of an other great Circle of the Sphere. For by the 23. proposition of Theodosius of the Sphere, a right line drawn from the Pole of his Circle unto the circumference, is equal to each of the four quarter sides, describe within the same Circle, which four quarter sides, do divide the Circle into four quarters. Yet are each greater Circles of a Sphere, equal between the one and the other. But seeing the equal right lines, do take away the equal compasses of the equal Circles, therefore should a line drawn from the Pole unto the circumference of his Circle, take away of the greater Circle, one quarter of the other Circle drawn by the Pole, even like as the sides of a quarter described within the Circle. By which appeareth, that the Poles of the greater Circles, do differ or be distant by a quarter from their Circles, as is above written. What the World is, and into how many parts the same is divided, with the motion of the celestial Orbs. THe World after Orontius, is defined to be a perfect and an entire composition of all things: a divine work, but finite, and continually to be marveled at: adorned with all kinds of forms and shapes of bodies that nature could make, which in all parts are procreated and appear: and those first created by God (so well in Earth as in Heaven) by his only wor● of nothing, to th'end the same might be a proper mansion place for man, in which he might daily behold, and make known. Aristotle teacheth two definitions of the world: the one, that it is an apt frame wrought, consisting both of heaven and earth, and of the celestial and inferior bodies aptly distributed, and of other natural things in them contained. The other definition is, that the world is a perfect body, and most perfect round form, containing the ordinance and distribution of bodies, created by God to tend unto a purpose, which by God, and through God is preserved. The parts or Regions of the world, are two: as the Ethereal, and Elementary. The aetherial region is the higher and upper part of the world, which encloseth the Elementary region, being wholly clear and the light perfect, and containing the Orbs of all the fixed stars and Planets, distinguished by a certain order, free of all mixture and all strange qualities, nor harmed by any alterations. In which the celestial bodies are drawn about by certain and continual orders and times of the motions, that they may so cause the diversities of times, days, years, and months: and as well in the Elementary nature, by his motion and light, engender, mix, and temper together the first qualities, and prepare also other effects. The Elementary region, is the neither part of the world, which is contained within the hollow upper face of the moons Orb and Sphere, in which are all corruptible bodies, and things harmed by diverse alterations, except the mind of man: the causes of which, are the contrary actions of the first qualities. Also the four Elements are simple bodies, which into parts of divers forms cannot be divided: yet through the mutual commixion of these, are diverse kinds of bodies caused. Therefore, whatsoever bodies are in the Elementary region, be either simple, mixed, or compound bodies: In that the mixed bodies, are all those which may be divided into parts of diverse kinds. To these of the four Elements, the next joining within the hollow upper face of the moons Orb, is the most thin Air (being the lightest of the Elements) kindled, through the daily moving about of the celestial circles: which for this congruency with the fire (named the elemental fire) that is daily drawn about by the Orbs compassing it, which may appear by the Comettes, and other fiery kinds, engendered in the same Element of a hot and dry vapour, that are likewise carried about. The next within that doth the air run, being a heavier Element than the fire, yet lighter than the water: which also is drawn about by a like motion, as may appear by the clouds, and other like impressions engendered in the same, but to the neither region of the same, consist the lateral motions, as we daily see by the blowing of the winds. Farther, Vitellio in his tenth book and 60. chapter affirmeth, that the clouds are distant from the upperface of the earth 25000. paces, or 13. German miles. But according to same writers, they are unequally distant from the earth: as somewhiles further off, and somewhiles nearer to the earth. For when the clouds are furthest distant from the earth, they are but 772000. paces, and being nearest the earth, are 288000. paces distant. To conclude, this Element compasseth and encloseth, both the earth and water by his largeness. The next Element to the Air which moveth, is the water, for the same is moved by a motion of flowing and ebbing which it maketh after the motion of the moon; in that it floweth six hours, and ebbeth so many, until the moon by the motion of the first mover, hath passed about all the quarters of heaven. Also the water hath a motion, and that downward into the earth, so that these two joint lie annexed make as it were one body. Yet the earth being the heaviest Element, hath a motion attributed as it were simply downward unto the middle: notwithstanding agreed of all men, that the same is immovable, and the Centre of the world. These four: that is, the fire, air, water, and earth, are named to be the four Elements, and both the simple, and Original matters, of which all mixed bodies are compounded and made. The proof that there is only four Elements, is this: that to each Element the two first qualities agree, and the Combynations the like of the four qualities: as of heat and drieth, which consist in the fire: of moisture and heat, which rest in the air: of coldness and moisture, which be in the water: of dryness & coldness, which is found in the earth. By these it is evident, that there are but four Elements: of which heat exceedeth in the fire, moisture in the air, coldness in the water, and dryness in the earth. To conclude, it appeareth, that heat with cold, and moisture with drieth, cannot aptly be joined. What the Stars are, and that, as to the motion of their Orbs, they are carried about. THe Ethereal region containeth the Stars, which are the thicker parts of their Orbs; perfect round, clear, most pure and simple, and free of any mixture, except the Moor which is darker than the others, yea variable and shadowed. And these fastened to their Orbs, by which in certain continual and appointed times and orders, are drawn about, and perform their returns in the determinate spaces of times, and those continually agreeing in themselves, that they may so engender the differences and orders of times, and in the inferior nature prepare and cause the first qualities, and other effects. The Sun the fountain of light, doth not only give light and make shine clear the inferior bodies, but the superior also, by the brightness and light of his beams. But the Stars seeing with a borrowed light they shine, which is far weaker than the suns, therefore with that strange light which they take properly of the sun do they shine, although unlike to the sun. For into all the stars, which by nature are round about thin, and penetrable, is the suns light equally shed and pierceth, and so filleth all, that they are subject to no times of increasing and decreasing of light. But the Moon, seeing it is an unperfit body, and that it hath the parts some where thin, & somewhere thicker and better compact: therefore doth it not equally, nor round about receive the suns light. So that the th'inner parts take more of the suns light, and of the same do clearer shine. But the lesser shadowed parts which also are seen, appear darker, as the spots in the moon do show. That the bodies of the stars are round, do the round forms in the Eclipses of the sun and moon show: yea in what parts of the world those Eclipses happen, do the bodies also of the stars at that time appear perfect round: Although the bodies of the stars be known (by sundry reasons) to be round as a bowl, yet by their great distance from the earth, appear to us as plain or flat. Nor the Stars are not moved by their own proper motions, but by the Accydentary, as unto the motion of the Orbs, to which they hang, as parts unto the motion of the whole. For to every round body do two proper motions only belong, as a moaning to and fro, and turning about. Therefore the Stars (seeing they be round) are by some proper and principal motion carried round. But the fixed Stars are not so moved round, in that they turned about, do not alter the same face or body which they once turned and showed to us: but that the same should of necessity happen like, being turned round in one place, about their Exetrée, with the others in the same motion being in the parts far distant, and the others then set and hid under the earth. Nor are they turned hither and thither, in that they never change the standing and place which they have in their Orb, which to those carried hither and thither would happen. Therefore, not by a proper and chief motion are they carried about, but by an accidentary drawing about of their Orbs, which what the same is, shall after appear. That Heaven is drawn round. THe Ethereal region, do the Philosophers also name quinta essentia, or as it were a fift body, constituted above the four Elements, being incorruptible & divine, consisting of the noblest and purest part of the air. Which also is placed above the hollow upper face of the moons Orb, that reacheth unto the hollow upper face of the highest heaven, being most pure, perfect round, continually carried about, and bright appearing. This part of the world being the aetherial region, is named heaven, which always drawn about by a marvelous swiftness, is divided into nine Orbs or Spheres. Although sundry Astronomers, as Alphonsus, johannes de monte regio, Purbachius, and others, have added a tenth Sphere, through the third contrary motion found in the eighth Sphere, named of Thebit benchore (the first inventor of the same (Motus trepidationis, or the going and coming of the eight Sphere. The first and uppermost Orb, is named the first mover. The second is that, which is named the ninth Sphere or Crystalline heaven, but of Ptholomy, named the firmament or Orb of the fixed stars. And the third is that, which (of them) named the eight Sphere, only added through that motion of the trembling, or as it were a moving forth and return of that eight Sphere; which properly is caused, in the two small Circles about the heads or beginnings of Aries and Libra: through which diverse motion of the eight Sphere, do the Equinoctials and Solstices come and begin sooner by certain days, and the sun's greatest declination diminished (and daily doth) to that in Ptolemy and Hipparcus time, which then was 23. degrees and 52. minutes, and 30. seconds. And for these have Alphonsus and sundry others, attributed divers motions to the eight Sphere, adding a ninth and tenth Sphere to it. That there are but eight celestial Orbs which may be seen. ALthough Ptholomy affirmeth, that there are nine Orbs equally distant, yet are there but eight which may perfectly be seen and discerned with the eye, both in the standing, variety of motions, and differing in the periods or courses. Also they are in such order disposed, that no Orb hindereth the motion of another near to it. As the Sphere of the fixed stars, and the seven Orbs of the Planets. And most certain it is, that some of the fixed stars are drawn by a swifter motion, and others by a slower motion, and that the Apogea or ascensions also of the Planets are changed, after the order of the signs. The Orbs of the Planets thus contain and compass one an other, as first the Sphere of Saturn being nighest the firmament (of which being compassed) doth like contain jupiters' sphere, and jupiters', doth in the same manner enclose Mars' sphere, and Marses in like order, the suns sphere, next the suns, doth contain Venus' sphere, which like doth compass, Mercury's sphere, and Mercuries doth contain the moons sphere, being the lowest and smallest sphere. And every of these spheres, hath a star a piece, named erratical stars or planets: which stars have every one their proper Orb several, his motion several, and unlike in time one to another, in that they appear one whiles near together, and another whiles are seen far distant asunder. By which it agreeth, that their equal motions, to appear to us unequal, either through the Poles of the Circles, divers from the Poles of the world about which they be turned, as are the Poles of the Zodiac, under which the erratical stars are continually drawn and move; rather for that the earth is not the Centre of those Orbs, by which the Planets are carried and moved about. So that when we consider those movings by the Centre of the world, then is caused, that they seem to us as they were increased in a greater bigness, when as we behold and see them near hand, and that lesser in bigness, when we see them placed far off. Even so in the equal circumferences of the Orbs, through the divers distance of sight, we like observe the unequal motions, by the equal times. Yet indeed neither of these happeneth, but that they are drawn about by unchangeable spaces, being a like distant, and keeping one manner of bigness. For if this were, than the sun, or any other star being in the middle of heaven, should seem or appear bigger (which it doth not) then being in the East, or West part. And the contrary we sundry times see, when as the sun or any other star, appeareth bigger in the quarters of the East, and West; which is not caused by reason of the shorter distance, but for that his beams in the vapours, which do thick ascend (both in the winter time, and in rainy weather) that hang in the air between our sight, and the body of the star, are then broken: which breaking of them, doth cause the star to appear far bigger to the eye, then in deed the same is. And that a readier and easier knowledge may be had (after the mind of Ptolemy) of the first mover, and celestial Orbs with the number of the Circles and Elements enclosed within the first mover, conceive this figure here following most aptly drawn and set out for thy further instruction. This Figure declareth the number, disposition, and order of the celestial Spheres, about the Globe of the Earth. That there are two first motions of the celestial Orbs. ALthough the celestial Orbs are severally drawn, by proper and unlike motions: yet be there two first motions, that are manifest, both by observation, and judgement of the eye. The one is of the first mover, which Ptholomy attributeth to the ninth Sphere, that is only drawn about by an equal swiftness, from the East into the west, and from thence again into the East, upon the Poles of the world or Equatour, in the space of a natural day or 24. hours. And this first mover draweth with it all the other Orbs, much like a ship, which being at full sail, doth draw and carry all her men, & other living things which are in the Ship. So that by this motion of the first mover, the neither Orbs, which the first mover compasseth, are drawn once every natural day, or in the space of a day and night, about the earth. Also this first mover, doth not only describe and measure a natural day, but causeth times, and diversities of days and nights, with the proper motion of the sun; and it daily bringeth up stars to be seen, and carrieth up to the highest, and after hideth them again, under our Horizont in the west. Besides it is the common measure of all the other motions. The other motion is proper to the eight Sphere, and to the Orbs of the seven Planets, in the which they are contrarily carried to the first mover, as from the west into the east, in moving under the Zodiac, and about the Poles of the same: and not in Parallels from the Equatour equally separated; but are drawn much slower, yea and unlike. As by a like example; when a ship by a most swift course is carried into the west, yet may the Mariners and others in the ship walk forward in the mean time into the East: Even so is this second motion of all the other Spheres under the Zodiac, upon the Poles of the Ecliptic. Also by a swifter motion are they carried, and sooner perform their courses, which are nearer to the earth▪ and contrariwise move by a slower pace, and in longer t●●e compass and wander about the signs of the Zodiac, which are further distant from the earth. Also in the middle of their courses (as it were) each do often stack or be slow, and often times stay as unmovable, and sometimes are retrograde, after again quicken their course, and by their swiftness recover that lost of the former tarriance. So that they never keep one manner of way, but one whiles from the middle journey of the Zodiac do wander into the North, and another while into the South. To conclude, they be ascended high from the earth, when they are named Apogei, and descended again unto the earth, when they are named Perigei. That there are two kinds of Stars, the fixed, and the Planets. ALL the fixed stars that hang to the firmament (or as Ptolemy affirmeth) to the eight Sphere, are named fixed: not for that they consist unmovable, but that they move so marvelous slow, that by judgement of the eye they cannot be perceived to move: yet the practitioners have and do find both by reason and observations, that they always separated by unmovable spaces one from the other, and are carried in parallels as it were in their Orb. Ptolemy, Aristillus, Timochares, with the observations of Hipparchus, joined unto those which he knew, noted that the fixed stars in a hundredth years moved one degree. But Copernicus being of later years (as about the year of Christ 1525.) that examined the observations of the ancient men, and compared them unto those noted of him, found that not so many as a hundredth years, but in seventy and two years, that the fixed had gone one degree: and that in every Egyptian year (which containeth 360. days) the fixed to have moved 50. seconds, and in a day 8. thirds, and ten fourths. And so performed their whole course, in twentyfive thousand, eight hundredth, and sixteen years, 25816. Of these known and numbered of the ancient men, are 1022. which they have divided into six differences of magnitudes; and to these have added certain obscure, and certain cloudy stars. The fixed stars of the first bigness, of which are numbered to be fifteen, and that both in bigness and brightness exceed all the other stars, and in body exceed the earth 107. that is, a hundredth seven times, with a eleven threescore fourths. The fixed stars of the second bigness, of which are accounted 45. do exceed the earth in greatness almost eighty seven times. The fixed stars of the third bigness, of which are numbered to be 208. do overpass or exceed the earth scutcheon two times, with a third part almost. The fixed stars of the fourth bigness, of which are reckoned to be 474. that are fifty four times greater than the Earth, with a half or a little more of the earth. The fixed stars of the fift bigness, of which are noted to be 216. that exceed by their greatness the earth 31. times. The fixed stars of the sixth bigness, of which are noted to be 50. do exceed the earth eighteen times, and a little more. The dark stars, are accounted 3. in number: and the cloudy stars, are reckoned to be five. The fixed stars do differ in brightness, standing, colour, twinkling, and especially in the configuration. Many of the fixed stars also with the effects both in the bigness and brightness, being notable and near together, the ancient men that divided them by a certain reason, have gathered, digested, and fashioned them, into forty and eight images or similitudes. And unto them through the congruence and similitude of the noted forms or figures, they gave apt names: and for the same cause especially, that they might the easier and sooner be discerned, known, and noted by their peculiar names. Also they divided the stars, by the standing into the North and South, and the signs of the Zodiac. The Northerly stars that decline from the Ecclipticke into the North, are twenty and one in number. The Southerly, that decline from the Ecclipticke into the South, are fifteen in number. The images that are named the signs, are twelve in number, which consist in the Zodiac. Of the celestial Images, and of their divers names, being in number, 48. Of the Northerly. 1 THe little Bear hath seven stars, and of those, that star which is in the top of the tail, is named the Pole star. 2 The great Bear, hath 27 stars, 8 without form. 3 The Dragon hath 31. stars. 4 The image named Cephe us, hath 12 stars. 5 The image Boötes or Lauceator, hath 22. stars. 6 The boreal or Northerly crown hath 8. stars. 7 The image kneeling or Hercules, hath 28. stars. 8 The Harp or Griepe falling, hath 10. among these the brightest is that named the Harp. 9 The wild Swan or Griepe flying, hath 17. 10 The image Cassiopia, hath 13. stars. 11 The image Perseus carrying the head Algoll, hath 26. stars: of which, those which are on the left hand do make the head Algoll or Gorgon's, 3. without form. 12 The Cartare, hath 14. stars, among those, that which standeth on the left shoulder, is the Goat: and the other two are named the Kids. 13 The image Ophiulcus or Serpentarius, hath 24. stars. 14 The Serpent, hath 11. stars. 15 The figure named the Arrow, hath 5. stars. 16 The Eagle hath 9 stars, 6. without form. 17 The Dolphin, hath 10. stars. 18 The division of the Horse, hath 4. stars. 19 The winged Horse or Pegasus, hath 20. stars. 20 The image Andromeda, hath 23. stars. 21 The triangle, hath 4. stars. The Sum of all the Stars, are 360 The 12. Signs of the Zodiac. 1 THe image named Aries hath 13. stars. 2 The image Taurus hath 23. of these five in the forehead of Taurus, named Succulae or Hiades, and the greatest star of Hiades in the Southerly eye, named Pallilicium, and Pleyades on the back of▪ Taurus, 11. without form. 3 The images named Gemini, are 18. stars: of which Castor or Apollo goeth before, Pollux or Hercules, followeth. 4 The image Cancer hath 9 stars, among these Presepe, and the cloudy star in the Breast. 5 The image Leo hath 27. stars: of these, that which is in the heart of the Lion, named Regulus, 8. without form; among which is that constellation, named Berenice's bush of hair, between the tops or ends of the Lion and great Bear. 6 The image Virgo hath 26. stars: of these, that which is in the right wing, especially Northerly, is named Vindenuator, but in her left hand a bright star, named the ear● of corn, 6. without form. 7 The image Libra, and klées of the Scorpion, have 8. stars, and 9 without form. 8 The image named the Scorpion, hath 21. stars, the middle star (of the three stars) placed on the Body, is named the heart of the Scorpion, and 3. without form. 9 The image named Sagitarius, hath 31, stars. 10 The image named Capricornus, hath 28. stars. 11 The image named Aquarius, hath 24. stars, and 3. without form. 12 The images named Pisces, have 34. stars. The Sum of all the Stars, except Berenice's bush, are 364. Of the Southerly. 1 THe image named Coetus, hath 22. stars. 2 The image named Orion, hath 38. stars. 3 The image named the river, or Eridanus, or Potamos, hath 34. stars. 4 The image named the Hare, hath 12. stars. 5 The image named the Dog, hath 18. stars, of which that in the mouth, is named Alhabor, 12. without form. 6 The image named the little Dog, or Caniculare star, hath 2. stars; of which the brightest is that named Proion or the dog-star. 7 The image named the Ship, hath 45. stars, of which a bright star going before in temone. 8 The image named the Water Serpent, hath 25. stars and 2. without form. 9 The image named the Bucket or great Cup, hath 7. stars. 10 The Raven or Crow, hath 7. stars. 11 The image named Centaurus, being one half like a man, and the other half like a horse, hath 37. stars. 12 The Beast which the Centaur doth hold, being a Wolf, hath 19 stars. 13 The image named the Altar, hath 7. stars. 14 The Southetly Crown, hath 13. stars. 15 The Southerly fish, hath 11. stars, and 6. without form. The Sum of all the stars, are 316. THe milky way, which Ptolemy nameth Galaxian of the white and milky colour, is a heap of most small stars, and dim to sight; of which is a certain confused gathering together, and abundance as it were increased, that no several light is discerned: and the same (in the manner of a girdle) compasseth and encloseth heaven about. The same also is unequal, and differeth in the standing, latitude, haunt of stars, and in the colour very much. It is somewhere discerned cleft, but the part going before, is neither whole, nor maketh a whole swath or enclosure about, but lacketh about the swan and Altar. And the part following whole, being in no place broken off with a space, and stretched thwartly in heaven: and from the parts of the Zodiac Northerly, it passeth by Gemini, and Sowtherly by Sagitarius, and Capricornus. Of the Planets. THe Planets, named otherwise the erring and wandering stars; not for that they err by a wandering and uncertain motion, but in that they are carried about by a divers and unlike motion. For sometimes they go forward, and sometimes retrograde; sometimes are hidden and clean out of sight, after they appear and show themselves. Again, they go before, and follow the Sun. They are carried swift, and their motions again so stayed, that they are moved in a manner nothing at all, but seem as they were stayed for a time. From the suns way, one while carried into the South, and another while carried into the North, and then unto the same way drawn back again: so that their journeys being passed and finished, they steadyly repeat their old courses by the like order. Of these are seven, and each carried in their proper Orbs, and compass about the Zodiac, in unlike spaces of time, SAturne highest of the Planets, and most slow in course, being cold and dry, pale to a leady colour, and performeth his course in 30. years, being ninety times, with an eight part greater than the earth. And the highest ascension or point of Saturnus Orb (which at this day is in the 29. degree of Sagitarius) is from the earth 20072. semidiametres, with a fourth part almost, and 15. minutes. But the lowest point of Satur's Orb, is distant from the earth, 14378. with a third part, and 20. minutes. IVpiter being next unto Saturn, temperate, and so clear or bright, that he giveth in a manner a shadow (especially when he is Perigeus or lowest descended to the earthward) and he compasseth about the Zodiac in twelve years. But jupiter giveth this proper shadow, when neither the lights be above the earth, nor Venus near to him. He is greater than the earth, by ninety five times, and a half part almost. And the highest ascension of jupiters' Orb, which possesseth the seventh degree of Libra, is from the earth 14369. with a fourth part almost, and 15. minutes, but the lowest point of jupiters' Orb, is from the earth distant 8853. semidiametres, with a ninth part and 45. minutes. Mar being hot and dry, and shining with a fiery colour, doth go about the Zodiac, in the space of two years. He is named the fiery Planet, of his shining with a fiery colour, or of the effect which followeth by him, in that he burneth and drieth up. He is one time greater than the earth, and a little more than a third part. The highest ascension of Mars' Orb, that obtaineth the 28. degree of Leo, is now distant (after Albategnius) from the earth 8022. semidiametres: but the lowest point from the earth, is 1176. semidiametres. THe Sun obtaineth the middle place between the Planets, wholly and thoroughly bright, being the fountain and Author of light: which by his motion expresseth and divideth the spaces of the Zodiac, and by his going about, have the signs their names. He is greater than the earth (after Ptolemy) a hundredth threescore and six times, with three eight parts. But after Capernicus, the sun exceedeth the earth, a hundredth threescore & two times, with eight parts less. The highest ascension or point of the sun's Sphere, which n●w possesseth the seventh degree of Cancer, is from the earth distant 1179. semidiametres, but the lowest point of the suns Orb, is from the earth distant 1065. semidiametres. Venus' next to the Sun, being cold and moist, white in colour, clearer and brighter shining then jupiter, and is carried about (like the Sun) in a years space, and both goeth before and followeth the sun; nor is further distant in the spring of the morning from him, than 46. degrees, and 47. minutes: but in the evening, she is seen digrssed from him, unto 47. degrees, and 35▪ minutes. When she goeth in the morning before the sun, thee is named the day star: but when she followeth the sun in the evening, she is then named the evening star. Lesser she is then the earth, but her true quantity is yet unknown: for that some affirm her quantity to be the 28. part, and others the 37. part of the earth. The highest ascension of Venus' Sphere, that obtaineth the 18. degree, & 20. minutes of Taurus, is from the earth after Albategnius 1070. semidiametres, but the lowest point, is 166. semidiametres distant from the earth. MErcurie being lower than Venus, is variable and apt to be changed, bright, but not white in colour; and is carried about the sun like to Venus, as one whiles moving before, and an other whiles following the sun. Nor is he further distant in the morning from him, than 29. degrees, and 37. minutes, and at the evening westward, 27. degrees, and 37. minutes. He performeth his whole course, in the space of a year, as the sun doth. Also he is judged to be the seventh part of 2●. or 22000. part of the earth. Albategnius affirmeth, the Star of Mercury, to be least of all the stars, and supposeth or accounteth him to be as one part, of 19000. parts of the earth. The highest ascension of Mercury's Sphere is from the earth▪ after Albategnius) distant 166. semidiametres, but the lowest point in the same Orb, is 56. semidiametres distant from the earth. THe Moon being lowest of all the Planets, doth compass about the whole Zodiac, in 27. days, 7. hours 43. minutes, and 7. seconds. She is lesser than the earth (after the judgement of Ptolemy) by three hundredth nine times, and a unity more than eight parts. For the triple proportion of the diameter of the earth unto the moon, by dividing above the fift parts, is even the like, as 27. unto 5. But lesser she is then the sun, by six thousand, five hundredth, thirty and nine times. Copernicus (by his observations) found the earth greater than the Moon, by forty three times: less than an eight part: and of this, the sun also is found greater than the moon, by seven thousand parts, lacking threescore seconds. And the greatest distance of the new and full mòone from the earth: after the mind of Ptolemy, is 64. semidiametres, and 10. scruples: but after later observations, 65. semidiametres, and 30. scruples. And the lowest to the earth, is 55. semidiametres, and 8. minutes. THe Moon digressing from the Sun every month, and taking or receiving a new light as it were, in that she (is changed, & taketh a new light of the sun) doth after increase by little and little, conceiving daily a bigger form and light, until she come in right line against the sun; at what time she shineth with full light: after returning again unto the sun, she waxeth old by losing of her light by little and little: and in the contrary manner cometh unto the like forms of light, until she coming under the beams of the sun, be quite out of sight. Also for that the moon hath a body, partly thin, partly thick, soil, and shadowed; therefore is she not equally filled round about with the beams of the sun, but that the same half of her Globe or body, which turned again in heaven (that beholdeth the sun) is it which shineth, and the other half turned away from the sun's light, is that which shineth not, but remaineth shadowed. That Heaven hath a round form and to be carried circularly. FIrst, heaven is equally distant round about from the earth, and of this is heaven perfect round, after the definition of the Sphere. Which reason is thus proved; that if heaven should have any other form then perfect round, then of necessity must the stars change their distances from the earth, what place upon earth they should purchase, as somewhere more, and somewhere less they should be distant; and the standing of them changed, should also alter their apparent bigness, in that they should appear greater being seen near hand, and lesser, being seen far off. Yet neither of these happeneth, but that they continually keeping a sunder, are drawn about by unchangeable spaces, and holding a like bigness and distance, to all places of the earth. That the stars about the quarters of the East or West, appear sometimes greater, is not caused by reason of the shorter distance, but for that their beams in the vapours, which often times consist in the air between the stars and our eye, are then broken; which breaking of them, causeth the body of the star seen, to appear much greater in the eye, then in deed it is. That heaven is drawn circularly, is thus known; in that we always see all the Stars, from the East into the West, to be drawn upward, and that the hemisphere in our sight, is carried continually in distant circles equidistant, never changing the standing or distance, one from another, neither in bigness, as far as the judgement of the eye can discern, neither any whit lessoned. For they being drawue from the neither place (as from the earth) are carried by little and little. And after they be thus come unto the highest of their journey (as unto the noonstéede) they decline again by little and little, till they be brought down unto the west quarter, and there set and hidden, under the earth: and these places and times, both of the rise and settings do they repeat in certain order. Therefore by these it appeareth, that they are drawn and carried by round. By the second it is evident, that the Stars, which be near the Pole Arctic, are never hidden out of our sight, but are continually and uniformally drawn round about the Pole as the Centre: in such sort, that the stars near to it make the lesser compasses, and the stars further off, do define greater compasses. So that the stars fastened to their proper Orbs (as aforewritten) are cyrcularly carried. By which two motions of the stars, as well tending unto the West, as otherwise; it plainly appeareth that heaven is drawn about and carried round. A manifest demonstration appeareth of the former argument, by this figure here following. That the Water and Earth are round Bodies, and by a mutual embracing do make one Body, and one hollow upperface. THat the earth is round, is thus proved. Whereas in every upper face, the length and breadth is considered. The length of the upper face of the earth, is from the West, into the East, or contrariwise. The breadth is from the South, into the North, or contrariwise. That the earth also to be round, appeareth after length: in that the Sun, Moon, and Stars, do neither arise, nor set at one instant time alike, to all persons dwelling in any part of the earth. But do much sooner appear and shine to them dwelling unto the East, and within a while after they show to them dwelling in the West. By the second appeareth, that one and the like Eclipse of the moon in divers hours, is seen both in the East and West. For that which appeareth in the first hour of the night to them in the West, is seen to them in the East part, in the second, third, or fourth hour, even as they come nearer unto the East: which would not be caused, if the night to both places should happen and be at one moment, nor sooner would they appear to them in the East part. Again, there be certain stars, which in their rising, do appear sooner to them in the East parts, then to them in the West, as Pliny writeth of Arbelis (being a town in Asiria) where an Eclipse of the Moon was seen in the second hour of the night, which in Sicily, was seen in the first hour of the night. For the Assyrians are more Easterly than the Sicilians, and therefore doth the sun set sooner with them, then with the Siciliaus. And when it was also the second hour of the night in Assiria, the Sun first set in Sicilia, about the first hour of the night. Moreover the Pole of the world (according to the diversity of places) is elevated and depressed. So that the cause of the diversity of this appearance, is only the swelling of the earth. To be brief, the beginnings and spaces of the days and nights, and that in divers places of the earth do vary, and yet following in a manner, one order. But this variety could not happen, if the earth were not Spherical, and all about equally round, herein excluding both valleys, and the tops of hills, which applied (unto the body of the earth) cause no inequality or diversity at all. For the swelling of the earth causeth, that the stars be not seen together in all countries, but drawn about by little and little, by a certain succession and order, that they so appear sooner to them in the East part, then to them in the West, through the swelling as yet not above carried, which swelling being high between both, is a let and cause of the later appearing of them to the west: and by that means also keepeth and hideth the stars the longer from their sight. So that by these it evidently appeareth, that the only cause, is the swelling of the earth. If the earth were fashioned with a deep hollowness, and compassed round about with a light enclosure, then should the stars risen, be soon seen to them in the West parts, and much later appear to them in the East. For that the higher enclosure to the hollowness, as a wall built about, should be a let and hindrance to the sight of the beholders; in such sort, that those stars arising, it should hinder their sight. If the earth were form with places standing in sharp pillar form, or in right line up; then should the stars appear set, and be hidden alike to those places, and no differences of days should be caused, but that they should have one like day, and the sun also appearing to that fide, which they showed: so that whiles the Sun runneth and compasseth about the back parts, they should be without light of the sun, and should remain all the time in shadow and darkness. And if it should have a Cubic for me, than should they see the sun six hours, and lose or be without light and sight of the sun, other eighteen hours. If in round piller-wise, as if the hounds were plain unto both the Poles, and the hollow parts should decline unto the East and West, then should no stars continually appear to them dwelling in the hollow: but that certain stars should arise up and set in the West, and other certain stars near to both the Poles, should always be hid. To conclude, if the whole earth were framed with an equal plainness throughout, then should the stars appear at one moment to all countries; and setting again, should hide the like out of sight: and by that means should the days begin and end alike, and no differences should be observed. To all such arguments, seeing experience only doth repugn or contrary them: It is therefore manifest, that the earth from the West toward the East, riseth up into an equal swelling. If the earth also were plain from the East unto the West, then should the stars arise so soon to them in the West, as to those of the East, which is a manifest error. Also, if the earth wéere plain, from the North unto the South; and like from the South unto the North: then the stars which were to some of a continual appearance, should always seen the fame and like, which way or into what quarter soever a man goeth, which also is untrue. But the cause which maketh the earth seen plain, is through the over great quantity, which causeth it so to appear to every man's sight. But that the earth is round (according to latitude) the divers elevations of the Pole and stars (either always in sight, or continually hidden) doth evidently declare. For from the Equatour, in going forth easily towards the North, and that the Pole Arctic be higher raised, and the stars near to the Pole raised up; then are the stars right against like depressed, and as they were out of sight, and so much the more as they go further from the Equatoure: nor the Northerly stars never set, but continually drawn about (in sight) with heaven. But the contrary happeneth, by going from the said Circle or Equatoure, unto the contrary part. So that there is no greater cause of this diversity, than the swelling of the earth, which if the same should be plain, the stars opposite or right against (according to latitude about the Poles) should offer and appear together to all countries, which the swelling of the earth hindereth to be seen. An instrument, by which the roundness of the Earth (according to latitude) may be proved, and all those may easily be showed which are taught of the days Artificial. That the Water hath a like swelling, and runneth round. THis by two reasons is proved, the first is most certain, by a mark or marks standing on the sea bank, like as a tower, steeple, or such like erected of purpose, so that a ship sailing into the deep, and carried so far off, that no more of the sides or bottom can be discerned, saving the top of the mast, which only appeareth to the sight. Or thus, that a mark stood on the sea bank, and a ship passing forth of the haven, sailing so far into the sea, that the eye of the beholder being near the foot of the mast cannot decern the mark (the ship in the mean time staying or standing still) so that his eye being in the top of the mast, shall perfectly see that mark: but the others eye being near the foot of the mast, should rather better see the mark, than he which is in the top of the mast, as may more evidently appear, by lines drawn from either place unto the mark: so that the manifest cause of this, appeareth to be none other, than the swelling of the water. But here are all other impediments excluded that may otherwise hinder; as mists, fogs, and such like vapours ascending. Also a like reason of the impediments of this above written, is, for that the water ariseth into a swelling, which hindereth the sight of the bottom or sides of the ship (that being in a high place doth not hinder the sight of the same) as the top of the mast, which either exceedeth or is equal with the swelling of the water. For men sailing on the main sea, see nothing round about but the Sky and the Sea: but coming nearer the banks, do by little and little descry and see, either high hills or cliffs, as if they were rising forth of the water. Also to those that dwell on a high ground, the sun first ariseth, and last setteth. And to this agreeth, that out of the higher places, both more and further may be seen into the sea, then in valleys or lower places. By all these therefore it is evident that the upper face of the water swelleth, as by the example following more plainly shall appear: but an other example of the same shall be here rehearsed, by a similitude of one part as the whole. The similitude of which matter conceive by this example, that experience daily teacheth us of the drops of water, which although they be small, yet powered on dry woollen cloth, run into a round or bunching form; which without doubt should not be caused, if the part followed not the nature of the whole of his kind. Now the example above promised doth here appear, in which by the letter A. is the ship meant to come unto the mark C. In which being in the point A. that is in the bottom of the ship, cannot see the mark standing in C. through the swelling of the water. But he which is in the top of the mast, as in the point B. without all impediment may see the said mark. That the self same or like to it, may be on land, as from the point D. none except he be foolish or stark mad will affirm the like. By the second it is manifest that the water by nature is carried and runneth downward, and stideth or falleth from higher unto lower places, so long, until it hath filled and be even with the earth, through the staying of high heaps of earth, hills or such like mighty and high banks enclosing it about that it run no further, nor make no hollowness in the middle of the earth, as a Centre of the earth. Which therefore gathereth between the empty places, so long, until it hath filled and be even with the earth; and that the whole together, through the hollowness thus made equal, doth fashion and keep a round form. So that the earth, with the sea, and waters running about it, do make one round body, and fill all the whole upper face: the earth also gaping and open somewhere, receiveth water into those hollow places, but a part of the earth appearing somewhere above it, staying and enclosing it about with strong enclosures and banks (wrought by divine miracle) that the bare places of the earth, might be a commodious dwelling and feeding for all beasts, and other living creatures. And that this is true, shall be proved by other two reasons. The first, by sundry perygrinations, in which many and most large parts of the earth are found toward all the quarters of the world, which evidently witnesseth, that the earth is not as Pliny and others writeth; which imagined that the earth is compassed about with water, and appearing so out of the water, like an Apple or Ball swimming above the water, whose one half showeth out of the water, and the other half hid in the water. Which reason Ptolemy doth not allow, but simply affirmeth, that the earth with the sea and waters, make one round body, by filling of the empty places, and both to have one upper face. Also vitrvuius in his ninth book writeth, that the earth is placed in the middle of the world, and is naturally joined together with the sea in the place of the Centre. But what the form of the earth is, above the waters, is yet not thoroughly known, by reason of the sea which runneth between it in divers parts, and breaketh it into sundry parts, like to gobbets or pieces. Ptolemy affirmeth the earth to be known, unto the longitude of the half Circle, that is 190. degrees, without any running between of the sea in that space; for that the earth is wholly joining together. But into latitude, he affirmeth the space to be much lesser, as 79. degrees, and of this opinion, is both Strabo and Aristotle. By the second it appeareth, that the water with the earth, doth equally make one hollow upper face, and the same to be perfect round; but whether is bigger, is greatly to be doubted: although the learned Novius, and sundry other late writers, do affirm the face of the earth to be bigger than the water. By the third (which is the Eclipses) In that of necessity the earth must have such a form with the waters running in it, as the shadow of the earth frameth and counterfeiteth in the moons Eclipses; in that the shadow showeth and expresseth the form of the body shadowed. But the shadow of the earth to be included round about with a round upper face, the wise both see & know. Therefore the whole Globe, compounded of the earth and waters, is comprehended with a round upper face. For it is manifest, that the moon before and after the full, is seen horned, and the part shadowed of the whole circle, is easily to be discerned from that bright circumference. So that the moon entering into shadow, or going out of the same, is likewise in the same manner horned: and the part darkened, is always discerned from the clear circumference of the whole Circle embossed. Therefore of necessity must the beginning of the shadow, which separateth the part lighted, from the shadowed, not be fully strait, nor unequal, nor vallied or winding, but round: and for that cause appeareth the upper face of the shadow not to be plain, but round. By these is also manifest, as by the first, that there is no difference between the Centre of the earth, and Centre of the water: but that the one, is the Centre of both the Elements, joining together into one round body, and tending unto the one and the same Centre of the earth. For the earth (seeing it is the heavier) is opened, and receiveth the waters falling into those places. By the second it is evident, that the place of the water, which ought to run over and cover the whole earth, is otherwise changed and appointed by the Divine will, for the benefit of all living creatures. By the third appeareth, that the opinion of certain Peripateticans is false; which affirmeth the water to be ten times greater than the earth; and that to one part of the earth, is ten portions of the water increased. But seven times greater than the earth it cannot be, unless the earth round about were wasted and impaired, by the Centre of the gravity (as it were settling and resting upon) should yield, and give place to the waters, as the heavier. Seeing the Spheres are together in a triple reason of their measures, then if the earth were an eight part, to seven parts of the water, the diameter of it could not be the greater; as from the Centre of the waters unto the circumference of them: that is, by double so much unto the diameter of the water, as by this figure here under drawn appeareth: where this letter A. is the Centre both of the earth and water, B. the Centre both of the magnitude and earth, G. A. D. the diameter of the waters, A. B. D. the diameter of the earth. If the waters are seven times bigger than the earth, the diameter of them must needs be double so much unto the diameter of the earth, as here from G. D. unto A. D. By which example thus drawn, the whole earth receiveth the Centre of the weight, giving place to the waters, and all covered with waters; to which general experience gainsayth and denieth, much less therefore can it be greater ten times. By which is to be concluded, that the water is but little in quantity, in respect of the earth, although it may seem very big, being up to the edges of the upper face of the earth. And if the waters had been more bigger than the earth, they had drowned or covered the whole earth, even of late years. That the earth employeth the middle place of the World, and is the Centre of the whole. A Ristarchus Samius, which was 261 years, before the birth of Christ, took the earth from the middle of the world, and placed it in a peculiar Orb, included within Marses and Venus' Sphere, and to be drawn about by peculiar motions, about the Sun; which he feigned to stand in the middle of the world as unmovable, after the manner of the fixed stars. The like argument doth that learned Copernicus, apply unto his demonstrations. But overpassing such reasons, lest by the newness of the arguments they may offend or trouble young students in the Art: we therefore (by true knowledge of the wise) do attribute the middle seat of the world to the earth, and appoint it the Centre of the whole, by which the rise, & settinge of the stars, the Equinoctials, the times of the increasing and decreasing of the days, the shadows, and Eclipses are declared. The earth round about is equally distant from heaven: therefore, according to the definition of the Centre, the earth is the Centre of the world. That the stars have always one bigness, in what place soever any shall behold them: therefore are they in an equal distance from the earth. The roundness of the earthly globe, hath a proportion unto the roundness of heaven; that is, the certain and proportional parts in the earthly Globe, do answer to certain proportional parts of heaven: therefore is the earth the Centre of the world. In that siftéene German miles on earth, do answer to a degree of the Meridian: and that in every hour do fifteen degrees arise of the Equinoctial; which could not be, if the earth were not in the middle of the world. For the unequal Arks, should otherwise appear in the equal times: and the equal parts of the Meridian, should the unequal spaces on earth answer: which experience daily witnesseth unto the contrary. And hereof it ensueth, that the earth stands in the middle of the world. In every Artificial day, do six signs appear, and six like set under the earth: therefore is the earth in the middle of the world, and is also as a prick, to which the half doth regularly move daily. The like is in the opposition of the Sun and Moon, when either light is in the Horizont: which could not be, if the earth should approach or come nearer unto one part, then unto the other. If it were nearer to either of the Poles, than could not the universal Equinoctials be: for that the one Ark always (either in the day and night time) should be greater than the other. The Eccclipses also could not be in the changes and full moons: For that there should then be uneven spaces from the South unto the North, and from the East unto the West. If the earth were not as the Centre of the world, then of necessity should these ensue, that the earth should approach, either nearer to the East, or West, or South part: and when any of the stars (aswell the fixed as Planets) shall come unto that part, they shall appear nearer to us, then being in any other part of heaven: and by that above said, they shall also appear greater: which is altogether untrue, and we also see the contrary in that (as above written) they always appear of one greatness, either being in the East, or in the West. Also one half of heaven is always above the earth, and the other half under the earth: and this is not only found and known in one quarter of the earth, but the like in every place (as the Equinoctials do witness) than which there can be no more evident trial. A third reason may be alleged, if any imagined the earth upon the Centre, to be parted into two equal halves, and that the eye is placed in the Centre: then shall the eye see no more than the half of heaven. By which appeareth, that the swelling of the earth, from the Centre unto his compass about, in making a comparison unto heaven is as in a manner nothing. And it is known to the learned in Astronomy, that any of the fixed stars, is by many times greater than the earth: which if any behold them, they appear as points in heaven. Now how much lesser would the earth appear, if a man should behold it from his place. Here learn by this demonstration following, that the earth standing without the Centre, in the point B. being to the Meridiane, as is the point A. nearer; and when a star shall come unto that point, then shall it be nearer to the earth, and in the opposite point, as is I. shall be from the same much further, than in any other place, and shall even there lesser appear, which by experience, is quite contrary. Further grant that C. D. be the thwart Horrizont, yet the contrary, for the second reason, E. B. K. being the Equatour, which from the said Horrizont is divided into two unequal parts, and by this consequent also must the Zodiac be divided into two unequal parts, from the said Horrizont: for that those two Circles, (as hereafter shall be taught) do cross one another into equal parts. Therefore when the sun, by his proper motion, carried from the East into the West, shall come unto the cross of the Equatour and Zodiac, and that the greater part of these Circles shall be under the earth, it cannot be that the Equinoctium or a like day and night, can be through out the earth, no not under the right Sphere, much less can it be under the thwart Sphere. IF this be unpossible, it shall be also as unpossible, that six signs may always be above the earth, and the other six under the earth; but rather that more of the signs shall be under the earth, and more of them above: even as the earth is imagined to be divided from the Horrizont aforesaid, into two equal parts; like as when it shall be in the Centre of the whole, and that from each Centre of the greater Circles, the earth is divided into two parts. As all these (to any beholding the material Sphere) are forthwith known at the first sight: so by a third reason is to be noted, that when any imagineth, by the line E. F. that the earth in the point G. standing as in the Centre of the whole, is divided by the middle, as well being in G. as H. for the exceeding distance from the Cyrcumference, is unpossible to see always the half heaven. If the Earth be not in the middle of the World, then of necessity shall it possess some of these standings. FIrst, the earth is placed without the Are tree of the world, yet in such sort, that it is equally distant from either Pole: that is, that the Equinoctial may be in the plain upper face, as in the letter D. appeareth. Secondly, that it is standing on the Exetrée of the world, yet without the plain upper face of the Equinoctial; that is, that it be nearer to either of the Poles, as in the point B. or G. Thirdly, that it is neither standing in the Exetrée of the world, nor in the plain of the Equinoctial, as in the points, A. C. F. E. The first standing being granted, these absurdities should then ensue, through the divers placing, in divers and sundry places of the plain Equatoure. 1 In the right Sphere, should never the Equinoctium (or a like day and night) be caused, in that the Horrizont should never cut or part the Equinoctial into two equal halves. 2 In the thwart Sphere, should no Equinoctial Bee, and somewhere again should the Equinoctial be, but not in the middle Parallel, between the two tropics; that is, it should not happen the sun being in the Equinoctial, but in an other lesser Parallel Circle, being nearer to either Tropic point. 3 The time from the rising, unto the Noon tide, should not be equal to the time from the Noon tide unto the setting of the sun. 4 The magnitudes and spaces between the fixed stars, both in the East and West, should not be seen equal or a like. In the second standing, if that the earth should be placed on the Exetrée, and not in the middle of the world, then should these absurdities ensue. In every Climate, the plain of the Horrizont should cut heaven into two unequal halves, except those places having the right Sphere: yea, and the Zodiac should be divided into two unequal Arks, so that there should be somewhere more, and somewhere less than six signs of the Zodiac seen above the Horrizont, which is contrary to all experience. 2 The Equinoctial shadows, both of the rising and setting of the sun, should not agree, in such sort that they might fall in right line. Neither the shadow of the rising of the sun in the Solstitial or longest day, should make or stretch in right line, with the shadow of the suns setting, in the Brumal or shortest day, et econuerso In the third standing, if neither it should be on the Exetrée of the world standing, nor in the plain of the Equatour; then should the same absurdities ensue, which are uttered in the two former. To conclude, wheresoever the earth is generally placed without the middle of the world, there is the reason of the days equal increasing & decreasing in the thwart Sphere confounded, and there shall either no Equinoctials at all be caused, when the sun occupieth the middle way between either Tropic. Nor the Moon always shadow the sun's light, although she cometh right against the body of the sun. And the earth not standing in the middle of the world, shall not shed or stretch his shadow to the moon. So that all these absurdities and vain arguments do grant, that the earth cannot be in any other place, then standing in the middle of the world. That the Earth abideth fixed and unmovable, in the middle of the world. THat neither the earth, in right nor Cyrculare motion is drawn about the Exe tree of the world, nor about any other Exetrée, but to rest and stay in the middle of the world; both holy scriptures confirm, and Physic reasons prove. For the Psalm saith, which established the earth upon his foundation, that it shall never be moved. And Ecclesiastes in the first chapter saith: that the earth standeth for ever, and the sun both riseth, setteth, and goeth about unto the place where he arose. Also that the sun is drawn about, the Psalm doth manifestly witness, where it is said: that for the sun, he hath placed a Tabernacle in them, and he, as a Bridegroom going forth of his chamber, doth rejoice as a Giant to run his course, which goeth forth from the uttermost bound of heaven, and returneth about unto the end of it again. Also it is known and numbered among miracles; that God would have the sun to continue. The Physic reasons are these. THat of one simple body, is only one simple motion. That the earth is a simple body: therefore thereunto agreeth but one simple motion. But of the simple motions, I have before taught, that the one is in right manner, and the other in Cyrculare form. That the right motion seeketh downwards unto the middle, whether being carried, they settle and rest. Therefore is the motion of the earth not cyrculare about. By the second appeareth, that every grave or heavy matter by nature, is through his weight carried after a most strait line unto the Centre, and both fetleth, stayeth, and resteth at the same; where it neither falleth, or is carried any further. So that all grave matters, as the parts of the earth, and those which consist of the earth, are sent or carried by a most strait leading unto the earth, and at his upper face shall stay and rest. And wear it not that they are stayed through the fastness of the earth, they should so long be carried downwardly, until they came unto the Centre. Also the earth through his fastness, receiveth and beareth all things falling on it. Therefore doth the earth much more (being within the Centre) stay and rest fixed and unmovable, bearing all other heavy things falling on it, seeing the earth is heaviest of all others. By the third it is evident, that if the earth should be moved or carried, it should of necessity be either drawn in right, or cyrculare motion. If it should be carried in a right manner (seeing it is the heaviest of all others) it should by his swiftness move and go before all other heavy things, and should leave behind the living creatures, and other things fastened to it, and should also leave them hanging behind in the Air. If the earth should be drawn about by a cyrculare motion, & should in a days turn (at the least) be carried about the Exetrée, from the West into the East, as either alone or with the first Orb: then every day, should many most disordered things, and contrary to experience happen. For it should be a most speedy motion, and swiftness inseparable, which should draw cyrcularly all the whole earthly body round about in 24. hours. And therefore that the earth is carried with so swift motion, should not only overthrow buildings, but high hills, and greatly shake and harm all things fastened and growing on the earth: yea all living beasts, and other creatures dwelling on the face of the earth, should be likewise shaken and harmed. Also the clouds, fowls, and whatsoever liveth and hangeth in the Air, should be carried and left behind at the setting in the West. For by the swift turning about of the earth should all things be over turned, and left behind by a great and long space; if by such a swiftness, the earth should be turned about the Exetrée of the world. Or if by the motion of the earth, the air, and all things hanging in the air, should be drawn with a like swiftness; then should they appear to stay, or not to be moved at all. And further, if a stone or any weighty thing cast upward should not light again down right on the same place: as may be seen in a ship, at sailing. So that to all these, doth evident experience deny, that by no motion, the earth is any thing moved, dut continually stayeth and abideth. By the fourth it is manifest, that in the motion and turning about of the Circle, the Centre abideth unmovable: which is the earth, placed in the middle of the world, and is as the Centre of the world. Therefore is the Earth known to be unmovable. That the Earth compared unto Heaven, is as a point. ALthough to the unskilful in this Art, the magnitude and largeness of the earth seemeth to be of an exceeding greatness, that no bond or end can be discerned with the eye; nor any having travailed into far countries, could hitherto find any bounds of the same: yet the greatness of the earth compared unto the mighty largeness of heaven is accounted but a prick; as the geometrical rules declare. The earth also is a very small thing, in respect of heaven: yea so little in comparison, as a pepper corn, or seed of Colliander, unto a Circle of a thousand paces compass. For if the earth compared to the firmament, were of any sensible greatness, a man should not see the half of heaven, nor the half Circle of the Equinoctial or Zodiac. And how much greater the earth should be, by so much the lesser should a man see the half of heaven. But the contrary is known, in that on any plain of the earth or upper face of the sea, a man always seeth the half Sphere of heaven, the other half (in the mean time) remaining hid: and of this the half dyameter of the earth is so small, unto the distance of the firmament, that it may take away nothing in a manner of the half Sphere, extant to the eye. Besides these, if the earth should be imagined to be placed in any of the Orbs of heaven, it would appear but small in respect of them: for being imagined in the moons Orb; the earth should appear thrice as great as the moon is discerned from thence, and somewhat bigger. And from the sun's Orb, the earth should be discerned twice so large as Venus doth here appear to us. And if in Mars' Sphere you would say that the earth is equal to a small star; But from the firmament, Satur's Sphere, or jupiters' (if a man could decern it) the earth should appear so small, that a man would be abashed at the sight of it. And here an ignorant man, might greatly wonder, that so small a body, yea rather a prick (as it is accounted of the learned) should contain in it so many Realms, Provinces, Cities, Towns, Floods, Mountains, Woods, Ualleyes, Seas, Rivers, Lakes, and many other great matters, over long to be written. That the earth also is as a Prick, is declared by sundry reasons following. By the first, that round about the earth, the magnituds and distances of the stars, in their times, are discerned and seen every where equal and alike. By the second, that the Gnomon or dial shadows, and the Centres of the Spherical borderes or Circles, placed in any part of the earth, do somuch avail, and keep the considerations and guydings about of shadows, so regularly, and agreeing to the rule and matter, as if those (in very deed) should be placed in the middle point of the earth. By the third, that the Horizont doth every where divide the whole heaven into two equal halves. For that in every moment, do six signs of the Zodiac appear above the Horizont, and in the night time being a fair sky are they to be seen with the eye, and so many (at that in. stant) hid within the Horizont: so that by a continual drawing about of heaven do six signs appear, and as many right against those six, set under the earth. If the magnitude of the earth should be of any light portion unto heaven, than so much of the Centre (the upper face drawn about) should part or divide heaven into equal half Spheres. The other Spheres reatching from any part of the upper face, should divide the same into unequal portions. Neither half the Zodiac should always appear, but a portion, much lesser than half the Zodiac should be seen above the earth, so that the greater part of the earth, through the folydnesse excluded and hidden, should not after be seen. By the fourth, the Equinoctial shadows, both of the rising and setting of the sun, do make a right line, even as if they should be streached out and lie on the plain, carried by the Centre of the earth. So that all these should not be caused, if the magnitude of the earth in respect of heaven, should be of a sensible, or of any portion to it. To conclude, Ptolemy useth always the body of the earth for the Centre of the world, not dividing the upper face from that which is not in sight of the earth. Certain affirm, that one degree of the greatest Circle in heaven containeth 57051. common German miles. Of which one degree of any earthly Circle in the upper face of the earth, doth amount to 15. German miles. And that one minute of the celestial degree, expresseth, 9509. German miles, which (if this be true) and certainly known, then is it not vainly thought and guessed, that the earth is as a Prick, in respect of heaven. To find the compass of the Earth, and by it the Dyameter. THe whole compass of the earth, according to Ambrose, Theodosius, Macrobius, and Eratostenes, doth contain 5400. German miles, and the dyameter of the same, doth contain 1718 4/22. German miles. But the authority of Eratostenes (after the mind of Pliny) is more to be regarded, than the other three Philosophers, which proveth by demonstration and reasons, that the compass of the whole earth is, 252000. furlongs. Yet Hipparchus finding fault at Eratostenes, doth affirm the compass of the earth, to be of 277000. furlongs. And a furlong is here (after the agreement of the Geometricians) of a hundredth, twenty, and five paces. And this sentence is not here mente, that there is any ambiguity or uncertainty in this reason: but that the one affirmed lesser, and the other more furlongs. For after Eratostenes, do 700. furlongs answer to one degree: but after Hipparchus, 774. furlongs answer to a degree. So that there is no other diversity in the matter, but only the number. Ptolemy that was after Eratostenes, attributed seven hundred fifty furlongs of the earthly merydiane, to one degree of the celestial meridian. So that by all these appeareth, that the magnitude of the earth is as yet unfound out, through the difficulty of measuring. And this whole compass is not only meant of the earth, but of the earth and water jointly together, both which are said to make one Sphere. Also Eratostenes gathereth the compass of all the earthly Orb, by the proportion of the particular, or the degree of the celestial Circle, unto the like space on earth. For he affirmeth, that to one degree of the celestial Equatour, answer 700. furlongs, or 15. German miles, but Ptolemy attributeth to a degree, 500 furlongs. Which is thus to be understood, that a Circle be imagined on earth, directly under the Equinoctial or Merydian line, dividing the earth into two halves: and that this Circle be likewise divided into 360. parts or degrees as the celestial Circles are. And each of these parts doth like unto the celestial parts, contain 700. furlongs, or 15. German miles. This now being tried and found, what the whole Sum either of the furlongs, or miles of the whole cyrcumference of the earth, which containeth 360. parts or degrees: you shall easily find and know the same by this manner. Multiply the whole compass of the earth; that is, the 368. degrees, by the 700. furlongs, or fifteen German miles, and the whole compass shall either appear to be 252000. furlongs, or 5400. German miles. This whole compass of the earth, divide by 22. and the number coming thereof, shall be the 22. part of the compass of it; that is, 11454 12/22. furlongs, or 254 ●0/22. German miles. And abate this 22. part, from the whole Sum of the circumference, and the number in furlongs shall remain and be 240545 10/22. and in German miles 5154 1●/22. And if any of these sums be divided a part by 3. it shall be found in furlongs to be 80181. a half, and a third part, or 3/2. 10/ 66. And in German miles 1718 4/22. that is; the dyameter of the earth, aswell in the furlongs, as German miles. And Archimedes by sundry labours, and witty inventions, and by Geometrical practice, hath found, that the like proportion is of the Circumference of the whole Circle un to the diameter of the same, as is 22. unto 7. that is, the diameter thrice, with a seventh part and a half. But whensoever any man will (by the cyrcumference of the Circle) gather and find his diameter, work the numbers thus, as this example teacheth. First, set down 22. at the left hand, toward the right hand 7. and the cyrcumference between those two numbers, 22. 5400. 7. After multiply the first by the second, that is, 7. by 5400. the number increased, which is, 47800. divide by the third, that is, 22. and you shall find in the quotient, 1718 4/22. German miles. Or thus in furlongs, the number being set down alike 22. 252000. 7. then multiply the first by the second, as 7. by 25200. and the increase shall be 1764000. after the increased number: divide by the third, as by 22. and the diameter shall be, 80181 18/22. If any covet to find the upper face of the earth, by the dyameter, and cyrcumference known, work one into the other, and you shall have that you seek. But if you desire to know the thickness of the earth, then join the superficial solydenes of the Sphere, unto the sixth part of the diameter, and you shall obtain your desire. THE SECOND PART OF THE SPHERICAL Elements of the Celestial Circles, with the uses of the same Circles. What is the Sum of this Second Part. WHereas in the first part, were only teh rudiments of the Sphere handled and taught (which are also written and contained in divers Phycite books) as of the World, and the many parts thereof: that is, of the Ethereal and Elementary Region: And also of the parts, motion and forme● of ●he aetherial Region: as Heaven, and the for●●●e, 〈◊〉, and quantity of the Earth. Here in this second part shall fully be ●et●●● th● and largely handled, the manifold uses of the Circle, of which the material Sphere is framed and made. Further this second part is divided into three parts, the first teacheth the division of the Circles (in that the ancient Astronomers, for a plainer instruction, divided heaven into sundry Circles) and of these some in greater, and other some in lesser Circles. In the second part, are the definitions, descriptions, and utilities of all the Circles taught. In the third and last part, are the places of the Zones, learnedly described, and the utilities of them. So that this second part doth especially entreat of the Circles (seeing the principal point of the Sphere, is of the celestial appearances) which by reason of the celestial Circles, or of the first mover are caused; as may appear of the ascensions and descensions of the signs, by which the whole knowledge aswell of the natural as artificial day is learned. Wherefore in that this instruction of the ascensions of the signs, consisteth in the Circles (which the ancient Astronomers imagined to be in the first mover) therefore is this second part of the celestial Circles, aptly placed, and necessarily before taught. That the Sphere of the world, is either right, or thwart. THe roundness of the earth, as is afore taught, both altereth the standing of the Poles, and the whole Sphere of the world, in divers parts of the earth. For to them which dwell under the Equatour, either Pole falleth to the plainness of the Horizont. But to others dwelling without the Equatoure, the one Pole is raised, and the other depressed & hid: through which diversity of the standing of them, are these differences caused; that the rise and settings of the signs are altered; the spaces between the days and nights varied, whose causes ought diligently to be sought. Therefore is the right Sphere, distinguished from the thwart Sphere of the world. In this manner, as here you may be hold by these figures following. That is called the right Sphere, in which either Pole resteth and standeth on the plain of the Horizont and the Equatoure, which there doth exactly possess the middle place between the Poles, and doth with the Horrizont make a right spherical angle: of which it is so named a right Sphere. For they have such a standing upon the Sphere of the world, as that neither of the Poles is elevated above the Horizont, to them which dwell under the Equatoure. The thwart, declined, or bending Sphere, is that, in which either of the Poles of the world elevated, is seen above the Horizont, and the other just somuch set and hid beneath the Horizont: and also that the Equatoure frameth and maketh with the Horizont thwart and unequal angles. And that is called a blunt angle, which seeth the Pole elevated: and that a sharp angle, declining unto the contrary. They which dwell on this side, and beyond the Equatoure have such a Sphere. But the same form and condition of the thwart Sphere, is not every where; nor the positure of it, the same reason: but that the thwartness of the Sphere is so much the more increased, as by how many degrees either of the Poles are near to the earth: and being further distant from the Equatoure, is raised and carried higher, which is the cause of many obscure differences: which that they may the plainer be expressed and understanded, the skilful practisioners have divided Circles in the first mover, by lines drawn unto certain stars or pricks from the Centre of the earth, and drawn about either by a continual or daily motion, by which they imagined them to be described. That the Circles of the Sphere, be some greater, some lesser, and the number of the Circles. HEre it is not to be omitted, that one Circle is greater than another, by four means. First, by reason of the magnitude of the celestial body in which it is imagined to be. And of this is the Equinoctial Circle of the first mover, greater than the Equinoctial Circle of the eight spher, in that the first mover is greatest of all the bodies. And although the Equinoctial of the eight Sphere, doth divide it into two equal halves, yet of the first mover it is named the greater, for that the same includeth all other bodies. By the second, it is evident that the Equinoctial Circle is greater, by reason of the appearance, in that the whole is seen above the Horizont. And by the same reason the Northerly Circle (which is named the Arctic Circle) is the greater, for that it always appeareth to us, above the Horizont. By the third, the Equinoctial is accounted greater than the other, in regard of the influxive virtue: and for this cause also is the Zodiac called greater than the others, through his greater working into these inferior bodies. For that under it, the sun and all other Planets are drawn. And Happarchus writeth, that this Circle is the life of all things which are in the world, etc. In that by the ascending of the sun to us, generation is caused, and by his falling or going from us, diminishing, that is corruption getteth the upper hand. By the fourth, is a Circle called greater than the other, insomuch as it is one Sphere, and thus the equinoctial, is greatest of all the Parallel Circles, in the first mover: which is evidently demonstrated, by the diameter of the Circle. Therefore by the definitions and reasons above showed, the equinoctial is the greater Circle, described in the upper face of the first mover, according to each part, or the whole of it, being equally distant from either Pole of the world. And it is further to be considered, that all the Circles of the Material Sphere, are imagined to be in the first mover, which also a material Sphere doth especially represent So that these Circles, may also be imagined in the other Spheres, aswell as in the eight Sphere, etc. And although a man may enter into conference between these Circles and the diameter, yet he shall be forced to confess that they be on such wise unto the sphere, as the Circle is unto the diameter. So that as the diameter divideth the Circle into two equal parts (in that it passeth by the Centre of the same) even so doth every of the greatest Circles divide the Sphere into two equal parts, because the plain upper face of it passeth by the Centre. And by this it may easily be perceived, that those which are named the lesser Circles (of which is a far greater number than is here set down) have divers Centres from the Centre of the Sphere; and yet the plain upper face of them passeth not by the Centre of the same Sphere. Of which ensueth, that they cannot divide the sphere into two equal halves: no more than the line drawn without the Centre, into a Circle; can divide the same into two equal halves. And both the greater and lesser of these is mente, according to the distance of his Centre, from the Centre of the sphere. The inward Circles that be movable, are those, which are describe in the first mover, and are drawn with it about: as is the equinoctial, the Zodiac, the Colours, the tropics, the Polare Circles, and others describe from the points of the first mover. But the outward Circles, are they that are as immovable, and not drawn about with the first mover, but abide steady. The number of which are these: the Meridiane, the Horizont, the hour Circles, the verticiall Circles, and Circles of the progressions. Further it is to be noted, that many are the Celestial Circles (as is above declared) whose use partly unto Astronomy, and partly unto Astrology, is necessary. As the verticiall Circles, the Circles of the altitudes, the Circles of the celestial houses. The Circles with the which the material sphere is describe: and to be brief, there are so many celestial Circles, as there may be points imagined in the first mover. Yet are there but only ten Circles, which are required unto this spherical treatise; whose names are the Equinoctial, the Zodiac, the two Colours, the Meridian, the Horizont, the two tropics, and the two Polare Circles. The greater Circles are those, which have the same or a like Centre with the earth, whose plain upper face doth pass by the Centre of the earth, so that they divide the sphere, into two equal parts (and especially the equinoctial) which for that it is a greater Circle, doth cut the spher into two equal halves; so that his plain upper face passeth by the Centre of the earth, according to the definition of the greater Circles. And by this consequent, when the Sun is in the equinoctial, he falleth into the Centre of the earth; that is, he is in the upper face which passeth by the Centre of the earth. And the sun is never in such an upper face, but when he is in the two equinoctial points for other wise, he runneth without that upper face. For the greater Circles are a like unto the Sphere, as the diameters unto the Circle: in that as the diameter cutteth the Circle in two equal halves (for that it doth pass by the Centre of the same) even so doth the greater Circle divide the Sphere into two equal halves, in that the plain upper face of the same, doth pass by the Centre of the sphere. But the lesser Circles are those, which have diverse Centres, from the Centre of the sphere, so that the plain upper face of them doth not pass by the Centre of the sphere. For how much nearer the Centre of the same is to the Centre of the sphere, and somuch the greater is that Circle, as the Tropic. But the further it is from the Centre, even so much ●he lesser in sight is the Circle, as are the Polare circle. And here none may suppose, that either these or other like circles, to be verily in the first mover, but only to be understood or imagined. For the cause of dividing heaven into certain spaces and regions, through the help of which, the courses of the Planets are observed, & brought unto a rule. Further the office of the celestial circles; are these. 1 That they divide heaven, into certain spaces, or regions. 2 The courses of the Planets, the firmament, and first mover, by the help of these circles are observed, and brought unto a rule. 3 They show the points of rising and setting; the nearness and differences both of days and nights. 4 The times and varieties of all the celestial appearances, may be observed and known of the circles by a certain reason. The six greater circles are numbered by names, standing, and use distinguished. As the Equinoctial. Zodiac. Colour of the Equinoctials. Colour of the Solstices. Meridiane. Horizont. But there are many others, as the Circles defined or describe by the Poles of the Zodiac, and Centres of the stars, which are named the circles of the latitudes. The Circles drawn by the verticial points of divers places, which may be named the circles of the distance, or space between places. For that the tops do knit or join together by the nighest space of the differences of places, and do show the distance of them. The circles by the Centres of the stars, and Poles of the world drawn, are named the circles of the declinations of the stars. The six circles of the positions (through which by the thirty parts of the Equatoure, and the points, touched of the Horizont and meridian drawn over the Equatoure) doth Regiomontane part and divide the whole heaven into twelve equal spaces, which he nameth the houses of heaven. The six greater circles (through which by the Poles of the Zodiac, and the thirty parts of the same bended and writhed) doth julius Firmicus divide the Zodiac into twelve equal parts, but the Equatoure into as many unequal arks. But that former distribution and disposing of the Circles by Regiomontane, both devised and demonstrated of him, doth bring and cause a reason of the framing of the figures of heaven, which they name Rational: in that the same invented and taught by principles and demonstrations, is declared by certain reasons. The other invented and exercised of others, doth bring and cause another reason of the forming and erecting of the figures of heaven, which of the same they name the equal manner; in that it parteth or divideth the Zodiac into equal arks. Many other circles there are, which for brevity be here overpassed: for that they belong not unto this determined treatise of the principles. The lesser circles, although there are in a manner infinite of them, yet are there four only recited and especially known, which also are named Parallels. As the Tropic of Cancer. Tropic of Capricorn. The Arctic or Northerly Circle. The Antarctic. Of the four greater circles, afore written, they both are movable, and are continually drawn about with the first mover and never changed. But the two neither circles, as the Meridiane and horizont, do remain and abide fixed and immovable, in the going about of heaven, and the standing always changed on the earth, toward what quarter soever they are varied, as they may be and are in a manner infinite in number. The Astronomers divide, both the greater and lesser circles, into 360. degrees, which they so named through the sun's passage or journey in the Zodiac, measuring and defining by his daily course such like parts and spaces. And of these parts or degrees of the greater circles, it is found and known, that each degree containeth in the upper face of the earth, either 62500. paces, or 500 furlongs, or 15. German miles. But each part of the lesser circles, do comprehend a lesser space by somuch, as by how much more from the magnitude of the Parallel, which is the middle and greatest, by reason of the distance they lack or differ. And each of the three hundredth threescore degrees, are also parted or divided into three score minutes: and each minute, into three score seconds: and each second into three score thirds: and so forth from thirds unto fourths: and so unto tenths, they distribute them. The description, names, and utilities, of the Equinoctial. THe Equinoctial, which the Greeks name 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, is a greater circle, placed in the middle place of the Sphere, between either Pole of the world, and dividing both by equal spaces movable, and crossing the Zodiac in two points, which when the sun doth come unto, he than causeth a like day and night throughout the earth: whereof this circle first purchased that name; in that the day is equal to the night, which happeneth twice in the year, as in the beginning and entrance of the sun, both into Aries and Libra. And a strait line drawn out by imagination doth describe this circle, reaching out of the Centre of the earth by the Centre of the sun's body on a plain or flat, of the Equinoctial being unto the first mover, or unto any of the fixed stars to the Equatoure, fastened to the eight Sphere, as that either of them, which with the third being somewhat lower and darcker do fashion the girdle of Orione, and that by a daily and continual turning drawn about of the first mover, until the same be returned unto the place, from whence it began. And likewise the sun, or any other constellation placed or being in it, doth in every region describe the half of the Parallel above the Horizont, and the other half, under the Horizont: which Ptolemy nameth the circle of the Equatoure of the day: and Alphraganus, the circle of the Equinoctial, and swath or girdle of the first mover, in that it compasseth about the first mover (as Strabo writeth) that it parteth the Northerly half Sphere, from the Southerly. For this greater circle of the first mover, is the first measurer, both of time, and motion. In that it causeth the proportional cyrcumferences by the spaces of times: and whiles it is once drawn about, a natural day is performed. And whiles the compass also of the whole, have moved one four and twentieth part, an equal or Equinoctial hour hath passed: by which it doth evidently appear, that this circle, belongeth unto the first mover. This Worthy Circle hath divers names. 1 IT is named the Equinoctial, in that it causeth a like night, to the artificial day. 2 It is by the same reason named the Equatoure; for that it maketh equal the night, to the day. 3 It is named the girdle of the first mover (not unproperly) for that as a girdle doth gird or divide our body into two equal halves; even so this circle divideth the sphere or first mover, by the middle. 4 It is named the line of the equality of the day, or the line of the equation of the Orb of the day, or the just division of the day and night. 5 Of Pliny it is named the Centre of the earth, and that not incongruently; seeing all the Parallel circles described from the Centre of the sun by the motion of the first mover, have their Centres from the Centre of the earth: and that the Equatour only, which when the sun shall be in the Equinoctial point, is then imagined to be drawn about with the motion of the first mover, that hath the same Centre with the earth at that time, by which the plain of the Equatoure, is then noted to pass. So that this is the cause why Pliny giveth that name to it: seeing a like day and night is caused, the sun then running under the Equatoure throughout the earth, as no man of skill maketh doubt of. It is named the circle of the high solstice; but this cometh to pass, by reason of those which dwell under the equinoctial, and have four solstices; as two on high, & two below, having four shadows in the year: and the sun passing twice a year by the Zenith, right over their heads (as when the sun is in the beginning of Aries and Libra.) And to them also dwelling under the Equinoctial are two summers and two winters: and the heat is mightiest and strongest, when the sun draweth from them into the North, or South; yet doth the sun always burn the earth right under it, causing a burning Zone, and not parteth far from their heads. So that their winters are not perfectly and simply named winters, as with us which are cold seasons in deed; but rather with them is a continual summer: yet for that the causes of heat with them, are not unformally, and in a like manner always, for that the sun doth not approach equally the Zenith of that part, as the same is known to many: whereof the heat to them is not uniform and a like in burning. But sometimes hotter, and sometimes slacker and meaner of heat. So that when the sun is in the Zenith, as in the beginnings of Aries and Libra, and that they are in their high solstices; then is the heat most vehement with them, yet not without the sun, this heat can be called mighty. But when as the sun is gone from their Zenith, which happeneth in the beginning of Cancer and Capricorn, where their low solstices are, the heat is then slacker: that is, dat burning. So that the weaker heat happening in the low solstices, may in a manner be named cold, in respect of the most burning heat, happening in the high solstices, yet it hath the nomination of winter, although no cold may be felt. What the offices or utilities of the Equinoctial are. THe causes why the skilful practisioners took and used the Equinoctial, with the offices which they attributed to it, and the many fold uses that it offereth, is herein declared. 1 It measureth the motion of the first and uppermost Orb, and showeth the same to be drawn about by a continual and equal swiftness. For that in every equal hour, do fifteen of the three hundredth and three score degrees of the same arise, and so many degrees right against, set and are hidden under the Horizont: and that all the three hundredth and three score degrees, in 24. hours, are turned about in the appointed times, and in their periods continually agreeing. And as the Equatour from the Poles of the world (about which the first mover is drawn, and is of either side distant by equal spaces) nor the Angle, which is comprehended & fashioneth with the Horizont doth never change: even so (by the same order and like motion) doth the first heaven or mover evidently show itself to be carried about. For the Equinoctial measureth and determineth the motion of the first mover, in declaring his revolution and year: which year of the first mover, is the time of 24. hours equal. But by what means the ancient astronomers first found, that the Equinoctial is drawn about in so many hours: and it is supposed they came to the knowledge thereof, by the office of some star, either in the Equinoctial, or placed near it, they perceived the same: as that the Equinoctial from some note marked of them, did return to it in such a certain space, as afore showed. 2 The divers motions of the Zodiac (which happeneth to it through the twart standing or lying▪) as a cannon or rule, doth direct and point out the beginnings, bounds, and time, with the which each parts or degrees of the Zodiac arise, or do set: and with which they touch these or those quarters of the world. For all the arckes of the Equatoure, are drawn by a certain and agreeable motion continually. The parts of the Zodiac drawn thwartly, the Equatoure doth not vary or is distant by like spaces from the Poles of the world, nor turned about his, but the same Poles of the world, which do differ by a long space from his, and drawn about by a most unlike motion and nothing at all agreeing in itself: For that some parts or degrees are carried up sooner or quicker, and others appear slower and later. So that these useth a more space of time in the rising slower, and those other pass up by a shorter and quicker space. But seeing that in the Zodiac the wandering stars or Planets, do wander continually hither and thither, and from one side of it to another: and that unto the middle circle of it or ecclipticke line, the places of all the fixed stars are referred and applied: therefore cannot the times of the rising or setting of the stars, be known and noted, except they should be guessed and attained, by the next arks of the equinoctial. It also declareth the equinoctialles, which are caused in those proper days, in which the sun happeneth to come into the equinoctial circle. For these are caused the sun being in the first degrees of Aries and Libra, in that the Zodiac and Equinoctial do cross each other in those places; whereof Manilius thus writeth. That these signs Aries and Libra cause a right, Throughout the earth, a like day and night. 3. It defineth and measureth the spaces, both of the natural and artificial days. And although the sun (which drawn about with the motion of the first mover, and in the proper motion, carried forth in the mean time by force into the contrary, when as he causeth the times of the days and nights, so well as the differences of the natural days) moved, and runneth in the Zodiac; yet of his motion, the day and night spaces cannot be gatherrd, through the diversity and unlikeness of the ascending or arising of divers parts or degrees of the Zodiac. But seeing the same motion is of all the parts of the Equatoure; therefore are the ascensions of the arcks of the Zodiac, carried up with the ascending of the nighest parts of the Equatour, like arising. So that both the days and hours, by the equal motion of these, are not found and distinguished by the unlike and unequal motion of them, in that these ascensions can be, of these two circles. The Greeks' by no means like of the same, in that by a steadfast order, they do mark the day and night times; therefore they part and divide them into equal hours, which they named times, that from the degrees of the Zodiac they might distinguish them. For every fifteen parts or degrees of the Equatour in his motion and rising above the Horizont, do make an hour, and every degree four minutes of an equal hour: so that the quarters or fifteen minutes of each degree, do produce and cause one minute of an hour. Also they observed the ascensions and descensions of the signs in this circle, for that in any region or country, a man may know the length of the artificial day and night, by having a spherical instrument, and the sun placed in the East Horizont, let the note of the Equinoctial be moved, and after the sun being turned into the West Horizont, let the note again of the Equinoctial be moved into the East Horizont. So that the degrees of the Equinoctial numbered, marked with these notes, do cause an artificial day, counting always fifteen degrees of the Equinoctial, for an equal hour. To conclude the length of the artificial day, known by subtracting the same from 24. hours, the quantity of the night remaining shall appear how much it is. Last the sun being entered into this circle, doth rise in the just East point, and setteth full West: but in the highest of summer being come to Cancer, he riseth North-east, and setteth Northwest: at what time the noontide is highest. But in the shortest time of winter when the sun is come to Capricorn, he contrariwise riseth Southeast, and is in the noontide lowest. 4 It distinguisheth the Equinoctials and crosseth the Zodiac thwartly wreathed and bended to it, in two opposite points, which when the sun cometh and is in it, he causeth like spaces of the day and night: and of the same, those entrances of the sun, are named the Equinoctial points. And there are two Equinoctials caused in every year: as the one, the sun entering the beginning of Aries, or the spring point of the crossing of the Zodiac and Equinoctial, in the beginning of the spring, which the Latins name the equinoctial spring, and the Greeks, Isemerian earinéns. And the celestial point of the same equinoctial, the Greeks name the point of our equinoctial spring. The other equinoctial is caused, when the sun hath his beginning of Libra, in the entrance of harvest, called the equinoctial harvest. And the celestial point in which the sun happeneth, they name the point of our Equinoctial harvest. These points remain not fixed in one place of heaven, but in the going before do proceed or move forward under the eight Orb, and turn before the places of the fixed stars. For the point of the equinoctial spring, that in the first year of Olimpias followed the first star of Aries of the eight Sphere, 4. degrees, and 52. minutes. And in the year of the death of Alexander, one degree, and 58. minutes. The same after the beginning of the years of julius, Cesar, followed 4. degrees, and 50, minutes. And in the year of Christ's birth, 5. degrees and 16. minutes. In Ptholomies' time, 6. degrees, and 40. minutes, it went before the same star: and in these years it went before that star, 27. degrees, and 35. minutes. So that the yearly times of the Equinoctials are come back, from the ancient time, and move before the marked days by a long space: For that the Equinoctial spring which about the beginning of the years of Olimpias, happened in the first or second of April. In the beginning of the years of Cesar, in the 25. day of March. In the time of Christ our saviour's birth, in the 23. or 24. day of March. In Ptholomies' time, in the 22. or 23. day of March. But in our time it happeneth, in the 11. or 12. day of March, and in this year 1570. it happeneth in the 11. day of March, and in the 11. hour before noon, on Saturday. The Autumnal or harvest Equinoctial, which happened in Christ our saviours time, in the 23. or 24. day of september, is brought back and come in this our time, unto the 13. or 14. day of September, and in this year 1570. shall happen in the 13. day, and in the 10. hour, and 21. minutes after noon, on Wednesday. And through this variation of the fixed stars, and Equinoctials, is caused, that the later practitioners have found an other quantity of the year, contrary to the ancients. For Hipparchus and Ptolemy, have established in their time the quantity of the Tropic year, to be of 365. days, 5. hours, 55. minutes, and 12. seconds. The Alphonsines, of 365. days, 5. hours, 55. minutes, and 12. seconds, Albategnius, 365. days, 5. hours, 46. minutes and 56. seconds. Cardanus, of 365. days, 5. hours, 48. minutes, 41. seconds, and 47. thirds. And Thebitius hath established the starry year to be of 365. days 6, hours, 9 minutes, and 32. seconds, which is the space of time, in which the sun returneth unto the same fixed star. But the Tropic year, is the sun's return, after his measuring of the whole Zodiac, unto the Equinoctial or soisticiall point. So that by the said points changed, either in the increasing or coming sooner, as hitherto hath been observed, is the quantity of the year, found to be in diverse and sundry wise of the practisioners. By it also is learned and known which stars and images celestial, are toward the North or South from it. And by it is the starrieskie divided into two equal halves, of which the one half is toward the North, and the other toward the South. So that the denomination, so well of the Planets, as fixed stars, are there by learned; whether they be Southerly, or the Northerly. another author writeth thus of it; that it divideth heaven into two parts, of which the one is named Northerly, of the seven stars in the great Bear; the other Southerly, in that the sun about the South, seemeth always to abide with us in that quarter. And if the same may be known, which stars are named Northerly, and which Southerly: and when the Planets are named Northerly, and when Southerly. So that by this reason, all the stars and images from it, tending toward the North, to be Northerly: and from it tending toward the South, to be Southerly. The Northerly images, in respect of the Equinoctial, are these. THe Bull named in latin Taurus, is adorned with 33. stars, although an other writer mentioneth but of 32. Of these, 5. are in the face, and about the eyes, and in the places where the horns are described to be, are one star a piece, which make seven in number; named Hyades in Greek, and Succullae in Latin, in that they stand like to the letter Y. These in the 10. 11. and 12▪ degrees of Taurus, having their latitude Southerly: of which 4. are of the third bigness, and one brighter than the rest in the Southerly eye, named properly Aldebaran, of the first bigness, and of the nature of Marse. The seven stars on the back of this sign, named Pleiades, and in Latin Virgiliae, but in English the clustering stars; in that they stand so near together that they can scarcely be numbered: yet these more regarded than any of the others, in that at the appearance of them, Summer is signified; and at the setting of them, (which is six months after) winter is then in entrance, like which is not showed in the other signs. And in our time, they are in the 22. and 23. degree of Taurus, the sun joineth with them every year, in the third and fourth day of May. So that after those days, through the suns departing from them, they are known to arise Heliace before the sun, and then is summer entered: which in our time happeneth about the 7. 8. 9 or 10. day of may. And when the sun is come (by his course) unto the 22. and 23. degree of Scorpio, which happeneth in our time, in the 5. and 6. day of November, then is the sun directly against Pleiades: and the sun then arising in the morning, they do set: and about these days, (as in the 5. 6. 7. 8. 9 and 10. day of November) winter is entered. These as Ptolemy writeth, are of the nature of Mars and the Moon: but all the others, being some of the third and fourth, and some of the fist bigness, are of the nature of Saturn, and a little of Mercury. THe sign Gemini is placed in heaven, as that between them and Taurus, is that constellation Orion standing Their headed devideb from the rest of the body, yet embracing one the other by bodies, and do directly set with the feet, and arise together bended, as they were lying. Of which those two be the notablest, that stand in the heads: and that clear star in the head which goeth before (named Castor, and of some Apollo) having beside in either shoulder a clear star, in the right elbow one, in either knee one, and in either foot one star. And the other which followeth, being next to Cancer, hath in the head a star named Pollux, of others Hercules, on the left shoulder one, in the right another, and in the other parts sundry other stars, to the number of 18. known in both. There is an other star standing without the form of Gemini, going before the foot of Gemini, and following after, called Propus: and is in our time, in the 24. degree of Gemini. Of which two are of the second bigness, as those in the heads, but the others are of the third, fourth, and fift bigness. And are all of the nature of Saturn, saving the head going before is of the nature of Mercury: and that in the head following, of the nature of Mars. THe sign Leo looking unto the West, is placed on the body of Hydra, and not in the head, by which Cancer is nigh unto the half of it, having the middle divided by the summer circle, in such sort, that under that Orb he hath the fore feet placed, setting and rising with the head. Also he hath in the head three stars, in the nape of the neck two, in the breast one, in the space between the shoulders under the neck or behiude the neck three, in the middle of the tail one, in the end of the tail another, and in the belly one clear or bright star (named the heart of the Lion) which also is called aroyal star, in that it is more about the Zodiac than the other great fixed stars; and for this cause called a star of the first bigness, although in truth, it is but a star of the second bigness, being of the nature of jupiter and Mars. All the stars which this sign hath (as Ptolemy writeth) are 27. Of which many are of a great brightness, as the two in the nape of the neck, of the second bigness: that on the heart, of the first bigness, another on the back, of the second bigness: another in the end of the tail, of the first bigness: and all the rest, of the third, fourth, and fift bigness. THe image named the Carter or dri●●● of the Car, Ptolemy doth deck with 14. stairs, being all now in Gemini, and of the 1. 2. 3. 4. 5. and 6. bigness, of the nature of Mars and Mercury. Also this image named the Carter, hath a clear star, named the Goat standing on his left shoulder, being a star of the first bigness, and in our time in the 15. degree of Gemini: borrowing nature of Mars and Mercury. And that image or constellation named the Kids, (being two small stars, standing on the left hand of the Carter) are in our time, in the 12. degree of Gemini, of the fourth bigness, and of the nature of Mars, and Mercury. THe image named Perseus, hath 26. stars which form two particular images: of which that which is seen on his left side, is named Gorgon, or the head Algoll. And hereof it cometh that they are called the Gorgon stars. The other seen on his right side, the ancient astronomers name the Circle o● scythe. Also Ptolemy in the description of Perseus, attributeth to the head of Algoll (that is Medusa) as to a particular image, four stars. And the brighter stars of them (being in the head of Algoll is the 12. star) is in our time, in the ●9 degree, and twenty minutes of Taurus. The following star (being of the fourth bigness) is in our time in the 18. degree of Taurus. And Ptolemy writeth, that the head of Algoll being of the second bigness, is of the nature of Saturn and jupiter: and that on the right side of Perscus', of the second bigness, is of the nature of Saturn and jupiter, and is in our time in 24. and 28. minutes of Taurus. ON the head of Aries (not far from the feet of Andromed●) standeth a figure, which the Greeks (for the likeness of the letter Delta) ●a●e Deltoton; and the Latins, for the similitude of the form called a triangle. This figur● hath 〈◊〉 equal sides, but the third not so perfect fashioned, yet easily to be known; for that it shineth brighter than many other stars about it: To which the stars of Aries are a little Southerly. And to it Ptolemy attributeth four stars, although all other authors affirm only three stars, except Alphonsus, which in our time are in Taurus, being of the third and fourth bigness, and altogether of the nature of Mercury. THe image of Andromeda (placed in heaven with the arms stretched abroad, and each hand bound) Ptolemy declareth it to have 23. stars, of the third, fourth, and fift bigness, and in our time are in Aries and Taurus, whose nature resembleth Venus. This Cassiopia is figured like to a woman sitting in a chair, with the hands lifted up after a wailing manner; and in the turning of the world about, she is drawn with the head always upward. Ptolemy doth number 13. stars in that image, of the 3. 4. 5. and six bigness, which in our time, are in the signs Aries and Taurus, and of the nature of Saturn and Venus. Among the Astrologians only Ptolemy and Alphonsus do place two horses in heaven: or (as I may more rightly speak) the two parts of horses: of which the one is called the fore horse, or head of the horse, to which Ptolemy attributeth four dark stars, which in our time are in Aquarius. The other figure named of the Arabians, Alpheratz, in English the second horse, the half horse winged, or Pegasus, whose fore part is described unto the navel: and of this, doth the greater number of authors write. Ptolemy decketh this image with 20. stars, being of the 2. 3. 4. and 5. bigness, which in our time are in Aquaries, Pisces, and Aries, altogether having the quality or nature of jupiter and Mars. THe celestial image of that fish named the Dolphin, the ancient men placed in heaven among the starred (not far from that constellation named the Eagle.) And many of the ancient astronomers, attributed but 9 stars, to this Dolphin, which are of the third, fourth, and sixth magnitude, and in our time be in Aquarius, retaining the nature of Saturn and Mars. THe figure named the celestial Arrow, placed in heaven without a bow, to which the Swan flieth, is near to the North. To this Arrow doth Ptolemy attribute five stars, which in our time are about the end of Capricornus, being of the fourth, fift, and sixth greatness, and having the quality of Mars, and a little of Venus. The figure named the Eagle (whereon Aquarius seemeth to fly) which many affirm to be Ganymedes, Ptolemy doth deck with nine stars, of the second, third, fourth, and fift bigness, that in his time were in Sagitarius and Capricornus, and in our time are in Capricornus, which follow the qualities of Mars and jupiter. Many ancient authors used for the celestial Harp, the Griepe falling, which for that there is so little thereof mentioned, shall here be overpassed. But Ptolemy giveth to this celestial Harp, 10. stars, being all of the first third, and fourth magnitude, and in his time were in Sagitarius (except the fift and sixth star) which then were in Capricornus, and have the qualities of Venus and Mercury. The image Hercules (named of Aratus and sundry others Eugonasis) is thus placed in heaven, it maketh the Dragon appear to have his head upright, and Hercules with the right foot, the knee being bended or bowed, seemeth with the left foot to thrust down the right side of his head, and in his right hand holding up a great nail as it were to strick, and covered on the left side with a Lion's skin, seemeth earnestly to fight and ●●ea the same unarmed. This image doth Ptolemy describe with 29. stars, and others only 28: which in our time are all in Libra, Scorpio, and Sagitarius, and of the quality of Mercury. Where Aratos, Ptolemy and Alphonsus write of two manner of Crowns (as the Northerly, and Sowtherly) therefore shall first be showed of the Northerly Crown, and after of the Sowtherly in their proper place. This bright constellation named the Northerly Crown, doth Ptolemy declare to have 8. stars, which in his time were all in Virgo, and at this day are in Scorpio. And in the same constellation is a bright star, of the second bigness, by the name of the whole image: of the Arabians named Alpheta of Virgil, Geor Guofia. The image named the Swan, the Fowl, the Hen, and the Griepe flying, doth Ptolemy deck with 17. stars, of the second, third, fourth, and fift bigness, and in his time were in Capricornus & Aquarius, but in our time are in Capricornus, Aquarius, and Pisces, and be all of the nature of Venus and Mercury. The image named Arctipholax, or Boötes, which in English may be named the herdman, or rather the keeper of the waggon, in that he seemeth to follow the waggon: that is the Northerly stars. And Pliny writing of Boots, (which he otherwise nameth Arcturus) doth affirm, that this constellation in a manner never riseth, but a stormy hail ensueth. Also Arcturus is a bright star not in fashion of the first bigness, standing between the legs of Boötes, as Ptolemy writeth: but Hyginus, Rufus, and others, do place that star in the girdle of Boötes. This Boots, (after Ptolemy) hath 22. stars, which in his time were in Virgo and Libra, and in our time are only four of the first in Virgo and all the others in Libra. But as touching the natures of them, Ptolemy doth only write hf Arcturus, which he affirmeth to have the nature of jupiter and Mars. The image named Cepheus, Ptolemy affirmeth to have twelve stars, of the third, fourth, and fift magnitude being in his time in Pisces and Aries: and in our time in Pisces, Aries, and Taurus, and following the nature of jupiter and Saturn. The image named the celestial Dragon, that other ancient men name the Serpent, hath (after Ptolemy) 13. stars placed over all: which in his time were in Libra, Scorpio, Sagitarius, Capricornus, Aquarius, Pisces, Aries, Taurus, Gemini, Cancer, Leo, and Virgo, and in our time are in these; Scorpio Sagitarius, Capricornus, Aquarius, Pisces, Aries, Taurus, Geminini, Cancer, Leo, Virgo, and Libra: being of the 3. 4. 5. and 6, bigness. Those that shine brightest are eight, and of the third greatness, as that third star, which is on the eye; the fift star which is on the head called Rastaben; the 24. and 25. declining unto the North, the 29. which standeth beyond the furthest winding, the 30. which is near the end of the tail, and the 31. which is at the very end. And these brighter shining stars are of the nature of Saturn and Mars. The image named the greater celestial Bear, and of many (for the form of the Stars standing together) Charles-wain. All the seven stars, of which two be alike, and are seen in one place, called of the ancient the two Oxen, in that they seem equally to move, as yoked Oxen. The other 5. stars they imagined to fashion the waggon and the sign or image next to it, to be Boötes, or in English the waggon driver, which seven stars (being the greater Bear) are drawn once about the Pole of the world in 24. hours, and never set out of sight: For one while it carrieth three unto the highest, and the other four unto to the lowest: and an other while it draweth the four unto the highest, and bringeth the three to the lowest. This constellation named the greater Bear, doth Ptolemy declare to have 27. stars, which in his time were in Gemini, Cancer, and Leo, and in our time in Cancer, Leo, and Virgo, having all the quality of Mars. But here I overpass all the stars of that constellation, and only take those which form the waggon (being 7. in number) of which four in the order of the stars of the greater Bear, being the 16. 17. 18. and 19 that go before the waggon, or the wheels of the same. The 16. 17. and 19 are of the second greatness, but the 18, is of the third bigness. The 25. is of the second sign (named Alioth) that is before the beam which containeth the yoke. The 26. and 27. that stand in stead of the places of the two Oxen. All these are described, in a manner after the mind of Hyginius, but Cesar the German attributeth the three stars of the tail, to the beam of the waggon, and the other Stars to the wheels of the waggon. The figure named Cynosura, the little Bear, or lesser waggon, did the men of Syria more diligently regard, supposing to sail the truer and surer by it: and of this thought through their first finding of the same (to have it called after them, Phenicen. This little Bear after Ptolemy, called the Northerly stars, or lesser waggon (as above said) hath seven stars, which in Ptholomies' time were in Gemini and Cancer, and in our time are in Cancer and Leo. Of these the first star, which is on the end of the tail, is named the Pole star, about which the first mover is supposed to be drawn, and is of the third bigness. The two following stars in the tail, and the two fore wheel stars, are of the fourth bigness, and the two hinder wheel stars following, are of the second greatness, and these stars have the quality of Saturn, and a little of Venus, as Ptolemy in primo Quadri, writeth. The Southerly images, in respect of the Equinoctial, are these. The sign Libra is a part of Scorpio, which through the magnitude of the members is divided into two signs, of which the figure of the one they called Libra. And that part was rightly named Libra, in that when the sun is entered the beginning of that sign, the day and night is divided a like as by an equal balance. For the Equinoctial harvest like happeneth, at the entrance of the sun into Aries as the Equinoctial spring doth. This sign hath eight stars (which are in form) of which one in the Southerly balance and another in the Northerly balance, and of the second greatness. But the others which either do follow or move before either balance, are of the fourth and fift bigness. Nine others there are which be not in form, placed within and without the balances. Being all of the nature of Mars and Mercury. The fore part of Scorpius is so hidden of the Equinoctial circle, that it appeareth to stay or hold the same up. It setteth with the head inclined, and ariseth right up. The sign Scorpio hath in those (which are called the Klées) in each of them two stars, of which the fore stars are the clearer, and have the quality of Mars, and a part of Saturn. It hath also in the forehead three stars, of which the middle stars is the clearest, and of the third bigness. In the space between the shoulders under the neck, three stars. In the belly two. In the top of the tail five, with the which he is spposed to strike, two stars. In the whole the sign hath 24. stars. That one star which is named Antares (or the heart of the Scorpion) is of the second greatness and of the nature of jupiter and Mars. And many stars (especially those which are placed on the body) are of the 3. greatness, and have the quality of jupiter and Mars. The stars by the forehead, of the nature of Mars, and part of Saturn. The stars on the legs and feet, are of the fourth and fift bigness, and have the quality of jupiter, Saturn, Mars, Mercury, and part of Venus. THe sign Sagitarius looketh unto the West, and is figured with the body of a Centaur, as it were shooting arrows, beginning from the feet, unto the shoulders. It is so placed in the winter circle, that his head only may seem to appear without the same Circle: whose half Bow is divided by the milky circle. And before his feet standeth the Crown decked with certain stars: he seateth headlong, and ariseth strait up. This sign hath in the head two stars, of the fourth bigness, of the nature of Mars and the Sun. In the right elbow one, and in the forehead one. In the belly one, in the left shoulder one, of the third bigness, and quality of jupiter and Saturn. The stars of either side the root of the tail, of the fift bigness, and of the nature of Venus, and part Saturn. In the fore knee, one star etc. This sign in the whole, hath 31. stars. Of which those on the Bow, on the North, South, and middle part, are of the third bigness, and of the nature of jupiter and Mars. And two on the left foot, of the second bigness, the one on the right ankle, of the third bigness: and that star in the right elbow, of the fourth bigness, and having the quality of jupiter and Saturn all the others are of the fourth or fift magnitude. THe sign Capricornus looketh unto the West, and is wholly figured in the Zodiac circle. The tail with the whole body, is divided by half (of the Winter circle) and reacheth to the left hand of Aquarius, he setteth headlong, and ariseth right up: he hath a star on the nose, and another going before the two stars in the mouth, another following them, and another Southerly of the three in the mouth: all of the sixth bigness, and of the nature of Saturn, and part Mars, and Venus. A star going before the three, under the right eye of the fift bigness, and of the nature of Mars and Mercury. The Southerly of the three following behind the horn, of the third bigness; the Northerly of the three behind the horn, of the third bigness. The Northerlier, and Southerlier of the stars in the neck, of the fift and sixth bigness. In the neck between the shoulders seven, on the breast two, on the belly and body seven of the fift bigness, and of the nature of Mars and Mercury. The stars on the tail, of the third, fourth, and fift bigness, and of the nature of Saturn and jupiter. In the whole he hath 28. stars known, of which the two on the horns are of the third bigness, but all the others be of the fourth, fift, and sixth bigness. The ancient astronomers as Aratus, Hyginus, and others, do assign three images in one constellation: as the Hydra or monstrous serpent, on whose tail they describe the Raven to sit, & almost in the middle of the same figure, they affirm the cup to stand. It is a sign in the South part, having the head declining unto Cancer: the half of whose winding body is placed under Leo, but he reacheth the tail unto the Centaur, on which the Raven doth sit. To this Hydra or water serpent, doth Ptolemy give 25. stars, being of the second, third, fourth, fift, & sixth bigness, his beginning in Ptholomies' time was in the fourteen de 'gree of Cancer, but the end almost in the fourteen degree of Libra: and in our time the beginning is in the 4. degree of Leo, and the end in the third degree of Scorpius, being of the nature of Saturn and Venus. The great water Cup or pitcher, doth Ptolemy deck with seven stars, being of the fourth bigness, which in his time were in Leo and Virgo, and in our time in Virgo, and of the quality of Venus, and a little of Mercury. The Raven (after Ptolemy) hath seven stars, being of the third, fourth, and fift bigness, which in Ptholomies' time were all in Virgo, & in our time are in Libra, having the quality of Saturn and Mars. The cellestiall figure named the Altar, doth Aratus place in heaven, under that beast called the Wolf, near to the South, and standing under the tail of Scorpius. To this figure doth Ptolemy assign seven stars, that in his time were in Scorpio, of the fourth and fift magnitude: but in our time are in Sagitarius, and have the quality of Venus, and a little of Mercury. The image named the Centaur, is thus described of Aratus, that the parts of this image likened to the man, do lie within the sign Scorpius; but the hinder half likened to the Horse, lieth or standeth under the Klees. And is likened to one having his right hand continually open, toward the round altar. And as one offering sacrifice on the altar, which sacrifice the monster holding in his right hand to offer on the altar, they call a wild beast. In that monster or Centaur named of Hyginus, Chiron, doth Ptolemy number 37. stars, of the first, second, third, fourth, and fift magnitude, which in his time were all in Libra, but in our time in Libra and Scorpio. The stars standing fashioned in the form of a man, have the quality of Venus and Mars, and those which represent the form of a horse, are of the nature of jupiter and Venus. The image named the celestial Wolf, doth the Centaur seem to hold: yet it is a several constellation from the other. To which Ptolemy doth assign 19 stars, being of the third, fourth, and fift magnitude, that in his time were in Libra and Scorpio, and in our time are all in Scorpio. The celestial figure named the River streached from Orion, do some name Eridanus, which otherwise Padus, some Gyon or Nilus, and some Oceanus. To this River Eridanus, that cometh from the left foot of Orion, doth Ptolemy give 34. stars, of the first, third, fourth, and fift bigness: that in his time were in Aries and Taurus, and in our time in Aries, Taurus, and Gemini. The last star of the 34. in the row (of the first magnitude) hath the quality of jupiter, and all the others, are of the nature of Saturn. The long Ship (named Argo) not the whole form of it is described or seen among the stars (in that it is divided from the fore part unto the mast) that may signify to men little to despair, although the Ship happen to break. Aratus writeth, that the fore half of Argo, is turned about right with the tail of the great Dog. But in a contrary order moved, in that the fore half is seen, and the other half hid; much like a ship rising with the swelling of the Sea, whose fore half is seen, and the other half hid, through that hinder part darkened or hid, and without stars. To the ship Argo doth Ptolemy ascribe 45. stars of the 1. 2. 3. 4. and 5. magnituds. The greater of these in order 44. of the first bigness, is that star (named of the Arabians Rubail, of the Latins Canopus') which standeth at the end of the Rother stéerer of the ship, that in Ptholomies' time was in the 17. degree, and 10. minutes of Gemini, having the Southerly latitude 75. degrees, and the declination Southerly 51. degrees, and 41. minutes. And in our time is almost in the 7. degree of Cancer, having his latitude Southerly 75. degrees, and declination of 51. degrees, and 34. minutes. All the other stars are of the quality of Saturn and jupiter, and were by Ptholomies' time, unto our time in Gemini, Cancer, Leo, and Virgo. The celestial Hare placed under the feet of Orion, is as he were running before the hounds of Orion, being feigned to be a hunter. To this celestial figure doth Ptolemy assign 12. stars, of the third, fourth, and fift magnitude, that in his time were in Taurus and Gemini, and in our time are all in Gemini, and have the quality of Saturn and Mercury. The image named Ingula, and also Orion, lieth thwart under to the section of Taurus, and hath stars standing and shining before the feet of Tautus; named Orion of the word Vrina: that is, of the flood of waters. For in the winter time (when this image or constellation ariseth) he troubleth both the Sea and Land, with showers of rain, and tempests. The Romans also name him Ingula, for that he appeareth armed, as girded with a sword, whose shape is terrible and most clear to be seen in the shining of the stars. For if it shineth bright and clear, then doth it portend fair weather to follow, if it appear dim, then doth it threaten a tempest to ensue. The head of this sign is drawn by three stars, of which the two clear stars, are called the shoulders, between which stars the neck is imagined to be, one thereof named Ingular. Pliny doth often make mention of Orion, as of his rising and setting whole, and in some places of part, as his girdle, or sword. Also he doth number Orion among the fearful stars, causing tempests. To this Orion doth Ptolemy assign 31. stars, which whiles he lived, were all in Taurus and Gemini, of the 1. 2. 3. 4. 5. and 6. magnitude, and one cloudy. The second star is of the first bigness, and the third is, of the sedond bigness, in the order of the stars of Orion, which are in the shoulders, and have the quality of Mars, and Mercury. The constellation named the Zone or girdle of Orion, hath three stars shining very bright, of the second greatness, in the order of the stars of Orion, being the 26. 27. and 28. That figure named his sword hath 6. stars of the third and fourth bigness, decked in the order 29. 30. 31. 32. 33. and 34. The figure named the Club that Orion bore in his right hand, when he fought with the dreadful Bull, that possesseth four stars, of the fift and sixth bigness. In the order 9 10. 11. and 12. of these the 9 and 10. are in the right hand. Further the other stars, either of the first or second bigness, as the 26, 27. and 28. be of the nature of jupiter and Saturn. But the other stars which are in the 3. 4. 5. and 6. and the cloudy star, do imitate the quality of Saturn, the 35. which is on his left foot, is of the Arabians named Rigel, of the first bigness, and referred to the nature of jupiter; but the others unto the quality of jupiter and Saturn. The ancient astronomers placed two Dogs in heaven, as they were following the Hare running: of which the one they named Protion, and the other the Dag. The image named Proceon (in English the fore-Dogge) hath no other name with the Romans, than the canicular: that is, the lesser Dog▪ And of Tully (in fragmentis Arati) he is named the fore-Dog. But the other doth Aratus place under the hinder feet of the fore-Dog. To this fore-Dog doth Ptolemy attribute only two stars, others do number three, that in Ptholomies' time were in Gemini, and in our time are in Cancer. Of which the fore star which is in the addition of the same, doth possess the magnitude. The scond star, which standeth on the leg shining bright, is Protion; of the first bigness, all are of the nature of Mercutie, and a little of Mars. The other Dog being the greater, is named of the Arabians Alhabor, which properly is named the greater dog. And this understand, that the same star is brightest shining, which standeth on the mouth or tongue of the Dog, being of the first bigness, and named by authors the dog, in the name of the whole image. The star named Syrius or the Dog, is placed in the middle Centre of heaven, unto which when the sun shall come, the heat is then doubled, and men's bodies affected with faintness. Also they suppose that star to be called Syrius, though the brightness of his fiery shining. The Latins name him, the canicular or Dog-star. Of which the canicular or Dog days were named: in that whiles the sun runneth in that part, it is dangerous, and this through the quality of the season then being, that disposeth the time to health or sicknesses. And hercos it is, that whiles for a time it ariseth, the season is not always contagious. Ptolemy nameth that Star which is on the mouth of the Dog; and assigneth him to be of the first bigness, most clear and bright in shining. And to that star which standeth or is placed on the head, he giveth a small quantity: that is, to be a star of the fift bigness. Avicen thus writing of the Dog-days, willeth men to beware, and learn the time in which the greater Dog ariseth, and the season in which the snow lieth still on the high hills or mountains, and the frosty or sharp cold time, for than is no apt time of ministering medicine. But a medicine may safely be drunk, or otherwise given, in the spring and harvest time. Hypocrates being of the same mind, affirmeth that in the Dog-days, and before them no purgation may safely be ministered. The beginning of the Dog-days varieth, according to the diversity of Regions, Climates, and Latitudes. In our time the Dog-days begin at the sun's entrance into the 10. 11. and 12. degree of Leo. That which above was said, that the star Syrius is in the middle Centre of heaven, is meant that the star is in a celestial circle, as the Solsticiall colour, whose Centre is the Centre of heaven, in which that circle is described. This understand, that the sun is then joined with the star Syrius, when they both arise together in the Horizont above the earth, and setteth Heliace West with the sun, though it cannot be seen rise in the morning, for the bright beams of the sun: but after the suns daily moving from it, the star beginneth to arise and be seen in the morning before the sun. To a man of knowledge this is not strange, that the Dog-star ariseth once every natural day: yet the words of Avicen are thus meant, that in what time the Dog-star ascendeth with the sun, and this at the horizontal meeting and joining together of them in the morning: which pestilent Caniculare time do the physicians determine to be of 40. days long. But the malice of that season is many times overcome & changed through the strong beams of the Planets happening in this time: as of jupiter, Venus, and sometimes of Saturn. Ptolemy doth assign to this constellation named the Dog-star, 18. stars, of the first, 3. 4. and 5. magnitude, that in his time were all in Gemini, and in our time in Cancer (except the 17. star) which is in the end of Gemini. And that which is brightest shining in the Dog's mouth, is named Alhabor, having the quality of jupiter, and a little of Mars, and all the others applied to Venus. Hyginus writing of this image, named the Southerly Crown (which of many is named Vraniscus) as if the same appeared fashioned hollow from heaven. The same doth he thus describe, that before the fore feet of Sagitarius, are a few stars, fashioned into a roundness, which form his Crown, that many have imagined as cast from him in bondage manner. And many mean by this Greek word Ouraniseos, the palate, in that this crown appeareth fashioned like to the Palate, which is a hollowness above the tongue. To this celestial Crown, fashioned like a little Palate, doth Ptolemy assign 13. stars, of the fourth, fift, and sixth magnitude, that in his time were all in Sagitarius, and in our time are in Sagitarius and Capricornus, of the nature of Saturn and Mars. This image do some name the monstrous Fish, the terrible fish, the monstrous sea beast, and sea Lion or Bear. This huge fish named the celestial Whale, is placed under Aries, and both the fishes, lying a little above the starry River in the Region of heaven. Ptolemy doth assign to this celestial Whale 22. stars, of the third, fourth, and fift bigness, that in his time were all placed in Pisces and Aries, and at this day are in Pisces, Aries, and Taurus, and most of them are of the nature of Saturn and Venus, and some only of Saturn. This Meridiane fish (named the Southern or Southerly fish) and great, whose alliances are the fishes named, which are placed in the circle of the Zodiac. This sign or image is placed in the South part, and seemeth (as it were) with the mouth to drink of the water coming from the sign Aquarius. Ptolemy doth number and give to this Southerly fish, 11. stars, being of the first, fourth, and fift magnitude, that in his time were all in Capricornus and Aquarius, and in our time are all in Aquarius. The brghter star in his mouth, hath the quality of Venus and Mercury. But those stars placed on the body of the same, are agreeable and a like to the nature of Saturn. These hitherto for the images placed on the North and South side of the Equatoure. 5 By the fift, is the declination of the parts of the Ecclipticke from the Equatoure, as at the bound from which it is known, and both the declinations of the stars, and the latitudes of places learned. The declinations of the stars are called the distances of them from the Equatour, toward either of the Poles of the world. The latitudes of places, the spaces from the Equatoure unto the highest of them raised in the Meridiane, as by the tops gathered and learned, in the standing right over. Also by the Equatoure do we learn the declinations of the Planets, aswell Northerly, as Southerly moved, as more evidently doth appear, in the soiled Sphere or Globe. So that by the declination of the stars known, a man may easily place them in proper instruments, by which great utility ariseth. And it is the measure of time, in that the length of the natural day is known thereby. 6 By the sixth is learned, that in the same Circle (as by the subject) is both the length of the whole earth, and particular places standing in divers parts of the earth, considered and measured. For according to the exact doctrine of the spherical tryangles, the longitude or length of places, and the difference of longitudes is always the Equinoctial Ark, and not any Parallel. By it also the declination of any degree of the Zodiac is known, which being had in any day at noon (the sun then shining clear forth) the Northerly latitude or elevation of the Pole of any Town, may artificially be known. It is beside the measure of time, in that a natural day is performed by one whole return of the Equinoctial, with an addition or inerease to that part of the Ecclipticke, which the sun in the mean whiles accomplisheth by his proper motion, against the motion of the first mover. 7 By the seventh, it much availeth and helpeth the doctrine of astrology, in that by the guide and leading of the same, are the beginnings of the twelve houses of heaven found, when astrologiall figures are erected and fashioned to prognosticate or judge by: which can never so perfectly be searched and found without the Equatoure, and this through the unlike motion and ascension of the parts or signs of the Zodiac. By it also are all Towns according to their longitude and latitude, easily placed and found in the earthly Globe: so that by it a man may readily know which Towns are Northerly, and which Southerly. It hath beside a most great use in Geography, unto finding the distances of places, and unto placing of Cities in the earthly globe, in having the true longitude and latitude of them. 8 The eight instruction, that by it a man may attain the knowledge of all the celestial Parallel circles, and the earthly Zones lying under them. As by this example, the Parallel streached along by Rhodes, cannot otherwise be known, but by his distance from the Equinoctial as by his principal & fore noted Parallel: which a man may learn and know to be from the Equatoure, toward the North 36. degrees. The same knowledge may aptly be had, of all the other Parallel circles rightly known, so that none (otherwise) can be prompt and saillfull in Geographical matters. Cleonedes affirmeth (prima Meteor) that it afterwards behoveth to know how to describe each turning about of the fixed stars with the first mover, about his Centre circle, as that all the Parallel circles are known. Seeing among those circles, the Equinoctial is greatest, and those Parallel circles lest which are drawn about the Poles of the world: even the like are those the greater circles according to proportion from them, which are described unto the Equinoctial. 9 The niuth showeth, that no description of the earth, (although in platefourme) can be expressed, neither by strait nor crooked lines, without the knowledge of the Equatoure. 10 By the tenth appeareth, what commodity of the same hath and serveth in the judging of genitures, is here by silence overpassed, seeing with brevity it cannot be uttered. The description, names, and offices of the Zodiac, and Ecclipticke line, or way of the Sun. AFter the ancient Astronomers had divided heaven into two equal halves by the Equinoctial, and diligently observed and noted the thwart drawing and standing of the Zodiac, and a like form of a larger Zone, the divers courses, motions, and wanderings, both of the sun, moon, and other Planets which being drawn about with the first mover, kept no equal spaces in themselves agreeing to the first mover, nor a like distant in their motions from the Equatoure: but that whiles they were daily drawn by a contrary motion of the first mover into the East, they in the mean time wandered one whiles into the North, and anotherwhiles into the South, unto a certain elongation and distiance, and so returned unto that circle. They abserued also that the Planets kept always one manner of journey and way, and that way cutting or cressing heaven and the Equinoctial by a thwart manner, the same of these, they named the Zodiac. This circle of the 12 signs, commonly called the Zodiac (which also is a greater circle, and thwart lying) having a latitude movable unto the motion of the sphere to which it fasteneth, and every where is a like, under which the planets by a continual motion are drawn and run. This circle also do the Latins name thwart, through the thwart standing of it: for the Equatour doth compass the sphere of the world, by the just middle space between either Pole: but the Zodiac is thwartly drawn both to the sphere of the world, and to the Equatoure: so that in some parts it is nearer to the Poles of the same, and in some parts further distance from it. It is crossed also of the Equatoure into two eqnall half circles; of which the one is called the boreal or Northerly half circle, and the other the Meridional or Southerly half circle: therefore by the continual turning of heaven drawn about, unto any right and thwart Horizont, inclined according to the thwart Angles, it doth both change and vary those Angles by the continual motion and turning about. For to certain Arks it figureth and formeth righter, and to certain others thwarter Angels, through that divers inclination unto the Horizont, which ensueth after the standing of it. And the diversity of the inclination of it unto the Horizont, doth also cause a variety in the motion. For those do slower arise, which make right Angles with the Horizont, and those are sooner drawn up and appear, which do cause thwart Angles. In the thwart Sphere, (with that thwartness of the Sphere and the Angles, which the Horizont and Zodiac perform) is the thwartness increased. What the names are of this Circle. 1 THis Circle is named the Zodiac, of this Greek word zoes; that is in English Life: in that it is the path, or the coming and going of the sun, which is called the author of life, & causer of generations (as Aristotle writeth.) Or of the Greek name zódion, which in English is the figures of Beasts, with the which this circle is imagined to be form by the concourse of stars. 2 This Circle is named thwart or bowing, in that it crosseth thwartly the Equinoctial and first mover, and doth appear thwart in respect of the Poles of the world, from which it is not equally distant. Or for that it maketh not right but thwart Angles, with the Equinoctial, and Colours, or tropics. Or for that it doth not regularly ascend and descend according to his parts (like as the Equinoctial doth) but that certain parts or signs of the same do righter and slower; and certain thwarter and swifter arise in either Sphere. But the Zodiac is not named thwart (compared unto the proper Poles) seeing from them it is equidistant according to each part; as the Equinoctial from the Poles of the world. Yet compared unto the Poles of the world (in that the one half of it declineth unto the North, and the other unto the South) and seeing upon these it is thwartly drawn by the daily motion, unto the moving of the Orb in which it is: In this respect, is the circle named thwart. 3 This Circle is also called Signifere, of the 12. signs carried in it, with the which the Zodiac is described. Or for that this Circle is divided into twelve equal parts, (which are called signs) and each having a name of some proper beast: or for the disposing of stars being in the sign, or for some property common to the beast and sign (which Ptolemy nameth the Orb of the signs) Pliny, Capella, and sundry Poets do name Signifere: but Aristotle nameth a thwart circle, in that it doth thwartly cross the Equatour, as witnesseth Proclus. What is the cause of the thwartness of the Zodiac. 1 THere are two causes, why the Zodiac is thwart: the one is, that the neither Spheres upon the other Exetrée, and Poles, may be carried contrary to the motion of the first mover. 2 The other is, that there may be diversities of times, and varieties of qualities and tempearances: that the sun also may wander and go about divers parts of the earth, running in the thwart circle; whereof Aristotle writeth, that it is necessary, that the proper motion in the Zodiac is unlike to the motion of the first mover, that it may thereby cause the variety of cresent or growing things. For if there were only one motion, there should no variety of growing things be caused. 3 A like reason to this, that of the same, one part of it doth draw nigh to the top and highest over our heads, and the other, that it is removed and distant from us, doth cause most commonly the diversity in effects, which unto the life of things is requisite. As for example, when the sun is in the Northerly half of this circle, and near the Zenith and highest over our heads, he doth cause a strong and mighty heat on all things of the earth▪ as by trial we find and see in the summer. If therefore the Zodiac were not thwart, but should equally approach or draw nigh according to all the parts of it, than should the sun be always a like near us. And when in a short time of summer he should cause such a heat, that his heat undoubtedly should be so mighty, that nothing should grow or be increased, but that those things already grown up and dried should be consumed and burnt up: wherefore the Zodiac is thwartly placed, that the sun moving into the further half, his heat may thereby be slaked and weakened, in which he being carried departeth from our Zenith, and cold then taken place, as appeareth in the winter. And if the sun should continually run in the South part of the Zodiac, then through extremity of cold should all things be destroyed in the North part. And as neither heat nor cold is continual, but successively, as those which be engendered and caused by heat, and consumed by cold. So that the sun procureth (by coming nigh, and going from us) in the Zodiac, that it behoveth the Zodiac to be thwart. Also a diversity of the Planets in the Zodiac. To conclude, we see that by the coming of the sun to us, generation is caused, & by his departure from us, things whither and dry. This circle called the Zodiac (according to longitude) is divided into twelve parts or signs, and neither more nor fewer. And according to latitude or breadth, into 12. degrees. This circle divided into twelve signs, in that of the ancients it hath been noted, that in every revolution of the sun, the moon is twelve time changed and new, and so many times hath he full light. And that so many changes and full moons do happen within the compass of one year: by which it pleased them to divide the Zodiac into so many parts, according to length. But the division of the breadth, hath another cause; that is, of the other Planets, (except the sun) diversly wandering from the same circle. To be brief, this whole circle is divided into 360. degrees, for the commodity of this number; in that the days of the year exceed this number by certain parts: for the common year hath 365. days, and 6. hours. There is a latitude attributed to the Zodiac, by which it differeth from the other circles, in that they are describe with one simple compass, that it might by the larger space, contain the wandering of the planets, on either side the Ecclipticke line, lest they should exceed the bonds. Yet the sun keepeth one manner of way and journey continually in the middle of the Zodiac, and never declineth from it, neither unto the right nor left side, but still keeping his proper places immovable; both in the rising and setting in either quarter, and is all alike in the winter and summer seasons. The declinations also of the sun, do show and appear to be equal, being on either side the Equator. So these do witness, that the sun continually 〈◊〉 his yearly motion, describeth and keepeth under that line named the Ecclipticke. But the other Planets do neither keep continually the sun's way, nor is drawn in a right path like him, but digressing on either side the sun's way, do wander the Zodiac by a crooked or bending course; as one whiles moved into the North, and an otherwhiles into the South: and from thence returning unto the suns way, as the like knowledge may be had and discerned by the eye. For this cause, the learned practisioners described the sun's course in the middle place of the Zodiac, and imagined from it a latitude to be attributed to the Zodiac, which the ancient astronomers determined to be of either side 6. degrees. But the late writers have increased the same, by adding two degrees to either side, through the digressions of Mars and Venus from the suns way; which hath been observed and noted to digress and decline little less than eight degrees. So that the latitude of the whole Zodiac (in our time) is concluded and agreed to be of 16. degrees, and the latitude is reached on either side, from the middle space of the suns circle toward the Poles of the Zodiac, eight degrees. The beginning of the longitude of the Zodiac (although in the compass of the circle, neither the beginning nor end can be assigned) which bendeth or is drawn perfectly round into itself; and both closeth and containeth itself: yet the practisioners have assigned by the principal and most ancient doctrine of the godly fathers,, to be in the poiut of the Equinoctial spring, which is by the suns coming unto the Equinoctial point: or truer by the change of the moon that followeth next the Equinoctial spring, is not to be doubted that the year then begun. So that they began to reckon the Zodiac from that point, where the motions and workings of the sun (the author and shower of the yearly space ensued) which after the day and night being alike, the day increaseth, and he ascending to us ward, doth after abate the cold on the earth, and both slaketh and melteth the frosts and ice, and the hidden virtues again of the earth, he than beginneth to lose, open, cherish, and stir up by his lively heat, and both looseth and sheddeth forth the due moisture enclosed; and draweth up and procureth young plants to spring, through his comfortable warmth daily showed upon the earth. They divided the whole Zodiac according to length into twelve equal parts (which they named signs) through the moon as guide and ruler of the same: which passing yearly by the Zodiac 13. times, to the suns slower going twelve times; & conjoined with him in twelve places of heaven. Those signs the ancient Greeks name zòdia, either by the figures of creatures, (which the fixed stars in their standing show and express) or by some natural agreement, they so assigned names to them. Or else they appointed the names of beasts to the signs, through the congruent nature betwixt Stars and beasts. Also through the effects which the sun hath in those places. Besides these, the ancient astronomers described the other stars without the Zodiac by images, that placed into images, they might be the commodiouser taught and expressed in heaven to the understanding of young students, and that their rising and setting might also be the more readily demonstrated. Ptolemy named those Dodekatemòria, that is, the twelve parts. The Latins called them signs, and constellations. Also they named those parts signs, for that in those twelve parts, all the seasons of the year are noted. Again they named the parts of the signs degrees, of the daily journey of the sun in the Zodiac, for that in journeying by little and little, he passeth through the whole Zodiac. They also divided each sign into 30. parts or degrees, through the suns daily journeys gained of the first mover, which in thirty days they declare by experience, to have measured and gone almost a twelve part of the Zodiac. Or for that the space from one conjunction unto an other is of 30. days, which space (of all writers) is named a month. Or else in that the sun by the same number of days, hath measured almost this Ark or space of the Zodiac. Whereof they named the self same, the thirty part of a sign, through the sun's motion every 24. hours, which the later Latines call degrees, and the Greeks Merè, that the ancient call parts. But the ten parts or degrees of every sign, the Greeks name Dekatas, and the Latins Faces; of which each sign doth contain three. The names and characters of the signs of the Zodiac, are these ♈ Aries, ♉ Taurus, ♊ Gemini, ♋ Cancer, ♌ Leo, ♍ Virgo. These in that they make the half circle of the Zodiac, declining into the North from the Equatoure, therefore do they name them, the boreal and Northerly signs. The names and Characters of the other signs of the Zodiac, are these. Libra ♎, Scorpio ♏, Sagitarius ♐, Capricornus ♑, Aquarius ♒, Pisces ♓. These in that they possess the opposite place, and the half circle reaching into the South of the Zodiac: therefore do they name them, the Meridional and Southerly signs. The sun also iourneyeth by these signs (as from the West into the East) by a contrary order to the first mover, as this figure plainly demonstrateth: beginning nevertheless at Aries, and from Aries, passing into Taurus, and from Taurus into Gemini, and so to the end of the signs. They divided each sign, into 30. degrees of length, in that the whole Zodiac (like as the other greater or lesser circle) containeth 363. parts, or degrees. And as the Zodiac hath in length 12. signs, even so it is requisite the same should be so many degrees broad (as Capella writeth. And as a degree is in the sign the thirtieth part or length, the compass of the whole Zodiac should be the like in breadth. Although Mars and Venus do sometimes digress from those bonds, yet that excess is little, and very seldom: and there can be no other reason of the same, then that such a latitude is permitted or assigned to the Zodiac. To this demand, why there are only twelve signs, and no more, doth Albumaser answer: affirming, that the first observers of the stars, noted 48. images in the 8. heaven, placed and decked with the stars, that represent sundry forms, and called by them, for the form, standing, or nature of the stars, of which they appointed 12. for the suns way: and therefore so many, are the signs of the Zodiac. But here may be demanded, where the Circumference of the Zodiac is, to which is thus answered that all the circumferences of the circles imagined are in that hollow of the first heaven, and likewise the signs are conceived there to be. And where the signs with the images of the eight sphere are movable, and the stars in them separated after a time. Yet the number and names, both of the signs and images remain. So that it is not material, if that the starry Aries separate from the first Aries of the zodiac, and the other signs the like from one another, by a most slow course are carried, and separated. The ancient men divided the parts or degrees of the signs into lesser portions, for the better attaining the precise point in the sun's place. So that they appointed to each degree 60. minutes, to each minute 60. seconds, to each second, 60. thirds, etc. For the infinite commodity of the numbers in calculating, by reason of multiplication and division. They also divided the signs after two conditions, as in the standing, and qualities. In the standing, they distinguished them into principal, fixed, and common signs. The principal and movable signs, are those which nighest succeed the four principal points of the zodiac: of which two possess the Equinoctial points of the whole circle (as Aries and Libra). The other two nighest to the Solstitial points, are named the tropics (as Cancer and Capricornus.) The firm or fixed signs, next to the principal, are Taurus, Leo, Virgo, and Aquarius. The common, or mean (or of two bodies, being the other four) which placed (as in the middle between the principal and fixed signs) do so obtain a common nature of both, as Gemini, Virgo, Sagitarius, and Pisces. In the qualities, they assigned them into four Trients, which the Latins name Tryangles, and three cornered the common writers nameth Triangularites, or Tripli ' cities. The first trient containeth Aries, Leo, and Sagitarius, which are by the space of four signs inclusively distant, or of 120. degrees: that are hot and dry, fiery, choleric, and masculine. The second Tyient comprehended Taurus, Virgo, and Capricornus; which being distant by the like space, are cold, and dry, earthly, melancholic, and feminine. The third Trient hath Libra, Gemini, and Aquarius, which being distant by the space of four signs, are hot and moist, sanguine, aereal, and masculine. The fourth Trigon or Trient, doth contain Cancer, Scorpio, and Pisces, which are distant by the space of four signs, and are in quality cold and moist, watery, phlegmatic, and feminine. All which signs, are agreeing to the four Elements, in their qualities. Of the Ecclipticke line, or way of the Sun. HEre it is diligently to be considered and noted, that it behoveth not only to know and understand the places of the Planets in the Zodiac (according to the longitude of the same) but also to learn and find their places (according to latitude) whether they be in that part of the zodiac which bendeth or declineth into the North, or in that part which leaneth into the South: which the better to understand and know, the ancient astronomers imagined a certain line, going round about the zodiac, and dividing the same after length by the middle, in such sort, that it parteth and leaveth eight degrees toward the North, & as many toward the South. So that this line is a greater circle, dividing the latitude of the zodiac into two equal halves, and hath sundry names: as the sun's way, the suns ●yr●uite, the sun's journey, the sun's place, the sun's circle, the Ecclipticke line, and the Ecclipticke place. This line named the sun's way, in that the sun keepeth always the middle under this line, not digressing to the one side nor other: but describeth the same in his yearly motion. But the other Planets do wander one whiles under it, and an other while on either ●oe, which if a Planet tendeth in that part of the latitude which is unto the North, wandering there, he is then named to have a latitude Northerly, as to us dwelling Northward: but if on the other side they have a latitude Southerly, then are they named descending and running low, And by the like reason, the same line is named the sun's journey. Also of Cleomedes, called the sun's circle, in that under the same the sun continually runneth. And he alone being drawn by the middle of the zodiac, never wandereth into the North nor South part from that line (as we have afore written) but continually iourneyeth about by the middle of it. So that of the same, it is called the sun's circle. It is named the sun's place, in that under this circle the sun continually abideth. To conclude, it is named by the usual name the Ecclipticke line. For that no Eclipse or abating of the suns or moons light happeneth, but when the sun and moon are linally under that line (or near come unto the moon) as in the same degree right against. For in the same degree, at the change, is the moon come right between our sight, and the sun's body; thereby abating his light. But the Eclipse of the moon happeneth at the full, when as the sun is right against the moon; & that the shadow of the earth falleth between both, whereby the moons light is darkened. So that the moons Eclipse is none other, than the falling of the earth's shadow between the sun and moon. The measure of the large space of either side, occupied by the Planets, limited and included by two lines, and the third drawn or described by the middle, is named the Ecclipticke line, and sun's place. The Eccliptick line is a greater circle consisting in the middle of the Zodiac, and dividing it into two equal compasses, defined to be eight degrees in breadth on either side, which the sun maketh by a yearly motion, going thwartly in one continual way, is divided by the four principal points; as the two Equinoctials, and the Solstices, into four quarters. For as the whole Zodiac, even so the Eccliptick to the Equatour, resting as it were in two only points, but in the rest of the circle it bendeth ●●om either point toward the opposite Poles of the world declined by the one half circle into the North, and by the other half into the South. The points that touch, are the Equinoctial (as we have above written) but the other two, furthest distant from the Equatoure (which are as marks or bounds for the sun's departure) that when he cometh to the one, he is carried no further, but stayeth there, and from thence drawn unto the contrary bound: through which turning back of the sun, they are named the tropics of the Greeks, and of the Latins; the solsticiall points. Not for that the sun being carried unto them, stayeth and remaineth any space, but never resteth, nor leaveth of his courses: seeing within certain days the Meridiane or Noon shadows are varied, the day & night spaces either lengthened and increased, or decreased and shortened notably; as the like is yearly seen. Of these, that which in the Northerly half circle is furthest distant from the Equatoure (named the point of the summer solstice) the other standing or being right against that, the point of the winter solstice. These points change their places two manner of ways, as well according to length of the zodiac by creeping further in the fore going, as in going to and coming short unto the Equatoure. First that the Equinoctial points, do over go the places of the fixed stars, against the order and course of the signs; and therefore do the days of the solstices begin and go before. For the summer solstice about the beginning of Olimpias the first day of july, which began the year with the Greeks at the morning rising of that constellation Syrius, being notably known to many: but in the year of Christ's birth, it happened in the 24. day of june, And in the year 1570. it happeneth in the 12. day of june, about 11. of the clock before Noon. The winter solstice in the first beginning of Olympias, happened the first day of january, or there about. In the year of Christ's birth it happened the 15. day of Decmber (in which day at the hour of 12. in the night, they affirm our saviour to be borne. The same winter solstice happeneth in the same year 1570. on the 12. day of December, about 2. of the clock at after Noon. In the second then happen unto the Equatoure by the Ecclipticke (as it were winding) and removed again in the same departing. For the observations of many times do witness, that the ark of the Colour of the Solstices reached to these points and Equatoure (which they name the sun's greatest thwartness or declination) is diminished by little & little. For before Ptholomies' time by forty years Aristarchus, Samius, found the same to be of 23. degrees, 52. minutes, and 20. seconds. And Ptolemy noted, that he found it to be just as much. Mahomates Aratensir which was after Ptolemy 749. years, found this declination to be of 23. degrees, and 35. minutes. Arzahell the Spaniard that was 190. years after Albategnius, found it to be of 23. degrees, and 34. minutes. Prophatius judius which was 230. years after Arzahell found this declination to be of 23. degrees, and ●2. minutes. Dominicus Maria being in the year of Christ 1491. found this declination to be of 23. degrees, and 29. minutes. Vueruerus being in the year of Christ 1514. found this declination to be of 23. degrees, and 28. minutes, and 30. seconds. Copernicus' being a later writer, as in the year of Christ 1525. found this declination to be of 23. degrees, 28. minutes, and 2. fifts of a minute. Of these (but by many notes considered) that the equalities have decreased by the regulare motion, and yet shall decrease, until an extreme term of diminishing ensueth, which he affirmeth to be of 23. degrees, and 28. minutes: the same Copernicus after gathered shall again increase; and that the greatest thwartness which may be caused on the sun or Ecclipticke line, is 23. degrees, and 52. minutes: & the least declination to be of 23. degrees, and 28. minutes. So that the established the difference of the greatest and least to be of 24, minutes. But he defineth the period motion of the increasing or diminishing to be in 1717. years: and that so many years, the motion of the decrease and increase shall be, and that the whole restitution also of the thwartness, to be in 3434. years. So that as the thwartness failing or diminishing; even so the points of the greatest declination (which are named the solstices) are yearly drawn and moved nearer unto the Equatoure by 6. minutes, 27. seconds, 24. thirds, and 9 fourths: but daily by one second, two thirds, and so many fourths, carried near unto it. And the thwartness increasing, may by the like order and condition, and in the same motion be again abated. As the Equinoctial points divide the Ecclipticke line into a Northerly and Southerly half circle, even so the solstitial points part the same into a half circle (ascending and descending) as to us. The ascending beginneth from the beginning of Capricornus, and endeth at the last point of Gemini, and containeth Capricornus, Aquarius, Pisces, Aries Taurus, and Gemini. And the descending from the beginning of Cancer, reacheth unto the end of Sagitarius, and comprehendeth Cancer, Leo, Virgo, Libra, Scorpio, and Sagitarius. So that the sun in that half circle, ascendeth from the Southerly region unto us, in that from us it is digressed into the South, and of the same they received those names. What the latitude of a Planet is, after two definitions. FIrst, that the ark of the great circle is crossed between the Ecclipticke, and true place of the Planet, (and that is named the latitude of the Planet) for that according to the same, the Planet into latitude, that is, into the South or North, swerveth from the Eccliptick line: whereof the Planets are named to have a latitude, one whiles into the North, and another while into the South. But the degree expressed and showed by that great circle in the Eccliptick, is called the degree of the longitude of the star or planet, which according to longitude from the beginning of Aries unto that place, is the Planet moved. The other instructeth, and by demonstration showeth, that from this line the other five planets wander, one whiles into the North, & another while into the South being not equally carried. This wandering from the said line, is named the latitude of the Planets, and is the ark of the great circle, passing by the Poles of the Zodiac and true place of the Planet, comprehended between the Ecclipticke, and Centre of the star. According to this distance, he is named a Planetary star (what star soever the same be) that to latitude from the ecliptic, is carried either Northerly or southerly. So that it cannot be said that a planet is without the Zodiac, seeing the ancient observers of the stars (being moved) did attribute to this circle a latitude. As may be (the Ecclipticke line) noted with A. and B. and the letter C. the Pole of the Northerly Ecclipticke, by which the Circle noted with C. G. D. and Q. is meant, being the shower of the Latitudes, and when a star shall be in the point G. he shall then be without or have no latitude, but if in the letter E. he shall then have a latitude Northerly, whose quantity, the ark G. E. showeth. If so be a star shall be in the point D. then shall it be Meridional, unto the quantity of the ark G. D. and L. D. K. the letters M. E. N. are the Parallels drawn about the said latitudes, on either side. So that this demonstration evidently showeth, what the latitude of a star is; that is, when such a latitude is attributed to the Zodiac. What the longitude of a Star is, and where he beginneth. THe longitude of a star, is the ark of the Zodiac or ecclipticke line, from the beginning of Aries, reckoned even unto that point of the eccliptickes, which is touched by the great circle, drawn by the Poles of the Zodiac, and true place and degree of the longitude of the stars. As may be conceived in the figure above, where the point A. representeth the beginning of Aries, the letters A. G. the longitude of the star, if the same shall be in the Ecclipticke, the letters C. G. D. the circle ending the longitudes. The difference between a declination and latitude: is this, that a latitude is the distance of a star or Planet from the eccliptick, toward either of the Poles: which distance is measured in the great circle drawn by the body of a star, and Poles of the Zodiac. But the declination is a distance from the Equinoctial, when as the sun is carried by a continual and daily course in the upper face of the Ecclipticke, and hath no latitude, but a declination only: yet the other six Planets, have a latitude and declination. The declination of Planets, is the distance of them (or a degree of the eccliptick) from the equinoctial. And this measured by the circle drawn by the body of a star, or degree of the ecclipticke, and by the Poles of the world. The Planets also are said to ascend and descend, by reason of the thwartness and bending of the Zodiac: for the sun doth ascend in the Northerly signs, but he descendeth in the Southerly. In the like manner do all the other Planets, as well by the reason of the ascension, as also of the place. For planets being in Northerly signs, have the ark of ascension greater than in the Southerly. Besides, this part of the world which declineth into the North, is supposed and judged as to us, to be raised higher, by reason of the Horizont. Further the definition of a sign shall here be declared, that the same is meant sundry ways: one whiles to be a circumference, an other whiles an upper face: and sometime to be a soiled body. The Zodiac (as I have afore declared) is one whiles a line all circumference (which is named the Ecclipticke line) an other whiles a swath, of eight degrees in breadth of either side: Sometimes the zodiac is called the plain upper face of that Ecclipticke: and in an other place the same called a soiled body, which of the said swath, and by the two imagined upper faces is crossed; of which the tops or highest places over the head are joined together in the Centre of the earth, and the feet are those Parallels of the Ecclipticke ending the swath, which may worthily be called a solid zodiac. Further a sign in the fift manner, is a portion of the spherical upper face (enclosed between two half circles) ended at the Poles of the ecclipticke. To conclude, a sign in the sixth manner is mente a soiled divider of the Sphere, contained in the said half Circles and Spherical upper face, which is a sign understood in the fift manner. These divers divisions serveth (as they writ) unto that end, whereby all things might be enclosed within the signs. For if signs be described in the first manner, then on such wise those stars only, and those points are said to be in the signs, whatsoever shall be in that cyrcumference of the ecclipticke. And in the first signification also is meant to be under the ecclipticke, which agreeth only to the sun, as at this day the sun is (being the 23. day of August) in the 9 degree, and 9 minutes, of Virgo at Noon, which is meant to be under that part of the eccliptick, that is named the 9 degree of Virgo. If in the second manner planets shall be in signs, which do not exceed six degrees of latitude; or thus in the second signification, to be under the zodiac is monte, that here a sign is expressed, enclosed within a square pinnacle portion. This signification agreeth to the other planets (except the sun) which decline from the ecclipticke, as Mars in this year 1599 is in the 15. degree of Virgo, which is under that part of the zodiac, that is said to be the 15. of Virgo. Also he hath a latitude Northerly of two degrees, and 28. minutes. If in the third manner, the sun or any star shall be in signs (placed in the plain of the eccliptick, or in the third signification to be in a sign) signifieth to be referred unto any sign of the zodiac. For the whole heaven is divided into twelve Regions (in circles passing by the beginnings of the signs, and Poles of the Zodiac) of which Regions each is named a sign. And this signification agreeth to the stars, standing without the zodiac: as the Northerly Crown, which in our time is in Scorpio, and referred unto the sign of the zodiac that is called Scorpio; in that it is between those two half circles which pass by the beginning and end of Scorpio. If in the fourth manner, the planets and stars also, not further distant than six degrees from the ecclipticke. Or in the fourth signification, is meant or referred unto any of the twelve Regions of heaven; into which, heaven by those six Circles which pass by the beginnings of the signs and Poles of the zodiac (as is afore written) is divided. This signification agreeth to those which are in the air, (as be the Comets.) As if I wrote that a Comet were in Leo, here I mean the six circles passing by the Poles of the zodiac, and beginnings of the signs, dividing both heaven and the whole neither Region of the world into twelve equal parts. So that a Comet is said to be in Leo, seeing it is in that twelve part which the two half circles describe, running or stretching by the beginning and end of Leo. If in the fift manner, all the stars and points meant in the upper face of the sphere, be included in signs. If in the sixth manner, than whatsoever is in the world (whether the same be in the Ethereal, or Elementary region) is accounted to be included within a sign. Here conceive, where the cyrcumferences of the circles are meant. And first imagine the circumference of the Zodiac, and all the other circles (as I have afore written) to be in the hollow upper face of the first mover, and runneth as it were in the first (after the second condition of motions) and demonstrateth alike distance and continuing of the circles without impediment. Although the Horizont, the Meridiane, the Uerticiall, and other circles (in respect of the habitation or dwelling place) remain immovable in that upper face of the first mover: yet doth it nothing hinder (although heaven or the first mover be drawn about) that such circles be imagined to be immovable. For there is nothing more agreeable, then to imagine circles fixed, and those abiding in any upper face of the earth. So that it is necessary, that the Zodiac, the Equatoure, and the other circles be described movable in the hollow face of the first mover, as the bound and enclosure of the whole world. The Horizont and Meridiane, and the others, placed immovable in that hollow and fixed upper face, in which the whole earth is placed, by this means the fixed circles should stay in the fixed upper face, and the movable circles should be drawn about with the movable. As in a material instrument, and solid sphere a man may see, in which the zodiac, the Equatoure, and other movable circles, are drawn about upon the Exetrée, between the two Circles remaining steady, of which the one representeth the Horizont, the other the Meridian. Whether the same may be described in the hollow, or in the embossing of the first mover of the said cyrcumference, it is little or nothing regarded: yet consider this, that all men may behold and see within the heaven or first mover, the hollow upper face of his enclosure, to describe and imagine the circles in the same. The Circles placed without the material instrument, must of necessity force a man to describe the cyrcumferences of the Circles in that outward face of the Instrument. To conclude, the Zodiac is meant and described according to his definition (being a greater Circle) whose cyrcumference in the hollow of the first mover described into signs, degrees, and minutes, (as was afore written) is divided. And seeing that Circle described by the suns yearly motion, is imagined strait drawn and defined or determined from the Centre of the sun's course by the Centre of the sun, which with the sun is drawn by a perfect revolution toward the East. For this line in that motion cutting the hollow upper face of the first mover, doth describe the cyrcumference of the Zdiacke. So that if the plain upper face of the sun's course be extended, until it cutteth the foresaid hollow upper face, which common section or cutting shall be the self same cyrcumference of the Zodiac, unto which the place of the force and virtue of any star is applied. Therefore by the same means that virtue of the moon, or any of the planets, drawn in the same hollow of the upper heaven, shall be like the same described. cording to the divers elevation of the Pole, whereof the Colours are called unperfect circles. There are two manner of Colours, as the Colour of the solstices, and Colour of the equinoctials. These two greater circles are drawn by the Poles of the world: of which the one goeth by the Poles of the Zodiac, and the other by the sections of the Zodiac and Equatoure. That which passeth by the Poles of the equatour and Zodiac, doth divide in two parts each half circle, as well of the equatour, as the Zodiac. Therefore the one condition of the Colours goeth by the solsticiall points of the Zodiac (which are the beginnings of Cancer and Capricorn, and the furthest points from the equatour) whereof it is named the solsticiall Colour. The other is named the equinoctial Colour, seeing it entereth by the said equinoctial sections, which are the beginnings of Aries and Libra; that is, the equinoctial points. So that these Colours divide aswell the equinoctial as the Zodiac into four quarters, in that they go by the four principal points of them. The Colours generally are called all the greater circles drawn by the Poles of the world, which take their name thereof, insomuch as they never are discerned or seen whole in the turning about of the world, as the other circles, but unperfect and lacking. For both the arks right against one another about the Poles, in the thwart sphere are not seen both at once. For they are either continually in sight to us, and never drawn away or hid like unto those which be near to the elevated Pole. Or else they never appear in sight to us, but are continually hid from us, as those which be the opposites. But the reaching of the Colours fasteneth in the two circles, extended and passing by the four principal points of the ecclipticke, as the equinoctials and solsticials, which touching one another in the Poles of the world, do in their cyrcumferences make right angles, and part the Zodiac and equatoure into four equal quarters. The Colour of the equinoctials, resting in the equinoctial points. The other containing the solstiticiall points, is called the Colour of the solstices▪ The Colour of the equinoctials is a greater circle, movable, and every where alike: drawn by the Poles of the world or equatour, and the equinoctial points, as the beginnings of Aries and Libra, making with the equatour right spherical angles, with the Zodiac thwart angles. For oftentimes the greatest circles (by a mutual touching together) do make right angles in the sphere, as they cut in two parts or into equal half circles, and by the Poles one another: and contrariwaise when they cut one another by the Poles, then do they form and make right angles with their cyrcumferences, and part one the other into equal parts (as writeth Theodosius in his first Book de Sphera, and in propositi, 18. 19 20. and 21.) Or thus, the Colour of the equinoctials (which is named the equinoctial Colour) is a greater Circle passing by the poles of the world, and the first points of Aries & Libra; where the two Equinoctial points are said to be: in that the sun causeth a like day and night in every place; or for that these points are in the Equator, whereof it is called the Colour distinguishing the equinoctials: so that the two Colours cross one another on the Poles of the world, at right spericall Angles. It is called the Colour of the equinoctials, for that it passeth by the equinoctial points, as by the beginnings of Aries & Libra (which they call the Equinoctial points) for that when the sun happeneth into either of them, the day and night is of equal length throughout the Earth; which cometh to pass twice in the year (as in the Spring and Harvest) whereof the one is called the Equinoctial spring (and at this day is about the eleventh of March) which is the day before Gregory: the other, the Harvest Spring, and happeneth in our time the 14. of September, that is, three days afore Lambert, whereof ariseth this ancient verse: Lampert, Gregori, nox est aequata diei. The Colour of the Solstices is a greater circle, movable, and every where alike drawn by the solsticiall points or the beginnings of Cancer & Capricornus, and the Poles of the Zodiac and Equatoure, making right spherical angles with both, for of both is the Poles comprehended. And according to Theodosius propo. lib. 2. de Spera, that by any two circles crossing one the other (when a third divideth the parts of both equally and in two parts) the same is the greater circle, and passeth by the poles of both. But that which passeth by the Poles of the other Circle, doth part it in two parts, and at right angles. Here may be demanded, why the other two are called the solsticiall points, seeing the Sun stayeth no where. Which is thus answered, that the sun digressing from either equinoctial point by his proper motion, doth daily departed from the equinoctial circle, till he come unto the solstitial point, where he is furthest distant from the equatoure. But immediately after he beginneth to return and come again unto the equatour, till he come unto the other equinoctial point. So that the point of the sun's furthest distance (which is the beginning of Cancer or Capricornus) and of the same called the solstice, in that the sun stayeth there: that is, ceaseth from his further going or departure, and beginneth again to come to the Equatoure. For the sun after his coming unto that point departeth, and cometh again to the equatour: so that the end, the departure, and beginning of his coming, is the solstice. Therefore not for that the sun stayeth there, are they called the solstices, although about those points of the going and coming of the sun, it is so small, that for four, sire, or more days after, he seemeth in judgement as it were to stay in one declination: and therefore for that cause may be named the solstitials. These of sundry (as of Campanus) are also called Tropic points, through the suns returning. And these may be called Uerticiall or Cardinal circles (seeing they go by those tops of the world) and express or show the four quarters of the Zodiac. Moreover seeing certain parts of these circles being near the pole are hid, and the other right against them nothing at all discerned at any time: therefore is it that they are called in Greek Kolouroi, which is in English, maimed and unperfect, as Proclus, Diadochus, Mocrobius and Capella, writ. But this agreeth not in the right Horizont, seeing there is no part of heaven, which doth always remain there hid. But in the description of the astrolobie, how large soever the same be, yet only these circles appear continually unperfect. Yet further, the Colour of the solstices, or the circle distinguishing the solstices, which also is called the solstitial circle, is a greater circle drawn and passing by the poles of the world, and Zodiac, and the greatest declinations of the same: and by the beginnings of Cancer and Capricornus. It is called the Colour of the solstices, in that it passeth by the solsticiall points (as by the beginnings of Cancer and Capricornus) which are named the solsticiall points; for that in them the solstice is caused: that is, the suns coming unto those points, departeth not further from the Equinoctial, but cometh) again unto the Equinoctial, which is caused twice in the year, as in summer and winter: whereof the one is called the summer solstice (which in our time happeneth the 12. of june or thereabout) being the next day after S. Barnaby the Apostle, where the longest day is holden to be. The other the winter solstice, which in our time happeneth about the 11. or 12. day of December (being a day or two before Lucy) where the day is accounted shortest: whereof is this ancient verse extant. Vitus est Lucia, daunt tibi solstitia bina. Of the former also ensueth, that there is certain fixed and movable Colours. For there is a fixed Colour of the equi●octiale, which passeth by the poles of the world, and section of the equatoure and Ecclipticke of the first mover. The fixed Colour of the solstices doth cut this at right angles in the poles of the world, and passeth by the middle of the sun's greatest declination. Seeing neither the equinoctials nor solstices, are caused according to the true meaning of the astronomers (as afore may appear) both in these points, aswell as in others: Therefore a man must conceive, that the Colours be movable: of which the one goeth by the true equinoctial; that is, by the section of the sun's way, and equatour, and by the Poles of the world, and the other of the solstices, passeth by the sun's greatest declination. These hitherto written, may more plainer appear, by this demonstration here following. In this figure, are the circles, and parts of the circles noted with their names. In which the letter F. expresseth the true and movable equinoctial. The letter E. is a note of the fixed Equinoctial. The letter D. pointeth out the head of Aries, of the eight sphere. The letter C. the centre of the eight Sphere. The letter A. of the ninth and tenth sphere. The letters K. N. represent the sun's greatest declination truly. The letters R. M. the suns middle declination greatest. How much the Equinoctials are distant one from another, the former large instruction of the equinoctials, may easily show at any time, unto which a man must always resort. The sun's greatest declination, is the ark of the Colour of the solstices, contained between the equatoure and either Tropic: this of sundry practisioners is diversly noted. For Ptolemy found the same in his time to be of 23. degrees, 51. minutes, and 20. seconds: of which the whole circle is noted to be 360. degrees, but after Alnieon, of 23. degrees, and 33. minutes. But the later practisioners have found the same to be 23. degrees, and 30. minutes. Purbachius hath found the same to be of 23. and 21. minutes: which variation of the sun's greatest declination is, through the coming and going of the eight Sphere, (which is named the trembling motion.) But this is demonstrated and taught more at large in the Theoricks. If any desire to observe the sun's greatest declination, let him take the altitude of the sun about the winter solstice, in the shortest day at Noon: which altitude being kept a part, work the like, the sun being about the summer solstice, and the sun's greatest altitude at Noon found by the rule of the astrolobie; look that in the bordure of the same, and take the middle of that ark, which is between the sun's least and greatest elevation at Noon, which possesseth the middle, and shall be the Sun's greatest declination. The knowledge of the sun's declinations, with the other stars, is very profitable; in that by the same, and the perfection of the elevation of the pole, the true place of the sun (if the same be unknown) may be known, the sun's greatest declination presupposed, after this manner as followeth. Mark and consider diligently (the sun being in the Noonestead circle) carried up from the Horizont: which found, if the sun run in the Northerly signs, abate from the said elevation the complement of the elevation of th● Pole. If the sun be carried in the Southerly signs, then work contrary; for that which remaineth, shall be the suns particular declination. As by a like example use this. The sun being imagined to be elevated above the Horizont 63. degrees. 21. minutes, and 4. seconds, the elevation of the Pole is 41. degrees, and 30. minutes, and the compliment of the same altitude of the Pole to be 48. degrees, and 30. minutes; with the which subtract the sun's altitude at Noon, and the remaurer shall be the sun's declination, which is 14. degrees, 51. minutes, & 4. seconds. being the distance of the sun from the beginning of Aries, abated for the suns running in the Northerly signs, at the time of the observation before the summer solstice. What the offices or utilities of the Colours are. 1 SHe common offices in general of the Colours are, to show the four principal points of the zodiac, in which through the sun's motion the greatest changes and alterations of time is caused. 2 They serve to demonstrat the solstices and equinoctialles, and to divide the Zodiac into four equal parts, to which the four seasons of the year do answer. 3. The use of the one is to express and make manifest the points of the equinoctials, and the other to show the points of the solstices. 4 They both cut the Zodiac and equatour, into two equal half Circles, and both divide either Circle into four equal quarters. 5 But the Colour of the solsticis offereth many other uses: for in the same is the suns greatest declination or thwartness measured and numbered, in that the suns greatest declination, is the Ark of the Colour of the colsticis (enclosed between the beginning of Cancer and the Equatour) which ark is either increased or diminished, according to the winding in and out of the ecliptic unto the Equatour, as is afore mentioned. 6. They serve to distinguish the Equinectiall, the Zodiac, and all heaven into four equal parts: the use of which matter shall appear in the place of the ascensions of the signs. 7 Each Colour beside, hath his private office or utilities: as the Colour of the solstices, which hath four offices. The first demonstrateth the solsticiall points. The second containeth and measureth, the sun's greatest declination. The third, that it stayeth up the poles of the Zodiac, and showeth their distance from the poles of world. The fourth, that it divideth the Zodiac into two halves, as into the ascending and descending. Also the same in the thwart Sphere, doth separate the signs rightly arising, from the signs thwartly rising. 8 The Colour of the equinoctials hath two offices. The first, that it demonstrateth the Equinoctial points. The second, that it divideth the Zodiac into two halfs; as into the Northerly and Southerly half, 9 To conclude, the Colour of the solstices doth often supply and is used in the stead of the Meridiane, when as in every daily revolution of the first mover, it doth twice enter into the place of the meridian, or is twice joined in the plain of the same. The descriptions, names, and offices of the Meridiane Circles, and Horizont. THe four greater circles which we have already described, that with the motion of the sphere are drawn about, and every where are alike, which the other two Circles are contrary; as the meridian and Horizont, that are not turned in the drawing about of the Sphere, but remain as immovable and fixed; neither are they alike in all places, but are continually changed, standing or placed on the earth. In that all places have their proper meridians, and Horizonts. For both by a mutual touching and joining together do make right angles, and they continually divide the whole heaven into four equal parts, and make the four angles and quarters of heaven, unto which by a continual turning about of heaven, both the one and the other stars (as it were by an orderly succession drawn) work and send forth their virtues more effectuous, and excercise their qualities in the Elements, then in any other places: especially the sun being drawn unto those bonds, for he both beginneth and endeth the days and nights, and distinguisheth them equally, as it were in the middle parcels of time. The sun also come unto the meridian, doth then more heat, dry up and consume vapours. The Meridiane of any place, is a greater circle, which goeth or reacheth by the poles of the world and height of any place: and for that it passeth by the poles of the equatour, Parallels, and the Horizont, through the same doth it make right angles with them. And of this it divideth all the arks of the Parallels as well in sight as not in sight into two equal halves. This circle hath sundry names, for Varro nameth it the Meridian or midday circle of the noonestéed, in that when the sun is in the meridian, or any other star above the earth, then hath it performed half the day ark, and is then at the bound of the Noon time. But the other half of the night is caused, at the instant point of midnight, the half then reaching from East and West. So that of the same (this circle of all writers in this science) named the meridian, but of Ptolemy the circle of midday and middle heaven, by the same reason. The astrologians call this circle the royal Cusp, the regal quarter, the beginning of the tenth house, and the middle of heaven: in that this place is principal, and of worthier dignity than the other quarters, of which shall further be written in his proper place. Further it behoveth by the addition (31. Primi Theodosijs) that the Equat●ure and Horizont, in the contrary manner, to pass by the poles of the meridian: & of the same that those poles is none otherwise placed, than in the common sections of the equatour and Horizont. By which sections, & by those poles of the Horizont, is a certain third circle greater drawn, which johannes (a Regio monte) nameth the verticial circle: so that by the foresaid Corolary or addition ensueth, that of these three circles of each Exetrée and Pole, are they in that common section of the other two circles. Like as of the Equinoctial, and two colours by right may be concluded. So that a triple division is caused by the three circles, which appeareth on this wise: that as the meridian tendeth by our top and height from the South into the North; even so by the same top it behoveth the other circle to be drawn and pass from the east into the west that both cutting one the other at right angle, should express the four foresaid quarters of the world. As the Horizont distinguisheth the upper half sphere, from the neither, and the meridian from the East to the West; even so it falleth out, that the third circle, as that verticiall, should separate the Northerly from the Southerly half sphere. To these, while any standeth upright toward the Welt, on such manner, that the middle of his body is in the common Centre of three circles; then doth the Horizont divide his upper half from the neither, and the Meridiane, the fore part from the hinder; and the vertical circle the right part from the left. The three common sections of these circles, are their Exe-trées (as is afore written) do indicate or show the four principal points of heaven (which are the fix poles of the circles) placed in the sections of the cyrcumferences, as the highest or lowest point (which are the poles of the Horizont) the point also most Easterly and Westerly, which are the Poles of the Meridiane: to conclude, the point most Northerly and Southerly, which are the Poles of the verticiall circle. Those people that seem to have their feet against ours (in respect of the roundness of the earth) that they dwell as it were under us have alike horizont agreeable to ours, alike meridian, and alike verticial circle. But of these two, the half circles which be extant to us are hid or as it were under them. Contrariwise, those which be hid to us, are to them extaunt. The point also highest to us, is lowest to them: contrariwise the lowest to us, is highest to them. The figure afore placed, doth plainer express that afore taught: where the letters A. B. C. D. represent the Meridiane, the letters B. E. D. F. the Horizont: the letters F. A. E. C. the vertical circle: the letter G. the centre of the circles and world: the letters A. C. the Exetrée of the Horizont, the letters B. D. the Exetrée of the verticiall circle: the letters E. F. the Exetrée of the Meridian. To conclude, the point that to us is most Easterly, is to them most Westerly, et è contrario. For the point most Northerly and Southerly, do not change the surname, except you list to change or alter the names, like as of the Poles of the world. For that which is to us apparent, is to them hid: and contrariwise to us hid, to them manifest. Here may be demanded whether that point of heaven most Northerly, be not the Northerly Pole of the world, and that point most Southerly, the Southerly Pole of the world. To which is thus answered, that if regard be had unto the Equatoure and right Horizont, which passeth by the Poles of the world, and hath the equatour for the verticiall, or in steed of the verticiall circle. But we which have not the Poles of the world in the Horizont (in whose cyrcumference these four principal points of the East, West, North, and South, are accustomed to be noted) are forced to call that Northerly section of the Meridiane and Horizont, the most Northerly point, and that section right against the most Southerly point. For in every place there are two sections which the meridian and verticiall circle do make with the Horizont, which are two right sections in the plain of that Horizont (cutting at right angel's one an other in the Centre) that express and show those four quarters of the world, from which the principal winds blow; as East, West, North, and South. So that the foresaid right sections do part the Horizont, and cyrcumference of the same into four quarters. The four principal winds (of the common sort) are thus called, that which bloweth from the East, the Levant wind, and that right against it the Ponent: that from the North, Transmontanus, and that right against it the Meridional. These four of later years, they have divided into 32. winds, after the noted lines and points drawn in the sailors card, and other Maps every where to be seen. Also the sailors compass doth express so many winds, directed by the adamant or loadstone, which how the same doth direct and show the winds, needeth not here be showed, seeing the same is sufficiently known to every sailor, which by the guide of their compass, direct their course in cloudy weather (either by day or night) in marking diligently the points of the compass, how they coast. To return unto the matter of the Meridiane: the diversity of Meridianes is no otherwise caused, than the swelling of the earth, as in the first part I have sufficiently written: the cause of which is, that one like part of heaven cannot be the top or height of every place. Therefore one meridian cannot serve all places, but that in all places a proper Meridiane is caused over the head. The meridian also is that which when the sun cometh unto the highest over us, foreshoweth by his working and heat the midday. This meridian is a greater circle, passing by the poles of the world and Zenith, or a direct point over the head, abiding immovable at the motion of the sphere. This circle is differing to every City and people, by reason of the East and West, and is a proper meridiane caused over the head. For this is manifest, that at the changing of the verticiall point, there is caused an other Meridian, through the swelling and roundness of the earth. Also a man may of one meridian line, describe many (as writeth johannes a regio monte) for in that instant of the noontide, by letting down right a plum line, the shadow of the line causeth a new Meridiane line on the platform. Therefore these with the verticiall line in the the Centre to the Horizont (crossing one an other at right angles) do indicate the four quarters of the world: as the meridian line, the North and South, the verticial line, the East and West. The Horizont formeth the quarters of the east and west: of which the one is called the East rising, or easterly quarter or end: the other called the West setting, and quarter of the West. The Meridiane defineth the bounds of the lowest and highest of heaven, and the quarters or middle motions of the day and night time: of which, that consisting the upper half Sphere, is named the highest place and middle of heaven, the other which containeth the lowest place right against it, called the bottom or lowest of heaven. The Meridiane is a greater circle, immovable, not one and the same every where, but to every place peculiar and proper, drawn by the top of the place and Poles of the world (unto which the sun carried by the motion of the first mover) doth in the day time cause high Noon, and in the night time drawn right against it causeth midnight. If this circle were movable like others, then at the motion of the sphere would it depart from our Zenith, and so lose the name of the Meridiane: neither would it divide in proper place under it, the artificial day into two equal parts; seeing by that motion, the Meridiane should approach nearer to one part of the Horizont, then to the other part. Nor should it stay the Horizont at right angles, of which it is numbered and accounted amongst the outward circles of the sphere. The like affirmeth Proclus, writing that the Meridiane is none of those circles which is noted and decked with stars. For the circles of the sphere are distinguished by stars, whereby those circles may more easily be known in heaven. The meridianes are changed by the continual changing of place in the swelling or embossing of the earth (according to longitude.) For by going continually right forth toward the East and West, it doth purchase new Meridianes: as by going three miles forth, then is an other point of heaven, differing from the first over a man's head and gone further by four minutes of a degree. Proclus affirmeth, that 300. furlongs cause no sensible alterations to happen of the Meridian: and this is meant of those which are placed under divers Meridianes, and Parallels. For those which are placed under one Parallel and divers Meridianes, perceive and see no alteration at all. He which goeth straight from the North into the South, or they which directly journey toward either of the Poles of the world, do continually travail under one Meridiane. In that all Merdianes do go from one Pole to another, therefore no journey causeth by this means an other meridian. There are as many meridians in number, as there be differences of verticiall points (right over divers parts of the earth) in going toward the East and West. The half of the equinoctial hath 180. degrees, whereof the Cosmographers do assign and distinguish so many meridians, in such sort, that each Meridiane doth pass by the two opposite degrees of that Equinoctial, and Poles of the world. The longitude of a place is the ark of the equinoctial circle, or of any Parallel contained between two Meridianes, of which the one lieth over the fortunate Isles, and the other streacheth over the top of the proper place noted, where the same distance of place is gathered from the fortunate Isles at the equinectiall, or at the Parallel of the place. The fortunate Isles are situated and lying in the sea, called Oceanus Libicus beyond Mauritania (between the Equatoure and the tropic of Cancer) which in our time is called the Isles of Canary, and lie further into the North from the equatour, than Ptolemy noted or accounted them. But the latitude, they accounted to be a space of the earth lying between either pole, accounted in the Meridiane drawn by the poles of the world, or a whole tract of the earth known and streached beyond, and on this side the equatoure, toward either Pole of the world. They established the beginning of the latitude in the equinoctial (as in the middle circle exquisitely between either pole) and common bound to both the Southerly and Northerly places, So that the latitude of a place, is the ark of the meridian, between the equinoctial and Parallel drawn by the top of the place: or it is the distance of a place from the equinoctial. This always is accounted in that meridian, which hangeth directly over the top of the place, and to one degree of the same, do 500 surlongs, or 15. German miles answer. The arks of the latitudes do not differ from the elevations of the pole, but in the standing only. For the elevation of the pole is the ark of the meridian, from the Horizont unto the Pole, raised on high from the plain of the Horizont. The latitude of a place, is the ark of the same meridian, placed between the equinoctial and verticiall point. To conclude, the latitude of a place, and elevation of the pole do not differ in the magnitude or largeness, but in standing only. By the former figure appeareth, that the Ark of the longitude of places or cities known, is forthwith offered at the first sight: as the ark E. P. or P. O. or O. N. etc. And seeing the equatour (being in compass about 360. degrees) doth wholly ascend in 24. hours above the Horizont regularly: of this it cometh to pass (whiles in each hour 15. degrees of the equatour do ascend) that through the longitude of cities, it is easily known the hourly distance of one place unto an other, seeing the sun cometh later to the meridian to them which are nearer to the East then to them in the West, whereof if a city shall be situated in L. and an other in K. the ark L. K. shall be of 30. degrees: then shall the sun come sooner unto the Easterlier meridian K. by two hours, then unto the Westerly. But if one city shall be in P. and the other in Z. then (in latitude only) shall they differ, and shall be under one meridian; which is declared in the last part of the description of the meridian. What the offices and utilities of the Meridiane are. 1 THe utilities and uses of this circle are many, of which the first is, that it distinguisheth the days and nights into unequal spaces: it determineth the forenoon time or morning, and the after noon or evening time of the artificial day: the like of the night into hours (which are before night) and those which follow unto morning. Many of the astronomers account their beginning of the natural day from this circle. It doth beside represent (without the equin●●tiall) the Horizont of the right sphere, and in every habitude of the sphere it doth represent the right Horizont, and showeth the points of the midday, and midnight. 2 This circle in the thwart sphere giveth and suprlyeth the office of the right Horizont: for to every thwart Horizont it leaveth or stayeth at right angles. So that the astronomer maketh or accounteth not his day, from the rising or setting of the sun through the thwartness of the Horizont, which causeth the variety & notable difference of the inclination of the Zodiac, unto the horizont of the angles, and largeness of the rising. But they begin to account from noon or midnight (the sun then occupying the Meridian) through the Sun, which congruence all the meridianes have with the right horizont. And that a lesser variety of the inclination of the Zodiac happeneth unto the meridiane and angles, which it maketh with the meridian. Also in this circle is the Zenith or direct point noted, from which the distances of the stars, and Parallel circles are gathered. 4 In the meridianes (as in the subject) the distances of the stars from the equatoure, the latitudes of places, and the elevations of the Pole are accounted. For the studious and skilful practisioners, observe the latitudes of places and the elevations of the pole, not to differ in the quantity, but in the standing only. For the elevation of the pole, is the ark of the meridian from the horizont, raised unto the pole. The latitude of the place, is the ark of the same meridian, contained between the equatour and verticiall point: so that it is manifest that these arks differing in the standing, do agree in magnitude, whose verticiall points, one meridian containeth, but not one Parallel, by an equal space from the west) be unequal distant from the equatour, and are then said to differ in the latitude only. Contrariwise, to whose tops one and the same Parallel, and not one meridian, but each place proper; those by like spaces from the equatour, be distant by unlike spaces from the fortunate Isles, and are said to differ in the longitude only. So that in both they are said to differ; to whom the Parallel only serveth, and they to whom the proper meridian serveth: for they have their spaces unequal to either bound. Therefore the difference of latitude is the ark of the meridian, contained between the Parallels of the two places, distant from the equatour. The quantity of the same is thus known; if from the half Equatour toward either pole of the places standing, the lesser latitude of the nearer, be abated from the greater latitude more further off: if from the half equatour the places be divided under (that the one half leaneth into the North and the other into the South) by the latitudes of both joined, whether one or both lie under one meridian or divers meridians. For it forceth not in the meridian of both, that the latitudes be joined together, seeing all meridians are alike in the sphere. The difference of the longitude, is the ark of the equinoctial or Parallel, enclosed between the meridianes of the two places, distant from the fortunate Isles, and in themselves: by which the longitude of one place exceedeth the longitude of another. The same longitude is the ark of the equinoctial, seeing the places be under the equatour. For in the only longitude the places, the common Parallels, and tops of both bended, do differ: in that the Parallels (from the equatour) toward the opposite quarters of the equal Parallels (as places to which they be right over) do likewise differ. The meridians (as is afore declared) are the greatest circles of the sphere of the world, bended by the verticiall points of all places, but drawn to the equatoure (as by the Poles) of which they pass unto right angles, and by a mutual consent, make angles in the Poles of the world, which the arks of the equatour being placed between those meridians, are measured, that by so much as a quarter of the circle they be distant from them: even so the equatoure from his Poles, is on either part distant by a quarter of the greatest circle. Those arks do contain the difference of longitude, by which one of the meridianes is further distant into the East than the other; so that the angles unto the Poles between the meridianes, are rightly named the angles of the difference of longitude; and by the arks of the equatour, those also come into knowledge: for there is a mutual relation between the angles and arcs each one of them towards another, which do measure the angles. The latitude of places, is the distance of the verticiall points from the equatour, gathered in the meridian. If then from the whole quarters of the meridians (which to the equatoure and Pole of the world, toward which the places decline the equal arks be stretched to the latitudes, than the seats of the places given, or the verticiall points of them shall be found. And the other arks from these points unto the Pole (which by a mutual section do make an angle) the compliments of the latitudes, be known by the degrees abated from 90. in the degrees of the latitudes. Further by the sun's meridian had and found, you may easily conceive the elevation of the pole, and habitude of the sphere. For the whole quarter is, of 90. degrees. Seeing the sun's meridian altitude in the equinoctial, must be subtracted from 90. degrees, the rest show the elevation of the Pole. As for example, the sun's meridian altitude of Viteberge in Germany, in the time of the equinoctial, is of 38. degrees, and 10. minutes, the rest of the degrees of the quarter shall appear to be 51. degrees, and 50. minutes, which elevation of the pole near agreeth to London. So that by so many degrees, is the Pole there elevated above the Horizont. And as the quadrant is from the pole unto the equinoctial: even so is the quadrant from the Zenith unto the Horizont. If therefore in the time of the Equinoctial, the distance of the Horizont unto the sun's altitude be of 38. degrees, and 10. minutes; which is not the half part of the quarter, the same yet being subtracted from the whole quarter, doth show that the rest shall be more than half part of the quarter: that is, 51. degrees, and 51. minutes. For those spaces which are from the pole unto the Equinoctial, and from the Zenith unto the Horizont, are alike: what the distance of the Zenith is from the equinoctial, the same likewise is the Horizont unto the Pole; that is, the latitude of the place, is equal to the elevation of the pole. To declare that the latitude of a place is equal to the elevation of the pole, these four propositions are to be conceived. First, the quarters of one and the same circle, any where taken, are equal one to the other. Secondly, the poles by the quarter; that is, 90. degrees be distant from their circle. Thirdly, the Zenith is the pole of the Horizont. Fourthly and last, the equals abated from the equals the equals still remain. So that two quarters of the meridian taken (as that which is from the equinoctial unto the pole, and that which is from the Zenith unto the Horizont) which seeing they are quarters of one and the same circle, therefore are they likewise equal one to the other; that is, either containeth 90. degrees, when from these two quarters the common ark is abated; which is between the Zenith and Pole of the world: and the rest of the equals remain (as the ark which is from the equinoctial unto the Zenith) and called the latitude of the place; and the ark (which is from the Pole of the world unto the Horizont) also called the elevation of the Pole, as may be understanded of the former Viteberge, that is of 51. degrees, and 50. minutes. Yet that you may easilier find and know the elevation of the Pole of your City or Town, you must first obtain and have the sun's meridian altitude; which workmanly may be had and observed by the shadow. As when the sun's altitude in the time of the equinoctial is precisely of 45. degrees, the shadow than is like to the Gnomone, which is at Venice (as Pliny writeth) also of Milan and Lions: for the sun to them is in the time of the equinoctial, in the middle of the quarter. But when the sun's altitude exceedeth 45. degrees, then is the shadow caused lesser, as of Rome, where the suns meridian altitude in the equinoctial is of 42. degrees, and 10. minutes: so that the shadow is there shorter. Also Pliny writeth of Rome, that the ninth part of the Gnomon in the equinoctial, doth lack of the noon shadow. But when the sun's altitude is lesser than 45. degrees, the shadow of the Gnomon is caused longer. The like is with us through all winter and the time of the equinoctial: for we see the shadows of men's bodies to be longer, for that the sun's altitude in that time is never 45. degrees. For how much the shadow is longer than the half part of the quarter, so much the lesser is the sun's altitude then 45. degrees. As of Viteberge in the 10. day of September, the sun's meridian altitude is then of 39 degrees, and 21. minutes: but when the sun is further distant by the 45 degree of the quarter (or by the half of the quarter) then ensueth, that the shadow is so much longer than the Gnomon, or 45, degrees. For the Noon shadow in the 10. day of September is the like unto the Gnomon, as the 50. degrees, and 39 minutes, are unto 45. degrees. Hear you see how by the meridian shadow, you may find the sun's altitude; which obtained, you shall easily find the altitude or elevation of the Pole (especially in the time of the equinoctial.) For the sun's altitude then from the whole quarter; that is, from 90. degrees, must be subtracted, and the elevation of the pole shall remain and appear to be, as is above taught. Seeing it is somewhat hard to find the height of the Pole unto any day prescribed, & that the same may more easily and surer be attained and found, you shall use this table here following: by the help of which you may without great labour, find and know the elevation of the pole. For to proceed and work by this manner, seek first the sun's meridian altitude at the day offered, either by an astrolaby or quadrant; but rather by the instrument named the quadrant, in whose bordure are 90. degrees drown or written, expressed by reason of the Gnomon and shadow upward. After seek the degree of the Ecclipticke by the Ephemerideses, which the sun obtaineth at noon of the day offered: next by the table following, take the declination of the degree found (by mean of the equinoctial) if the sun than shall be in Northerly signs, abate or subtract from the sun's altitude afore found: but if in Southerly signs, then add unto the sun's altitude. The produce or rest is the elevation of the equinoctial, which abstracted or abated from the whole quarter; that is, from 90. degrees, leaveth & showeth the elevation of the pole, as in the 10. day of September, the sun's altitude in the twelve hour (or at noon) is of 39 degrees, and 21. minutes. To find this elevation of the pole, I enter the table following, where I find and see the 27. degree of Virgo, to have the declination of one degree, and 11. minutes: which degree and minutes (seeing they are in the Northerly part of the world) are to be subtracted from the sun's altitude that day, and the degrees which remain are 38. and 10. minutes. The altitude of the equinoctial that day, which subtracted or abated from the whole quarter; that is, from 90. degrees, the elevation of the pole which remaineth, is 51. degrees, and 50. minutes. This Table of the Sun's declinations, containeth the number of the degrees of the Zodiac, increasing in descending on the left hand, and increasing by ascending on the right hand, with the Signs decently placed: the Arks or roots of the declinations follow those numbers: which roots are no other than the arks of the circle of the Latitude: that is, the circle passing by the Poles of the Ecliptic, included between the Ecliptic and Equatour. The general Table of the Declinations. ♈ ♎ arks. ♉ ♏ arks. ♊ ♐ arks. G ●r. m ●r. m ●r. m G 0 0 0 12 16 20 38 30 1 0 26 12 37 20 40 29 2 0 12 12 37 21 0 28 3 1 18 12 58 21 11 27 4 1 44 12 58 21 21 26 5 2 10 13 19 21 31 25 6 2 36 13 40 21 40 24 7 3 2 14 0 21 49 23 8 3 28 14 20 21 58 22 9 3 53 14 40 22 6 21 10 4 19 14 50 22 14 20 11 4 45 15 18 22 21 19 12 5 10 15 37 22 28 18 13 5 25 15 55 22 35 17 14 6 0 16 ● 22 41 16 15 6 25 17 31 22 47 15 16 6 50 17 48 23 52 14 17 7 15 17 5 23 57 13 18 7 39 17 22 23 2 12 19 8 3 18 ●8 23 7 11 20 8 27 18 54 23 11 10 21 8 ●● 18 0 23 15 9 22 9 15 18 25 23 18 8 23 9 39 19 40 23 21 7 24 10 2 10 55 23 23 6 25 10 25 19 9 23 25 5 26 10 48 19 23 23 27 4 27 11 10 20 36 23 28 3 28 11 32 20 49 23 29 2 29 11 54 20 36 23 30 1 30 12 16 20 30 23 30 0 Ecli● ♏ ♓ ♌ ♒ ♋ ♉ Ecli● THe meridianes with the Horizont, in any right or thwart, & in the other four greater circles, do distinguish all heaven into twelve spaces, which they call the houses of heaven. Of these four, which occupy the angles of heaven, are called the quarters: the four next to these, are named the succedents: the last (included by the succedentes and angles) are named the declining houses, and the cadent from the angles. The meridian also hath a most great use in cosmography: for by it the describers of the world measure the longitudes and latitudes of places and cities: which being known, the distance of cities may easily be found. That you may understand what the longitude and latitude of a place is, it behoveth you to know the distinction of the earth after the Geographers, which is on this wise, The Geographers do assign or imagine two points on the earth, right under the poles of the world: after that they devise a circle equally distant on either side from these these two points (right under the equinoctial) which divideth the whole Globe of the earth and water into two equal halves. This circle thus described on earth, they distribute into 360. parts or degrees, in proceeding from the West into the East, by each degrees of this circle; and by the points right under the poles, they imagine and draw 180. circles; which, for that they are under the celestial meridians, they also call meridians, and those they divide into three hundred & threescore parts or degrees; by which parts they imagine and draw the Parallel or equidistant circles to the equinoctial, proceeding from the equinoctial on either side, towards the points in the poles lying under these Parallels, & although they be not of the same bigness or largeness (for how much nearer the poles they are, so much the narrower and straiter they run together. Contrariwise, how far of they be from the Poles, and nearer to the Equinoctial, so much the wider and larger they run) yet do they divide as the Equinoctial, or any other great circle, into three hundredth and three score parts or degrees. How this division of the earth being learned and understood, a man may the more easily conceive what the longitude and latitude of places is. The longitude of a place (as I have afore written) is the ark of the equinoctial circle, or Parallel, passing by the Zenith of the place which is sought after, included between the two meridians; as between the first meridian (which by the Zenith of the Isles of Canary (and further off) is imagined to be drawn, and the Meridian of the place offered: that is, the longitude of any place, is the distance thereof from that westerly point, from which the beginning of longitudes is accounted toward the East. They began to account the longitude from the west, through the proper motions of the Planets, which are carried unto the contrary quarter from the West: or rather for the Moon, at whose Eclipses it is well known that it more availeth, than the true finding out the longitudes of places, or as some rather think likelier, that the places which end and stand furthest Westward inhabited, have been sures and perfecter found. For through the dearness and opportunity of the journeys (which they in ancient time were moved to f●aua●le and sail ●●●●) as the two Isles (named Gades) which lie by the furthest parts of Spain beyond Granade, and since through the passage by West Ocean, men of later years have sailed about the furthest parts without stop or impediment. But unto the Eastward, they were stopped of their course by a great distance through the difficulty and peril of the journey. And since beyond the half circle almost threescore degrees, men have sailed to Scythia besides Imaus (which now is named the great Tartary) that reacheth bordering to the upper India, where the most large kingdom of Cathagia under the parallel of Thracia flourisheth, where Bebeid Cham was governor. And that is the part of Tartary, which beginneth from the river Tanais, so that the largeness of Schithia Asiatica (from the West to the East) doth almost take up 84. whole degrees. America in the sea Atlanticus, is of such greatness, that the same is supposed to be a fourth part of the world inhabited: the middle or half of it hath the longitude of 330. degrees, and the latitude of ten degrees Southward. The sea Altanticus hath many large islands in it; among which, the most notable are Spagnolla, Cuba, Parias (otherwise Chersovesus) by the strait that reacheth upward into the north. The middle of the same hath the longitude of 285. degrees: the latitude Northerly 44. degrees. For from 11. unto 50. almost, it reacheih unto. America streacheth far into the South, beyond the tropic of Capricorn, although his bound or furthest part Southerly be not yet found or known. To the ancient it was no further known Southward, than 17. degrees beyond the Equinoctial: and the furthest known to them Northward, exceeded not three score and three degrees, which (as Ptolemy witnesseth) was unto the Island Thylen. So that the whole latitude found by them, appeareth to be 80. degrees, both of the one and the other side of the equinoctial: and on earth the same containeth 40. thousand furlongs, to which 50. hundred paces answer, but German miles two hundredth thousand agree. Also the Island Thilen or Thulen, standeth beyond Scotland, and the Isles Hebrides and Orchades, that be into the North and East, which is distant from the furthest bound of Scotland, but three days sailing, if prosperous winds be their help. At this day men have found beyond Thylen (but somewhat into the East (and most large bounds stretched and found beyond the arctic or Northerly circle, & these are whole without breaking of any sea between; and contain Suetia, Norway, Iseland, Grunland and Lapeland. The kingdom of Suetia appeareth most large, and containeth sundry nations and people; among which, they are of most account, the East and West Gutland people, inhabiting near to Norway. And under the King of Suetia are the Lapeland people, (as the Finelapons and Dikilapons) where are a wild and fierce people, dwelling almost under the pole arctic (especially the Lapeland people) to whom the sun never setteth in the summer for 40. days space. Above these inhabit a people of a cubit long or high, having small and crooked bodies (named of some Pygmalion's) that live under a very dark and bitter cold air or sky. And above Scania (near to the West bounds of Suetia) doth Norway stretch into the North, whose uttermost limit extendeth unto the 71. degree almost of the Northerly latitude. Above this is the country named Iseland, by reason of the frozen waters and sea: where throughout the year it so bitterly freezeth, that through the icy seas there thick frozen, it permitteth no ships to come unto them, except in the three hottest months of the year. It aboundeth with brimstone, and burneth in many places through the sulphur & brimstone veins. Pliny writeth, that the Ocean sea in North is very large, which in these our days is well known. This also was learned of certain skilful sailors (which inhabited and very much had travaled this coast) that they knew not the limits or bounds of this sea toward the North, but supposed that this sea did compass the whole earth. By this sea dwell many and mighty people; as the Danes, the Swedens', Norway's, Gotelandes, Finelands, Russians, and Pruchenians: and under the pole artic the Lapland's. The reason why in these places such force of moisture aboundeth, is for that a daily and continual cold of these places gathereth and thickneth the air, and by a continual working resolveth into water. For when the air is not thoroughly purged by the sun's beams, than the weakness of them, and far distance of the sun from these places, must of necessity be continually thick and dark, which afterwards yieldeth and giveth plentiful floods by dews and rains. Albert mag. in his book de natura loci, and 8. chapter, assigneth a witty and laudable reason, why the Northerly be inhabitable. The cause he setteth down, in that sundry skilful Mariners affirm (that have many times sailed into the Northerly parts of the Ocean sea) that in those places is a continual darkness, which when men saw they returned for fear, supposing (nay rather doubting) that none could sail any further in that quarter of the world, through the darkness, and thick mist, which hindereth the direction of their journey. So that the nature of those places cannot be sufficiently known to us, seeing no man (as the learned report) hath attempted thither, through extremity of cold their bearing sway. And for that exceeding cold is a mortifying quality, therefore a man may conjecture, that few living creatures and beasts can there live etc. Yet the part of the Northerly Ocean (unto the Easterly side) is sufficiently known to many travailers. Although the uttermost bounds of the earth are not wholly known, yet the nearest aprroaching to them shall here be applied, as the longitude of the earth distant between Peru (the Realm of America) and Cathaya, to express 315. degrees: or if any mind to account the longitude from the fortunate Isles, they may by a whole circle contain them, even as the whole Orb about in a manner doth partly give place to the water, and are partly dwellings for men, beasts, and other living creatures; although some places of the earth be more inhabited than others. But as touching the latitude; if toward the North in the country of Lapous, & the south (toward the utmost coast of America shall end) seeing the utmost distance of the earth hath very little been noted, of this shall small error be caused. If two places offered or given be placed under the Equatour, of which the space is sought, than the ark of the difference of latitude, is the same with the ark of the distance, neither doth the verticiall circle differ from the Equatour. For the equatour of either place doth contain the verticiall points, as may appear in this triangle, noted with A. B. C. Of which, if 15. german miles be wrought into parts of the difference of longitude, and any scruples after remain, divide those by 4. For (by so many minutes of a degree, doth a german mile answer) that the distance shall make. As Ptolemy writeth, of the places under the Equatour. The high land or mountain of the satires, in the country of Syna, whose longitude is of 175 degrees, and no minutes, nor hath any latitude. Myrica an Isle of Ethiope under Egypt, whose longitude is of 85. degrees, the angle of the difference of longitude between the meridians of these places, is strait or right, and containeth a whole quarter or 60. degrees. The like are these places standing under the equatour. Colipolis a city of India beyond the river Ganges, which hath the longitude 194. degrees, and 20. minutes, & Essina the great Mart-towne of Aethiope under Egypt, whose longitude is of 70. degrees, and 3. minutes. The angle of the difference of longitude (which the meridians of these compass) is blunt, and containeth 94. degrees, and 17. minutes. Again the same or the like meridians contain and make a sharp angle of 43 degrees, as of the city Nubarta of Taprobane, which at this day is Sumatra, and Colipolis of Ind beyond or above Ganges: for it is distant from the west 122. degrees, and 20. minutes, and this containeth 164. degrees, and 20. minutes. If two places be given, the one standing under the Equatour, and the other distant toward any other quarter from it. The first, that the angle of the difference of longitude is strait to these here placed. In that if two places given the one shall be under the equatoure, but the other distant from the same toward some quarter, them must the angle of the difference of longitude be considered. If the same shall be right, then shall the distance of either place be the quadrant of the greatest circle. As in this triangle A. B. C. where the letter A. representeth the Pole of the equatour and the places given, that the one be standing in the point B. under the equatour, and the ark A. B. be the quadrant: and that the other consisteth in the letter C. the angle then of the difference of longitude, being C. A. B. is right. By Regio a montano de trangulis appeareth, that C. B. the ark of the distance of places which reacheth out right, is a quarter of the greatest circle. Wherefore if the degrees be multiplied by 15. and the minutes divided by 4. the distance than shall be known. As for example, Nubarta of Taprobone hath the longitude 121. degrees, and 20. minutes, but no latitude: the city Pyse of the Tuscans in Italy, hath the longitude 31. degrees, and 20. minutes almost, the latitude of 42. degrees, and 11. minutes: then the angle of the difference of longitude is right, for the difference is of 90. degrees, or a whole quadrant. These then multiplied by 15. do procreate or bring forth the distance to be of 13▪ 50. German miles. Essina a Mart-towne or principal ●itty of Aethiope under the government of Egypt, hath the longitude of 70. degrees, and 3. minutes, but it hath no latitude. The I'll of Tyrus hath the longitude of 67. degrees, and no minutes the latitude of 33. degrees, and 20. minutes. The difference of longitude, between the one and the other, is of 3. degrees, and 3. minutes. The complement of the difference of longitude, is of 86. degrees, and 57 minutes, of the latitude of the place not standing under the equatour, the complement is 56. degrees, and 40. minutes. The royal city Colipolis of Ind (above the river Ganges) hath the longitude of 164. degrees, and 20. minutes, but no latitude known. The longitude of Tyrus is of 67. degrees, and no minutes, the latitude hath 33 degrees, & 20. minutes. The difference of longitude greater than the quadrant, is of 97. degrees, and 20. minutes. The quadrant being abated, there remaineth 7. degrees, and 20. minutes. The complement of the latitude of Tyrus, is of 56. degrees, and 40. minutes. If of two places given, either standeth without the Equatoure toward some one of the opposite quarters; and the other under the equatoure: then is the reason of the standing considered, and the angle of the difference of longitude. For the one differeth either by like spaces from each bound, and is nearer to the Pole, the other to the Equatoure. The same appeareth by the compared latitudes, which like tops of either place contain the same Parallel, the unlike being distant, and the Parallel by a space separated, toward each place, do argue peculiar and proper tops. But the angle of the difference of longitude, either it is right, blunt, or sharp. This of the placing and diversity of the angles, doth much vary or alter the reason & method of the searching of these. If two places given have equal arks of the latitudes, and from the middle or half of the equatoure be alike distant, and how much so ever the angle of the difference of longitude be, as here under the difference of longitude is in the first, of the example taught: yet are the arks of the latitudes agreeing and equally found, so that in this example appeareth no difference, but in the only longitudes of the places offered. As for example. The longitude of Dansk is of 39 degrees, and two scruples or minutes: the latitude of the same hath 54, degrees, and 48. minutes. The longitude of Lubeck is of 28. degrees, and 20. scruples, the latitude hath 54. degrees, and 48. scruples. The difference of longitude consisteth, of 10. degrees, and 42. minutes. The half difference is, of 5. degrees, and 21. scruples. The distance on earth, between Dansk and Lubeck, is of 92 German miles, and a half. The great city Alexandria under the Turk (after Ptolemy) hath the longitude of 122. degrees, the latitude of the same, is of 41. degrees. That famous Toletum or Toledo of Spain, hath a longitude to the same, of 10. degrees, the latitude of the same is, of 41. degrees. The difference of longitude between the one and the other, is of 102. degrees. The half difference, hath 51. degrees. The complement of the equal latitudes of either, is of 49. degrees. The whole distance between both appeareth to contain 1077. German miles and a half. If of two places given, the one be further distant from the equatour than the other, and the greatness of the compliments of either latitude differing (as that the arks of the latitudes be unequal) so that the diversity of the angle included with the arks of the compliments, shall vary the method or reason of the search, for that the one giveth and formeth a right angle, another a sharp, another a blunt angle: yet to these, the angle of the difference of longitude is right. The example of two places differing alike (both in the longitude and latitude) here appeareth. The city Tacola (which at this day is called Malchaia or Magna) a place of much resort of Merchants. This from the West hath the longitude of 160. degrees, and 30. minutes, of latitude from the equatour, it is 4. degrees, and 15. scruples distant. The other city and place in the country of Pontus (named Trapezus) being a head city of Cappadocia and was the ancient seat of the Emperors. This hath the longitude of 70. degrees, and 30. minutes, and the latitude of the same is of 43. degrees, and 5. scruples. The difference of longitude between the one and the other, is of 90. degrees. The ark of distance between both places is of 87. degrees, and 6. minutes: to which 1306. & a half German miles answer. If the unequal arks of the latitudes, and angle of the difference of longitude be lesser than the right, it causeth a divers reason of the search, by which the ark of the complement of the greater latitude doth vary three ways, as it is greater or lesser, and as with the ark by the second in quisition surely known, and being joined, form either more or less a quarter of the circle. Or thus, that the angle which the unequal compliments of the unequal latitudes include, be sharp; that is, and if the arks of the latitudes of either place be unequal, and the difference of longitude be lesser than the quadrant. As in this example more plainer appeareth, of two places being of sundry longitudes. That worthy city Trapezus of Cappadocia, whose longitude is of 70. degrees, and 30. minutes, the latitude 43. degrees, and 5. minutes. The longitude of that well known city of Rome, hath 39 degrees, and 8. scruples, the latitude 41. degrees, and 8. minutes. The difference of longitude, between the one and the other, is of 33. degrees, and 22. minutes. Another example not unlike the former, and not much varying from the former: as the longitude of jerusalem, which is of 66. degrees, and no minutes, the latitude, of 31. degrees, and 40. scruples. The longitude of Viteberge, being of 30. degrees, and 30. minutes, the latitude 51. degrees, and 50. scruples. The difference between the one and the other of longitude is of 35. degrees, and 50. scruples. If in places unequally distant from the equatoure, the angle of the difference of longitude shallbe blunt, by which the difference of longitude shall appear greater than the quadrant. Or thus, that the angle of the difference of longitude be blunt, seeing the places are further distant than a whole quarter, and thereby causeth a divers reason and way of search from the former; which semblably the divers quantity of the complement of the greater latitude doth three manner of ways vary, as in the same ark (which perfectly known by the second) is either greater or lesser. The example of this appeareth of these two places: the noble city Antiochia in Syria, which was after called Seleucia, hath the longitude of 106. degrees, and no minutes, the latitude is of 40. degrees, and 40. scruples, The other of Toletum, whose longitude is of 7. degrees, and 4. scruples, the latitude hath 37. degrees, and 50. minutes. The difference of longitude is of 98. degrees, and 56. scruples, which deducted from the half circle (or 180. degrees) the difference that remaineth unto the half circle, is of 81. degrees, and 4. minutes. The like example not much varying from the former of these two places: as the noble city of Portugal named Lysebone, whose longitude is of 4. degrees, and 18. scruples, the latitude hath 39 degrees, and 38. scruples. The other named Calecute (although the latitude differeth) hath the longitude of 112. degrees, and no minutes, the latitude is of 5. degrees, and no minutes. The difference of longitude, containeth 107. degrees. and 42. scruples more than the quadrant. The same deducted from the half circle, doth express the difference remaining unto the half circle to be of 72. degrees, and 18. minutes. The complement of the greater latitude, is of 50. degrees, and 22. scruples. The complement of the lesser latitude, is of 85. degrees, and no scruples. Another example of two places distant from the Equatour, of which the one is distant from the middle of the Equatour into the North, and the other into the South, as this example further instructeth; the one being the isle of Thilen (which in Ptholomies ●●me was the uttermost bond of the earth known, Northward) that hath the longitude of 33. degrees, the latitude Northerly, of 63. degrees. The other called the isle of S. Thomas, hath the longitude of 27 degrees, and 20. minutes, the latitude Southerly, of 16. degrees. The difference of longitude, is of 5● degrees, ●nd 40. minutes. The complement of the latitude Northerly, is of 26. degrees. A third example of the difference of other two places, as Bas●a of Taprobane, which Ptolemy affirmeth to be in longitude 126. degrees, and in latitude toward the South 6. degrees, and 30. scruples. The other named Stocholma, in the Realm of Suecia, hath the longitude of 42. degrees, and 38. scruples, and the latitude of 60. degrees, & 30. scruples. The complement of the latitude Boreal, is 29. degrees, and 30. minutes. The common way of measuring of places, with their spaces, by the rules of longitudes and latitudes. HEre before I have somewhat written of sundry habitable places on the earth, whose sundry points differ between the one and the other; either in the only longitude, or in the only latitude, or in the longitude and latitude both together. Those places which do differ in the only longitude, be distant by equal spaces from the equatoure, toward either of the Poles of the world: the verticiall points of those places ended by the same Parallel joining next the same space between: yet each have their own proper meridians, being not distant by a like space from the Westerly bound. The distance of these is always gathered and noted in the same Parallel, which commonly belongeth to either place standing or hanging right over the tops of them. Those places which do differ in the only latitude, are standing ●●der the same meridian, but they have divers Parallels▪ ●●d each proper; and those continually distant unequally, either toward one pole from the middle of the Equatour (if either place declineth unto one and the same quarter) or otherwise from the middle of the equatoure severed and distant into the contrary quarters, by equal or unequal spaces. If that one of the places look into the South, and the other into the North, the distance of these is always accounted in the common meridian. Those places which do differ both in the longitude and latitude together, or both decline toward one Pole of the world, or separated and distant from the midst of the equatoure toward the opposite Poles (as the one looking into the North, and the other into the south) or else by equal Parallels distant from the equatour; of which two only are in the Sphere. If they be reduced and applied unto one great circle (per 3. secundi Theodosijs) or else be under by unequal Parallels, and by an unequal space. The difference of the longitude of those (which either be toward them, or toward the Poles equally distant) is always gathered in the middle Parallel between either of the bonds by arithmetical proportion, as afore taught. But in those places which have equal Parallels, and equally dastant unto the opposite quarters, the difference of longitude is imagined & noted in either of the equal Parallels. Therefore the ark hath the distance of the places standing, by the next space drawn overthwart by the points of those places, which with the arks of the difference of either (both of the longitude and latitude) doth form and make a spherical triangle right cornered, always in the upper face of the Globe. If that two meridianes meet and end at the poles of the world, and being cut by the overthwart cyrcumferences of the Parallels, do make with the included arks of them right cornered tryangles, through the four right lesser angles: but the angles being not right, the ark of the distance of the places doth divide them into two right cornered tryangles. One of those tryangles is used in the common account for the right cornered; because in places not far distant from the equatoure, the angles contained between the mutual sections of the meridians and Parallels, do not so much vary from the right angles: but in places far distant from the equatour, they vary very much. Now the rules for the divers standing of places shall be taught in an easy and common manner. If places do differ in the only longitude. TO the searching and knowing of this, like as in the former, are the longitudes and latitudes of places given required; by which they being found (seeing in the latitude there is no diversity) the difference of longitude is only to be considered, by deducting the lesser longitude out of the greater, and then howemany miles by proportion of the Parallel, under which the places stand or lie to the equatoure, answer to one degree of the same. The same doth that rule (set forth in the form of a table here following) declare, being drawn and made unto this use by the learned; in which, the miles that answer to one degree of each Parallel, are there found and noted unto one degree of the distance of the Parallel from the equatour. If to the whole degrees of the distance of the Parallels do minutes depend, then from the difference of the two next numbers to one degree, may the proportional part be deducted or drawn: which from the number of the miles expressed unto a whole degree is abated, that the Parallels succeeding, may be little & little be caused to stretch & appear narrow. To be brief, the miles with the scruples or quarters (if any be adjoined) let them be reduced into the whole ark of the difference of longitude, which then shall manifestly show and express, the measured space by the German miles. Ptolemy when he had learned the longitudes and latitudes of certain notable places, he could extract and gather by them the other unknown places, by the distances truly learned from travailers. For by the longitudes and latitudes known of two circles, and the distance also of them from any third place, there is then offered and given to know, as well the longitude, as the latitude of the third place. Further, in any two places lying and being in the upper face of the earth, are five notes commonly learned. The distance of them, converted into degrees: the latitude of the one, and the latitude of the other: the difference of longitudes: the angle under the circumferencial distance: and the meridians contained by the other. Of the which five, if three only be known, it is certain that the other two may easily come to knowledge by the practice and skill of the spherical tryangles. An example of these former words (as touching the difference of longitude of two places) the latitudes being alike. As the city Byzantium now called Constantinople, whose longitude is 55. degrees, and no minutes, the latitude hath 43. degrees, and 5. minutes. The other city Trapezus hath the longitude of 70. degrees, and 50. minutes, the latitude of 43. degrees, and 5. minutes. The difference of longitude is of 15. degrees, and 50. minutes to one degree of the common Parallel, and to each place, do 10. German miles with 29/30. answer or agree. These now brought into the difference of longitude, do cause & make 174. German miles almost. The like example to the former, is Arbela of Assiria, which hath the longitude of 80 and no minutes, the latitude of 37. and 15. minutes. The other Athens, whose longitude is of 52. degrees, and 15. minutes, the latitude 37. degrees, and 15. minutes. The difference is of 27. degrees, and 45. minutes. Other brief examples. Lon. Lati. Areca in Comagena being a part of Syria. 70. 10. 37. 15. Megara the country of Euclid. 52. 0. 37. 15. The difference is of 18. 10. Lon. Lat. Philippi a city in Thracia or country of Alexandria. 50. 45. 41. 50. The royal city of Room. 36. 20. 41. 50. The difference is of 14. 25. longitude. Lipsia, 29. 58. 51. 24. The difference of long. is 9 degr. & 42. min. The difference of long. is 6. degrees, & 4. min. Antwerp, 20. 16. 51. 28. Vratislavia, 34. 34 51. 10. Erphordia, 28. 30. 51. 10. If places do differ in the only latitude, or that both be placed toward one pole, or either distant from the middle of the equatour, so that in the only latitude the places differ, when the longitudes be like, the standing of the places is to be considered toward either Pole, whether either place declineth toward one Pole, or that the one be Southerly, and the other Northerly. If they decline unto one place and quarter, then deduct the lesser latitude, out of the more, and the difference of latitude shall appear. If either be distant from the middle of the equatoure, the latitudes joined do show the difference. The degrees, of the difference wrought by 15. and the scruples divided by 4. shall offer & give the estimate distance in German miles. As in this example, the city of Noriberge hath 28. degrees, and 20. minutes of longitude, the latitude is of 49. degrees, and 24. minutes. The other is Mylayne, whose longitude is of 28. degrees, and 20. minutes, the latitude hath 45. degrees, and 6. minutes. The difference of latitude, is of 4. degrees, and 18. minutes: the space between, is 64. miles and a half. Like examples are these. Trapezus, 70. 15. 43. 5. The difference of latit. is 5. degrees, & 45. min. The difference of latit. is 6. degrees, & 44. min. Antioch, 70. 15. 37. 20. Padua, 31. 50. 51. 0. Budissina, 31. 50. 44. 16. If two differ together in the longitude and latitude, and that either declineth toward one Pole, then in either toward the places differing, as in the longitude and latitude are the differences of the spaces from either bound of the latitude and longitude gathered. The half difference of the latitude added to the lesser altitude shall show the Parallel in which the difference of longitude is accounted. With that Parallel by this rule are the miles gathered and known, which answer or agree to one degree. These found, reduce into the whole difference of the longitude, and that which proceedeth (agreeably) of the same; that is, multiplied in itself or arising of the multiplication keep. After the degrees of the difference of longitude reduce into 15. and the minutes annexed (if any such be) distribute or divide by four, that which ariseth of either working, reduce jointly one to the other, and add to the number kept afore. For of the whole gathered may the square root be attained, which showeth the distance of places. As by a like example, the city of Witeberge hath the longitude of 30. degrees, and 30. minutes: the latitude of 51. degrees, and 50. minutes. The other being jerusalem hath 66. degrees of longitude, and no minutes: the latitude is of 31. degrees, and 55. minutes. The difference of longitude is of 35. degrees, and 30. minutes: the difference of latitude is of 19 degrees, and 55. minutes. The middle Parallel in which the difference of longitude is accounted, doth differ or is distant from the equatour 41 degrees, and 52. minutes: to one degree of the same do 11. miles, and 10. scruples of a German mile answer, which reduced into the difference of longitude, do procreate or bring forth 396. German miles: these wrought together make 156816. The degrees of the difference of latitude being wrought by 15. & the scruples divided by four, do make 266. German miles; which multiplied one in the other, do perform and make 89401. Either of these square numbers joined, and the root extracted, the distance shall appear to be 4●5. miles. The finding of the distances of places or cities, in a more easier manner. THat you may know how by the longitudes and latitudes of two places or cities, the distance of them may be found: thus do, when two cities be offered (whose largeness is to you unknown) sée● the longitude and latitude of both by the cosmography of Apian, or Pto lomies Geography; which being found, writ down the longitude of the one under the longitude of the other, and the latitude of the one under the latitude of the other (as the former examples show) in such sort, that the degrees of the other, and likewise the minutes under the minutes. After seek the difference as well of the longitudes and latitudes, in this manner: subtract the lesser longitude from the greater, the remainder is called the difference of the longitudes. After deduct the lesser latitude out of the more, and the difference of the latitudes shall remain. By the differences of the longitudes and latitudes, shall the distance of cities given be gathered. But in that there is three manner difference of places, as that there be certain places which differ in the only latitude; that is, under one meridian, and yet lie under divers Parallels: and certain that differ in the only longitude; that is, under one Parallel: yet are divers meridians: and certain that do differ both in the longitude and latitude; that is, they lie under divers meridians, and Parallels, three rules also of the searching of distances, between two places, are taught of the Geographers. The first rule. WHen two cities having one longitude are offered (but having sundry latitudes) deduct the lesser out of the more: the rest of degrees, in that they be the degrees of the great circle, multiply by 15. (for that 15. German miles answer to one degree of the great circle) and then shall you have the distance of the cities. But if minutes depend to the degrees of difference, them divide them by four, the quotient add to the fore number of the miles. For seeing one degree or 60. minutes do make 15. German miles; it ensueth, that four minutes make one German mile, etc. An Example. MAdeburge and Egra agree only in longitude; that is, they be equally distant from the West or from the meridian, which is drawn or stretched by the fortunate Iles. For the longitude of either town is of 29. degrees, the latitude of Madeburge is of 52. and 20. minutes: the latitude of Egra is of 50. degrees, and 5. minutes: therefore is Egra more Southerly than Madeburge. The difference of the latitudes, is 2. degrees, & 15. minutes; that is, 33. German miles, stith a half & a quarter of a german mile. Another. TThe longitude of Trydent is of 30. degrees, and 30. minutes. The longitude of Viteberge is as much. The latitude of Trydent is of 45. degrees, & 14. minutes. The latitude of Viteberge is of 51. degrees, and 50. minutes. These now differ in the only latitude, which difference of the latitude is of 6. degrees, and 36. minutes; that is, 99 German miles. So much is the distance almost between Trydent and Viteberge. Another. THe longitude of Thunis is of ●6. degrees, and 50. minutes: the longitude of Salerne in a manner the same. The latitude of Thunis is of 32. degrees, and 30. minutes. The latitude of Salerne is of 40. degrees, and 30. minutes. The difference of latitude is of▪ 〈◊〉 degrees, & 〈◊〉 minutes, that is, 120. miles. And somuch is the distance between Thunis and Salerne. Another. THe City of York, and the Town of Berwick, agree in longitude, for the longitude of either place, is of 17. degrees, and no minutes. But they differ in latitude, in that the latitude of York is of 54. degrees, & no minutes, the latitude of Berwick, is of 56. degrees, & 50. minutes. The difference of the latitude is of 2. degrees, and 50. minutes: that is, 210. English miles. So much in a manner is the distance, between the City of York, and Berwick. Another. THe City of London and Northampton, in a manner is of like longitude. For the longitude of London is of 16. degrees, and 30. minutes approved. But they differ in latitude, in that London hath the latitude of 51. degrees and 34. minutes, the latitude of Northampton is of 52. degrees, and 50. minutes. The difference of the latitude, is of 1. degree, and 16. minutes; that is, 7●. English miles. So much in a manner is the distance between London and Northampton. Another. THis example differeth both in the longitude and latitude somewhat. For the longitude of Colchester, is 18. degrees, and 30. minutes, the longitude of Oxeforde hath 15. degrees, and no minutes. The difference of longitude between the one and the other, is of 3. degrees, 38 minutes, that is, 109. English miles. The latitude of Colchester hath 51. degrees, and 59 minutes. The difference of latitude, is no degrees, and 16. minutes. So that 16. English miles, is the distance between the one and the other, after their standing Northward. Another. CYgnea and Ratisbone, agree in longitude, for either is of 29. degrees, and 51. minutes: but they differ in latitude, in that the latitude of Cygnea hath 50. degrees, and 46. minutes, the latitude of Ratisbone, of 48. degrees, and 56. minutes. The difference of latitude between the one and the other, is 1. degree, and 50. minutes, which make 27. and a half German miles. The second rule. BEfore the second rule be here taught, it behoveth that you know how many German miles answer to each degree of the parallel (passing by the Zenith of Cities offered.) Here conceive that not as in the former rule, to every degree of each parallel, but to each degrees only of the parallel Circle, which streacheth and is under the Equinoctial, and as principal of all the parallels, divideth the whole earth into two equal halves, to which are 15. German miles attributed, as to a degree of it. Where the other circles (as afore written) be not of the same bigness, but how much nearer they be to the poles, so much the lesser they are: and how further of they be from the ●n●●s, so much the greater they are. Whereof it is manife●e mile▪ aswell the greater as the less Circle of the parallels, ●●tes, stributed or divided into 360. degrees, and that those degrees (according to the distance of those parallels from the poles) be greater or lesser. For the same cause shall you here find in the table following, how many German miles answer in each elevations, to the degrees of the parallels. A Table, containing the degrees of the differences of each Parallels, from the Equator unto the proper Pole, by whole degrees of the Latitudes converted into Miles. Degrees. Miles. Scruples. Degrees. Miles. Scruples. Degrees. Miles. Scruples. Degrees. Miles. Scruples. Degrees. Miles. Scruples. 1 14 59 19 14 11 37 11 59 55 8 30 73 4 23 2 14 59 20 14 6 38 11 49 56 8 23 74 4 8 3 14 58 21 14 0 39 11 39 57 8 10 75 3 53 4 14 58 22 13 54 40 11 29 58 7 57 76 3 38 5 14 56 23 13 48 41 11 19 59 7 43 77 3 22 6 14 55 24 13 42 42 11 9 60 7 30 78 3 7 7 14 53 25 13 36 43 10 58 61 7 16 79 2 52 8 14 51 26 13 29 44 10 47 62 7 2 80 2 36 9 14 48 27 13 22 45 10 36 63 6 48 81 2 21 10 14 46 28 13 15 46 10 25 64 6 34 82 2 5 11 14 43 29 13 7 47 10 14 65 6 20 83 1 50 12 14 ●● ●0 12 59 48 10 2 66 6 6 84 1 34 13 ●● ●● 31 12 51 40 9 50 67 5 52 85 1 18 14 ●4 33 32 12 43 50 9 38 68 5 37 86 1 3 15 14 29 33 12 35 51 9 26 69 5 23 87 0 47 16 14 25 34 12 26 52 9 ●4 70 5 8 88 0 31 17 14 21 35 12 17 53 9 12 71 4 53 89 0 16 18 14 26 36 12 8 54 8 49 72 4 38 90 0 0 An Example for the use of this Table. LVneburgum and Stetinum, have the elevation of the Pole precisely of 54. degrees, to know how many German miles answer to one degree of the Parallel, passing by the Zenith of either City, enter your Table, and there diligently looking, you shall find by the degree of that latitude 54. noted eight miles, and 49. scruples of a mile. For so many miles in that Parallel answer to a degree; that is, eight, a half, and the third part almost of a German mile. And this is easily found, if the elevation doth only consist in whole degrees. For in each elevation are certain miles, and the scruples of a mile, answering to each degree assigned. But if the place or city have minutes depending to the latitude as Viteberge whose latitude is of 51. degrees, and 50. minutes: then seek in this table how many miles and scruples of a mile, are attributed to the whole degrees, and you shall find by the degree of the latitude of 51. noted 9 miles and 26. scruples of a German mile. After seek the miles and minutes that next join to the elevation following, being 52. and you shall find right against 9 miles, and 14. scruples of a mile: which so set down or placed, that the miles be under the miles, and the minutes under the minutes, after this manner. mile's minutes 9 26. 9 14. Subtract the lesser number out of the more and upper written, and there will remain 12. minutes, of this rest; that is, of the 12. minutes, seek the number proportional, according to the proportion of one degree or 60. minutes, unto the minutes depending to the latitude offered, as of the latitude of Viteberge to the whole degrees, do 50. scruples depend. Of which so place the numbers by the Rule of three, working and saying on this wise, 12 Z 50 60 10 that if one degree or 60. minutes of the degree do give 28. minutes of a mile, how many scruples of a German mile, do 12. minutes of a degree give. To know this, multiply the first by the second, that is, 12. by 50. & the increase shallbe 600. this product divide by the third number which is 60. and the part proportional shallbe 10. This proportional part found, subtract out of the miles, and minutes of the former elevation; that is, from the 9 miles, and 26. minutes: deduct the 10. and there will remain 9 miles, and 16. scruples, precisely answering to one degree of the Parallel passing by Viteberge. Here the second rule followeth, which is easy to conceive, if you work according to the former taught. The second Rule. IF two Cities be offered, which differ in the only longitude, first seek by the instruction above taught, the miles, and minutes of a mile answering to one degree of the Parallel, passing by the Zenith of those Cities. After, seek the difference of longitudes in the degrees and minutes: then multiply the difference of longitudes, with the miles and scruples of the miles, and the distance shall appear of the Cities given. An Example. VIteberge and Westphalia agree in latitude: that is, they be both standing under one Parallel. For the latitude of Viteberge is 51. degrees, and 50. scruples, and exceedeth the latitude of Westphalia by certain minutes, which here we pass, but they differ in longitude, in that Westphalia lies more to the West. The longitude of Vite berge is 30. degrees, and 30. scruples: the longitudes of Westphalia is 24. deg. & no min. To find the distance, see how many miles answer to one degree of longitude in the parallel, passing by the Zenith of the cities given. Before was taught, that in the Parallel of Viteberge 9 miles and 16. scruples do answer to one degree: wherefore seek the difference of longitudes of the two Cities, and deduct the lesser number out of the more; that is, let the 24. degrees and no minutes be deducted from the 30. degrees, & 30. scruples, & the difference resting, shall be of 6. degrees, and 30. scruples. Last, multiply the 6. miles and 16. scruples, with the difference of longitude; that is, with 6. degrees, and 30. minutes, and you shall have the distance of the two Cities. But here observe and note diligently in the multiplication of the degrees, miles, and minutes, what proceedeth and cometh of the same. For the miles multiplied by the degrees, do bring forth the miles: and the miles multiplied by the minutes of the degrees, do bring forth the scruples of the miles. The minutes of the miles multiplied by the degrees, do produce or bring forth the minutes of the miles. And last, the minutes of the miles multiplied by the minutes of the degrees, do produce the seconds of the miles. But that this may the readier be conceived, use this example, the former Westphalia and Viteberge: where the 9 miles and 16. scruples, are to be multiplied by the 6. degrees, & 30. minutes on this wise. Multiply the 9 whole miles, by the 6. whole degrees, thus: as six time 6. bringeth out 54. miles. Multiply after that, the whole miles by the minutes of the degrees; thus, that 9 times 30. do make 270. minutes of miles. After multiply the minutes of the miles by the whole degrees, and by the minutes of the degrees: as the 16. minutes of the miles multiplied by the 6. degrees, do make 99 minutes of miles. After this the 16. minutes of the miles multiplied by 30. minutes of the degrees, do make 480. seconds of miles; which minutes and seconds gather into whole miles, in this manner. First divide the 480. seconds by 60. and the quotient shall be 8. minutes. (For that one minute containeth 60. seconds, as one degree doth contain 60. minutes. These 8. minutes, add to the minutes proceeded of the former or upper working; that is, the 270. and the 96. & you shall have 374. scruples of miles, which divided by 60. the quotient will be 6. whole miles, and 14. scruples; that is, almost the fourth part of a German mile. These miles gathered of the seconds and minutes of the miles, add to the 54. miles gathered afore by the multiplication of the degrees and miles, and you shall have the true distance between Viteberge and the Monastery of Vestphalia; that is, 60. German miles, and almost a quarter. This manner of working in searching the distance of places (which differ in the only longitude) observe in the other examples following: in which you shall find their distance, by having their longitudes and latitudes. Here following shall be sundry examples, in which the young students and practisers may excercise them according to rule. An Example. COleine and Marburge do differ in the only longitude: for the longitude of Coleyne is of 23. degrees, and 28. scruples, the longitude of Margburge hath 25. degrees, and 45. minutes. The latitude of either (which agree) is of 51. degrees, and no minutes. The difference of longitudes is of 2. degrees, and 17. minutes. The miles answering to one degree (drawn in that Parallel by the Zenith of the Cities given) are 9 miles, and 26. scruples, as may appear in the former table. But seeing no minutes depend to the latitude, the 9 miles, and 26. minutes are to be multiplied by the difference of the longitudes: that is, the 2. degrees, and 17. minutes, in this manner: saying twice 9 do make 18. miles, twice 29. are 52. minutes of miles, nine times 28. do make 152. minutes of miles, and seventeen times 26. are 442. seconds of miles: which seconds and minutes divided by 60. do make three miles, 32. minutes and 22. seconds. These added unto the 18. miles, declare the distance of Coleyne and Margburge, to be of 21. German miles, and a half. Another. THe longitude of Franckeforde is of 25. degrees, and 38. minutes. Hasforde is of longitude 37. degrees, and 52. scruples. The latitude of either, is of 50. degrees, and 12. minutes. Now they differ in the only longitude, for that the difference of the longitudes is, of 2. degrees, and 14. scruples; that is, Franckeforde by two degrees, and 14. minutes, is more toward the West, than Hasforde. The miles according to latitude 50. are 9 and 38. minutes, and the miles according to the latitude following, as 51. are 9 and 26. minutes. The difference of these two manner of miles and minutes, is 12. minutes: the part proportional subtracted, is two. The miles answering to one degree, in the Parallel drawn by the Zenith of Franckeforde and Hasphorde, are 9 and 36. minutes. Now as above these miles and minutes (with the difference of the longitude) that is, two degrees, and fourteen minutes multiplied, you shall have the distance in German miles; that is, twenty and two, and almost a half. Another. The longitude of Gawnt (the native town of Charles the first Emperor) of 19 degrees, and 8. minutes. The longitude of Lipsia of 29. degrees, and 28. minutes. The latitude of either is of 51. degrees, and 24. minutes. The difference of longitudes is of 10. degrees, and 50. minutes. The miles according to the elevation 51. are 9 and 26, minutes: the miles ensuing the elevation assigned, are 9 and 14. minutes. The difference of these two manner of miles and minutes, is 12 minutes: the part proportional subtracted, is 4. minutes. The miles answering to one degree in the Parallel (to Gaunt or Lipsia) are 9 and 22. minutes. These miles and minutes multiplied with the difference of the longitudes, do offer and show the distance between Gawnt and Lipsia; that is, 101. German miles, and almost a half. Another. THe longitude of Straseborow is of 24. degrees, and 30. minutes, the longitude of Landunum of Bavier is of 30. degrees, and 25. minutes. The latitude of either is of 48. degrees, and 45. minutes. The difference of longitude, is 5. degrees, and 55. minutes, etc. Another. THe longitude of Direpsa is of 130. degrees, and no minutes; the longitude of Danaba of 104. degrees, and no minutes neither. The latitude of either is of 45. degrees, and no minutes. The difference of longitude, is 26. degrees, and no minutes. An easier working. IF this curiosity's in observing minutes trouble you, you may then with lesser pain and error leave them, especially in places being not far distant a sunder, where the minutes omitted do little force or hinder, how near soever you find the true distance. And by this means the second rule, is of no difficulty: for that every painful labour doth especially consist in the multiplying of the diffeence of longitudes, with the whole miles offered by the former Table, according to the degree of latitude, of the Cities given. An Example. AMsterdame and Brandenburge (which as unto whole degrees appartaineth) agree in latitude: for the latitude of either place in whole degrees, is 52. degrees. But they differ in longitude, in that the longitude of Amsterdame is 21. degrees, and 4. minutes, the longitude of Bradenburge of 30. degrees, and 35. minutes. They differ in longitude 9 degrees; that is, Amsterdame is nearer to the West then Bradenburge by 9 degrees, as the former table teacheth in the Parallel of the latitude 52. which containeth 9 miles. Now by so many miles is Bradenburge distant from Amsterdame. Another. NOrdlinga and Nicostadium, agree in latitude, for the elevation of the Pole, or latitude of either is of 48. degrees. But they agree not in longitude, in that the longitude of Nordlinga is of 27. degrees, and 54. minutes, the longitude of Nicostadium of 29. degrees, & 32. minutes: so that they differ 2. degrees, which make 20. German miles, as may appear by the former table, where 10. miles are assigned to the latitude 48. Now you shall understand that the distance of Nordlinga and Nicostadium, is of 20. German miles almost. Another. THe longitude of the City of Venice is of 32. degrees, and 30. minutes, the longitude, of Spoletum is of 36. degrees, and 30. minutes. The latitude of either, is of 44. degrees. The difference of the longitude is of 4. degrees. And 10. miles do answer to one degree in the Parallel of the latitude 44. The miles being multiplied by the difference of the longitudes; that is, by four degrees, do declare the distance of Venice and Spol●tum, to be of forty miles. If of two places, the one being Southerly, and the other Northerly. IF of two places given, the one hath a latitude Northerly, and the other a latitude Southerly: seek the difference of either space of the longitude; after subtract the lesser longitude out of the greater (but of the latitude Northerly and Southerly) according to the latitudes joined of either place. In the second place the standing must be cosidered, whether they be situated under equal Parallels, and both distant by a like space from the Equatoure, or else otherwise separated by unequal Parallels, and by an unlike space. For if the Paralles of the places given shall be equal, then must the difference of longitude be accounted in either alike: but if unequal (and that both shall be distant by an unlike space) than the half of the greater latitude applied to the lesser latitude, shall demonstrate and show the Parallel apt and meet to this instruction: with the same Parallel are the degrees answering to each degree, declared by the former rule, and the other is taught & showed, as in the precedent place is declared. Meroe a Region of Aethiopia under Egypt, hath the longitude of 91. degrees, and 30. minutes, the latitude of 16. degrees Northerly. The I'll of S. Thomas in the bordure of Aphrica hath the longitude of 27. degrees, and 20. minutes, the latitude Southerly is 16. degrees. The difference of longitude is 34. degrees, and 10. scruples. The difference of latitude which the conjoined latitudes do make) is of 32. degrees. And seeing both by an equal space be distant toward the opposite poles from the equatour, it therefore forceth not, that the difference of longitude be gathered in either Parallel Northerly or Southerly, in that they be equal. For to one degree of the Parallel (which is of 16. degrees, distant from the equatour) do 14. miles, and 25. scruples, answer or agree: which reduced into the difference of longitude, do bring forth 492. German miles; which multiplied together, do bring forth 241064. The difference of latitude wrought or multiplied by 15. do bring forth 480. German miles, which again wrought together do cause 230400. And by either quadrant conjoined, the square root drawn out of the same, doth then declare and show the distance to be of 686. German miles. The I'll of Thylen hath the longitude of 33. degrees, the latitude is. of 63. degrees Northerly. The I'll of S. Thomas hath the longitude of 27. degrees, and 20. scruples,, the latitude Southerly, of 16. degrees. The difference of longitude, hath 5. degrees, and 40. scruples, the difference of latitude, is of 79. degrees. The half difference of the greater latitude, applied to the Southerly latitude, bringeth forth that the Parallel is distant from the equatoure 47. degrees, and 30. scruples: in which the difference of longitude, must be accounted. And to one degree of it in the rule, do 10. German miles, and 7. scruples answer; which wrought into the difference of longitude, do bring forth 57 german miles almost. Those multiplied, do make the increase to be 3239. By the difference also of the latitude, those multiplied, do bring forth 1404225. Of the quadrants joined, the root hath 1189. German miles almost; that is, the distances sought of the places. That the studious and diligent practioners may easter perceive and perfecter understand these differences of the standing of places, let them often accustom themselves therein, that when the longitudes and latitudes of sundry places be offered, they then consider whether they differ in the only longitude, or latitude only, or in both, and what the latitude is of either, and into which part from the Equatour: and besides that, they learn to express the standing of them by proper lines drawn, and the places noted. If the numbers of the latitudes be alike, and the numbers of the longitudes be unlike, then do the places only differ in the longitude. Therefore by two meridians found and defined, lying cross to them in one Parallel, imagine and set the place of the greater longitude in the point of the crossing further off, that the other in the nearer may be placed unto the West. For the place always (whose longitude is lesser than the other) is nearer found to the West, and the other is further distant into the East. The ark also of the Parallel included between either meridian, doth demonstrate the difference of longitude. If the numbers of the longitudes shall be alike, and the numbers of the latitudes unlike, then is the diversity of the places in the only latitude. Therefore two Parallels drawn cross, of which the one being higher and the other lower and crossing them by one meridian, they do set the place of the greater latitude in the uppermost point of the crossing, and the other in the lowest point. If the latitudes be alike, as the one Southerly, and the other Northerly: then the middle ark of the Merydian being between, is equally crossed by the Parallels of the places drawn thwartly by the Ark of the Equatour, in such sort, that the Equatour is by an equal space distant from either. If both the numbers of the longitudes and latitudes shall be unequal, and either place distant into the North from the Equatour, therefore in both is there a diversity. Therefore two Meridian's being imagined, the one Oriental dextre, and the other Occidental synistre, and that by so marry Parallels drawn thwartly, which cross the Meridian's, the one Southerly, the other Northerly: and that the place whose greater longitude is touched in the lowest and furthest point, and the other to be noted right against; that is, in the upper and nearest point. Or thus contrariwise: If one place shall exceed the other, both in longitude and latitude, and be further standing in the higher point of the crossing, and thereby more farther distant, and the other noted to stand right against, and the seats also of the places unequally touch, which declareth and containeth the nighest distance of such places. In the same manner is the standing of places descending unto divers parts from the Equatour expressed; being observed in such order, that if the places of either be alike distant from the Equatour, the Equatour than is exquisitely standing in the middle of both: but if the places happen to be unequal, then is the Equatour by an unequal distance, placed farther off. A third rule. IF two Cities offered do differ both in the longitude and latitude, seek first the difference aswell of the longitude, as latitude. After half of the difference of latitudes add unto the lesser latitude, and with the produce enter the table which in the former examples hath been taught and practised: searching there the miles and minutes answering properly to one degree. The miles and minutes found, multiply with the degrees of the difference of longitude, and the produce multiply in itself, and you shall obtain and have the first quadrate. Thirdly, multiply the difference of latitude by the 15. German miles, and this produce also multiply in itself, and you shall have the second quadrate. Last, join or add together these tw●● quadrate numbers (and of that produced or increased) search out the quadrate root. The quadrate or square root●, is the distance of Cities offered. An Example of the third rule. Wischegarda and Verona, do differ both in the longitude and latitude, in that the longitude of Vuischegarda is of 41. degrees, and 17. minutes, the latitude is of 52. degrees, and 4. minutes. The longitude of Verona hath 31. degrees, & 18. minutes, the latitude is of 44. degrees, and 49. minutes. The difference of the longitudes is of 9 degrees and 59 minutes. The difference of the latitudes is of 7. degrees and 15. minutes. The half of the difference of the latitudes, is 3. degrees, & 37. minutes, which half added to the lesser latitude; that is, to Verona, which is of 44. degrees, add 49. minutes, doth then produce or bring forth 48. degrees, & 26. minutes. This produce or increase is named the middle latitude, in that it is distant by equal degrees and minutes from either latitude of Vuischegarda and Verona; that is, it exceedeth the latitude of Verona by 3. degrees, and 37. minutes, and Verona doth exceed Vuischegarda by so many degrees, and minutes. With this product or middle latitude; that is, with 48. degrees, & 26. minutes. I enter the former table, and according to the instruction afore taught in the second rule, I find in the parallel which is drawn by the middle latitude, to answer to one degree right against 10. german wiles, and 2. minutes. It was also taught in the second rule, that if minutes depended to the latitude, that those should be sought in the former table, and by the next elevation following, the proportional part to be sought. As in this example. The latitude 52. are 9 miles, and 14. scruples noted, and in that 3. degrees, and 37. scruples depend to a middle latitude, I seek in the table how many miles and scruples are noted next to the latitude following, 55. and there I find 8. miles, and 36. scruples. The difference between the miles and scruples of the elevations of 52. and 55. is 1. degree, & 22. minutes. By the proportion of this difference, is the proportional part gathered and found, according to the manner afore taught in the second rule. Another example of this third rule for thy further instructing of Viteberge and Lipsia, which differ in the longitude and latitude: for the longitude of Viteberge is of 30. degrees, and 30. minutes, the latitude hath 51. degrees, and 50. minutes. The longitude of Lipsia is of 29. degrees, and 58. minutes, the latitude hath 51. degrees, and 24. minutes. The difference of the longitudes is of thirty two minutes, the difference of the latitudes is of twenty six minutes. The half of the difference of the latitudes is of thirteen minutes, which half added to the lesser latitude (as to Lipsia) which is of 51. degrees, and 24. minutes, doth produce ●1. degrees, and 37. minutes. The product is called the middle latitude, in that by equal minutes it is distant from either latitude of Viteberge and Lipsia; that is, it exceedeth the latitude of Lipsia, 13. minutes, and by so many minutes is it exceeded of Viteberge. With this product or middle latitude; that is 51. degrees and 37. minutes, I enter the former Table, and by the Instruction afore uttered in the second rule, I find in the Parallel which is drawn by the middle latitude, that 9 miles, and 19 scruples do answer there to one degree. And in the second rule afore is taught, that if minutes depend to the latitude, which is sought in the former Lable, then by the next elevation must the part proportional be sought. As in this example to the latitude, 51. degrees, are 9 miles and 26. scruples noted. And in that 37. minutes depend to the middle latitude, I therefore seek in the table how many miles and scruples are assigned to the latitude next following; that is, 52. degrees: right against which I find noted 9 miles, and 14. scruples. The difference between the miles and scruples of the elevations of 51. and 52. is of 12. minutes: so that by the proportion of this difference unto the whole degree, or 60. minutes, is the proportional part drawn or gathered, according to the manner afore taught in the second rule. As thus, that as 69. minutes yield 12, even so do 37. give 7. minutes, which is the part proportional. The same minutes subtracted from the miles and scruples assigned to the latitude 51. that is, from the 9 miles, and 26. scruples, there remain 9 miles, and 19 scruples. And so many miles and scruples in the Parallel of the middle latitude doth answer unto one degree. Which being found and known, these nine miles and the scruples, with the differences of longitude, which is of thirty two minutes, I then multiply, and they show and bring forth 298. minutes: which multiplied again in itself, do bring forth the first quadrate to be 88804. minutes. And this is the first part of the working of these. Now followeth the other part. I multiply first the difference of latitude, as the 26. minutes by 15. German miles, and they bring forth 390. minutes, which multiplied again in itself do yield 151200. minutes, as the second quadrant is. Now these two numbers quadrate added, do bring forth and make 240904. minutes, of which the quadrate or square root is of 494. minutes of miles. These for that they are the minutes of miles, aught to be divided by 60. and then they bring forth 8. whole miles, and 14. scruples; that is, a fourth part almost of a Germaive mile. So that somuch is the distance, between Viteberge and Lipsia. Another. THe longitude of Buda is of 37. degrees, and 44. minutes, the latitude hath 47. degrees, and no minutes. The longitude of Aquisgranum is of 22. degrees, and 24. minutes, the latitude hath 51. degrees, and 6. minutes. The difference of the longitudes, is of 15. degrees, and 20. minutes. The difference of the latitudes is of 4. degrees, and 6. minutes. The half of the difference of the latitudes, is of 2. degrees, and 3. minutes. The middle latitude is of the degrees, and three minutes: here (in that 3. minutes do only depend to the middle latitude) are omitted, seeing the leaving of them bring or cause small error. Then must you take the miles assigned to the latitude 49. that are 9 miles, and 50. scruples, which with the difference of the longitude; that is, 15. degrees, and 20. minutes are to be multiplied, and they shall bring forth 150. miles, and 46. scruples: which miles contain as a quadrate; that is, one part in itself with the minutes, that may be multiplied and resolved also into minutes in the multiplication by 60. it shall then bring forth 9000. minutes▪ to these add the 46. minutes, and the number than shall be of 9046. minutes. These minutes again multiplied in itself do bring forth and offer the first quadrate, that is 81830116. The difference of the latitude, as the 4. degrees, and 6. minutes, multiplied by 15. doth produce or bring forth 61. miles and 30. scruples: which as they may be wrought and multiplied again in themselves, they may be resolved into minutes, and you shall have 3660. minutes. These further wrought in themselves do bring forth and show the second quadrate, which containeth 13395600. The two quadrate numbers also conjoined, do make 95225716. minutes. The root of this; that is, 9758. divided by 60. declareth the space between Buda and Aquisgranum, to be 162. german miles and a half. Another. THe longitude of Room is of 36. degrees, and 20. minutes, the latitude hath 41. degrees, & 50. minutes. The longitude of jerusalem hath 66. degrees, and no minutes, the latitude is of 31. degrees, and 40 minutes. The difference of the longitudes is of 29. degrees, and 40. minutes. The difference of the latitudes is of 10. degrees, and 10. minutes. The half of the difference of the latitudes, is of 5. degrees, and 5. minutes. The middle latitude, is of 36. degrees, and 45. minutes. The miles answering to one degree in the Parallel of the latitude next following, are 11. and 59 minutes. These subtracted from the miles and minutes of the former elevation, there do 9 minutes remain. These thus found and known seek the proportional part to be subtracted, in saying, if one degree or 60. minutes in this Parallel do yield 9 minutes of a German mile, how many minutes of a mile do 45. minutes yield or make, which depend to the degrees of the middle latitude. To know this, multiply 45. by 9 and the product divide by 60. then will 9 minutes remain in the quotient. The part proportional must also be subtracted, which deducted from the miles and minutes assigned to the latitude 36, as from the 12. miles, and 8. minutes, do 12. miles, and 2. minutes remain. By which appeareth, that so many miles and minutes, do answer to one degree in the Parallel of the middle latitude. This now is as a preparation and entrance, unto the second working. To have therefore the distance of the foresaid cities, multiply first the 12. miles, and minutes, with the difference of the longitudes 29. degrees, and 40. minutes, and they shall bring forth 356. German miles, and ●9. minutes, which 356. miles, that may be wrought together with the minutes 59, are to be resolved into minutes, the same is performed, if they be multiplied by 60. To the same product being 21369. add the 59 minutes, and they make 21419. These minutes again multiplied in themselves, do offer the first quadrate, that is, 458773561. Thus you have the understanding and knowledge of the working of the first place. After this multiply the 10. degrees of the difference of the latitude by 15. and you shall readily have the miles 150. to which add for the 10. minutes depending, 2 miles, and a half of a German mile, and you shall have in this second part of the working 152. miles, and a half or 30. scruples of a German mile. Which miles, as they may with the minutes be multiplied together in themselves, so are they to be resolved by that 60. multiplied into minutes, which then bring forth 9120. to which add the half or 30. miles, and you shall then have the whole to be 9150. minutes: which again multiplied in themselves do make the later quadrate to be 8372●500. Now unto the last, conjoin these two quadrates, and the whole sum shall be 542496061. minutes. The root of this number; that is, 23299. seeing it representeth the minutes of miles, divided by 50. doth then show the space which is between Icrusalem and Room, in German miles, to be 388. with a third part almost of a mile. Another. THe longitude of Hamburge is of 37. degrees only, the latitude hath 45. degrees, and 24. minutes. The longitude of Magdeburge hath 29. degrees, and 38. minutes the latitude is of 52. degrees, and 20. minutes. The difference of the longitudes is of 2. degrees, and 38. minutes. The difference of the latitudes is of 2. degrees, and 4. minutes. The half of the difference of the latitudes, is one degree, and 2. minutes. The middle latitude is of 53. degrees, and 22. minutes. The miles assigned to the elevation 53. are 9 and 2. minutes. The miles assigned to the degrees of the elevation following, being 54. are 8. and 49. minutes. The difference now of these two manner of miles and minutes, hath 13. minutes. The proportional part subtracted is of 4. minutes; which minutes, let four be deducted out of the 9 miles, and 2. minutes assigned to the elevation 53. there will then remain 8. miles, and 58. minutes. Therefore so many miles and minutes, do answer to one degree in the Parallel of the middle latitude. These miles and minutes now found, multiplied with the difference of the longitudes, do bring forth 23. miles, and 36. scruples. And these 23. miles, wrought together with the minutes; that is, multipled in itself, and that resolved into minutes, to the producte also add the minutes 36. and the whole then shall appear 1416. minutes. This number again wrought into itself, doth offer the first quadrate, which is 2005056, minutes. After multiply the difference of the latitudes, by 15. miles, and the increase shall be 31. miles. These miles again resolved do yield or give 1860. minutes, which multiplied again in themselves, do offer the later quadrante, which containeth 3459600. minutes. The whole sum, that is, the numbers increased of these two quadrats, are 5464656. The root of the minutes, which is of 2337. minutes, divided by 60. doth declare the distance which is between Hamburge and Magdeburge, to be 39 German miles almost. An easier working. and less curious. THis great labour perhaps after the kind, may fear some from the practice of these, and the rather in that this curious or diligent multiplication of the minutes, needeth not in all or at all times, especially if the space of the two cities doth not contain many miles, or that the cities offered be but a little space distant one from the other. For where the distance is great, as of Viteberge & Frankforde, Noriberge and Room etc. The minutes then neglected, do cause great error. But if the space be small between the cities given, without the account also of the minutes (for that seldom in the only minutes, as are the near places together, do they only differ) the distance then by the only degrees & miles whole, cannot be found. But if any be minded not so curiously to search the distances of places, then let him or them omit the minutes depending aswell to the degrees of the longitudes and latitudes, as the miles, and according to the instruction of the third rule, the minutes being neglected or omitted, you shall then find without any difficulty the distance of places given. An Example. THe longitude of Franckeforde is of 25. degrees, the latitude is of 53. degrees. The longitude of Viteberge, is of 30. degrees, the latitude hath 51, degrees. The difference of the longitudes, is of 5. degrees. The difference of the latitudes, is 1. degree. The half of the difference of the latitudes in whole degrees is nothing, wherefore the middle latitude, is the like nothing. The miles assigned to the lesser latitude, as to the 51. degrees, are 9, multiply now these 9 miles with the difference of the longitudes, with 5. degrees, and the increase shall be 46. which multiplied in itself, do offer the first quadrate; that is, 2025. After multiply the difference of the latitudes, that is, one degree with 15. miles, which 15 miles multiplied again in itself, do produce or bring forth 225. which is the later quadrate. These two quadrates conjoin, and of the increase seek the root, which then declareth the distance between Franckforde and Viteberge, to be of German miles about 74. Another. THe longitude of Brunsweeke is of 28. degrees, the latitude of 52. degrees. The longitude of Viteberge is 30. degrees, the latitude of 51. degrees. The difference of the longitudes, is of 2. degrees. The difference of the latitudes, is 1. degree. The miles assigned to the lesser latitude, are 9 The difference of the longitude multiplied by 9 miles, doth produce 18. miles, which multiplied again in itself do produce 324. that is the first quadrate. The difference of the latitude, being one degree doth make & contain 15. miles, which also wrought again in themselves do offer the later quadrate, which containeth 225. Now of these two quadrates conjoined, the root is of 23. which number is almost the distance of Viteberge, in germane miles, from Brunsweeke. Another. THe longitude of Dansk hath 39 degrees, the latitude of 62. degrees. The longitude of Noriberge, hath 28. degrees, the latitude is of 49. degrees. The difference of the longitudes is of 11. degrees. The difference of the latitudes, is of 5. degrees. The middle latitude, is of 51. degrees. The miles answering to one degree in latitude, are 9 The difference of the longitudes, that is multiplied with the 9 doth yield 99 miles, which again multiplied in themselves, do produce the first quadrate which containeth 9801. The difference of the latitudes (being 5. degrees) multiplied by the 15. doth then produce 75. miles, which wrought again in themselves do offer the later quadrate which containeth 5625. The increase now of the two quadrates, comprehendeth 15426. The root containeth 124. And so many are the miles almost, between Dansk and Noriberge. Another. THe longitude of jerusalem hath 66. degrees, the latitude is of 31. degrees. The longitude of Nazareth hath 67. degrees, the latitude is of 32. degrees. The difference of the longitudes is 1. degree. The difference of the latitudes, is the like one degree. The miles assigned to 1. degree in the Parallel of the lesser latitude, are 12. The first quadrate doth contain 144. The miles answering to one degree of the difference of the latitude, are 15. The later quadrate, comprehendeth 225. The increase of the quadrates, containeth 369. The root containeth 16. miles. Now the distance in a manner is so much, between jerusalem and Nazareth. And thus by other examples, may young practisioners excercise, without labour, tediousness, and pain, to find the spaces of places given, by the degrees of the longitudes, and latitudes. A demonstration of the third rule. THe demonstration of this working or instruction, is taken out of the last proposition of the first book of Euclid, where he doth teach and demonstrate, that in the tryangle right cornered, the quadrate which by the line or side drawn and stretching to, maketh a right angle, that is equal in the two squares, which are caused by the sides containing the right angle. Which that you may easier conceive and understand, in the page going before is placed an apt figure to this matter, by which, a reason not only of the third, but also of the rules of the first & second may be practised and declared. Also there is repeated those things, which afore were declared of the Theoric of the longitudes and latitudes, that the younger practisers may the readier and easier conceive the rules hereafter taught. The line E. F. doth represent the Equinoctial on earth, lying under the celestial Equinoctial circle. The line B. C. doth represent the Parallel; that is, the circle equ●ich ●unt to the Equinoctial circle, drawn over the head or Zenith of the city C. The line A. D. doth represent the Parallel, yea equidistant to that Equinoctial, drawn by the Zenith of the cities, A. and D. The line A. B. E. doth represent the meridian, of the proper city or place A. The line D. CF. doth represent the meridian, of the cities C. and D. The declaration of the first rule. THe two Cities C. and D. agree in longitude, in that they are under one meridian; that is, they be distant by like spaces from the West. But they have not alike latitude, for that the City C. is nearer to the Equinoctial than the City D. by three degrees. To have therefore the distance, or that space between, you shall easily find the same by the degrees of the meridian. The declaration of the second rule. THe two Cities A. and D. agree in the latitude, or they have one like elevation of the Pole, in that they are under one Parallel, and the Zenith of both is by five degrees distant from the Equinoctial. But the longitude of them is not alike; that is, they be not equally distant from the West: for the city A. is more Westerly than the city D. by four degrees. So that the distance is to be gathered and learned by those degrees between, in that Parallel. The declaration of the third rule. THe two Cities A. an● ●. be distant by unlike spaces, aswell from the 〈◊〉 from the Equinoctial. For they be under divers meridians and Parallels. The city A. is nearer to the West than the city C. by four degrees, and it is further distant from the Equinoctial than C, by three degrees. Wherefore by those degrees in which it is nearer to the West and furthest distant from the Equinoctial, must the distance of the two cities A. and C. be sought. For that the space between the meridian A. B. passing by the Zenith of the City A. and meridiane C. D. stretching by the Zenith of the city C. containeth four degrees: yet those degrees are not in the great circle, in that those two Parallels do not divide the earth into two just halves, but into unequal halves: so that of necessity it must follow, that the degrees of divers Parallels have unequal spaces. Wherefore in the third rule are not the miles answering to the degrees of the lesser elevation taken, except the difference of the latitudes be small: nor the miles taken, answering to the degrees of the greater elevation: but the miles are taken answering to the degrees of the middle latitude: for that it lacketh in one part, may be restored in the other. Of the same may the distance in miles be sought, according to the longitude. After this, in that the space between the Parallel A. C. passing by the Zenith of the city A. and the parallel B. C. reaching by the zenith of the city C. containeth three degrees, and these are the degrees of the meridian; that is, of the great Circle, where to one degree do always and every where fifteen German miles answer. So that the distance of those Cities are easily found, according to their latitude. And in the same by that multiplication of the miles and degrees, the adding of the product, by the increase and extraction of the root, that the distance of the Cities may necessarily and surely be gathered, is thus demonstrated. That in every tryangle right cornered, the square which is made by the side, is drawn against a right angle, and is equal to the two squares which are made by the sides containing a right angle. As the quadrate which is made by the drawing of the line A. C. into itself, that is equal to the squares, which are caused by the drawing of the line A. B. into itself, and B. C. into itself: which by Arithmetical practice may more readier and better be understood of young students and practisioners in this manner. First the side A. B. containeth three spaces, which multiplied, do bring forthus. The line B. C. comprehendeth 4. distances, which multiplied, do produce or bring for 16. which two squares conjoined, do make 25: & the square which proceedeth of the 5. multiplied (which the line A. C. containeth) do they equate. Even so in the instruction of finding the distances of places according to the third rule, the difference of the longitudes is represented by the line B. C. but the difference of the latitudes by the line A. B. Therefore as by the quantities known of the lines A. B. and B C. is the quantity of the line A C. attained. Also by the differences of the longitudes and the latitudes of places known, and those afore taught being multiplied and increased, the distance of them is easily known, which by the line A C. is represented. And in the Triangle and quadrate, is the side (but in the number) named the root. These hitherto, for the knowledge of finding the distances of places shall suffice. The definition, appellations, division, and offices or utilities of the Horizont. THe Horizont called the ender and Circle of the half Sphere, is the edge between the light part, that standeth for the same we see, and the dark half that we cannot see of the sky. The Horizont (as Proclus writeth) is a greater circle, immovable or fixed, not one and the same every where, but to each place proper from the verticiall point, and round about equally distant, and dividing the whole sphere of the world into two equal half spheres; of which, the one half appeareth in sight to us, and the other half hid under the earth. The description of the Horizont doth Macrobius teach; where he writeth, that the Horizont is after two conditions: the one, extendeth on every side unto the firmament and serveth peculiarly as it were for the division of heaven, in dividing justly the sky into two halves: of which the one appeareth in sight to us above the proper Horizont and the other hid under that Horizont from us. Which Horizont hath his name of the sky, and of the same called the celestial Horizont: whose diameter (after Macrobius) is as large as the diameter of the eight sphere, which (as he affirmeth) is the furthest and highest part of the sky, that men can readily see and discern with the eye. But the earthly Horizont, in that the same serveth for the sights only of the earth and water, and not stretching unto the firmament; nor that his half diameter (as Macrobius writeth) doth exceed 180. furlongs, which containeth 22. miles, and ½. So that the whole diameter after his account, is but 45. miles in length. Which if any man stand upon an even or plain ground (or else on the sea) may see round about him 22. miles & a half every ways. Which round compass of the whole Horizont (after Macrobius) doth contain 141. miles, and 3/7. parts. A comparison, that as the meridian is an immovable circle, even so is the Horizone: for if the same were movable, it would not cross the meridian at right angles: and unto these should be imagined, that if it were movable, in each day the same would move with the meridian circle. The appellations and divers names of the Horizont. 1 THis circle is called the Horizon, as it were the circle dividing the half spheres, or of the greek word Orizomai, which in English signifieth to define, determine, and set out, in that the same defineth the part of the world seen. Or of Oros or Orion, that is the bound or ender. 2 It is named also the girdle, or the circle of rising. 3 Macrobius calleth the Horizone that bound of heaven that is seen above the earth (lib. 1. cap. 15.) In that it is the end or bound separating the neither half Sphere from the upper. And of him also called the edge of the half sphere. And Alfragnus called it the circle of the half sphere. 4 The Horizone also is so defined of his office, in that his office is to divide that part of the world in sight, from that hid under the earth. Whereof it is not unworthily called the ender, seeing it permitteth nor suffereth any to see but the half sphere at one time, and therefore is called of some, the circle of the half sphere, as afore taught. This circle is always understood to be described by the verticiall point, in that as the vertical point is changed, even so likewise is the Horizone. The Horizone is divided after two sorts; first into a right and thwart: secondly, into a sensible and rational Horizone. The Horizone of the right sphere is called right or right cornered, above which neither of the Poles of the world is elevated, which they have whose Zenith is under the Equinoctial, or dwell under the Equinoctial. Their Horizone is the circle drawn by the Poles of the world, which divideth aswell the meridian as the Equatoure at right angle, through which rightness it obtaineth that name, that it is called the right Horizone. The sensible Horizone is a space of the earth defined by a compass round about, which the sight of the eye attaineth and comprehendeth in a plain and even field. Or thus, the sensible Horizone is that which the eye ●●●fectly seeth, and describeth according to the ●ounde of ●ight, and called of some the artificial Horizon, and that foe, the s●●● cause, that which is contained by sight, is by a certain similitude agreeing with the artificial day. And as the artificial day is so named, for that artificers do especially work in it, even so the like is the horizone named artificial, in that towers, foretresses, and castles in time past, were built like the horizone. The diameter of this horizone (after Macrobius) which nearer agreeth to a truth (than either Proclus or Albertus) as afore was taught, is of 36. furlongs, to which almost four German miles answer, and 22. English miles: and so far on a plain and even ground not hindered by hills or thick mists, may a man fully see. And in the same space the embossed rounds of the earth, being without hills, is increased, and groweth to 250. feel, or 125. cubits: so that this horizone is not suddenly changed, nor in a short space. Therefore of necessity must ensue, that those which are distant by a lesser space than 360. furlongs, to see always some part of the earth common to both. But those which are distant by many spaces, do comprehend divers compasses by sight of the eye and divers horizones. The rational horizone is that which afore was described, that the same is a greater circle, lying by the edge of the earth, and reaching round about unto the sky, and dividing the celestial Orbs into two equal half Spheres, as the one half in sight, and the other hid to us. Although the plain upper face of the horizone passeth not by the centre of the earth, yet by the edge of the same, through which we see and observe the celestial bodies, that rise above and set under it: so that they evidently show, that the same divideth heaven into two equal half spheres, as above remembered. For in every moment, do six signs of the Zodiac appear above the earth, as in the night to the eye may be numbered and noted, that six signs set under the earth, and be gone out of sight. This is also called rational, seeing the eye cannot discern unto the highest heaven, nor aptly frame this division of heaven into two equal halves: yet the mind by examining, gathereth and concludeth, as by a perseverance passing before, and in the showing of the stars that rise and set, and in considering the tarriances of them in either half sphere. This beside is called the artificial horizone, in that by the benefit of the astronomical art, it was invented. Or thus not much agreeing to the former, the rational horizone (which of some is named natural) and according to the mind of Ptolemy, Cleomedes, and Proclus, belongeth unto the Sphere of the fixed stars, and reacheth even unto the same Sphere, and divideth heaven into equal half Spheres, the one half appearing above the same circle, and the other half not appearing, hid under it. Such a manner of imagining is not in vain, nor without cause determined and devised, seeing that men in the night and in a clear season, standing on an even ground, may see stars arise unto sight in the East, which a little before appeared not to the sight: and those after drawn by the first mover unto the West horizone, that began to go down be set, and do not after appear. By which they concluded that there is a circle in heaven, dividing and ending matters in sight from those not seen. So that they nothing doubted to call this circle the rational horizon (which together with the upper face by the centre of the earth stretched round about unto heaven) and by the four quarters of the world, as East, West, North, and South, divided things seen, from those not seen. And a great help it giveth unto this imagination that the earth is perfect round and embossed, in that of a Globe through his embossing can be seen but the half at a time. This also yieldeth a help to reason, by the appearances in the celestial bodies, although our sight cannot attain unto the starry sky, nor fully discern heaven, although a man earnestly look up and behold it: yet do we see stars, whose light extend unto our eye. As by this example may evidently appear, of that royal star named the heart of the Lion, which in our time is in the 22. degree almost of Leo. And the star standing on the left buttock of Aquarius in the 22. degree almost of the same signe● that is diametraly or right against one the other situated. Which do on this wise, that as the one appeareth above the horizone, the other is hidden under it, et e contra. So that as the one riseth, the other setteth, and on this manner do they continually. Of which reason it is concluded, that a certain circle divideth heaven into two equal halves, and do part (as afore taught) the things seen, from those not seen. Although the tarriance be but small, in that this star appeareth a very small while above the earth, through the same, that this star of Aquarius is Southerly from the ecclipticke line, it greatly forceth not. The like examples may be applied of the superior planets, when they be situated or appear opposite in heaven, as they also may be evidently seen, in the opposition of the sun and moon, when they be seen near to the East and West horizone, and where the moon is near the sun's way. The diameter of the rational horizone, although the same cannot be found nor comprehended, through his exceeding distance by exterior sense and judgement: yet reason itself judgeth, that the same may extend unto the starry sky, whose sight from that not seen it doth describe and the same is of 32655932. German miles, and 20. minutes, which distance by the outward senses, is judged as infinite. The Pole of the rational horizon, is the vertical point. for it is distant by a quarter of the greatest circle, that is, 90. degrees, from the compass round about of the horizon, yet not to all places serveth one horizon, for that as a man changeth place and country, even so ariseth a new horizon, whether so ever he travaileth. And new horizons also appear and happen, if a man either travail toward either of the poles of the world, or in right line toward the East and West, and the like unto divers quarters, as into the North, the East, or West, or contrariwise journeying by the opposite course, the Horizones vary and change. And if the places be either situated partly toward the East or West, and partly toward the South or North, the horizones there decline and vary them partly toward the East or West, and partly toward the south or North: which happeneth, by reason that the City is not under one Parallel. And Cities or countries situated under one meridianes do vary their horizons directly; either toward the South or North. There be as many horizons, as there be meridians. And for so much as that of all places cannot be one manner of Zenith, therefore cannot one Meridiane serve for all places. And seeing the Pole of the Horizone is the Zenith of it, which is in the Meridiane, and that to each place belongeth a proper Zenith, and a proper Meridian, it followeth that to each place belongeth a proper Horizone. Toward the Poles by the changing of places are the horizons changed, and the divers elevations of the Pole by a certain occasion caused: also they evidently declare a like alteration to be caused in the respect of the opposite quarters of the East and West, and do procure and cause divers beginnings of the days and nights, insomuch that the stars generally appearing and seen, do by order of times and in sundry places, arise and set in the West and hide them under the Horizon. For the same manner of Eclipse, which is seen at Arbela (after Pliny) in the fift hour of the night, to them of Carthage it appeareth in the second hour: so that the sun sooner setteth to them of Arbela by three hours, then to them of Carthage. Therefore the horizon of Arbela is much further distant into the East than the horizon of Carthage. The same rational horizon (as it were on the plainness of the earth) drawn and streached unto the sky, doth the meridian extend to it downward, and divide the same into two half circles: of which the one declineth unto the East, and thereof called the East quarter, and the other unto the West, and of that named the West quarter. And the divers places of the suns rising and setting, do sundry wise divide either half circle. For the Equinoctial rising, and the Equinoctial setting, (which are points of the horizon, that the sun in the equatoure placed, by rising and setting passeth) do part and divide either half circle into equal quarters. And with these points do the Poles of the meridian join. And either quarters do the other two (as the rising and setting) divide into two unequal arks. For of the two Northerly quarters, the same which tendeth and looketh unto the East, is the solsticial rising, and the other the solsticiall setting. But of the two Southerly, the Easterly doth the winter rising divide, and the Westerly doth the winter setting part. But by what space these rise and settings may differ and be distant from the former middle in every horizon, and in the largeness of rising doth Ptolemy instruct in that elevation of 40. degrees, and fifteen scruples. Of the shadows which the sun arising and setting in these points of the horizon causeth, is worthy to be considered and noted, in that the Equinoctial shadows (which through the suns rising and setting in the Equinoctial points are caused) do fall and extend in strait manner. But the other shadows not in the same condition or not in strait line do fall, but that the solsticiall shadows in the rising, with the winter shadows in the setting, and contrariwise the winter shadows in the rising, with the Solsticiall in the setting do form and make right shadows. The offices or utilities of the Horizon. 1 THis circle (like as all the others) so that nothing in heaven is frivolous and of a vain imagination hath many utilities. First it divideth the whole heaven into two equal half spheres. 2 It declareth which stars be of continual appearance, and which continually hid under the horizon: which do set, and which do arise above the horizon. So that it appeareth, that the stars consist in a triple defference, as that certain do arise and set, certain never appear above the horizone, and certain continue and be always above the horizon. 3 The horizon therefore is caused of the habitude, as well of the right, as the thwart sphere. 4 The rising and setting of the stars are applied unto the horizon, by which settings and rise, the descriptions of times are changed, and it also declareth the degree of the Zodiac, with the which each star riseth and setteth. 5 The horizone showeth the rising and setting of the signs of the Zodiac, the exaltations, or elevations of the pole and the equatoure, the latitudes of places, to the largeness of rising, which is the ark of the horizon to the stars or points of the ecclipticke and equatour, arising together, included with the beginnings of the twelve houses of heaven. 6 By the office of the horizone, at any time we may learn and know the quantity of the artificial day and night: and likewise procureth or showeth the just cause of the inequality of the artificial days, it doth also declare the rising and setting of the sun. For as the horizons, according to the elevation or depression of the pole, are varied: even so are the verticiall days in themselves caused unequal, yea in those points of the Zodiac. 7 By the benefit of the horizon (the sun shining) we attain and come each day unto the knowledge of the unequal hour of the day. 8 It showeth to us the elongation of the stars from the rising and setting, which the astronomers call the largeness of the rising and setting, or the Zenith of the rising and setting. 9 By this circle we learn how much the rising aswell of the stars, as the other points of heaven, is distant from the true and the Equinoctial rising: that is, in the same are the latitudes of the stars accounted from the equinoctial, and also their rise and settings. 10 It manifesteth the degree of the Zodiac, with the which the purposed star riseth and setteth. 11 It iudicateth the stars, or the celestial images that be continually in sight, or always hid. 12 It maketh manifest the rise and settings of the signs of the Zodiac. It doth likewise make distinction, between the Sun and Moons Eclipses, seen as well above the horizon, as not in sight. 13 It helpeth and furthereth much unto the finding of the latitude of a purposed place, whereof (through the benefit of this circle and the meridian) may the distances of places be certainly found. Of the vertical Circles. BEsides the former circles at large mentioned, are there other circles which shall here be uttered and taught, as in an apt place agreeing to that aforesaid, which be● these: the vertical circles; the circles of the positions, and of the 12. houses. Of these in order shall here be written (as the necessary matter offereth) seeing a special part of astronomy dependeth of them, and the whole composition of the celestial instruments seemeth likewise one of them. First the verticals, be circles which from the top of any place given, are drawn unto each part of the horizon, and divide the upper half Sphere in sight into so many parts, as the Horizone is divided; and all concur and meet above in each vertical point or Pole of the Horizon. To the number of these, is the meridian adjoined. These circles, are likewise understood and noted immovable, as the meridian and Horizone; that is, they are not drawn about with the first mover, as the Zodiac, the Equatoure, the Colours, and the other circles infixed to the first mover. The Circles of the Altitude. THe Circles of the altitudes be● those, which are equidistantly described about the top of places. As the vertical circles do divide each of these circles into 360. degrees, even so do these divide a quarter of each vertical circle into 90. degrees. So that none of the altitude circles is greater than the horizone, nor lesser than that which is imagined and understood to be described about the verticiall point. The especial office of these circles is, that aswell the altitudes of the fixed stars as the Planets, may be measured and known, as the fixed stars above the horizone: by which altitude or elevation, the times; that is, the hours are known, and the places of the stars, as may appear in tables made for that only purpose. Seeing then it cannot be (and that through the roundness of heaven) but that any star given or supposed unto the motion of the whole, is imagined by his altitude to be distinguished in some Parallel: therefore is the altitude of the star or of any other celestial point, the ark of the verticiall circle, drawn by the Centre of the star, contained between the horizon and the star given, which (as afore written) is distinguished of the said parallel. The meeting and joining together of these circles with the verticals, is not moved, but at the motion of the vertical point; which is none other, than the pole of the horizon, from which all the parallels of the altitudes, are imagined to be described by equal distances. But this (in mine opinion) is not to be overpassed; that is, that any star, when it shall be equally distant from the meridian, either hath or may have the same altitude from the horizon, as to the eye is offered in this figure following. Where a b d c. is the Meridian: b e c. the greatest half of the Parallels of the horizon: f g. the least: b. the North, and c. the South: a. the point of the top: o. or q. the place of the star given, by which a o k. or a q n, the vertical Circle passeth, and the like doth the Parallel p l k. The Ark k o. or n q. is affirmed to be the altitude or elevation of the star from the horizon, that endeth at the parallel p oh l r. and p o. is the distance of the star from the noonestead a p d c. Now when the star (by the motion of the principal) is drawn unto the point q. in which when the same shall be, it will be equally distant from the Meridian Circle: wherefore through the equal distance of the parallels, of which they be named, shall the Ark oh k. be equal to the Ark n q. Of this proceedeth and is caused that in the hours equidistant from the noonestead, as is the seventh hour before noon, and the fift hour after noon: likewise the eight and the fourth, the ninth and the third, the tenth and second, and so of the rest. The sun obtaineth equal elevations above the horizon. This much availeth in the composition or making of dials, and giveth great light and brevity to the same practice, as may appear elsewhere: but the vertical Circles in the soiled Spheres and Globes, by one quarter of the Circle, depending of the vertical point unto the horizon (divided into 90. degrees) is declared. The hour Circles. IN that the whole work of dials dependeth upon the knowledge of the hour circles; it is therefore requisite and necessary to entreat fully of the circles distinguishers of the hours, or at the least utter a brief instruction of this. First you shall understand, that the Equatoure only, which (as afore taught) the sun being either in the beginning of Aries or Libra, is regularly moved, aswell in the right, as thwart Horizone; and thereof is always the one half above the horizon, & the other half hid under the Horizon. Through this his equal motion or regulare motions, is it judged worthy and laudable: seeing by it the equal hours (as well by day as night) are attained and had. And this conceive, that there are twelve greater circles understood, which cross the Equatoure at right angles, and pass by both the poles of the first mover, from which the said equatour, is distinguished into 24. equal parts, which are called the distances or spaces of the hours, in that each be distant from other by 15. degrees. For they divide the vertical, the Zodiac, and the horizone into 24. parts, but unequally: at which Poles the nearer parts to them are narrower than those which be and draw nearer to the equatour. And that these may clearer and perfecter be understood, imagine yourself to be under the equatoure; that is, in the right Sphere: in such a standing shall the half meridian Circle be the line of the twelve hour, and the half horizontal circle, the line of the sixth hour before noon: and the other half of it, the line of the sixth hour at after noon. By which imagination firmly conceived, may a man imagine between the half horizontal circle, and the half meridian circle, to be other five half circles firm and immovable, which are not moved but as the vertical point is moved, being distant each from other by an equal distance, as by 15. degrees of the equatour. The first after the horizon, is applied to the seventh hour, & so forth of the rest. And in like manner between the meridian half circle, and the occidental horizone are other five circles understood (according to the former division) and that which followeth the meridian, shall be applied to the first hour, that which next followeth to the second hour, and so forth of the others. Besides, imagine the sun to ascend from the horizon, and when he shall be come unto the first half circle from the horizon, then shall he shed a shadow furthest westward, and being drawn up unto the second, shall make a shorter shadow, and the shadow shall always (until the sun be come unto the half noonestéede circle, where he sheddeth or sendeth a shadow) plum down right to the earth: but descending from the Noonstéede unto the West, the Sun causeth then the like shadows contrary. Further conceive, that the Exetrée of the world, in whose poles (as is afore taught) all the hour circles meet together in one, doth perform & express the same, which the foresaid circles taught: as by the sun dials the like is readily understood and known. The Circles dividing the twelve houses of Heaven. NOw resteth to entreat of the circles distinguishers of the houses, and the circle of the positions: but first I will write of the distinguishers of the houses. As there are six circles that are imagined of the astronomers, by which heaven is divided into twelve parts; among which are the Horizone and meridian, whereby the whole is divided into four equal parts: and those twelve parts, are (of the astronomers) called mansions or houses. But as touching the constitution and forming of the celestial houses, there are sundry old and late opinions, but whether opinion is the worthier, or to be the rather allowed, is not here mente to be stood upon, nor aptly belongeth to the matter I entreat of, so well as in the proper place is agreeing: yet certain, and especially the ancient, which were Campanus, a singular mathematician and astronmer, divided the houses by the five circles of heaven, meeting an● joining at the Poles of the world; from which they divided the whole heaven (together with the meridian) into twelve equal houses. But for a better and readier instruction, they form and drew them in this manner. After the four principal quarters or angles of heaven were drawn, and that the right ascension of the middle of heaven was had, then were the parts of the Zodiac diligently considered (that occupy as well the Easterly as the Westerly Horizone) and then were the right ascensions sought of those parts: which being done, the constitution and making of the two houses in the Easterly part of heaven, was the right ascension of the mid heaven, deducted from the right ascension of the Horizone: and the remayner, was distributed into three equal parts. In the bound of the first part (in accounting from the Noonstéed toward the East) was there imagined a circle for the beginning of the eleventh house: but in the bound of the second part (from the Noonestéede) was the beginning of the twelve house placed. After in the bound of the third part, from the Noonstéed, was the beginning of the first house drawn: and the like was wrought and done in searching for the 2. Westerly houses, as the ninth and the eight house. For they deducted and subtracted the right ascension of the west part, from the right ascension of the mid heaven or noonestead, and the remainder or rest (as afore taught) was distributed into three equal parts. After that in the end of the first portion (from the noonstead towards the West) the ancients constituted or placed the bound of the ninth house, with the circle coming from the poles of the world: and in the bound of the second portion, was the beginning of the eight house form. These attained, the degrees and parts of the degrees of the Zodiac answering to each arks of the Equatoure, were sought in the Tables of the right sphere: but the houses standing under, were defined and made like to their opposites. And seeing this manner of forming the houses is unperfect, therefore shall here no further be taught of the same. In which a e. is the vertical circle, crossing a d e c. at right angles: f g b. the equatour: d g c. the horizon, d. and c. be the points in which the distinguishers of the houses concur and meet; which also do make equal distinctions in the vertical circle, and thereby be the houses noted and divided. But the later Astronomers, moved by the authority of the incomparable Mathematician Regiomontanus, inurnted and devised another order of the houses, more agreeing to reason than the former. For they divided the quarters of the equatour, comprehended between the horizon and noonstead, into three equal spaces, and by each section they imagined great circles, joining in the sections of the Meridian and horizon, as the former, Although all these are plainer and more evidently taught and known in the material Sphere, yet we thought good to speak somewhat (as our possibility serveth) in plain form. Wherefore grant that a f c. is the Meridian, a. the Top, n. the Northerly pole: k. the Southerly pole, b. and c. the points of the sections of the horizon and Meridian, where the distinguishers of the houses concur and meet, which also are imagined by the equal distinctions of the equatour e i l. as to the eye sufficiently appeareth, that b i c. is the horizon circle, d. the easterly point or rising of the equatour, from which the first house taketh his beginning. The Circle of position. ALL these Circles being set down, the Astronomers notwithstanding do write of another Circle, whose use and office serveth to great purpose, for the Art of directing & searching other more secret matters in Astronomy, and is thereof called the circle of Position, which passeth at all times by the former sections of the meridian and Horizone, and by the Centre of the star, or of any other purposed point in heaven, like to the soresaid circles, whether that star be above the earth, or under the earth. That this may clearly appear, mark and consider this figure here expressed, where the letter c. representeth the top point, d. the Northerly Pole, e. the opposite pole, a g b f. the circle of the position passing by the sections of the horizon and meridian, b c d e. the meridian a b. the Horizone, g f. the Centres of the stars (of which the one is in g. above the earth, and the other under the earth in the point f.) And many other circles besides all these, which hitherto have been described, may be invented and imagined in the sphere, for the necessity of the workings. The difinitions, names, and offices of the four lesser Circles. THe Parallels are lesser circles, which from either of the greater circles drawn thwartly on the sphere, do equally difand be distant from the Equatoure or Zodiac toward their poles: so that they do not divide the Sphere into equal half Spheres, but into unequal portions. For seeing the sphere from the middle streacheth or draweth by little and little straighter and narrower toward the furthest and highest tops: even so must the parallels which are distant from the middle and greatest, and that by equal spaces on each side agreeing, draw of necessity narrower, and so much the narrow, as they nearer approach unto the poles. As writeth Theodosius in the sixth proposition of his first Book of the sphere. And the same Author in the 14. proposition of his first Book of the sphere, and in the sixth, of his second Book writeth, that all the parallels have the same poles agreeing with the greater circles unto which the parallels are. And certain of the Parallels are applied unto the plain of the Equatoure, others unto the plain of the eccliptick. These do as well the fixed stars, as the planets placed without the ecclipticke, and drawn about the Exetrée stretched b● the poles of the ecclipticke and Centre of the world describe: yet do all their centres consist in the Exetrée of the Zodiac, and the middle circle of them, and the greatest is the ecclipticke. These also do the same stars, and the verticiall or top points of each places, or any other applied unto the plain of the equatour, drawn as it were by the first mover about the Exetrée and poles of the world define. And the Centres of these be in the Exetrée of the world or equatoure, but the middle and greatest of these, is the equatour. It is manifest by that afore taught, that the sun in every day doth gain toward the East (against the daily motion) one degree of the Zodiac: and of this happeneth, that he in each day through the thwartness of the Zodiac describeth a certain new circle in heaven, and in the next day another, and so forth by order, as the like may be compared by a small cord, wound close about a Nun or top, beginning from the foot upward, even so the sun beginning to turn again at the first degree of Capricorn, doth every day after change a new Parallel, until he become back unto the first degree of Cancer, and by and by after returned from Cancer, he in the like order goeth unto the Capricorn: so that in the next day following, the Sun riseth not with the same Parallel above the Horizone that he did in the morning before, nor shall not run the next morrow in that Parallel that he did in this day. And each of these Parallels (even as the greater circles) contain 360. degrees, which be so much lesser, than the degrees of the greater circles, and occupy or comprehend somuch the lesser space in heaven, as answereth to the upper face of the earth, as by how much the more from the compass and largeness of the greatest circle they lack, by reason of the distance. And although they yield and be less in the quantity, yet unto the degrees of the greatest circles be they agreeable and like, as (writeth Theodosius) in the 14. proposition of his second book of the sphere. These lesser circles, do offer and teach sundry utilities. First the Parallels, of which on this side and beyond the Equatour, are 182, that the sun yearly by his daily motion describeth: and do express the causes of the continual equality of the days in the right Sphere, and of the unequalness in the thwart or bowing sphere, and where the day spaces are increased and lengthened, there the night spaces be lessened and decreased: and being otherwise they show the contrary. In the second, the Parallels (which the verticial points form) when they express the bounds of the latitudes of places, then are they standing under, by which their longitudes or distances from the West are accounted. In the third, the Parallels (which either the Planets or the fixed stars describe) referred unto the Equatour, do express the bounds of their drawings or motions from the equatour. The others or rest, which applied unto the ecclipticke described, do show the bounds of the latitudes▪ and that for how long time they tarry above the earth, or otherwise hid within the earth, and under the Horizone, doth either show. In the fourth, the greatest and chiefest utilities of the Parallels are, that which on the habitable earth the practisioners sever by such distances, as by how much the greatest artificial days are by a quarter of an hour longer increased and extended. For they distinguish the habitable earth (and that by observation) into certain necessary spaces, and do judicate the regular increasings of the days, and what is common to each dwelling under those parallels, in as much as the quantities, the increasings and deminishing of the days and nights, the rise and settings of the stars, the Noonstéede shadows, and the nature of the Winter and Summer but those which are contrary, as that there is a difference & diversity of the dwelling places being under divers Parallels, they indeed be necessary unto the distribution and description of the climate. Although the number of these circles be so infinite, as is the infinite variety of the stars and vertical points: yet are there four usually rehearsed in these Elements or introduction, that be especially noted and described by peculiar names: and for the same cause (as seemeth to me) in that they divide the whole Globe of heaven and earth into five Zones, and these applied unto the plain or flat of the equatour. The tropic of Cancer, or summer tropic. The tropic of Capricorn, or winter tropic. The arctic or Northerly Pole. The antarctic, or Southerly Pole. Which Circles are called the tropics. THe Sun (according to the former words) through the motion of the first mover is in 24 hours, drawn once about: and for that he is carried in the thwart Circle, and in the same by his proper motion changes daily unto other places of the Zodiac, it must needs ensue, that he describeth in each day a new parallel. And those doth the sun repeat in the parts of the Zodiac, which be equidistant from the solsticiall points; in such wise, that they be in the whole 182. circles. And these do they call the circles of the natural days, of which the uttermost and furthest that include the sun's way, are named the Tropics, which is (in English) the sun bounds, in that the sun never passeth them, neither toward the North nor toward the South: but after his touching of each, he returneth again. The one of these called the tropic of Cancer, and the other the tropic of Capricorn. Why these are called the tropics. THey are named the Tropics, of the Greek word Tropikoi, which is in English, the turnings again; in that when the Sun is digressed from the Equatoure and come unto those, he turneth back again. Also the Tropic circles touch the Zodiac, at the beginnings of Cancer and Capricorn, of which the one is called the Tropic of Cancer, and the other of Capricorn, the one being Northerly, and the other Southerly. And as to our dwelling, the one is called the summer Circle, and the other the Winter. So that when the sun toucheth any of these, he turneth again, and is carried toward the other. As by this example further appeareth, where all that season and time (from the twelfth day of December unto the eleventh day of june) a man may perceive the Sun every day arising higher and higher: and when he is at the highest over our heads, that day doth he by his course describe the summer Tropic: from which again turning, the sun every day after draweth lower and lower from our vertical point, until he be come again unto the lowest. In which twelve day of December (not going any further toward the South, but being come unto the beginning of Capricorn) he describeth the winter Tropic. The Tropic of Cancer is a lesser Circle, which the sun describeth at the entering into the beginning thereof, and is drawn by the daily motion, whose plain or flat passeth not by the centre of the earth: and it is one of the natural Circles which is outermost, described of the sun toward the North, and drawn by the beginning of Cancer. And it hath also his name of the standing, in that the same is the bound of the suns journey or course toward the North, and the nighest coming unto us: unto which being brought, he turneth back, and directeth his course into the South; of which that place is called Trope. It is continually distant from the Equatour, by the quantity of the sun's greatest declination, which at this day is of 23. degrees, 28. minutes, and two fifts almost: and it encloseth also the sun's way, and doth beside, with the other 3. Parallels, divide the Zones of heaven and earth. Further, this is named the circle of the summer solstice, by the same reason, in that it is drawn by the point of the summer solstice. And the Northerly Tropic in that it is the Northerly part of the world. And the summer circle, for that the Sun in the summer falleth into this circle. Also this circle in all the Northerly tract is on this wise, that the greater part or portion is above the Horizone, and the lesser part (as to us) under the Horizon: so that the sun running in that circle, causeth the longest day of summer. And whiles the sun describeth these circles, the days be longer than the nights. For the longest day increaseth from minute to minute, from hour to hour, and from the latitude of one degree, unto the latitude of 66. degrees, and 30. minutes. In which the day artificial is of 24. hours, and is thereof called a whole day. For in the latitudes following, and beyond, he increaseth into many whole days. A like definition hath Proelus, where he writeth that the summer Tropic, is the furthest circle Northward that the sun describeth: into which when the sun is come, he than maketh his summer turn, and causeth also at that time the longest day and shortest night of the year: from which turning back, he goeth again toward the contrary coast of the world: so that of the same Proclus it is called a Tropic (which is in English) a returning circle. For it is evident to all men, that after the sun beginneth to turn, he may in short time after, or at the least within 5. days, but especially at Noon in every week, be well perceived to descend and go lower and lower, until he become unto the Tropic of Capricorn or the winter circle: where he turneth again, as you may plainly learn and understand by the former description of that circle. The Tropic of Capricorn is a lesser circle, and one of the natural circles, which is by the like space distant from the Equatoure into the South, and described of the sun in the beginning of Capricorn, as being uttermost toward the South (which is the bound of the sun's greatest departure from us, and of his longest digression unto the South) that he defineth and maketh. This circle also is called the winter Solstice, and winter Tropic; in that when the sun cometh into this circle, it is presently winter: that is, the shortest day of the year. Also the less●● portion of this circle is to us above the horizone, and the greater beneath or under the Horizon. Besides the sun's journey endeth at the south, and crosseth or divideth both the burning and temperate Southerly Zone. The Brumal or winter tropic (as writeth Proclus) that is furthest toward the South, of all those which the sun describeth by his drawing about of the first mover: into which when the sun falleth, he causeth his winterly return: so that the longest night of the year and shortest day, is at that time procured. From which he goeth no further toward the South, but returneth unto the contrary quarter of the world: and hereof this Circle is called a Tropic, or circle of return. Now these three are principally noted: the equatour, and the two tropics, for the course of the sun. That the instructions of the two Tropics afore spoken of, may more perfectly be understood, conceive this Figure here demonstrated: In which a h b e. is the meridian, a d b. the right Horizone d. the Centre of the principal a. the Northerly Pole, b. the Southerly Pole, g d c. the circle of the Zodiac, h d e. the Equatour, which here is meant to be abatingly described, when the sun shall be in the centre of the earth, or in the true section of the Equatoure and Zodiac, as in the letter d. from which point when the sun returns toward the Northerly pole a. under the circle g d c. he than describeth in each day by the motion of the first mover each Parallels, until he be come in the Meridiane unto the point g, from which he can not further ascend toward our Zenith in the meridian. Of which in the same day, the sun describeth g f. the parallel to the equatour, which is called the Tropic of Cancer, in that the sun beginneth from this place to approach or draw nearer to the Equatoure; unto which when the sun shall come, he than descendeth unto the neither half sphere, in the half circle d c. He being come again unto the point c, doth from his centre by the motion of the principal or first mover in the Poles of the world, describe the Parallel c i. that is, the tropic of Capricorn. The Polare circles, are two of the lesser circles near to the Poles of the world, being alike equal distant to the equatour which upon the Poles of the equatour described are drawn by the Poles of the Zodiac. And these are named the Polare Circles, in that they be near to the Poles: of which, that near to the Pole arctic, is called the arctic circle, of the greater or lesser Bear drawn in it, or for that this circle is described about the pole arctic: the other that is right against▪ is named the antarctic Circle, in that it is drawn about the Antarctic Pole. Or thus, the arctic is a lesser circle, which the Northerly pole of the Zodiac is so far distant from the Pole arctic of the world, as is the sun's greatest declination: or as Proclus writeth, that the fore foot of the greater Bear by the daily motion formeth. The same circle (after the mind of the learned) is distant from the equatour 66. degrees, and 30. minutes almost. To whom this altitude is higher by 23. degrees, and almost 29. minutes. To those parts of the earth is the pole arctic extaunt in sight, and continually appeareth. It also secludeth and parteth the untemperate Northerly Zone, from the next temperate Zone: where the Solsticiall Tropic is made the Northerly circle, and in that place under this altitude of the pole 66. degrees, and 31. minutes: there all the stars and images contained from the solsticiall Tropic unto the Pole are seen: as both the Bears, the Dragon, Cepheus, Cassiopia, Perseus, Auriga or the Carter, whole Boötes (except from the knees downward) the crown Hercules (except the head and right arm) the Harp, the Swan, the great Horse Andromeda (except the left Cubit) the half of the Northerly Fish almost, Deltoton, a part of the back of Taurus, the neck and Northerly Horn, a great part of Gemini, and the head and neck of Leo. And not unlike to the former, doth Proclus describe them: where he writeth, that the Northerly circle is the same, which of all those that to us continually be seen or appear, is for truth the greatest; and that also toucheth the Horizone at one only point, being wholly described above the earth. And the stars that are enclosed within this circle, do neither rise nor set, but are continually seen all the night drawn about the Pole. The South or antarctic circle, is thus defined of him, that the same is equal and equidistant to the Northerly or arctic circle, and toucheth the Horizon at one point. The whole of this circle is hidden under our Horizone, so that all the stars placed and drawn in it, abide ever out of sight to us. The like description that the antarctic Parallel is a lesser Circle, which the Southerly Pole of the Zodiac draweth about as it were by the daily motion, doth describe about the Southerly top of the world, and is by a like space distant from the Equatoure and the antarctic pole of the world, as the arctic is from his opposite. And doth separate or divide the untemperate Southerly Zone from the next temperate Zone. Further it is manifest, that the distance of the Poles of the ecclipticke from the poles of the world, do agree with the greatest bowing or declination of the ecclipticke or the sun: In that the poles from their circles, be always distant a quarter of the circle, and the colour of the solstices, is here taken for that which comprehendeth either Pole. And when the quarters standing between the poles, and the circles of the poles, be in themselves, or between one the other equal, as the ark of the same circle, than the middle ark common to both, which (as exempted) goeth between the poles of the world and the ecclipticke, and so parteth and leaveth them equal. For the one half of the other equal arks, is from the poles of the ecclipticke unto the poles of the world, and the other, is from the furthest point of the ecclipticke unto the equatour. By which it appeareth, that so much is the distance of the poles of the Ecclipticke from the poles of the world, as is the sun's greatest declination, being 23. degrees, and 28. minutes, and two fifth almost. Or thus, that the pole of the Zodiac is far distant from the pole of the world, as is the greatest declination of the sun from the Equinoctial circle: and by the equidistance also on each side of the arctic circle from the Pole of the world, that that part of the Colour comprehended between the first point of Cancer and the arctic circle, is almost double so much unto the greatest declination of the sun. And if circumspectly you consider the manner of the motions, you shall readily perceive that those circles which ever more be of like largeness, increase and decrease together with the two Tropic circles, according to the increase or decrease of the sun's declination. As appeareth by the letter n. in the foresaid figure, that representeth the Northerly pole of the ecclipticke or Zodiac, moved from the letter n. into o. by the motion of the first mover, and returning again into the point n, shall be moved the circle describing n o. being distant from the Northerly pole a. as much as is the sun's greatest declination h g. as hereafter by demonstration shall plainer appear. And this circle named the arctic, in that it is described by the arctic of the Zodiac. The like is described from the point r. being the pole antarcticke, by the motion from r. unto s. and returning again unto r. so that the antarcticke circle r s. is equal to his opposite, and equidistaunt to the Equatoure. This probation, that the distance of the Poles of the world and Zodiac, is equal to the sun's greatest declination, doth require before hand, these three propositions. The first that the quarters of each circle any where taken be in themselves or between one another equal. The second, that the poles by a quarter; that is, by 90. degrees, be distant from their proper circle. The third, that the equals deducted from their equals, then do the equals rest. As for example, if you borrow two fourths in one and the same Colour circle, that is the Solsticiall of the same part, where it passeth by the beginning of Capricorn, and is the like from the pole of the world unto the Equinoctial, and that other, is that which is from the Pole of the Zodiac unto the Zodiac or ecclipticke: and of this I thus reason, that when the equals be deducted or abated from the equals, the remainder shall be equal. Therefore are the foresaid quarters equal, in that they be in the same circle, and that from either is the equal or common ark deducted; that is, the same which is contained between the Equinoctial and the pole of the Zodiac, which ark doth contain 66. degrees, and 31. minutes almost. So that the arks, resting or remaining of these quarters be equal; that is, the distance of the poles of the Zodiac, and the Equinoctial, is equal to the sun's greatest declination. For if 66. degrees, and 31. minutes be deducted from either quarter, the remainder then shallbe 23 degrees, and 31 minutes: which is the distance between the foresaid poles and the greatest declination of the sun. This other example demonstrateth, that the sun's greatest declination and the distance of the poles of the zodiac or ecclipticke from the poles of the world, is equal and of like largeness, and that what soever happeneth to the distances of the said Poles. For as this increaseth or decreaseth, the like doth that decrease or increase. Of this it is manifest, that the two foresaid arctic circles, is now in our time lesser through the decreasing of the sun's greatest declination, and that the tropics are greater than they were in Ptholomies' time. The offices or utilities of the four lesser Circles. 1 THe office of the Solsticiall Tropic: (after the Greeks) is to define the longest summer day: and the winter Tropic, to determine the shortest winter day and longest night. For Proclus to find the longest day, did divide the summer solstice into 8. equal parts: of which so divided, he affirmed three parts to be continually hid under the horizon, and five above. The truth of which is known, if the Sphere be rectified for the latitude of 41. degrees, where by this division the longest day containeth 15 hours and the night but 9 hours. 2 Many and notable offices do the Tropic circles offer, as well unto the composition of dials, as unto the preparing many other Instruments in Astronomy. 3 They declare the places of the Ecclipticke, in which the sun's solstices are caused: whereof the longest or shortest days by them are known. Or thus, they declare in every standing of the sphere, the longest and shortest day, with their quantity. 4 They include the Sun's way, in that they be as the bounds including the Region in heaven, in which the sun is continually moved. 5 They declare the sun's greatest declination, as afore hath been often taught. 6 They separate in heaven, the burning Zone, from the two temperate Zones. But of the Polare circles, these be the chiefest and especialest utilities. 1 They judicate or show the Poles▪ of the Zodiac, and how far they be distant from the Poles of the world. 2 They enclose those stars which ever appear above our Horizone, and those in like manner right against being always hid unto us. But for that every several Climate (hath disagreeing from other Climates these circles) their distance therefore cannot be certain from the other Parallel circles, saving for one Region certain, as neither their quantities, nor their order. For in that place, where the altitude of the pole is lesser than 66. degrees and a half, these circles there are lesser than the Tropics, and in order are between them and the poles, and is from the pole continually distant by so many degrees, as the pole in that country is raised above the Horizon. So that in the same place, the Pole raised more than 66. degrees and a half. The Tropic than is above the horizone, as the like may be understood by that place called Wardehouse. So that in the same Climate, the arctic circle is greater than the Tropic of Cancer, as witnesseth the learned Stoeflerus, justingensis. 3 They distinguish (after the mind of the Greeks) the cold Zones, from the temperate. Which Ferio denieth, affirming that the arctic and antarcticke circles, keeping no uniformity to all countries and being uncertain and variable bounds, can limit any certain place. For the temperate Zones are places certain, the arctic and antarcticke circles be changeable limits, therefore cannot they be as bounds of the temperate Zones: yet doth he better allow and agree unto that, that the tropics be bounds of the temperate zones. So that changeable limits (by this argument) cannot be appointed as bounds to unchangeable places. 4 They divide together with the Tropics, all heaven into five parts or Regions, which they call zones. The descriptions, names, qualities, and utilities of the Zones. THe four lesser circles called Parallels (that were afore described, do divide the whole heaven toward the Poles into five spaces: which that heaven might be compassed about with these larger swaths, the astronomers of the same called them Zones, or otherwise of the Latins Gerdils. The Cosmographers by the same imagination applied, do also dispose and distribute the whole Globe of the earth into five rooms or spaces, lying directly under, and agreeable in proportion to them in heaven. Wherefore a zone (after the mind of the Greeks) is a portion, tract, or space of heaven, or earth, between the two Parallels or lesser circles, being nighest equidistant, or contained between the room equidistaunt and Pole of the world, and girdeth or compasseth as it were the heaven or earth. Or thus, a zone is a space of earth like to the two Parallels or lesser circles above, which the astronomers imagine to run on the upper face of the sphere. And as the whole portion included by the two Tropics called the burning zone, doth compass heaven as a girdle: even so imagine the room of the earth, lying right under the Tropics. The zones have sundry names, for of the Greeks they be called zóne, and of the Latins by a borrowed word Zona, as may appear by julius Firmicus, Macrobius, Virgilius, ovid, and other Latins. That heaven or earth is imagined to be girded about with these. Martianus nameth them swaths, Tully and Macrobius nameth them by the like reason girdles. ovid nameth them plagues; that is, rooms or spaces. And how many zones they be, may easily appear, in that the astrologians, Geographers, Physicians and Poets, do divide as well the heaven as earth into siue rooms or spaces, by the four Parallels or lesser circles: of which there be two manner of zones: the celestial and the earthly. The celestial, are the cause of the earthly, in that the earthly lie directly under them. And of the zones, the celestial be they which the astronomers by imagination describe and distribute in the hollow of heaven: the earthly, be they which lie perpendicularly under. And both also be temperate, and untemperate zones. The celestial zones, in that they have nothing of the elementary qualities, therefore do they not by heat burn and scorch, nor by cold make stiff: nor cause a temperate mixture of qualities or temperateness, yet are they noted and discerned by the names of the qualities; as the earthly zones, which being the author of the sun, and fountain both of light and heat, and running continually in the middle zone of heaven is diversly felt, according to the manner of the distance. Or thus, there are no qualities formally attributed to the celestial zones, but to them only virtually, which is on this wise to be understood, as that the celestial zones of themselves be neither cold, hot, nor temperate, but are so called through the sun's declination from the equatour, as well into the North, as into the South quarter of the world: In the which declination, is the like matter felt, as well in the suns right sending down of beams, as in the thwart projection of them on the upper face of the earth, which diversly changeth the heat 〈◊〉. The scorching or untemperate middle Zone (which through the heat and burning beams, the sun there causeth, when he is over the head or in the Noonestéed place) is contained between the bounds of the suns journey which the two Tropics make, and includeth 47. degrees of heaven. For the two Tropics are on either side the equatoure, so that it useth the middle room in the burning zone, from which the sun toward the North and South, never declineth above 23. degrees, and 29. minutes. By which appeareth, that it is there as hot in the middle of winter, as it is in Spain in the middle of summer: and therefore not disagreeing to that which the ancient Cosmographers wrote, that the countries lying under this space, or rather under the equatour, is unhabited through the burning heat: and of them for this cause, named the burning or scorching zone. But of later years it is found contrary, in that at Molucca, Good-hope, Calicute, and Samatra, rich drugs, and other fine spices have been there gotten by the Spantards and Portugeses, and yéerly haunted by them, as at this day the same is thoroughly known to many: which also confess that the places under the Equinoctial, and the rich City Calecute, being by the sea coast of Ind, standing between the equatour and our Tropic of Cancer, and unto the other Tropic South under the Burning zone, that the places is habitable and peopled, although very cumbersome with extremity of heat. Also that space on earth containeth 685. German miles, or 23500. furlongs. Ptolemy and Avicen affirm, that the places between the equatour and summer Tropic is habitable, and that many Cities be there, although the sun in those places through his direct beams (and especially under the equatour) doth by the over much heat and continual heat, burn and mightily scorch. The like do sundry others affirm, which writ, that those places is convenient for the life of creatures, in that under the equatour there be many waters, which although resolved and run through the heat, yet do they breathe and send upward cold vapours, which the sun continually maintaineth in drawing up through his vehement heat, and sending down mighty showers of rain: which vapours in the night (through the sun's furthest distance under the earth, and especially at midnight) cause a mighty cold and chilling air: which the sun after his rising, until he be somewhat ascended above the earth cannot suddenly overcome and put away that cold impression of the air. So that the people there inhabiting, be monstrous of form, and have rude wits, wondrous wild and terrible conditions, like to wild and furious beasts. The countries which lie under the Southerly Parallels, as those which are described by the Equinoctial line, unto the summer Tropic, where the sun is drawn and runneth over the tops of them: there through the abundance of vapours, rain, and night cold, is the sun's heat repressed, mitigated, and dulled; so that the heads of the Ethiopians or Moors be little, having but little and withered brains, their bodies short, having thick crisped hair on their heads, gross and dull of senses, black scorched or burned bodies, withered or wrinkled faces, crooked of stature, being in a manner hot by nature, and cruel conditions, through the mightiness of heat in those places. And the constitution also of the air is there such, that all living and cresent things on that earth, are found and known to agree with them. Further it is to be noted and understood, that any there travailing from the Northerly places, the further they go toward the South, somuch the stronger heat or burning they shallbe annoyed with. The two temperate zones be next adjoining to the burning zone, the one on the Northerly, and the other on the Southerly side of it. And the beginnings of either be the hotter, the ends colder, the middle of them exquisitely temperate: in the other parts doth the heat either so much the more exceed, or the bitter cold overcometh and ruleth, as how much the nearer they approach or come unto the burning Zone, or otherwise unto either of the extreme Zones, which continually cause a bitter and an extreme cold. The cause of this diversity, is through the sun's beams, for the sun continually moving in the middle journey of heaven (described between the two Tropics) and digressing or going beyond the prefixed bounds of nature, doth not show his beams unto divers parts of the earth in one manner, but unto the places right under, and in the burning zone the tracts or countries contained under them, doth he send down right beams, which stretcheth to the upper face of the earth at right angles. And unto the countries of either temperate zone, doth the sun send down thwart or slope beams. And unto the places under either cold zone, doth he stretch long beams on the plain of the earth, even the like as being near to the Horizone, which neither reach unto the upper face of the earth, nor cause angles, but keep an equal distance unto it, do stretch forth infinitely. But those beams of the sun do neither give light, nor heat, but turn backward: in that the property of the reflection which of the beam against a solider resistance, prohibiting or letting the penetration, is a certain repercussion and reverberation) that increaseth and doubleth the force of the direct beam, and by the reflexed beam to it adjoined, or at the least by his virtue applied and communicated. Seeing this reflection is the especiallest cause of the heat and that the angles of the reflections falling do continually make or be equal in the angles: for that cause do they much unlike increase the force of the direct beams, and their effects do notably vary. So that in the burning zone, the reflection stretcheth unto right angles, seeing the strait or right beams are carried & led into themselves, in such sort that as direct and re●lexen, they meet and be mixed, and in this, doubling as it were the virtue and force of the direct beams, is on such wise increased, that it kindleth, burneth, and consumeth. And in either temperate zone, is the reflection caused at right angles in that the sun beams do thwartly reach to the upper face of the earth, and are turned and extended backward unto thwart angles, which how much the nearer and liker they be to the right, so much the nearer do they join either beams together: by which they proceed and come into the nearer parts of the burning zone. But so much the blunter as they stretch, so much the longer do they separate either beams, as how much the more they are extended unto the extreme or outmost bounds. And for this cause do they more heat than the fore parts of the temperate zone, whose heat is a little gentler or milder than the heat of the burning zone, and the beams a little further of: whose cold notwithstanding differeth somewhat from the extreme or outmost untemperate zones. And those which stretch and fall into the middle region of either temperate zone, do cause a mean between the right and very sharp angles, and yet not directly matched or joined, nor do they by so near a space communicate their virtue, as in the beginning of it▪ neither by so large a distance as in the end, but in the middle in a manner: So that they cause and increase a temperate heat in the same zone. But in the extreme or cold Zones, is no reflection of beams caused, for those beams equally distant from the earth are streached forth infinitely: and for that cause do those neither give light nor move or procure heat, neither do those zones at any time warm, either perfectly clear, or appear bright: but that they continually be foggy, misty, dark, and bitter or extreme cold, through the continual mists, which more and more increase, especially toward the northerly pole. And yet many affirm, a reasonable dwelling in those places, yea and under the Northerly pole, but far colder and bitterer dwelling, through the far being from the way of the sun, and beholding of the comfortabler stars. For the Sun through his over far distance, cannot by his presence above the earth comfort and heat. This now is the perfect cause of the divers and universal coustitutions of the air and chief qualities in each zones: so that of the particular constitutions be other causes. But to return unto the temperate Zones, the latitude of either temperate Zone is of 43. degrees almost, of German miles 645. and of furlongs 21500. So that the Boreallor Northerly zone beginning from the Tropic of Cancer, endeth at the arctic circle, or at the degree of latitude 66. and 31. minutes. And the Southerly from the Tropic of Capricorn, is extended or reacheth unto the antarcticke circle, or the degree of the Southerly latitude 66. and 32. minutes. The untemperate cold zones that reach from either temperate unto the poles of the world, do move continual cold and frosts. So that the beams of the sun, although they pierce and enter through, yet seeing they extend not backward, nor through the reflection or streaching backward be strengthened and sharpened, therefore can they not so heat, that by the thawing they dissolve the earth and ice, nor put away or void the mist. Now the untemperate Northerly zone, beginning from the 66. degree and 31. minutes of the Northerly latitude, endeth at the Pole arctic: and the untemperate southerly zone, begun from the same bound of the Southerly latitude, extendeth and endeth at the pole antarcticke. Those people which dwell under the burning zone, be named of the Greeks Amphiskioi Amphiscij, in that the Noon shadows, at divers times of the year, go or be cast to them two ways, as toward the South or North. And twice also in the year runneth the sun right over their heads (as is demonstrated in the second Theorme of Euclid) so that at Noon it cometh to pass, that they have almost no shadow: for the sun being direct or in right line over their heads at Noon, he than sendeth down right Beams, which are cast or streached to the plain of the earth at right angles: so that their shadow falleth and is right under the feet, and not on any side of them. So that the sun in any other time of the year being without the vertical points, the shadows at Noon are one whiles cast into the South, and another while into the North unto them: even as the sun digressing from their tops or Noonstéed is either carried into the North, or otherwise declineth into the South. This sort of people which be under either temperate zone, are called of the Greek Cosmographers Eteroskioi, Heteroscij, in that they have a single shadow. For with them the Nooneshadowes continually run or go toward one quarter only. So that to them dwelling Northward the Noon shadow streacheth towarth the arctic or Northerly quarter. By which it appeareth that the sun never ascendeth over their heads, but continually casteth or streacheth his beams thwartly into those countries, which always form their thwart angles with the plain of the earth, or else fall a-slope upon the earth. Those people which possess, and dwell under either untemperate or cold zones, are named of the Greek writers Periskioi, Periscij: for that their shadows in one artificial day are carried and run round, as it were about them on the plain of the earth: so that the sun unto those places casteth or sendeth not strait, thwart, or slope, but long beams running on the horizone, which as they stretch along infinitely; even so the shadows going and lying on the flat of the earth, and extended along, do increase infinitely. And these zones also under the poles, extend to that proper place, where the Tropic circles, and the Arctic circles be all one. Strabo likewise writeth, that the cold zone reacheth to that place, where the Tropic is the arctic circle; that is, where this first Zone endeth, and the temperate beginneth: the Pole being 66. degrees, and a half above the horizon: so that this pole must be from the top of their heads in that place 23. degrees, and a half. Further, these people that have their shadows running round about them, dwell within the Polare circles: In that all people whose Zenith is within 23. degrees and a half of any of both the Poles, have their shadows compassing about them, but those people (as afore written) dwelling nearer under the Pole, the longer is their day, and by that reason do the shadows run the oftener about them. For where the day is of 24. hours long, the shadow doth run but once about, yet where the day is of half a year long, the shadows do run 183. times about. Here conceive that there be five zones on earth, answering to the five celestial zones, both in the heat, temperateness, and cold: which for a plainer understanding, use this figure here following demonstrated. Where the Orb or circle described on the plain of the earth, is distributed by the two unknown diameters into four equal parts: as to the outward points of the one diameter, note the letters a b. To the points of the other diameter, add the letters c d. The letter c. the Northerly Pole, and the letter d. representing the Southerly pole. The ark of the Orb a c. divide after the common manner into 90. parts or degrees, the number (as the use is) noted by 5. 10. 15. 20. 25. etc. And beginning to reckon at the letter a. in ascending by the number 5. unto the letter c. being the Northerly pole. Again set one foot of the compass unchanged on the letter c. representing the Northerly Pole, and with the other opened, make a point of the one side, and after on the other side, in drawing a line beside from point to point, and the ends of that line note with the letters ● k. that declare the arctic circle. And likewise set one foot of the compass on the note d. iudicating the Southerly pole, and after the marking with points on either side, draw a right line; at the ends of which, note these letters l m. that represent the antarcticke circle. These so finished, you shall then see on that plain or flat the five earthly zones rightly described. For the space here represented of the earth by the Tropic lines e f. and g h. included, doth demonstrate the burning zone. In that the sun's heat by his direct beams over it, doth continually strongly heat and burn that space of the earth: wherefore you may rightly draw a strait line from the letter g. unto f. representing the sun's journey. And the space of the earth included of the line i k. the arctic circle, and the ark answering to the Northerly line i k, doth iudiacate the cold and frozen zone Northerly. And that other Region or space contained right against, representing the antarcticke circle, doth demonstrate the cold Southerly zone. And the tract or space of the earth included within the lines i k. and E F. doth iudicate our temperate zone Northward, and that reasonably habitable: and the other portion of the earth contained within the lines g h. and l m. doth manifestly show the temperate southerly zone. Where Ptolemy and other ancient Cosmographers write, that the burning zone is unhabited, or as a desert, Aristotle, Pliny, and john de sacro bosco (in his treatise of the Sphere) writ the contrary: Besides these, it is well known at this day, yea by experience understood of those that have yearly gone and come from the countries lying under that zone; that is, between the two Tropics to be inhabited. Further this burnt zone is inhabited and well replenished with people that there dwell, as the same is thoroughly known to many that have passed to and froth Indies: so that it may evidently appear, that the heat there is not extreme, nor so distemperate, seeing the time of the heat that they suffer, continueth not long, nor the heat sharply worketh or causeth his uttermost effect. For the sun but a small time tarrieth above the Horizone in the burnt Region or Zone (as certain astronomers writ) as the space of twelve hours only: so that the heat there is much qualified and suppressed, through the cold rising in the night time; whereof it is manifest, that he causeth not his extreme hotness there, although he streacheth his beams perpendicularly on the earth. Therefore may many marvel, that sundry ancient men affirm these parts to be unhabitable, seeing they knew of Arabia, Foelix, Aethiopia, Taprobana, and divers other countries lying under the burnt zone: yea besides these, are Guinea, Calicute, Muluca and Gatigara, well known to lie or be under the burning Zone: and many of the people in those countries live long: and the same Region also is inhabited and replenished well with people. A like affirmation hath Albertus and Avicen (as afore written) that the middle zone is habitable, for they agree contrary to the old writers, that in the same Region of the world, which the ancient Cosmographers named to be the burnt Zone, that it is a far temperater dwelling, than under the Tropics it can be in any wise. And that people dwell under the tropics, the ancient never doubted. Wherefore if so reasonable dwelling be under the Tropics, it cannot be otherwise (as affirmeth Petrus de apono) that under the Equatoure, (notwithstanding the suns sharp heat) but that men may dwell there for all the untemperateness of heat. To be brief, all the writers of later years agree, that the middle zone is not only habitable, but found and known by many reasons, and by experience, that the same is most temperate, and the earth under it rich, both of gold and rich drugs, and reasonable well furnished of all things needful for man's life. So that in the same middle Region of the earth under the Equatour, it appeareth, that through the coldness of the night, it doth there temper sufficiently the burning heat of the day. Besides these, after the mind of Hiero. Cardane, in that Saturn, Mercury, and the moon (which properly are cold and moist planets) have a great force in the Regions under this zone, but especially the moon, that worketh her most force there in the night time, more than the other two: and of this cause more temperateness in the day time. Besides these, it is well known that those people have two summers, and two winters in the year. For in the year of our Lord 1530. at the will and charge of Charles the fift Emperor, a part of America westward was discovered, where Peru among the rest, was found richest both of Gold and other rich things and costly drugs, which is situated in longitude, of 290. degrees from the West toward the East, and is distant 5. degrees from the Equatoure toward the South. But what substance of Gold and other rich things hath yearly been brought from this isle, needeth not here any further rehearsal. And the like is to be considered and noted of the other two zones, contained between the Polare circles, and Poles of the world. Although Albertus Mag. denieth, a commodious dwelling for men in those places, and confirmeth the same by probable reasons, yet experience reclaimeth and denieth those opinions of his, and other ancient writers. In that it is well known that Gothland, Norway, Russia, Lapeland, Groveland, and divers other countries toward the North pole, is inhabited and well peopled. And Galeottus Naruiensis proveth, that men dwell under the North pole, affirming the same not to be true, that the cause of the cold there is only the far distance of the sun, as not of the heat by dearness of his coming. In that the sun by reason of the sign in which he is, either increaseth or diminisheth them with us. Besides he affirmeth, that the cold is not so dispersed round about, as that it compasseth round after the form of a circle, nor that the heat in like sort doth run round about the whole body of the earth. Further Cardane writeth, that under the poles, there is no such coldness as some suppose, in that the Moon, Venus, and Mars▪ have the greatest latitudes, in respect of the sun, and the others besides. For the moon hath five degrees to the North, Venus and Mars exceed unto eight degrees Northward, but Saturn which is the author of cold, scarcely performeth three degrees Northward. Besides these, the Moon more availeth Northward and Southward near to the poles, than the sun, in that she nearer approacheth those parts. For the Moon (as above said) hath five degrees of latitude: as well to the North, as South: so that when she shall be in the first degree of Cancer, with her greatest latitude Northward; that is, in the head of the Dragon, she shall then be nearer by five degrees to the Northerly pole, than the sun. And in like manner, when she shallbe in the tail of the Dragon (at the entrance and beginning of Capricorn) she shall be nearer the pole antarcticke by five degrees than the sun. Although in the winter the moon should be in the beginning of Capricorn with the Southerly latitude of four or five degrees, yet may she work and cause more in the change of weather, and shall cause more in Scotland than the sun, in that her power and virtue there is such. But in Brasilia and under the antarcticke pole for two causes, the one, in that she is there of such power, and the other for that in her working she is nearer. What the longitudes and latitudes of the celestial Zones are. THe longitude of Zones beginneth from the West, and is extended by the Noonestéede into the East, and from the East again by the midnight point into the West. The motions of the sun in the zodiac, and Poles of the zodiac, do describe the latitude of the zones. For the sun's motion or the zodiac do describe the burnt zone, seeing the sun on the one part of the zodiac goeth toward the North unto the elongation of 23. degrees, 28. minutes, and being by his daily motion in the beginning of Cancer, doth describe the Tropic of Cancer, which is the bound of the two zones, the burnt zone, and Northerly temperate Zone. And on the other part of the zodiac doth the sun go into the South unto the same elongation, and being in the beginning of Capricorn, doth likewise describe the Tropic of Capricorn, which is the bound of the other two zones: in that it distinguisheth the burnt from the southerly temperate zone. And the space also included in these two circles, using the middle place, is called the burnt zone, and thus the burnt zone, doth employ 46. degrees, and 57 minutes. The Poles of the Zodiac (which are daily about the Poles of the world) from which they differ 23. degrees, and 28. minutes, and are drawn by the motion of the first mover, do describe two circles in the divers parts of heaven as the Polare circles, which also be the bounds of the zones, that distinguish the two temperate from the cold zones. So that the latitude of either cold zone, unto the poles of the world, is of 23. degrees, and 28. minutes. The other degrees of the semicyrcle are attributed to the temperate zones; so that either zone containeth 43. degrees, and 3. minutes. What is the Longitude and Latitude of the earthly Zones. THe longitude of the earthly zones, is like to the longitude of the celestial, as from the West by the noon steed into the East, and from thence by the midnight point again into the West. And the latitude of them is like to the latitude of the celestial zones: for as the manner of the latitude of the celestial burnt Zone is unto the whole cyrcumference; even so is the manner of the earthly burnt zone, unto the compass about of the earthly Globe; that is, as 47. degrees is unto 360. and so likewise conceive of the others. And that this may plainer appear, use the figure following, in which a l h e. is the meridian, or Colour of the solstices, e x l. the Equatoure, a x h. the meridian, s u p. the earthly Globe, s n. the earthly Tropic of Cancer, k o. the Tropic of Capricorn t u. and q p. the arctic circles. To these answer f r oh k b b. and d s m c c. also c ff b a g e e i. the celestial circles. And what the proportion f d. is, unto the whole compass d a k g f the same is (as above written) the proportion r s. unto the whole cyrcumference of the earthly Globe: and on this wise conceive of the other circles. The letters f d. be the latitude of the celestial burnt zone, and r s. of the earthly, d c. and f g. be the latitudes of the temperate zones in heaven, and s t a c r q. of them on earth. The two outward zones, to these here drawn, be by themselves noted, as well in heaven, as on earth. Now that we have declared with the five circles, the latitudes either of the celestial or terrestrial zones are defined, it shall therefore be necessary to write here of the latitudes of the earthly zones in miles. And that you may readily find the latitude in miles, multiply the degrees by 15. (in that so many German miles, answer to one degree of the great circle in heaven) as the 43. degrees of the burnt zone, being the sun's greatest declination, multiplied by the 15. miles, do produce 705. german miles, which is the latitude of the burning zone. The latitude of either temperate zones, containeth 646. german miles almost. And from either Tropic, unto the points right under the poles, doth the space or distance contain 352. German miles. Where is the beginning and end of every Zone, according to latitude, and which places are in which Zones. THe middle of the burning zone is under the Equinoctial line, where either pole is in the Horizon. And both be his bounds (where the elevation of the pole, aswell Southerly as Northerly is) of 13. degrees, and 28. minutes. For either temperate zone doth there begin, and streacheth unto the same place, where the elevation of the pole is, of 66. degrees, and 30. minutes: which place, is the beginning of the cold zones. By these now may a man easily conceive, which places are in which zone: for if the elevation of the Pole Northerly, be lesser than 23. degrees, and 28. minutes, this place than is in the burning zone, as the inner Libya, Aethiopia, a part of Arabia Felix, and India. But if the elevation containeth precisely so many degrees and minutes, the place than is in the bound of the burnt and temperate zone; as is Siene a city of Egypt. Further if the elevation of the Northerly Pole be greater than 23. degrees, and 28. minutes, yet lesser than 66. degrees, and 30. minutes, this place then is in the temperate zone, as Greece, Italy, Spain, Germany, France, England etc. But if the latitude be precisely of 66 degrees, and 30. minutes, the place is in the bound of the temperate and cold zone, as is almost Lagenla●us of Suetia. Last, if the elevation of the pole exceedeth 66. degrees, and 30. minutes, the place is in the cold zone beyond which degrees hath Nicolaus Dovis a German added a table of Noreway, Gothland, Iseland, Greenland, Fineland, and Lapeland etc. How the Zones and Climates do differ. THe Zone is a space or room of the earth, from the West into the East, and from thence by the midnight point again into the West. But the Climate is a space of the earth, whose beginning is constituted in the west and end in the East. A Zone also is the space of earth, between two circles equidistant, but a Climate is the only space or room of the habitable earth, contained between two lines equidistant. What the qualities of the Zones are. TO the celestial Zones are qualities attributed, not formally, but only virtually; that is, the celestial zones are neither cold, hot, nor temperate, but of this named cold, burning, and temperate, through the sun, which one while coming into this, and another while declining into that part of the world, do●th send down his beams to the earth in sundry manner: as one whiles plum down right, when the sun runneth under the equinoctial, and another while by a thwart manner, as in the thwart sphere: which beams (besides how right angles they make on earth) so much the greater heat they cause, and how thwarter angel's they make, somuch the weaker heat they procure. So that under the Equinoctial the beams most rightly and down right falling, do make right angles on the upper face of the earth, which through the same causeth a most great heat. Also the beams falling toward either poles, do cause thwarter angles, and they make the angles more uneven or thwarter, and thereof the same heat is the lesser. And in the temperate zone (especially in the summer) the beams do make almost angel's falling unto a rightness, but in the winter unto a thwartnes; so that in the same Region is a commodious dwelling. But in the cold zones the angles are caused unlike or uneven, & thwartest or slopest, as in the burnt Zone they are rightest and most downward: in somuch that the cold zones even (as the burnt) are commodious to dwell under. For the beams falling and reflexed, how much nearer they fall and be together, somuch the stronger and mightier they move and cause the heat: as we daily see that the sun in the noonstéed being (as in the summer) to cast or stretch down almost perpendicular or down right beams: which beams also are almost reflected into themselves, of which the greatest heat of the day than is caused. And contrariwise, the sun being in the East or west, where the beams streaching downward and reflexed, are scattered and run abroad; the effects be lesser, and the heat much abated and feebled. Even so the beams in the burnt zone be perpendicular or plum downright, which reflexed into themselves do cause a most great heat. In the temperate zone do the beams bylitle and little fall sloper and sloper, of which they cause there a temperate heat. But in the cold zones the beams furthest decline or fall slopest, through which they procure no effect, & of the consequent cause there a very weak heat. What the utilities of the Zones be. 1 THe ancient considerers of the stars, have thus instituted the distribution of the zones for two causes. The one is, that by this reason they might show to us which places of the earth be reasonably habitable, & most commodious to dwell under. 2 The other is (as we learn by experience) that the wits of men, and nature of places by them appear and are known, in that the air compassing us, is a certain cause of the temperateness. For the manners and conditions of men (as writeth Galen) do for the most part ensue the temperaments of the bodies: yea the nature of trees, plants, herbs, and beasts do like ensue the temperament of air. Of which that we might be the surer and certainer of the natures of the foresaid matter, it pleased the ancient to divide them into five zones. Of which (it is well known) that the bodies of men or people dwelling under the burning zone (as the Moors) be shorter of stature, than those people dwelling under the temperate zones, wilder, and crueler. Also they be crafty and subtle of nature, having besides wrinkled faces, thick crisped hear on the head, and black scorched bodies, and crooked of stature. Also all living and cresent things, are found to agree according to the quality of the air in that Region. Further the people dwelling under the Northerly Parallels or Polare circles (where the places bound of cold and moisture) be white of body, having long hear on the head, tall and comely of stature and parsonage, cold of quality, yet in manners or conditions wild and cruel, through the force of the cold in those places, and agreeing with these is the greatness of the winter, and the greatness of fierce and cruel beasts, and other living things there breeding, with a furious people inhabiting, called generally the Scythians. Last, those dwelling under the temperate zones, be a gentler and civiler people being some tawny (especially toward the South) and others toward the North reasonable white of skin and body, being mean of stature, and temperate in nature and quality, and of the same like in conditions and behaviuor, etc. And thus much, for the second part of this Treatise. FINIS. The Table of all the special and several points handled in this Book. OF the Rudiments of the Sphere, of Heaven, of the Stars, of the Orbs of the Stars, and of the Earth. Folio 1 What a Sphere is. 2 What the world is, and into how many parts the same is divided, with the motion of the celestial Orbs. 8 What the Stars are, and that as to the motion of their Orbs, they are carried about. 11 That Heaven is drawn round. 13 That there are but eight celestial Orbs, that may be seen. 14 A general figure declaring the number, disposition, and order of the Celestial Spheres about the Globe of the earth. 16 That there are two first motions of the celestial Orbs. 17 That there are two kinds of Stars, the fixed and the Planets. 19 Of the celestial images, and of their divers names, being in number 48. 21 The 12. signs of the Zodiac. 22 Of the Southerly. 23 Of the Planets. 25 That Heaven hath a round form, and is carried circularly. 29 That the water and earth are round bodies, and by a mutual embracing do make one body and one hollow upper face. 31 An Instrument, by which the roundness of the earth (according to latitude) may be proved▪ and all those may easily be showed which are taught of the days Artificial. 33 That the water hath a like swelling, and runneth round. 36 That the earth emploieth the middle place of the world, and is the Centre of the whole. 42 If the earth be not in the middle of the world, then of necessity it must possess some of the standings described in the figure there demonstrated, 46 That the earth abideth fixed and unmovable in the middle of the world. 49 The physic reasons. 50 That the earth compared unto heaven is as a point. 52 To find the compass of the earth, and by it the Dyameter. 55 The second Part. What the sum of the second part is. 59 That the Sphere of the world is either right or thwart. 90 That the Circles of the Sphere, be some greater, some less, with the number of the Circles. 92 The description, names, and utilities of the Equinoctial. 62 That this worthy Circle hath divers names. 71 What are the offices of the Equinoctial. 73 What are the Northerly images in respect of the Equinoctial. 78 The description, names, and offices of the Zodiac, and Ecclipticke line, or way of the Sun. 98 What are the names of this Circle. 100 What is the cause of the thwartness of the Zodiac. 109 Of the Ecclipticke line, or way of the Sun. 113 What the latitude of a Planet is, after two destinctions. 115 What is the longitude of a Star, & where he beginneth. 116 What are the uses and utilities of the Zodiac and Ecclipticke. 124 The description, names, and offices of the Colours. 125 What the offices and utilities of the Colours are. 133 The description, names, and offices of the meridian Circles, and Horizon. 135 What are the offices and utilities of the meridian. 144 A Table of the Sun's declarations, etc. 155 The common way of measuring of places with their spaces, by the rules of longitude and latitude. 167 What is to be done if places differ in the longitudes. 169 Other brief examples. 171 The finding of the distances of places or Cities, in a more easier manner. 173 The first rule. 174 An Example. 175 Another. Ibid Another. Ibid Another. 179 Another. Ibid Another. Ibid Another. 177 The second Rule. Ibid Another excellent Table, etc. 178 An example of the use of this Table. 179 The second Rule. 180 An Example. Ibid Another. 183 Another. Ibid Another. 184 Another. Ibid An easier working. Ibid An Example. 185 Another. Ibid Another. 186 If of two places etc. Ibid. A third rule. 190 An example of the third rule. Ibid. Another. 193 Another. 124 Another. 196 An easier working and less curious. 197 An Example. 198 Another. Ibid Another. 199 Another. Ibid A demonstration of the third rule. 200 The declaration of the first rule. 201 The declaration of the second rule. Ibid. The declaration of the third rule. 202 The definition, appellations, division, and offices or utilities of the Horizon. 204 The appellations and divers names of the Horizon. 205 The offices or utilities of the Horizon. 215 Of the vertical Circles. 217 The Circles of the Altitude. 219 The hour Circles. 221 The Circles dividing the twelve houses of heaven. 226 The Circle of position. 230 The definitions, names, and utilities of the four lesser Circles. 231 Which Circles are called the Tropics. 235 Why they are called Tropics. Ibid. The offices or utilities of the four lesser Circles. 245 The descriptions, names, qualities etc. 247 What the longitude & latitude of the celestial zones are. 261 What is the longitude and latitude of the earthly Zones. 263 Where the beginning and end of every Zone, according to latitude, and which places are in which Zones. 264 How the Zones and Climates do differ. 267 What are the qualities of the Zones. Ibid What be the utilities of the Zones. 268 FINIS.