A LEARNED TREATISE OF Globes: Both Celestial and Terrestrial: with their several uses.  
Written first in Latin, by Mr. Robert Hues: and by him so Published.  
Afterward Illustrated with notes, by Jo. Isa. PONTANUS And now lastly made English, for the benefit of the unlearned.  
By John Chilmead Mr of A. of Christ-Church in Oxon.  
LONDON, Printed by J. B. for Andrew Kemb, an● to be sold at his shop, on S. Marga●●● hill in Southwark, 1659.   

To the Reader.  
THat nothing is at once brought forth, and perfected▪ is an observation we may make, as from other things so in a more especial manner from Arts and Sciences. For (not to speak any thing of the rest, which yet have all of them in succession of times, had their accessions of Perfection) if we but take the Astronomical writings of Aratus, or of Eudoxus, (according to whose observations Aratus is reported by Leontius Mechanicus to have composed his Phaenomena) and compare the same with the later writings of Ptolemy; what errors and imperfections shall we meet withal; And in the Geographical wo●…ks of the ●…ncients, whether we compare them among themselves, the later with the former; ere either of them with the more accurate descriptions of our Modern Geographers: how many things shall we meet wit haltherein, that need either to be corrected 〈◊〉 erroneous, or else supplied as defective? There shall we find Strabo, every w●…ere harshly censuring the extravagances of Eratosthenes, Hipparchus, Polybius, and Posidonius; Authors among the Ancients of very high esteem. For as for Pytheas, Euthemeres, Antiphanes, & those Indian Historiographers, Megasthenes, Nearchus, and Daimachus, whose writings are stuffed with so many fabulous idle relations, he accounts them unworthy his censure. In like manner, Marinus Tyrius, however a most diligent Writer, is yet hardly dealt withal by Ptolemy. And even Ptolemy himself, a man, that fo●… his great knowledge and experience may seem to have excelled all those that went before him: yet if a man shall but compare his Geographical Tables with the more perfect discoveries of our later times: what defects & imperfections shall he there discover? Who sees no●… his errors in the bounds he sets to the Southern parts of Asia & Africa? How imperfect are his descriptions of the Northern coasts of Europe? These errors of Ptolemy, and of the Ancient Geographers have now, at ●…ngth, been discovered by the late Sea voyages of the Portugals, and English: the Southern Coasts of Africa and Asia, having been most diligently searched into by the Portugals; as the Northern parts of Europe, have in like manner been by our own Countrymen. Among whom, the first that adventured on the discovery of these parts, were, Sir Hugh Willoughby, and Richard chancellor: after them, Stephen Borough. And farther yet, then either of these, did Arthur Pet, and Charles Jackman discover these parts. And these voyages, were all undertaken, by the instigation of Sebastian Cabot: that so, if it were possible, there might be found out a nearer passage to Cathay and China yet all in vain, save only that by this means, a course of traffic was confirmed betwixt us and the Moscovite.  
When their attempts succeeded not this way; their next design was then to try▪ what might be done on the Northern Coasts of America: and the first undertaker of these ●…oyages was Mr. Martin Frobisher: who was afterwards seconded by M John Davis. By means of all which Navigations, many errors of the Ancients, and their great ignorance was discovered.  
But now that all these their endeavours succeeded not, our Kingdom at that time being well furnished, in ships, and impatient of idleness: they resolved at length to adventure upon other parts. And first Sir Humphrey Gilbert, with great courage & Forces attempted to make a discovery of those parts of America, which were yet unknown to the Spaniard: but the success was not answerable. Which attempt of his, was afterward more prosperously prosecuted, by that honourable Gentleman, Sir Walter Raleigh: by whose means Virginia, was first discovered unto us, the General of his Forces being Sir Richard Greenvile: which Country was afterwards very exactly surveighed and described by M. Thomas Harriot.  
Neither have our Countrymen within these limits bounded their Navigations For Sir Francis Drake, passing through the straits of Megellane, and bearing up along the Western Coasts of America, discovered as far as 50. degrees of Northern Latitude. After whom, Mr. Thomas Candish, tracing the same steps, hath purchased himself as large a monument of his fame, with all succeeding ages. I shall not need to reckon with these, our Countryman, Sir John Mandivel, who almost 300. years since, in a 33. years' Voyage by land, took a strict view of all India, China, Tartary, and Persia, within the Regions adjoying.  
By these, & the like expeditions by Sea, the matter is brought to that pass, that our English Nation may seem to contend, even with the Spaniard, and Portugal himself, for the glory of Navigation. And without all doubt, had they but taken along with them, a very reasonable competency of skill in Geometry, and Astronomy: they had by this, gotten themselves a far more honourable name at Sea, than they. And indeed, it is the opinion of many understanding men, that their endeavours have taken the less effect, merely through ignorance in these Sciences. That therefore there might be some small accrwment to their study and pains, that take delight in these Arts; I have composed this small Treatise: which, that it may be for their profit, I earnestly desire. Farewell.   

The Contents of the Chapters, of this TREATISE.  
THe Preface: wherein is showed the Antiquity, and excellency of Globes, in comparison of all other Instruments, as being of a form, most apt to express the figure of the Heavens and Earth. The roundness of the Earth, is defended against Patricius. The height of Hills, how much it may detract from the roundness of the Earth.  

The first PART.  
Chapter. 1. WHat a Globe is, with the parts thereof; and of the Circles without the Globe: What the Horizon is, with the things described therein, in a Material Globe. What the Meridian is, the Poles: and Axis; as also the Hour-circle and Index.  
Cap. 2. Of the circles, which are described on the supersicies of Globes. Of the AEquator or Equinoctial circle. What a day is, both Natural, and Artificial: as also of Hours, both Equal, and Unequal. Of the Zodiac, and Eccliptick. What a year is, and the Indeterminate limits thereof: together with the divers opinions of Authors concerning the same; as also many of their errors. What the AEquinoctium, and Solstices are; with changing of their places, and Anticipation in the Calendar, confirmed by many observations. The error of Sosigenes, and Julius Caesar, in designing the place of the AEquinoctium. Of the Colurs. The Longitude, & Latitude of the fixed Stars,, are proved by observations, to have been altered. A place of Ptolemy, l ib. 1. cap. 7. Geograph. is vindicated from the injury of his Interpreters, and confirmed by the authority of Strabo. Of the Tropickes: with the changing of their declination. What the Arctic, and Antarctick Circles are: Of the Vertical Circles, and Quadrant of Altitude.  
Chap. 3. Of the three positions of Sphere, Right, Parallel, and Oblique: with their several affections.  
Chap. 4. Of the Zones, and their number. The vain opinions of the Ancients, concerning the temperature of the Zones, are rejected; both by the testimonties of some of the Ancients themselves, as also by the experience of later times.  
Chap. 5. Of the Amphiscij, Periscij, and Heteroscij.  
Chap. 6. Of the Perioeci. Antoeci, and Antipodes, compared to each other.  
Chap. 7. Of Climates, and Parallels.   

The Second PART.  
Chap. 1. OF such things as are proper to the Celestial Globe: as namely of the Stars. And first of the Planets, or wand'ring Stars.  
Chap. 2. Of the fixed Stars, and their constellations.  
Chap 3. Of the Constellations of the Northern Hemisphere.  
Chap. 4. The signs of the Zodiac: and first of the Northern.  
Chap. 5. The Constellations of the Southern Hemisphere: and first of those in the Zodiac.  
Chap. 6. Of the rest of the Constellations of the Southern Hemisphere.  
Chap. 7. Of the other Stars which are not expressed in Globes. Why the Stars appear sometimes in greater number, then at others times, and sometimes greater, and at other times less: with the confutation of some vain opinions concerning the same. The idle relations of Americus Vespasius, Cardan, and Partcis, concerning the extraordinary greatness of the Stars about the South Pole, are refuted out of the Authors own experience.   

The third PART.  
Chap. 1. THe Geographical description of the Terrestrial Globe, with the parts of the world that are yet known. The errors of Ptolemy, concerning the Southern bounds of Africa and Asia, as also of the Northern limits of Europe, are condemned, out of the Writings of the Ancients; and various experience of later Writers.  
Chap. 2. Of the compass of the Earth and the measure of a Degree: with divers opinions concerning the same of the Greeks; as namely. Eratosthenes, Hipparchus, Posidonius, Cleomedes, and Ptolemy: as also of the Arabians, Jtalians, Germans, English. and Spanish. Posidonius, and Eratosthenes are confuted out of their own observation and propositions. Ptolemy's opinion is preferred before the rest, and he freed from the Calumnies of Maurolycus, who is also taxed, in that without cause favouring Posidonius, he unjustly condemns Ptolemy.   

The Fourth PART.  
Chap. 1. HOw to find out the Longitude, Latitude, distance, and Angle of position or situation of any places, expressed in the Terrestrial Globe.  
Chap. 2. Of the Latitude of any place.  
Chap. 3. How to find the distance, and Angle of position of any two places.  
Chap. 4. To find the Altitude of the Sun, or Stars.  
Chap. 5. To find the place and declination of the Sun for any day, given.  
Chap. 6. To find the Latitude of any place, by observing the Meridian altitude of the Sun, or Stars.  
Chap. 7. How to find the Right and Oblique Ascension of the Sun, and Stars, for any Latitude of Place and Time.  
Chap. 8. How to find the horizontal difference betwixt the Meridian and the vertical circle of the Sun, or any other Star, which they call the Azimuth, for any time, or place assigned.  
Chap. 9 To find the hour of the day, as also the amplitude of rising and setting of the Sun, and Stars, at any time and Latitude of place.  
Chap. 10. Of the threefold rising and setting of Stars.  
Chap. 11. How to find the beginning and end of the Twilight, for any Latitude of place and time.  
Chap. 12. To find for any Latitude of place, and time, the length of the Artificial day, or night; or the quantity of the Sun's Parallel that remains above the Horizon, and that is hid beneath it: and to perform the same by any other Star.  
Chap. 13 To find the hour of the Day, and Night, both Equal and Unequal, for any time & Latitude of place.  
Chap. 14. To find the Longitude, Latitude, and declination of the fixed Stars, as they are expressed in the Globe.  
Chap. 15. To find the declination of the Needle from the true Meridian, which they commonly call, the Variation of the Compass, for any Latitude assigned: Where the errors of those are discovered, who assign to the Magnetical Needle a certain Meridian, and fixed po●…nt which it always respects; and that affirm this change of variation to be regular. All which vain conjectures of theirs, and ungrounded Hypotheses, are refuted both by more certain observations of others, as also of the Author himself.  
Chap. 16. How to make a Sun Dial, by the help of the Globe, for any Latitude of place.   

The fifth and last PART.  
OF the Rumbes that are described upon the Terrestrial Globe: wherein their nature, Original, and use in Navigation is declared.    

The Preface.  
THere are two kinds of Instruments, by which Artificers have conceived, that the figure of this so beautiful, and various fabric of the whole Universe, might most aptly be expressed, and, as it were, at once presented to the view. The one, exhibiting this Idea in a round solid, is called a Globe, or Sphere: The other, expressing the same in a plain, they term a Planisphaere, or Map, Both of which, having been long since invented by the Ancients, have yet even to our times, in a continued succession, received still more ripeness and perfection. The Sphere or Globe, and the use thereof, is reported by Diodorus Siculus to have been first found out by Atlas of Libya: whence afterward sprung the Fable, of his bearing up the Heavens with his shoulders. Others attribute the invention of the same to Thales. And it was afterward brought to perfection by Crates, (of whom Strabo makes mention) Archimedes, and Proclus; but most of all, by Ptolemy; according to whose rules, and observations especially, succeeding times composed their Globes, as Leontius Mechanicus affirms. And now there hath been much perfection added to the same, in these our later times, by the industry, and diligence Gemma Frisius, and Gerardus Mercator; as it may appear by those Globes, that were set forth at London, Anno 1593. so that now there seems not to be any thing that may be added to them. The Planisphaere indeed is a fine invention, and hath in it wonderful variety of workm●…nship, if so be, that the composition of it be rightly deduced out of Geometrical, and optical principles: and it wants not its great delightfullnesse, and beauty also. But yet that Other, being the more ancient, hath also the priority in Nature, and is of the most convenient form; and therefore more aptly accommodated for the understanding and fancy, (not to speak any thing of the beauty, and gracefulness of it) for it representeth the things themselves, in proper genuive figurs. For as concerning the figure of the Heavens, whether it were round, was scarcely e-ever questioned by any. So likewise, touching the figure of the Earth, notwithstanding many, and sundry opinions have, been broached among the ancient Philosophers, some of them contending for a plain, others an hollow, others a Cubic all, and some a Pyramidal form: yet this opinion of its Roundness, with greatest consent of reason, at length prevailed, the rest being all exploded. Now we affirm it to be round, yet so, as that we also admit of its inequalities, by reason of those so great eminences of hills, and depression of valleys. Eratosthenes, as he is cited by Strabo in his first book, saith, that the fashion of the Earth is like that of a Globe, not so exactly round as an artificial Globe is, but that it hath certain inequalities. The earth cannot be said to be of an exact orbicular form, by reason of somany high hills, and low plains: as Pliny rightly observes. And Strabo also in his first book of his Geography, saith, that the Earth and the water together, make up one spherical body, not of so exact a form, as that of the Heavens, although not much unlike it. This assertion of the roundness of the Earth, with the intervening Sea, is confirmed also by these reasons. For first, that it is round from East to West is proved by the Sun, Moon, and the other Stars, which are seen to rise, and set. first with those that inhabit more Eastwardly, and afterward with them that are farther West. The Sun riseth with the Persians that dwell in the Eastern parts, four hours soonner than it doth with those that dwell in Spain, more Westward: as Cleomedes affirms. The same is also proved by the observing of Eclipses, especially those of the Moon; which although they happen at the same time, are not yet observed in all places at the same hour of the day or night, but the hour of their appearing is later with them, that inhabit Eastward, than it is with the more Western people. An Eclipse of the Moon, which Ptolemy reports lib. 1 Geogr. cap. 4. To have been seen in Arbela, (a town in Assyria,) at the fifth hour of the night; the same was observed at Carthage at the second hour. In like manner an Eclipse of the Sun, which was observed in Campania to be betwixt 7. and 8. of the Clock; was seen by Co●…bulo, a Captain in Armenia, betwixt 10●… and 11. as it is related by Pliny. Now that it is also of a spherical figure from North to South, may be clearly demonstrated by the risings, settings, elevations and depressions of the Stars, and Poles. The bright Star that shines so resplendently, in the upper part of the stern of the Ship, Argo, and is called by the Greeeks 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, is scarcely to be seen at all in Rhodes, unless it be from some eminent high place: yet the same is seen very plainly in Alexandria, as being elevated above the Horizon, about the fourth part of a sign: as Proclus affirms in the end of his book, de Sphaera. For I read it, Conspicuè cernitur; not as it is commonly, Prorsus non cernitur; notwithst anding, that both the Greek text, and also the Latin translation are against it. Another argument may be taken, from the figure of the shadow, in the Eclipse of the Moon, caused by the interposition of the Earth's opacous body: Which shadow being Spherical, cannot proceed from any other than a round Globous body: as it is demonstrated unto us out of optical principles. But this one reason is beyond all exception: that those that make toward the Land at the Sea, shall first of all descry the tops of the hills only, a●…d afterwards, as they draw nearer to shore, they see the lower parts of the same, by little and little: Which cannot proceed from any other cause, than the gibbosity of the Earth's superficies.  
As for those other opinions of the hollow, cubical, Pyramidal, and plain figure of the Earth, you have them all largely examined both in Theon, (Ptolemy's Interpreter) Cleomedes, and almost in all our ordinary Authors of the Sphere: together with the reasons why they are rejected. Yet that old conceit of the plainness of the Earth's superficies, is again now at last, tanquam Crambe recocta, set forth in a new dress, and thrust upon us by Franciscus Patricius; who by some few eold arguments, and misunderstood experiments, endeavours to confirm his own, and consequently to overthrow that other received opinion of the spherical figure of the Earth. I shall only lightly touch at his chiefest arguments; my present purpose and intention, suffering mce not to insist long on the confutation of them. And f●…rst of all, the great beight of Hills, and the depression of valleys, so much disagreeing from the evenness of the plain parts of the Earth, scem to make very much against the roundness of the Earth. Who can hear with patience, saith he, that those huge high mountains of Norway, or the mountain Slotus, which lies under the Pole, and is the highest in the world, should yet be thought to have the same superficies with ●…he Sealying beneath it? This therefore being the chiefest reason, that m●…y seem to overthrow the opinion of the Earth, and Seas making up one spherical body; let us examine it a little more nearly, and consider, how great this inequality may be, that seems to make so much against the evennessc of this Yerrestitall Globe. Many strange, and almost incredible things are reported by Aristotle, Mela, Pliny, and Solinu●…, of the unusual height of Atho●…, an Hill in Macedonia, and of Casius in Syria, as also of another of the same name in Arabia, and of the monntaine Caucasus. And among the rest, one of the most miraculous things which they have observed of the mountain Athos, is, that whereas it is situate in Macedony, it casts a shadow into the market place at Myrrhina, a Town in the Island Lemnos; from whence Athos is distant 86. miles. But for as much as Athos lies Westward from Lemnos, as may appear out of Ptolemy's Tables, no marvel that it casts so large a shadow: seeing that we may observe by daily experience, that as well when the Sunriseth, as when it sets, the shadows are always extraordinary long. But that which Pliny, and Solinus report of the same mountain, I should rather account among the rest of their fabulous Stories; where as they affirm it to be so high, that it is thought to be above that region of the air whence the rain is wont to fall. And this opinion (say they) was first grounded upon a report that there goes, that the ashes which are left upon the Altars on the top of this hill, are never washed away, but are found remaining in heaps upon the same. To this may be added another testimony, out of the Excerpts of the seventh book of Strabo, where it is said, that those that inhabit the top of this mountain, do see the Sun three hours sooner, than those that live near the Sea side. The height of the mount●…in Caucasus is in like manner celebrated by Aris●…otle, the top whereof is enlightened by the Sun's b●…ames, the third part of the night both morning and evening. No less fabulous is that which is reported by Pliny and Solinus o●… Casius in Syria, from whose top the Sun rising is discovered about the fourth watch of the night: which is also related by Mela of that other Casius in Arabia. But that all these relations are no other than mere fables, is acutely and solidly proved by Petrus Noninus, out of the ve●…y principles ●…f Geometry. As for that which Eustathius writes, that Hercules pill●… called by the Greeks Calpe and Abenna, are celebrated by Dionysius Perlegetes for their miraculous height is plainly absurd and ridiculous. For these a●…ise not above an hundred els in height, which is but a furlong: whereas the Pyramids of Egypt are reported by Strabo to equal that height; and some trees in India are found to exceed it: if we may credit the relations of those Writers, who in the same Strabo affirm, that there grows a tree by the river Hyarotis, that casteth a shadow at noon, five furlongs long.  
Those fabulous narrations of the Ancients, are seconded by as vain reports of our modern times. And first of all Scaliger writes, from other men's relation, that Tenariff, one of the Canary Islands, riseth in height fifteen leagues, which amount to above sixty miles. But Patricius not content with this measure, stretchth it to seventy miles. There are other hills in like manner cried up for their great height; as namely the mountain Andi in Pe●…u, and another in the Isle Pico among the Azores Islands▪ but yet both these fall short of Tenariffe. What credit the relations may des●…rve, we will now examine. And first for Tenariffe, it is reported by many writers to be of so great a height, that it is probable the whole World affords not a more eminent place; n●…t ex●…pting the mountain Slo●…us it sel●…; which whether ever any other mortal man hath seen, besides that Monk of Oxford (who by his skill in Magic conveyed himself into the utmost Northern regions, and took a view of all the places about the Pole, (as the Story hath it) is more than I am able to determine. Yet that this Isle cannot be so high as Scaliger would have it, we may be the more bold to believe, because that the tops of it are scarcely ever free from snow: so that you shall have them covered all over with snow all the year long, save only one, or, at the most, two months in the midst of summer: as may appear out of the Spanish Writers. Now that any s●…ow is generated 60 or 70 miles above the plain superficies of the Earth and Water, is more than they will ever persuade us: seeing that the highest vapour●… never rise above 48 miles above the earth, according to Eratosthenes his measure; but according to Ptolemy, they ascend not above 41 miles. Notwithstanding Cardan, and some other professed Mathematicians, are bold to raise them up to 288 miles; but with no sma●… slain of their name, have they mixed those trifles with their other writings. Solinus reports that the tops of the mountain Atlas reacheth very near as high as the circle of the Moon: but he betrayeth his own error, in that he confesseth that the top of it is covered with snow, and shineth with fires in the night. Not unlike to this, are those thi●…gs which are reported of the some mountain, and its height, by Herodotus, Dionysius Afer, and his scholiast Eustathius: whence it is called in Authors, Coelorum columen, the pillar that bears up the Heavens▪ But to let pass these vain prodigious relations: let us come to those things that seem to carry a greater show of truth. Eratosthenes found by Dioptricall instruments, and measuring the distances betwixt the places of his observation, that a perpendicular, drawn from the top of the highest mountain, down to the lowest bottom or valley, did not exceed ten furlongs. Cleomedes saith that there is no hill found to be above fifteen furlong●… in height: and so high as this, was that vast steep rock in Bactriana, which is called Sisimitrae Petra, mentioned by Strabo in the 11 book of his Geography. The tops of the Thessalian mountatns are raiscd to a greater height by Solinus, then ever it is possible for any hill to reach. Yet if we may belieus Pliny, Dicaearchus, being employed by the King's command, in the same business, found that the height of Pelion, which is the highest of all, exceeded not 1250 pases, which is but ten furlongs. But to proceed yet a little further, lest we should seem too sparing herein, and to restrain them within narrower limits than we ought: we will add to the height of hills, the depth also of the Sea. Of which the illustrious Julius Scaliger in his 38. Exercitation against Cardan, writeth thus. The depth of the Sea (saith he) is not very great: for it seldom exceeds 80 pase●…, in most places it is not 20 pases, and in many places not above six, in few places, it reacheth 100 pases, and very seld●…me, or never exceeds this number. But because that falls very far short of the truth, as is testified by the daily experience of those that pass the Se●…s: let us make the depth of the Sea equal to the height of mountains: so that suppose the depth thereof to be ten furlongs, which is the measure of the Sa●…dinian Sea, in the deepest places, as Posidonius in Strabo affirms. Or if you please, let it be fifteen furlongs, as Cleomedes, and Fabianus, cited by Pliny lib. 2. c. 102. will have 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉. (For Georg. Valla in his interpretation of Cleomedes, deals not fairly with his Author, where he makes him assign thirty furlongs to be the measure of the Seas depth.) These grounds being thus laid, let us now see what proportion the height of hills may bear to the Diameter of the whole Earth: that so we may hence gather, that the extubcrancy of hills are able to detract little or nothing from the roundness of the Earth; but that this excrescency will be but like a little knob or dust upon a ball, as Cleomedes saith For if we suppose the circumference of the whole earth to be 180000 furlongs, according to Ptolemy's account, (neither did ever any of the Ancients assign a less measure than this; as Strabo witnesseth:) the Diameter thereof will be, (according to the proportion betwixt a circle and its Diameter found out by Archimedes,) above 57272. furl●…ng. If then we grant the highest Hills to be ten furlongs high, according to Eratosthenes and Dicaearchus; they will bear the same proportion to the Diameter of the Earth, ●…hat is, betwixt one and 5727. (Peucerus mistakes himself when he saith, that the Diameter of the Earth to the perpendicular of ten furlongs is as 18000. to one for this is the proportien it beareth to the whole circumference, and not the Diameter. Or suppose the tops of the ●…ighest hills to ascend to the perpendicular of ●…ifteene furlongs, as Cleomedes would have it: ●…he proportion then will be of one to 3818. Or if ●…ouplease, let it be thirty furlongs, of which ●…height is a certain rock in Sogdiana, spoken ●…f by Strabo, in the eleventh Book of his Geography, (notwithstanding Cleomedes is of o●…inion, that a perpendicular drawn from the top of the highest hill, to the bottom of the dee●…est Sea, exceeds not this measure:) the proportion will be no greater, then of one to 1908. Or let us extend it yet farther, if you will, to four miles, or thirty-two furlongs, (of which ●…eight the mountain Casius in Syria is repor●…ed by Pliny to be,) the proportion will yet be somewhat less than of one to 1789. I am therefore so far from giving any credit to Patricius his relation of Tenariffes being seventy●…wo miles high, (unless it be measured by ma●…y oblique and crooked turnings and windings: ●…n which manner Pliny measureth the height of ●…he Alps also to be fifteen miles;) as that I ●…annot assent to Alhazen, an Arabian, who would have the tops of the highest hills to reach ●…o eight Arabian miles, or eighty furlongs, as I think: neither yet to Pliny, who in his quarto lib. cap. 11. affirms the mountain Haemus to be six miles in height: and I can scarcely yield to the samc Pliny, when as he speaks of other Hills four miles in height. And whosoever should affirm any Hill to be higher than this, though it were Mercury himself, I would bardly believe him. Thus much of the height o●… hills, which s●…emed to derogate from the roundness of the Terrestrial Globe. Patricius proceeds, and goes about to prove that the water also is not round or spherical. And he b●…rroweth his argument from the observations of those that convey or level waters, who find by their Dioptricall Instruments; that water●… have all an equal and plain superficies, except th●…y be troubled by the violence of winds. On the contrary side, Eratosthenes in Strabo affirms, that the superficies of the Sea is in some places higher, than it is in other. And he also produceth, as assertors of his ignorance, those Water-levellers, who being employed by Demetrius ab●…ut the entring away of the Isthmus, or neck of land betwixt Peloponesus and Greece; returned him answer; that they found by their In●…ruments, that that part of the Se●… which was on Corinth's side, was higher than it was at Cenchraee. The like is also storied of Sesostris, one of the Kings of Egypt, who going about to make a passage out of the Mediterranean into the Arabian gulf, is said to have desisted from his purpose, because he found that the superficies of the Arabian gulf was higher than was the Mediterranean: as it is reported by Aristotle, in the end of his first Book of Meteors. The like is also said in the same place, by the same Author, to have happened afterward to Darius. Now whether the Architects or Water-levellers, employed by Demetrius, Sosostris, and Darius, deserve more cre●…it, than those whom Patricius nameth; I shall no●…●…uch trouble myself to examine. Yet Strabo in●…igheth against Eratosthenes for attributing any ●…ch eminencies, and depressions to the superficies 〈◊〉 the Sea. And Archimedes his doctrine is, ●…at every humid body, standing still and with●…t disturbance, hath a Spherical superficies, whose ●…enter is the same with that of the Earth. So that ●…ee have just cause to reject the opinions, both of ●…hose that contend that the superficies of the Sea is ●…aine; as also of those that will have it to be in ●…me places higher tben in other. Although we●…●…annot, in reason, but confess, that so small a por●…on of the whole Terrestrial Globe, conclude●…atricius ●…atricius his agreement, which he allegeth from ●…he experience of Water-conveighers, to be of no ●…eight at all.  
But he goes on, and labours to prove his ●…ssertion from the elevation and depression, rising ●…d setting of the Poles, and Stars, which are ●…served daily, by those that traverse the Seas: ●…ll which, he saith, may come to pass, al●…ough the surface of the water were plain. For 〈◊〉 any Star be observed, that is in the vertical ●…int of any place; which way soever you tra●…ell from that place, the same Star will seem 〈◊〉 be depressed, and abate something of its ele●…ation, though it were on a plain superficies. ●…ut there is something more in it then Patri●…ius takes notice of. For if we go●… an equal measure of miles either towards the North, or toward the South; the elevation or depression of the Star, will always be found to be equal: which that it can possibly be so in a plain superficies; is more than he will ever be able to demonstrate. If we take any Star situate near the AEquator, the same when yo●… have removed thence 60. English miles, will be elevated about a degree higher, above the Horizon, whether the Star be directly over your head, or whether you depart thence, that so it may be depressed from your Zenith, for 30. or 50. or any other number of degrees. Which that it cannot thus be; on a plain superficies, may be demonstrated out of the principles of Geometry. But yet me thinks, this one thing might have persuaded Patricius (being so well versed in the Histories of the Spanish Navigations, as his writings sufficiently testify) that the superficies of the Sea is not plain; because that the Ship called the Victory, wherein Ferdinand Magellane losing from Spain, and directing his course towards the South-west parts, passed through the straits, called since by his name, and so touching upon the Cape of good hope, having compassed the whole World about, returned again into Spain. And here I shall not need to maintain the famous Voyages of our own Countrymen, Sir Francis Drake, and Master Thomas Candish, not so well known perhaps abroad; which yet convince Patricius and the same error. A●…d thus have we lightly touched the chief foundations that his cause is built upon: but as for ●…ose ill understood experiments, which he brings 〈◊〉 the confirmation of the same. I shall let them ●…sse, for that they seem rather to subvert his opi●…n then confirm it.  
Thus having proved the Globe of the Earth 〈◊〉 be of a Spherical figure, seeing that the E●…inency of the highest Hills hath scarcely the ●…e proportion to the Semidiameter of the ●…rth, that there is betwixt 1. and 1000 ●…hich how small it is, any one may easily per●…ive: I hold it very superfluous to go about to ●…ove, that a Globe is of a figure most proper and ●…t to express, and represent the fashion of the Hea●…ns and earth, as being most agreeable to Nature, ●…siest to be understood, and also very beautiful 〈◊〉 behold.  
Now in material Globes, besides the true ●…d exact description of places, which indeed is ●…e chiefest matter to be considered; there are ●…o things especially required. The first where●… is the magnitude and capacity of them; that 〈◊〉 there may be convenient space for the de●…ription of each particular place or region: the ●…cond is the lightness of them, that so their ●…ight be not cumbersome. Strabo in his eleventh, ●…ok, would have a Globe to have ten foot 〈◊〉 Diameter, that so it might in some rea●…nable manner admit the description of particu●…r places. But this bulk is too vast, to be ●…nveniently dealt withal. And in this regard, 〈◊〉 think that those Globes, of which I intent 〈◊〉 speak in this ensuing discourse, may justly be perferred before all other, that have been●… set forth before them; as being more capacious than any other: for they are in Diameter two foot, and two inches: whereas Mercator's Globes, (which are bigger than any other ever set forth before him,) are scarcely sixteen inches Diameter. The proportion therefore of the superficies of these Globes, to Mercator's, will be as 1. to 2●… and somewhat more, Every Country therefore in those Globes will be above twice as large as it is in Mercator's: so that each particular place may the more easily be described. And this I would have to be understood of those great Globes, made by William Saunder●…on of London; concerning the use of which especially, we have written this discourse. For he hath set forth other smaller Globes also, which as they are of a lesser bulk●… and magnitude, so are they of a cheaper price: that so the meaner Students might herein also be provided for. Now concerning th●… Geographical part of them, seeing it is taken out of the newest Charts and descriptions; I am bold to think them more perfect than any other: how ever they want not their errors. And I think it may be the Author's glory to have performed thus much in the edition of these Globes. One thing by the way you are to take notice of: which is, that the descriptions of particular places are to be sought for else where; for this is not to be expected in a Globe. And for these descriptions of particular Countries, you may have recourse to the Geographical tables of Gerardus Mercator, whose diligence and industry in this Regard seems to exceed all other before him. To him, therefore we refer you.  
PONT. STRABO in the place above, cited by the Author, speaks of a Globe of that bigness, not such an one as himself had made but such an one as he could wish were made; that so it might be every way absolut●…. And indeed with in this age of ours, the magnificent and Illustrious Tucho Brabe, who is now deservedly celebrated with the titl●… of a Second Atlas, hath made a very fair Celestial Globe composed all of wood within, and covered over with plates of Copper, artificially wrought, containing six foot in Diameter, besides the Meridian, and Horizon, and other ●…ppendances which may be guessed at by the rest▪ the like whereof, so coldly and elaborately framed, and every way exactly answering itself, I think was never made by any. And indeed, it is a vast and magnificent piece of work: insomuch that many strangers came out of divers parts into Denmark, while it was there, only to see this Globe But Tycho●…fterward ●…fterward betaking himself to the Emperour●… Court, carried this Globe with some certaino other Mathematicll instruments with him. All which after the death of Tycho, were ●…ought for a great sum of money by the Emperor, and are now preserv●…d at Prage in the ●…mperiall Castle, and showed among other ●…arities there. About the Horizon are read thes●… words, written in letters of gold.  
Anno a Christo nato M. D. XXCIV. Regnante in Dania Frederico secundo, hunc Coelesti machinae conformem Globum, in quo affi●…a octavae Sphaerae sidera c●…litùs organis deprehensa, suis quaeque locis ad amussim repraesentare, Errant●…úmque stellarum per haec apparentias perpervestigare decrevit, coelo terrigenis, qui rationem eam capiunt, Mechanico opere patefacto, TYCHO BRAHE, O. F. Sibi & posteris. F. F.  
Which Globe, by reason of i●…s extraordinary magnitude, hath this prerogative above all other▪ that all things may be done upon it most exactly, and in the very minute, especially as far as concerns the doctrine of the First movable, together with the observations of the Stars, and their aspects in respect of the Ecliptic and AEquator: all which may be done mechanically, without any ●…edious computations.  
The great Duke of Tuscany hath also two very fair Globes, as large as this, but made after the ordinary manner; the one a Terrestrial Globe: but the other an Armillary Sphere, consisting of Circles, and Orbs only.  
Now concerning those Globes of Mercator, spoken of by our Author, the same have been since, accurately corrected, according to Tycho'●… observations, and set forth both in a great, and lesser form●… by I Hondius, and are still made, and sold by his Son.  
And because that in this ensuing discourse of Globes, there is often mention made of a Point, Line, Superficle●…, Angle, Rhombus; Axis, and other the like Geometrical terms: I have thought good to set down the several definitions of the same.  
A Point, is that which hath no parts: or a thing supposed to be Indivisible, or that cannot be divided into parts.  
A Lin●…, is a supposed length without breadth; whose extremes or bounds are t●… Points.  
A Right Line, is the shortest of all Lines, drawn from any two of the same Points.  
Parallels, are Lines equidistant from each other: which though they should be protended infinitely▪ would never meet in one point, but keep still the same distance mutally.  
A Perpendicular, is a right Line, falling directly on a Right Line, and making on each side that Point where they touch, two equal Right Angles.  
A Superficies, is a Longitude, having only Latitude: whose terms and limits are two Lines.  
A Figure, is that which is comprehended within one, or many bands: under one bound is comprehended a Circle: and all other Figures under many.  
A Term or Limit, is that which is the end of any thing.  
A Circle, is a plain Figure, comprehended under one round line: in the midst whereof there is a P●…int, from whence all Lines drawn to the Circumference are equal.  
The Centre of a Circle, is that point in the midst, from which all equal lines are drawn to the Circumference.  
The Diameter of a Circle, is a Right line passing through the Centre, terminated at each end with the Circumference, and dividing the Circle into two equal Parts.  
A Semicircle, is the half of a Circle, contained within the Diameter, and half the Circumference.  
An Arch, is a portion of a Circle, comprehended within a Right line, and any part of the Circumference. and is always either greater or lesser than a Semicircle.  
An Angle is, when two lines are extended upon the same superficies, so that they touch one another in a Point, but not directy.  
A Right Angle, is that which is produced of a Right line, falling upon a Right line, and making two equal Angles, on each side the Point, where they touch each other: As the Lines A, B, C.  
An Obtuse Angle, is that which is Greater than a Right Angle, as the Angle A, C, D.  
An Acute Angle, is that which is less than a Right: as the Angle A, C, B.  
A Solid Angle, is that which is comprehended under more than two plain Angles, which are not in the same superficies and meeting all in one point: as are the Angles of a Cube, or Die.  
Rhombus, is a Figure Quadrangular, having equal sides, but not equal Angles.  
Rhomboides, is a Figure having neither equal sides, nor equal Angles: yet the Opposite sides and Angles are equal.  
A solid Body, is that which hath length, breadth, and thickness; as a Cube or Die: and the Limits or Extremes of it are superficies.  
The Axis is that Diameter, above which the Sphere or Globe is turned.  
The Poles of a Sphere, are the Extremes, or ends of the Diameter, and are terminated in the superficies of the Sphere.  
A Sphere is defined by Euclid to be, when the Diameter of a semicircle remaining fixed, the Semicircle is turned about, till it return again to the place, whence it began to move at first.   

The first Part, Of those things which are common both to the Celestial and Terrestrial GLOBE.  

CHAP. I. What a Globe is, with the parts thereof: and of the Circles of the Globe.  
A Globe, in relation to our present purpose, we define to be an Analogical representation either of the Heavens, or the Earth. And we call it Analogical, not only in ●…egard of its form, expressing the Spherical figure, as well of the Heavens, as also of the Terr●…stiall Globe, consisting of the Earth itself, together with the interflowing Seas: but rather because that it representeth unto u●… in a just proportion and distance, each particular constellation in the Heavens, and every several region and tract of g●…ound in the Earth, together with certain circles, both greater and l●…sser, invented by Artificers for the more ready computation of the same. The g●…eater Circle we call those, which divide the whole superficies of the Globe into two equal parts, or halves: and those the lesser, which divide the same into two unequal parts.  
PONT. A Globe is also called a Sphere: only with this distinction, that a Sphere is properly such an one, as consists only of circles or little hoops of brass, or like matter, and is not a solid body, as is a Globe: the Latins call it Armillaris. Now those Circles whereof it is made, although we are not to cone eive that there are any such reallones in the Heavens, yet they have been invented by Artificers, to the end, that by means of the same, the doctrine of the true motions of the Celestial bodies might the more easily be apprehended. And what is said of the AEquator, Zodiaque, Axes, and the other Circles, is also to be understood of the other Orbs themselves, and their Hypotheses. For as concerning the objection made long since by Rhoeticus, and lately by Peter Ramus lib. 2. Scholar Math. touching the facility the ancient Egyptians had in searching out the courses of the Stars: I think it not amiss to let you see what the Noble Tycho's opinion is herein, and what answer he, once upon occasion gave Ramus himself, proposing the same unto him: as we find it related by himself in his book of Astronomical Epistles pag. 60. And thus it is.  
Quod celeberrimus ille noltri aevi Philosophus Petus Ramus, etc. Where as that famous Philosopher of our times, Peter Ramus, was of opinion, that the Science of Astronomy might be framed by some certain Logical ways of computation, with Hypotheses: this is nothing else but a mere groundless conjecture. Which con●…eit of his, he proposed indeed to me about sixteen ●…eares since, when as we were together at Au●…purge: wishing me withal, that when as I had ●…nce reduced the course of the Stars into some ●…xact order, by the Hypotheses now in use; I ●…ould then try what might be done without them. And that this might possibly be effected, he brought this for his reason, because that he had read, that the Egyptians, had anciently a most easy and facile way and method in their Astronomy. And therefore, seeing that this way of computation by Hypotheses is very intricate and difficult; it must needs follow, that they had a more plain and compendious way to the knowledge of the course of the Stars, and that without them But I opposed him herein, showing withal, that it was altogether impossible that the Celestial Apparen●…es should be reduced into any certain order or science, so as to be understood, without the help●… of Hypotheses. And that this facility of the Egyptians was only in the AEquators of the Planets, whereby they freed themselves from all tedious supputation; Whereas, the ease and facile use of the Ephemerideses was not as yet brought to light. But for as much as he (thought otherwise a man of an excellent apprehension and wit, and a great lover of the truth) seemed not to be so throughly acquainted with the hidden secrets of this intricate Science, and considered not that the course of the Heavenly bodi●…s did not keep a constant period at any set time: I neither could nor indeed desired to get any thing of him, in this matter. He hath many Sectaries at this day, who have a strong faith of the possibility of this thing: but such they are, that neither understand the matter themselves, nor will ever be able to bring it to any effect. For seeing that all things consist in number, weight, and measure: without these, there is no●… any thing in this visible world that can be explained or understood. Now the office of these Hypotheses is only to show the measure of the apparent motion of the Heavenly bodies, by circles and other figures: which are again resolved into numbers by Arithmetic without which, whosoever shall think to attain to the knowledge of the motion of the Stars: he may be said to invoke Fortune, (as the Proverb is:) and dreams of some strange incorporeal, and more than Seraphical way, above the reach of humane capacity.  
Besides the body of the Globe itself, and those ●…hings which we have said to be thereon inscribed, there is also annexed a certain frame, with necessary instruments thereto belonging: which we shall declare in order.  
The fabric of his frame is thus. First of all, there is a Base, or foot to rest upon: on which there are raised perpendicularly six ᶜ Pillars ᵇ or ᵃ Columns, of equal length and distance; upon the top of which there is fastened to a level, and parallel to the Base, a round plate or circle of wood, of a sufficient breadth and thickness, which they call the Horizon: because that the uppermost superficies thereof 
The Horizon.  performeth the office of the true Horizon. For it is so placed, that it divideth the whole Globe ●…nto two equal parts. Whereof that which 〈◊〉 uppermost, representeth unto us the visible ●…emisphaere, and the other, that which is hid ●…omus. So likewise that Circle which divi●…es that part of the world which we ●…ee, from ●…hat other which we see not, is called the Hori●…on. And that point which is directly over our ●…eads in our Hemisphere, and is on every side ●…quidistant from the Horzion, is commonly ●…ailed Zenith: but the Arabians name it Se●…th. But the former corrupted name hath yet ●…revailed, so that it is always used among Wri●…ers generally. And that point which is oppo●…ite to it in the lower Hemisphere, the Arabians●…all ●…all Nathire; but it is commonly written Nadir. These two points are called also the Poles of the Horizon.  
Furtheremore, upon the superficies of the Ho●…izon in a material Globe there are described, first, the twelve Signs of the Zodiaque: and ●…ach of these is again divided into twenty lesser portions: so that the whole Horizon is divided ●…nto 360. parts, which they also call degrees. And if every degree be div●…ded into sixty parts ●…lso, each of them is called a Scruple or Minute: and so by the like subdivision of Minut●…●…nto fixty parts, will arise Seconds, and of these Thirds, and likewise Four h●…, and Fifths, etc. by the like partition still of each into ●…xty parts.  
PONT. In the midst among these Signs are there described certain Characters, to denote the particular Planet, to whose dominion each Sig●… doth appertain. Next to this there is another Section, wherein are set down the several day●… of every week: after that, followeth the number of the days of every Month, throughout th●… whole year. Besides this number of the day●…s, each of them hath in their several orders some one of these three letters affixed, K. N. I. signifying the Kalends, Nones, and Ides, which terms the Ancient Romans used in their accounts, to sign●… fie the days of every Month. For they did 〈◊〉 reckon as we do now, from the first day of every Month to the 30. or 31. of the same; but their account was according to the Kalendes, None●…, and Ides. So that the first of each Month w●… the Kalends; and the rest of the days of the same month were not reckoned forward, but after a retrograde manner. As for example: The last day of December, with us is the 31. They called the second of the Kalends or January, and the 30. of the same month, the third of the Kalends of January Thus reckoning backward till they came to the Ides, which was the foureteenth of December, and the nineteenth of the Kalends of January,. The like order they observed in the Ides and Nones also. Now what months have more or fewer Kalends or Nones may be found upon the Horizon, as we have said: and as may be gathered also out of these old verses. 
Majus sex Nonas, October, Julius, & Mars:  
Quatuor at reliqui. Tenet Idus quilibet octo.  
Ind dies reliquos dic omnes esse Calendas.   
There is also described upon the Horizon the Roman Calendar, And that three several ways: ●…o wit, the ancient way, which is still in use ●…ith us here in England; and the new way, ap●…ointed by Pope Gregory 13. Wherein the E●…uinoxes & Solstices were restored to the same ●…laces, wherein they were at the time of the ce●…ebration of the Council of Nice: and in the ●…hird, the said Equinoctial and Solsticial points ●…re restored to the places that they were in, at ●…he time of our Saviour Christ's nativity. The ●…onths in the Calendar are divided into days ●…nd weeks: to which are annexed, as their pe●…uliar characters, the seven first letters of the Latin Alphabet. Which manner of designing ●…he days of the month, was first brought, in by Dionysius Exigum, a Roman Abbot, after the Council of Niee.  
The innermost border of the Horizon is divided into 32. parts, according to the number ●…f the winds, which are observed by our mode●…ne Sea-fareing men in their Navigations; by ●…hich also they are wont to design forth the ●…uarters of the Heavens, & the coasts of Coun●…ries. For the Ancients observe but four ●…inds only: to which were after added four ●…ore: but after ages, not content with this ●…umber, increased it to twelve and at ●…ength they brought it to twenty four, as 〈◊〉 is notes. And now these latertimes ha●…e ●…ade them up thirty two, the names whereo●…, ●…oth in English and Latin are set down in the ●…he Horizon of Material Globes.  
PONT. The true Horizon is either Rational or Sensible. The Rational or Intelligible Horizo●… divide th' the Sphere into two equal parts exactly; and these are called the upper and the lower Hemisphaeres. The sensible or apparent Horizon, is s●… called, because it only seems to divide the Heavens into two equal parts, or Hemisphaeres: whereas indeed it doth not divide it so exactly, but only seemeth so to do. The Rational Horizon, is also called the artificial, because that it was brought in, for the use of Astronomy.  
The use of the Horizon is manifold. First, it divides the Heavens into two Hemisphaeres. Secondly, it showeth what Stars never set, and so what never rise from under the Earth; and so, likewise what Stars do both rise and set. Thirdly, it shows the cause of the equality, and in equality of the artificial days and nights. Fourthly, it condueeth to the finding out of the latitude of any place. Fifthly, it is the cause of the Rectitude and obliquity of the Sphere; whereof we have occasion to speak more largely hereafter.  
There is also let into this Horizon, two notches opposite one to the other, a circle of brass, making right angles, with the said Horizon, and placed, so that it may be moved at pleasure up and down, by those notches, a●… need shall require. This circle is called the Meridian, because that one side of it, which is 
The Merinian.  in like manner divided in 360. degrees, supplieth the office of the true Meridian. Now the Meridian is one of the greater circles, passing through the Poles of the world, and also of the Horizon: to which, when the Sun in his daily revolution is arrived in the upper Hemisphere, it is midday; and when it toucheth the same in the lower Hemisphere, it is midnight, at that place whose Meridian it is.  
These two circles, the Horizon and Meridian, are various and mutable in the Heavens and Earth, according as the place is changed. But in the material Globe, they are made fixed and constant: and the earth is made movable: that so the Meridian may be applied to the vertical point of any place.  
PONT. The us●…s of the Meridian are these, especially. First, It determineth the paint of midday, and midnight: whence the Astronomers begin the day always from the Circle.. Secondly, in the Meridian is observed the Zenith or v●…rticall point of places, whence afterward the distances of Stars and Parallel circles are gathered. Thirdly▪ The Longitude and Latitude of places are taken from hence. Fourthly, It shows the greatest elevation of the Sun, and other Stars: which elevation is called their Meridian Altitude. Fifthly, By the Meridional eleudtion of the Sun, when he is in the Equinoctial point, may be found out the elevation of the Pole, and habitude or position of the Sphere. For the quarter of a circle being 90. degrees, if then we subtract the Mer●…dionall Altitude of the Sun in the Equinoctial from 90. degrees, the remainder showeth the elevation of the Pole. As for example, The elevation of the Sun at noon, when it is in the AEquinoxe, is about 38. degrees with us here at London: which being deducted out of 90. there remains 52. Which is the elevation of the Pole with us. So at Rome the Equinoctial altitude of the Sun is about 48. degrees; which being substracted from 90 degrees, which is a Quadrant, there remains 42. for the elevation of the Pole.  
In two opposite points, of this Meridian, are fastened the two ends of a●… iron pin, passing through the body of the Globe and its Centre. 
The Poles and Axis.  One of which ends is called the Arctic, o●… North Pole of the world; and the other the Antarctick, or South Pole: and the pin itself is called the Axis. For the Axis of the world is the Diameter about which it is turned. And the extreme ends of the Axis are called the Poles.  
To either of these Poles, when need shall require, there is a certain brass circle or ring, of a reasonable strong making, to be fastened, which circle is divided into 24. equal parts, according to the number of the hours of the day & night: and it is therefore called the Houre-circle. And this circle is to be applied to either of the Poles 
The Houre-Circle.  in such sort, as that the Section where 12. is described, ●…ay precisely agree with the points of mid day, and midnight in the superficies of the t●…ue Meridian.  
There is also another little pin, or stile to be fastened to the end of the Axis, in the very centre of the Houre-circle: and this pin is called in Latin, Index Horarius: and is so made, as that it turns about and pointeth to every of the 24. sections in the Houre-circle, according as the Globe itself is moved about: so that you may place the point of it to what hour you please.  
PONT. The use of this Houre-circle and Index is to denote the hours of the rising and setting of the Sun and other Stars, which must be practised after this manner. First, you must set the Globe to your elevation or Pole, and then apply the degree of the sign, in which the Sun at the time is, to the Meridian, and the Index to the twelfth hour which is uppermost. And so having thus done, you must turn the Globe about, till the degree wherein the Sun is, come to the Eastern side of the Horizon; which done, the Index will point out the hour of his rising, and if you turn it about to the West side, you shall in like manner have the hour of his setting.  
There is also belonging to the Meridian a Quadrant of Altitude, being made of a long thin plate of steel or brass, and fashioned crooked, so that it may be applied to the convexs' Superficies of the Globe, and having the fourth part of the circle in length. And this Quadrant is made in such a sort, as that 
The Quad●…ant of●… Altitude.  it may be fastened on the Meridian, and so be applied to the Zenith of any place whatsoever, being divided from one end to the other into 90. equal parts or degrees.  
There is besides at the foot of the Globe, a Mariner's compass placed: which serves to show, how to place the Globe rightly, according to the Four winds or quarters of the world.   

CHAP II. Of the Circles which are described upon the Superficies of th●… Globe.  
ANd now in the next place we will show wh●… Circles are described upon the Globe itself. And first of all there is d●…awn a circle, in an equal distance from both the Poles, that is 90. degrees, which is called the Equinoctial, or 
The AEquator.  AEquator; because that when the Su●… is in this Circle, days and nights are of equal length in all places. By the r●…volution of this Circle is defended a Natural day, which the Greeks call 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 For a day is 〈◊〉; Natural and Artificial. A Natural day is defined to be the space of time, wher●… in the whole AEquator 
A day Natural and Artificial.  makes a full revolution▪ and this is done in 24. hours. An Artific●…all day is the space, wherein the Sun is passi●…g through our upper Hemisphere: to which is opposed the Artificial night, while th●… Sun is carried about in the lower Hemisphere. So that an Artificial day and night are comprehen●…ed within a Natural day.  
The Parts of a dav are called hours; which are either Equal or Unequal. An Equal hour is the 24. part of a Natural day, in which 
Hours equal and un●…quall.  space, 15. d●…grees of the AEquator do always rise, and as m●…ny are depre●…ied on the opposite part. An Unequal hour is the 12. part of an Artificial day, betw●…xt the ●…ime of the Suns rising and setting again. Th●…se hours are again divided into Minutes. Now a Minute is the 60. part of an hour▪ in which space of time, a quarter of a degree in the AEquator, that is, 15. minutes do ●…ise, and a●… many set.  
PONT. The use of the AEqu●…tor consists chiefly in these things. First, it showeth the time of the AEquinoxes, which are always when the Sun falies upon the Equinoctial circle. And this is, when as the Sun enters into the first degree of Aries and Libra: according to that of Manil●…us.  
Libra Ariesque parem reddunt noctemque diemque  
In English thus.  
The Sun in Libra, and Aries placed, each year:  
The day and night are equal every where.  
Secondly ●…he AEquator divides the Heavens into two equal parts, or Hemisphaeres. whereof one is called the Septeutrionall or Northern Hemisphere: the other, the Meridional or Southern. Thirdly, it showeth the ascension and descension of the parts of the Zodiac: whence the length of the Artificial day and night, for any position of Sphere, may be known. Fou●…thly 〈◊〉 shows what Stars, and parts of the Ecliptic have any Declination.  
The AEquator is crossed, or cut in two opposite points, by an oblique Circle, which is called the Zodiac. The obliquity of this Circle is said to have been first observed by Anaximander Milesius, in the 58. Olympiad. as Pliny writeth in hi●… lib. 2. Cap. 8▪ who also in the same place affi●…mes, that it was first divided into 12 parts, which they call Signs, by Cleostretus Tenedius, in like manner as we see it at this day. Each of these Signs is again subdivided into 30. parts: so that the whole Zodiac is divided, in all, into 360. parts, like as the orher circles are. The first twelfth part whereof, beginning at the Vernal Intersection, when the AEquator and Zodiack cross each other, it assigned to Aries, the second to Taurus, etc. reckoning from West to East. But here a young beginner in Astronomy may justly doubt, what is the reason, that the first 30. degrees or 12, part of the Zodiac is attributed to Aries, whereas the first Star of Aries falls short of the Intersection of the Equinoctial and Zodiac no less than 27. degrees, The reason of this is, because that in the time of the Ancient greeks, who first of all observed the places and situation of the fixed Stars, and expressed the same by Asterisms and constellations, the first Star of Aries was then a very small space distant from the very Intersection. For in Thales Milesius his time, it was two degrees before the Intersection: in the time of Meton the Athenian it was in the very Intersection: in Timocharis his time it came two degrees after the Intersection. And so by reason of its vicinity, the Ancients assigned the first part of the Zodiac to Aries, the second to Tauru●…; and so the rest in their order: as it is observed by succeeding ages, even to this very day.  
PONT. Thales Milesius was the first that calculated the time of the AEquinoxe and Eclipses: and he flourished about the years of the Creation, 3370. which was about 634. years before Christ, Meton lived about 431 years before Christ, in the year of the Creation, 3517. He was the Son of 〈◊〉, and was a man of excellent knowledge in Astronomy. He also first invented the Moon's Circle of 19: years: whose first new Moon fell upon the 13 day of the month Scriophorion, which is the same with our 16 of June, being on a Friday. Vid D●…dorum Siculum. Censorinus writes of him thus. Praeterea sunt etc. There are (saith he (besides, many other great years: as the Metonicall year which Meton the Athenian invented and consisted of 19 common years etc. Timochares was by nation an Alexandrian, and he lived 300 years before Christ.  
Under this Circle, the Sun and the rest of the Plane●…s finished their several courses and periods, in their several manner and time. The Sun keeps his course in the midedst of the Zodiaque, and therewi●…h describeth the Ecliptic circle. But the rest h●…ve all of them their latitude and deviations ●…rom the Sun's course, or Ecliptic. By reaso of which their digressions and extravagations, the ancients assigned the Zodiaque 12. Degrees of Latitude. But our moderen Astronomers, by reason of the Evagations of Mars, and Venus, have added on each side two degrees more: so that the whole latitude of the Zodiaque is confined within 16. degrees. But the Ecliptic only is described on the Globe, and is divided, in like manner as the other circles, into 360. degrees.  
PONT. The whole latitude of the Zodiaqu●… is divided into two parts by the Ecliptic, which is the circle, or Circumference under which the Sun steers his course continually. whence it is called in Latin, Via Solis, & Orbita Solis, the Sun●… high way. And in G●…eek, 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, a Circle divideing the Zodiac in the midst. And it is called the Ecliptic, because the Eclipses of the Sun and Moon never haeppen, but when they are either in conjunction or opposition under this line, or very near the same.  
The Sun runneth through this Circle in his yearly motion, finishing every day in the year almost a degree by his Mean motion, that is 59 minutes, 8. seconds. And in this space, he twice cro●…seth the AEquator; in two points equally distant from each other. So that when he passeth over the AEquator, at the beginnings of Aries and Libra, the days and nights are then of equal length. And so likewise when the Sun is now, at the farthest distance from the AEquator, and is gotten to the beginning of Cancer, or Capricorn, he than causeth the Winter and Summer So Istice●…. I am not ignorant, that Vitruvius, Pliny, Thco●… Alexandrinus, Censorinus, and Columolla are of another opinion; (but they are upon another ground,) when as they say, that the  
AEquinoxes are, when as the Sun passeth through the eighth degree of Aries and Libra, and then it was the midst of Summer and winter, when the Sun entered into the same degree of Cancer end Capricorn. But all these Authors defined the Solstices by the returning of the shadow of Dial's: which shadow cannot be perceived to return back again, as Theon saith, till the Sun is entered into the eighth degree of Libra and A●…ies.  
PONT. The office and use of the Zodiac is. Fi●…st, in that, it is a rule or measure of the proper motion of the Planets. Secondly, By the help of the Zodiac the true place, of all the Stars are sound: besides it may be known in what sign any fixed Star or Planet may be said to be. Thirdly, It showeth the Latitude of the Planets and fixed Stars, Fourthly, All Eclipses happen when the Sun and Moon are under the Ecliptic. Fifthly, The obliquity of the Ecliptic is the cause of the inequality of the artificial days and nights.  
The space wherein the Sun is finishing his course through the Zodiac, is defined ●…o be a Year, which consists of 365. days, and almost 6. hours. But they that think to find the exact measure of this period, will find themselves frustrate: for it is finished in an unequal time. It hath been always a controversy very much agitated among the Ancien●… Astronomers, and not yet determined. Philolaus a Pythagoraean determines it to be 365. d●…yes: but all the rest have added something more to this number. Harpalus would have it to be 369. days and a half: Democritus 365. days and a quarter, adding besides the 164 parts of a day. Oenopides would have it to be 365. days and almost 9 hours. Meton the Athenian determineth it to be 365. days 6. hours, and almost 19 minutes. After him Calipius reduced it to 365. days and 6. hours, which account of his was followed by Aristarchus of Samos, and Archimedes. of Syracuse. And according to this determination of theirs, Julius Caesar defined the measure of his civil year, having first consulted (as the report goes) which one Sosigines a Peripatetic, and a great Mathematician. But all these, ●…xcept Philolaus, (who came short of the just measure) assigned too much to the quantity of a year. For that it is somewhat less than 365. days, 6. hours, is a truth, confirmed by the most accurate observations of all times, and the skilfullest Artists in Astronomical affairs. But how much this space exceedeth the just quantity of a year, is not so easy a matter to determine. Hipparchus, and after him Ptolemy would have the 300. part of a day substracted from this measure: (for Jacobus Christmannus was mistaken, when he affirmed, that a Tropical 〈◊〉, according to the opinion of Hipparchus and Ptolemy, did consist of 365. days, and the 300 part of a day) For they do not say so, but that the just quantity of a year is 365. days, and 6. hours abating the 300. part of a day: as may be plainly gathered out of Ptolemy, Almagest. lib. 3. Cap. 2. and a●… Christmannus himself hath else where rightly observed. Now Ptolemy would have this to be the just quantity of a year perpetually and immutably: neither would he be persuaded to the contrary, notwithstanding the observati●…s of Hipparchus, conc●…ning the inequality of the Sun's periodiacall revolution. But yet the observations of succeeding times, compared with those of Hipparchus, and Ptolemy, do●… evince the contrary. The Indians and Jews subtract the 110. part of a day: Albategnius the 600. part: the Persians the 115. part: according to whose account Messahalah and Albumasar wrote the tables of the Mean motion of the Sun. Azaphius, Avarius, and Arzachel affirmed that the quantity assigned was too mcch, by the 126. part of a day. Alphonsus abateth the 122. part of a day: some others, the 128. and some the 130. part of a day. Those that were lately employed in the restitution of the Roman Calendar, would have almost the 133. part of 1. day to be substracted, which they conceived in 400. years, would come to three whole days. But Copernicus observes that this quantity fell short, by the 115. part of a day. Most true therefore was that conclusion of Censorinus, that a year consisted of 365. days, and I know not what certain portion, not yet discovered by Astrologers.  
By these divers opinions here alleged, is manifestly discovered the error of Dion, which is indeed a very ridiculous one. For he had a conceit that in the space of 1461. Julian years, there would be wanting a whole day for the just measure of a year; which he would have to be intercaled, and so the civil Julian year would accurately agree with the revolution of the Sun. And Galen also, the Prince of Physicians, was grossly deceived, when he thought that the years consisted of 365, days, 6. hours, and besides almost the 100 part of a day: so that at every hundred years' end there must be a new intercalation of a whole day.  
Now because the Julian year, (which was instituted by Julius Caesar, and afterward received, and is still in 〈◊〉) was somewhat longer than it ought to have been: hen●…e it is that the AEquinoxes and Solstices have gotten before their ancient situation in the Calendar. 
The mutation of the AEquinox. and Solstices,  For about 432. years before the inca●…nation of our Saviour Christ, the Vernal AEquinoxe was observed by Meton and Euct●…mon, to fall on the eighth of the Kalends of April, which is the 25. of March, according to the computation of the Julian year. In the year 146. before Christ it appears by the observations of Hipparchus, that it is to be placed on the 24. of the same month, that is the 9 of the Kalends of April. So that from hence we may observe the error of Sosigenes (notwithstanding he was a great Mathematician) in that above 100 years after Hipparchus, in instituting the Julian Calendar, he assigned the Equinox●… to be on the 25. of March, or the eight, o●… th●… Kalends of April, which is the place it ought to have had almost 400. years before his time, This error of Sosigenes was derived to succeeding ages also: in so much that in Gallen time, which was almost 200. years after Julius Caesar, the AEquinoxes were wont to be placed on the 24. day of March and September: as Theodorus Gaza reports. In the year of our Saviour's Incarnation, it happened on the 10. of the Kalend●… of April, or the 23, of March. And 140. years after, Ptolemy observed it to fall on the 11. of the Kalends. And in the time of the Council of Nice, about the year of our Lord 328. it was found to be on the 21. of March, or the 12. of the Calends of April In the year 831. Thebit Ben Chorah observed the Vernal AEquinoxe to fall on the 17. day of March: in Alfraganus his time it came to the 16. of March. Arzachel a Spaniard in the year 1090. observed to fall on the Ides of March, that is the 15. day. In the year 1316. it was observed to be on the 13. day of March. And in in our time. it is come to ●…he 11. and 10. of the same month. So that in ●…he space of 1020. yea●…s. or thereabout, the Equinoctial points are gotten forward no less than 14. days. The time of the Solstice also about 388. years before Christ, was observed by Meton and Euctemon to fall ●…pon the 18. dav of June: as Joseph Scaliger, and Jacobus Christmannus have observed. But the same in our time, is found to be on the 12. of the same month.  
The Ecliptic and AEquator are crossed by two great circles also, which are called Colours both which are drawn through the Poles o●… 
The Colours.  the world, and cut the AEquator at ●…ght Angles. The one of them passing through the points of both the Intersections; and is called the Equinoctial Colour: The other passing through the points of the greatest distance of the Zodiac from the AEquator is therefore called the Solsticiall Colour.  
PONT. The office of the Colours in general is. First to show the four principal points of the Zodiac, in which, by reason of the motion of the Sun, there are caused the great changes of the Seasons of the year. Of which points, two are in the AEquator, at Aries and Libra, determining the place of the AEquinoctial Colour: and Capricorn, which constitute the Solsticiall Colour. Secondly, To distinguish the AEquator Zodiac and the whole Sphere of the Heavens into four equal parts. The use of which is principally seen in examining the ascensions of the Signs. These Colours differ from each other, in that the Solsticiall Colour passeth through the Poles of the world, and also of the Zodiac: but the Equinoctial Colour passeth through the Poles of the world only.  
Now that both the Colours, as also the Equinoctial points have left the places, where they were anciently sound to be in the heavens, is a matter agreed upon, by all those that have applied themselves to the observations of the Celestial motions: only the doubt is, whether fixed Stars have gone forward unto the proceeding Signs, as Ptolemy would have it: or else whether the Equinoctial and Solsticiall points have gone backward to the subsequent Signs, according to the Series of the Zodiac, as Copernicus' opinion is.  
PONT. What the opinion of Joseph Scaliger was, concerning the procession of AEquinoctial points thus diversely thought on by Ptolemy and Copernicus, you have expressed in an epistle of his ●…o Isaac Casaubon, there having been not long before a disputation holden concerning some certain Mathematical question, at the entreaty of some of the chiefest of the States of the Low Countries; among which number Scaliger was chosen also, as an Arbitrator: which Epistle of his, was afterwards Printed, amongst some other of his Epistles at Paris. What the Illustrious Tycho also thought concerning this point, you have in his Progym●…asmata Instaur. Astron. p. 255. But I will first set down Scaliger's opinion: and afterward add Tychoe's, and some others also. Scaliger speaks thus.  
Alterae literaetuae, etc. I received (saith he) ●…eur second letters, the next day aster your former. In which you make mention of one that undertakes ●…o discourse of the Magnetical direction of the Needle. Many indeed have endeavoured in this matter, and doc daily endeavour, being thereto encouraged by the rewards proposed by the Illustrious States. To whose hands some have delivered up their opinions in writing: and Arbitrators forthwith have been called about it. O●… which number, it was my chance to be chosen f●… one: there being indeed amongst them many excellent, both Mathematicians and 〈◊〉 But those that professed the Mathematics, were altogether unexperienced in Nautical affairs: an●… the Navigators were as ignorant of Astronom●…call. Besides these Authors of whom we were 〈◊〉 pass our judgements, performed nothing worth 〈◊〉 great expectation. Neither hath that Englishman, who wrote a Book three years since, of the Magnet, produced anything answerable to th●… great opinion was raised of it. I myself hav●… often proposed, to these Mathematicians that profess in this place, a thing which it seems can never sink into their heads: insomuch that they entertained it with scorn and laughter. Hipparchus was the first that brought in that merry conceit of the eight spheres moving toward th●… East: and so persuaded Ptolemy, that the fix●…d Stars in the eighth sphere moved all in the same order, situation, and distance from each other, toward the East. Which Ptolemy so confirmed, that it had been a heinous matter for posterity to have doubted of the same. And first of all within the memory of our Fathers, Nicolaus Copernicus, that great restorer of Astronomy, perceived the weakness of this conceit of Hipparchus: and withal observed, that the eight Sphere did not move toward the East, but that the Equinoctial points went forward in●…o the precedent Signs: and this he calls 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 But this observation of his, he only nakedly proposed, without any demonstration at all. But I have observed, that the Stars have not (as Hipparchus and Ptolemy dream) gone on to the subsequent parts: and that the Cynosure, or Polar Star was at the same distanoe from Pole in Eudoxus his time, as it is at this day. For proof of which assertion I have collected many instances. which being granted, the procession of the Equinoctial point must necessarily follow. For one of these two must needs be granted; to wit, either of the motion of the eighth Sphere toward the east, or else the progress of the Equinoctial points into the precedent Signs. Now that the first is not to be admitted appears manifestly, because that the fixed Stars have not 〈◊〉 all ●…hanged their situation in respect of the Pol●…, since Eudoxus his time. Therefore the other must needs be granted. The Equinoctial points therefore, have gone forward to the ant●…cedent Signs. Which proposition notwithstanding the great Copernicus had no way to demonstrate, 〈◊〉 out of the Phaenomena; by which that other motion might as well be defended▪ as ●…his. We therefore now have this 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 But what is it? Even nothing else, b●… the motion of the Equinoctial points into the precedent Signs. Now if the Equinoctial points be●… movable; and the Equinoctial C●…cle b●…e de●…cribed by these points; the Equinoctial Circle ●…hen must needs be movable also: which is as true, as truth itself. And if the Equinoctial circle be movable; his Pole must be movable also; and so the Poles of the Equinoctial must be divers from the Poles of the world. for the Pole of the World is immovable; but this movable. Besides, all the Meridian circles do pass through the Poles of the Equinoctial: and in the superficies of stone dials, the Meridian line, which is drawn for the placing of the Sun Dial, is understood to pass through the Poles of the Equinoctial; which is confessed by all men, and is most true. But because the Poles of the Equinoctial are movable, the Meridian line. that passeth through the same, must be movable also. And therefore it necessarily followeth, that after some certain number of years, there will be no further use of these Meridian lines in the designing of the hours in dials; but a new Meridian line must be taken, and the situation of the Dial altered, though not the Dial itself. We may therefore conclude, that the Sun dials, after some certain time, will prove false, unless the Meridian line be rectified. This is demonstrated of the very principles of the Mathematitcks. But besides this, we have some notable instances out of the Ancients, which do manefestly evince, that after some term of years, Sun dials do not agree to their first designations: all which I have diligently collected. These things thus demonstrated, I proposed them to these Mathematicians, that, because the whole businesses of the Magnetical Needle had dependence upon these Meridian's, they would consider, whether or no, this doctrine, by me first proposed, might open the way to the matter in hand, etc.  
Thus far Scaliger. Let us now hear Tycho. Inaequalitatis, inquit, circa motum, etc. That the reason (saith he) of the inaequality observed in the motion of the fixed Stars, or as Copernicus calls it, the Anticipation of the Equinoctial points (which is a very subtle and ingenious speculation of his own, that so he might reconcile and maintain the inventions of all that went before him) that this conceit, I say, doth not constare sibi, these 70. years' observations of the Star called Spica Virgins, since his first observing the same; do manifestly prove. For in this space of time, the reciprocation of the Equinoctial points, or promotion of the Stars, is swifter, by much, than he conceived it would have been. So that, whereas now they ought to have finished but one degree in an hundred years' space, or thereabout, they finished the same in 70. the quantity of the years being not so slow as he imagined it to be: as appears plainly by that we have delivered in the former Chapter. For these two things do mutually cohere together in Copernicus, that when the quantity of the year is greatest, the motion of though fixed Stars should then be slowest. But these things the accurate observat●… on's of these present years do manifestly elude, for as much as they do not answer his periodical restitutions.  
Thus these two great lights of our times, Tycho, and Scaliger, to whom we may add the opinion of our Countryman Dr. Gilbert, who in his 6th book de Magnete, will have the praecession of the Equinoctial points to depend upon the Magnetical mot●…n of the Poles of the Earth▪ And this is that Englishman, as far as I can gather, whom Scaliger mentions in his forecited Epistle: Unto whom I refer you for satisfaction in this point, in his lib. 6. cap. 8.  
The first Star of Aries, which in the time of Meton the Athenian, was in the very Vernal Intersection, in the time of Thales Milesius was two degrees before the Intersection. The same in Timochares his time, was behind it two degrees 24. minutes: in Hipparchus time, 4. degrees, 40. minutes: in Albumasars' time, 17. d●…grees, 50. minutes: in Albarenius his time, 18. degrees, 10 minutes: in Arzachels' time, 19 degrees, 37. minutes: in Alphonsus his time, 23. degree●…, 48. minutes: in Copernicus and Rhoeticus his time 27. degrees, 21. minutes. Whence Franciscus Baroccius is convinced of manifest error, in that he affirms that the first Star of Aries, at the time of our Saviour's Na●…ivity, was in the very Vernal intersection: especially contending to prove it, as he doth, out of Ptolemy's observations, out of which it plainly appears, that it was behind it no less than 5. degrees.  
In like manner the places of the Solstices are also changed, as being always equally distant from the Equinoctial points. This m●…tion is finished upon the Poles of the Ecliptic, as is agreed upon, both by Hipparchus and Ptolemy, and all the rest that have come after them. Which is the reaso that the fixed Stars have always kept the same latitude, though they have changed their declination. For confirmation whereof, many testimonies may be brought out of Ptolemy, lib 7. cap. 3- Almag. I will only all dg one, more not able than the r●…st, out of Petolomies' Georgr. lib. 1. cap. 7. The Star which we call the Polar Star, and is the last in the tail of the Bear, is certainly known in our time to be scarce three degrees distant from the Pole: which very Star, in Hipparchus his time, was above 12. degrees distant from the Pole: as Merinus in Ptolemy affirms. I will produce the whole passage, which is thus. In the Torrid Zone, (saith he) the whole Zodiac passeth over it, and therefore the shadows are cast both ways, and all Starrrs there are seen to rise and set. Only the little Bear begins to appear above the Horixon in those places, that are 5 0 furlongs Northward from Ocele. For the Parallel that passeth through Ocele 〈◊〉 distant from the AEquator 11. gra. ⅖. And Hipparchus affirms, that the Star in the end of the little Bear's tail, which is the most Southward of that Constellation, is distant from the Pole 12. degrees▪ ⅖. This excellent testimony of his, the Interpreters have, in their translating the place, most strangely corrupted (a●… both Johannes Wernerus, and after him Peter Nonius have observed) setting down in stead of 500 Quinque mille, 5000▪ and for Australissimam, the most Southern, Borealissimam, the most Northerly: being led into this error, perhaps, because that this Star is indeed in our time the most Northern. But if these testimonies of Marinus and Ptolemy in this point be substracted, Strabo in his lib. 2. Geogr. shall acquit them of this crime. And he writes thus. It is affirmed by Hipparchus (saith he) that those that inhabit under the Parallel that runneth through the Country called Cinnamomifera (which is distant from Meroe Southward, 3000. furlongs▪ and from the Equinoctial, 8800.) are situated almost in the midst, betwixt the AEquator and the Summer, Tropic, which passeth through Syene (which is distant from Meroe 5000. Furlongs) And these that dwell here, are the first that have the Constellation of the little Bear, enclosed within their Arctic Circle, so that it never sets with them: for the bright Star, that is seen in the end of the tail (which is also the most Southward of all) is so placed in the very Cirele itself, that it doth touch the Horizon. This is the testimony of Strabo, which is the very same that Ptolemy and Merinus affirm; saving that both in this place, and elsewhere, he always assigns 700. Furlongs in the Earth, to a degree in the Heavens, according to the doctrine of Eratosthenes: whereas both Marinus and Ptolemy allow but 500 only: os which we shall speak more hereafter.  
Let us now come to the lesser Circles which are described in the Globe. And these are all Parallel to the AEquator: as first of all the Tropickes, which are Circles drawn through the points of the greatest declination of the Ecliptic, on each side of the AEquator. Of which, that which looks toward the North 
The Tropic  Pole, is called the Tropic of Cancer: and the other, bordering on the South, the Tropic of Capricorn. For the Sun, in his yearly motion through the Ecliptic, arriving at these points, as his utmost bounds, r●…turneth again toward the AEquator. This Retrocession is called by the greeks 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, and the Parallel Circles, drawn through the same points, are likewise called Tropickes.  
PONT. The use of those tropickes is, First, to show when the Sun, in an oblique Sphere, is nearest the vertical point of any place, and so likewise when the farthest off. Secondly, they show, when the Sun, in his Diurnal motion, maketh the longest or shortest days in the year. Thirdly, they are▪ as it were, the limits and bounds, wherein the Sun finisheth his yearly course. Fourthly, they distinguish the Torrid Zone in the heavens, from the two temperate Zones.  
The distance of the Tropics from the AEquator, is diversely altered, as it may plainly appear, by comparing the observations of later times, with those of the Ancients. For, not to speak any thing of Strabo, Proclus, and Leontius Mechanicus, who all assigned the distance of either Tropic from the AEquator to be 24. degree●… (for these seem to have handled the matterbut carelessly) we may observe the same from the more accurate observations of the greatest Artists. For Ptolemy found the distance of either Tropic to be 23. gr. 51. min. and ⅓▪ just as great, a●… Eratosthenes and Hipparchus had found it before him: and therefore he conceived it to be immutable. Machomethes Aratensis observed this distan to be 23. degrees, 35. minutes, right as Almamon King of Arabia had done before him. Arz●…l the Spaniard found it to be in his time, 23. degees, 34. minutes. Almehon the Son of Albumasar, 23 degrees, 33. minutes, and half a minute. Prophatius a Jew, 23. degrees, 32. minutes, Purbachius and Regiomontanus, 25. degrees, 28. minutes Johan. Wernerus, 23 degrees, and 28. minutes, and an half: and Copernicus found it in his time to be just as much.  
PONT. This distance of the Tropickes from the AEquator, is caused by the Sun's greatest declination, as the Astronomers call it. which greatest declination of the Sun hath been, at divers times, found to be variable. For beginning as sar backward, as possibly we can, and so driving it down by the Olympiads, and the year of Christ, even to these present times, according to Tychoes' calculation. we find it to be thus, both in the degree and minute, as is here expressed in this ensuing Table.  
 gr. m. 11.  Aratus 24. 0. 0. Olympiad. Hipparchus 23. 51½ 124. Eratosthenes  127. Ptolomaeus 23. 51. 20, An Christi 140. Albategnius 23. 35. 0. 749. Arzahel 23. 34. 0. 1070. Almeon 23. 33 ½. 1140. Prophatius Judaeus 23. 32. 0. 1300. Purbachius 23. 29. 30. 1458. Regiomontanus 23. 30. 0. 1490. Copernicus' 23. 38 30. 1500. Tycho Brahe 23. 31. ½. 1592.  
To which we may add these words out of Tychoes. 1. Book of new Star which appeared An. 1572. p. 101. where he saith, that by certain observations it hath been found, that both the Sun's greatest declination, as also the other Intermediat by the same reason are altered, as it is testified by the whole current of the most skilful Artists, in a continual succession of time: so that Ptolemy's time, & some certain years before him, it was found to be 23. gr▪ 51. ½ but it doth not appear by any certain testimony to have been ever greater. Whence may be collected, that Aratus, whom we have set in the first place, who assigns 24. gr. speaks with the largest, and as it were, at random, and (as our learned Author hath also observed of Strabo, Proclus and Leontius Mechanicus) not so accurately as he should have.  
There are also two other lesser circles described in an equal distance from the Poles, to that of the Tropickes from the AEquator? which circles take their denomination from the Pole on which they border. So that one of 
The Arctique, and Antarctique circles.  them is called the Arctic or North circle; and and the oppsite circle the Antarctick or Southern. In these circle's the Poles of the Ecliptic are fixed, the Solsticiall Colour crossing them in the same place. Strabo, Proclus, Cleomedes, all Greek Authors, and some of the Latins also, assign no certain distance to these circles from the Poles: but make them various and mutable, according to the diversity of elevation of the Pole, or divers position of the Sphere: so that one of them must be conceived to be described round about that Pole which is elevated, and to touch the very Horizon, and is therefore the greatest of all the Parallels that are always in sight: and the other must be imagined, as drawn in an equal distance from the opposite Pole; and this is the greatest of those Parallels that are always hidden.  
PONT. The Arctique, and Antarctique circles do show, 1. The Poles of the Zodiaque and their distance from the Poles of the world, 2. They do distinguish the frigid Zones from the Temperate, and with the Tropiques and AEquator they help to divide the whole Heaven into five parts or regions which they call Zones.  
Besides these circles expressed in the Globe, there are also some certain other circles in familiar use with the Practical Astronomers, which they call Vertical circles. These are 
The Vertical circles,  greater circles drawn from the Vertical point through the Horizon, in what number you please: and they are called by the Arabians Azimuth, which appellation is also in common use among our ordinary Astronomers. The office of these circles is supplied by the help of a Quadrant of Altitude, which is a thin plate of brass divided into 90. degrees. This Quadrant must be applied to the vetrex of any place, when you desire to use it, so that the lowest end of it, noted with the number of 90. may just touch the Horizon in every place. This Quadrant is made movable, that so it may be fastened to the vertical point of any place.  
PONT. Concerning the moveableness or mutability of the Arctique, and Antarctique Circles, Joseph Scaliger reports himself to be the first that observed it, out of the Ancient Greek Authors: as you may see in his Commentaries upon Manilius, revised, and published by himself a little before his death. Neither doth he think that any ancient Latin Author within 400. years after those Greek Writers, nor scarcely any before Sacrobosco's time, can be found to have determined them to be immovable. But because there are many excellent things to be met withal in that pssage of his, and that he sets down the same by way of demonstration; I have thought it not impertinent, seeing our Author hath given a touch at it, to set down Scaliger's opin●…n in his own words: as you have them upon those verses of Monilius, lib. 1. Astron.  
Circulus ad Boreā fulgentem sustinet Arcton, Sexque fugit folidas a coeli vertice parts.  
He proceeds after this manner. Describantur circuli AEquinoctiali paralleli XC etc. Let there be described (saith he) 90. Parallel circles to the Equinoctial, and these will be the same that Gaminus calls, 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, always appearing. Now among all those, That which toucheth the Horizon in the point of intersection of the Horizon and Meridian, will be 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, the greatest of those that always appear, and so conseqvently, the Arctique Circle of that place: now because the Orisons are movable, the Arctique Circles must also be movable. So in the Climate wherein Cnidus lies, the elevation of the Pole being thirty six degrees, Eudoxus determines the Arctic Circle also to be so many degrees from the Pole▪ in like manner in another Climate, it will be divers, according to the diversity of the elevation of the Pole. Thus Hipparchus 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉. At Athens (saith he) the greatest of the Circle always appearing is distant from the Pole thirty seven degrees: but that in Rhodes thirie six degrees: and look how great the Altitude of the place is, the same must the distance necessarily be, betwixi the Pole and that point, by which the Arctic circle is described. And therefore the Ancient greeks always defined the Arctique circle to be 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉. Sive 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉. The most Northern point that their Horizon, or place of habitation had. So that the Arctic circle is nothing else, but the point of their habitation which toucheth the Horizon. For in describing, they have both one common point. Only in this they differ, that the centre of the Arctique circle is the Pole of the world; but the centre of the Horizon is the Vertical circle, or Zenith of the place,  
As for example. A. F. D. E. is the Horizon: A. G C. H. the Arctic circle A. D. the Meridian: A. the point of Intersection of the Horizon with the Meridian; in which place also the Arctic and Horizon in describing do mutually touch each other. B. the Pole: C. the Zenith of the place. I. the opposite point of the diameter of the Actique circle, Now if the elevation of the Pole be full 45. degrees, as it is at Vienna in Franc●…, than the point I. will be the same with C that is to say, the opposite part of the Arctique cir●…le will touch the Zenith of the place. Ent if the elevation of the Pole be less than 45° degrees, the Zenith will then fall without the circle: but if it be greater, it will fall within. S●… that by this means it will come to pass, that the nearer we are to the AEquator, the lesser these circles will be: and contrariwise, the farther we live off the AEquator, the greater they are: But under the Equinoctial itself, that is in a right position of Sphere, there is no Arctic circle at all: Pytheas writes, that those that inhabit Thule, now call Iseland, have a Tropic for their Arctique circle. Whether therefore this Circle fall within or without the Tropic, the distance of it from the poi●…t, l. Will be as great, as is the difference betwixt the elevation of the Pole, and the elevation of the Equinoctial above the Horizon of the place. As for Example: The elevation of the Pole at Rome is 41. degrees, therefore the Equinoctial is elevated above the Horizon 48. gr. 20. m. and the difference is 7. degrees 40▪ m. And therefore the Zenith, or vertical point of Rome, falleth 7. degrees, 40. m. without the circumference of its Arctic circle. So this distance which those that inhabit Iseland, is 43. gr. as having their Pole elevated 66. degrees 30. m. So that the Trepick with them toucheth the very point of intersection of the Meridian and Horizon. And therefore, Martianus Cappella designs the Arctic circle to be. Semper apparens, & contingens confinia Finitoris, nunquam mersus assurgent. A circle that always appeareth, and toucheth upon the skirts of the Horizon, yet never goeth under it. By these words Confinia Finitoris, he meaneth the intersection of the Horizon and Meridian 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, in the most Northerly point.  
These grounds being thus laid, we see that as many habitations as there are, so many Arctic circles there are also, and the same not 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, fixed and unchangeable, but different according to the diversity of paces. So that, by this we may plainly ●…erceive the error of our modern Artificers, who, in their Artificial Globes, describe this circle contrary to the doctrine and practice of the Ancients, drawing it on the Poles of the Ecliptic above the Pole of the world. Fur such an Arctic circle there cannot be, but only to those that inhabit Syene by the Nile: for with them, the Pole is elevated 23. gr. 30. m. These things considered, the Arctic circle ought not to have any place in the Material Globe, unless it be made for the inclination of some certain place: otherwise there can be no such Arctic circle.  
These things, when I first proposed in Aquitaine, where were many, both learned and unlearned, Noble and Paedants, it cannot be imagined with with what scorn and hissing they entertained them. And at length, when my constancy would not give place to their stubborn ignorance; I thought I should have been beaten among them. Yet at last, having nothing to defend themselves with, they said, that, however it were, these circles were useful for the distinction of the Zones. At which answer of theirs, I had much ado to forbear laughing. For this division of the world into Zones, is quite cashiered in these our times, when as the whole world hath at length been fully discovered by the Navigations of the Portugals and Spaniards. And for this purpose, to confute these Mathematicians, I alleged these words of Strabo, 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉. Polybus therefore did not, (saith he) in making certain Zones, which are to be limited by the Arctic circles: two of which line under the said Arctiques, and other terminated betwixt the Arctiques, and the Tropiques. For this is a Maxim: That determinate things cannot be bound by uncertain and indeterminate limits. This their Philosophy therefore is vain and frivelous. But yet their impudence ends not so. For you shall hardly meet with any of those Mathematicians, that will not presently conclude him mad, that should but dare to descend any whit from the doctrine of John de Sacrobosco, in the point of these circles. Yet one of them, not long since, being as it seems, advised thereto by the former edition of Manilius, confesseth by the way, and as it were unwillingly, that the Ancients made other use of the Arctic circle s; then we now do. And yet he would not be thought to have learned this of me: notwithstanding these kind of fellows are the most ignorant in matters of Antiquity, in the world. Who should be the first broacher of this ridiculous conceit, I cannot guess, otherwise, then that it must needs be some latin Writer, and thaet 400. years later than any of the Greek Authors. And I know not whether any other taught this doctrine before John de Sacrobosco: ceartainely he is the most ancient I can readily think on. As therefore our men are in an error, in making the Arctic to be an Immutable circle, so likewise are the Ancients, and those among us that follow them, to be blamed, for making this circle to be Parallel to the other three: whereas the Parallel circles in a Sphere have the same Pole with the Sphere itself. But the Pole of the Arctique is the same always with the Pole of the World: whereas the Pole of the other three altereth, as do the Tropical, and Equinoctial points. For the Equinoctial and Tropical points do anticipate their places in the Zodiaque: insomuch, that in a certain term of years, they are removed forward a degree. Now the Equinoctial, and Tropical circles, are no other than what are described by those points, which in themselves are movable. Therefore are their Poles also movable. But we shall suffer for these things too, I doubt not, until that length of time shall have beaten this into the heads of such men, with whom strength of reason is able to prevail nothing at all:  
And this is the opinion of Scaliger, and the Ancients, concerning the Arctic circles: which Johanne●… Pincierus, a learned man, in his lib. 2●… cap. 13. Parergor. Otij▪ Marpurg. hath lately examined, and indeavonred to confute the Arctique circle (saith he) is thus described by Proclus. Arcticus circulus, etc. The Arctique circle is the greatest of all those circles that are always in sight, and it toucheth the Horizon in one point, and is seen also above the earth. And the Antarctique he defines thus. The Antartique is a circle equal and Parallel to the Arctique, and lies wholly hid under the earth. These circles therefore, in the opinion of Proclus, are movable, andare described by a point that toucheth the Horizon about the Pole that is nearest to it: and they are also changed, with the Horizon, as often as a man moveth either Northward or Southward. So that the nearer they are to the Pole, the lesser they are: and so chose, the farther off they are from the same, the●… are so much the greater: and consequently it follows, because they have no fixed place, that therefore they cannot be described upon a Sphere or Globe.  
But from hence there ariseth three inconveniencies. First, that these Arctiques described by Proclus, are not of any use in distinguishing the Frigid Zone from the Temperate, by reason of their uncertain situation, and mutability. The next is, that with those that inbabite within twenty three degrees and an half of the Pole, (which is as much as the Sun's greatest declination from the AEquator) the Arctique circle will be the same with the Tropic of Cancer, and the Antartique with that of Capricorn. So that they will have but two lesser circles or Parallels, which will make but three Zones in all, two cold ones; and a torrid. For in this confusion of the circles, there will be no distinction betwixt the cold, and the temperate Zones, And which is more, they that dwell under the AEquator. will have no Arctiques at all. Lastly there are certain accidents proper to, certain Climates, which cannot he assigned them, unless there be fixed and certain limets set to distinguish the cold Zones from the temperate.  
As for example, If it be enquired, what properties are incident to those that inhabit betwixt the Tropic of Cancer and the Arctique circle: and what to those under the Arctique circle itself: and lastly, what betwixt the Arctique circle and the Pole of the World. To these questions there can be no answer made without these fixed Arctique circles. Besides this, it would take away much light and futhera●…ce, both from Geographical Maps, and Astronomical instruments, if these Arctique circles might not be described in them: Which could not possibly be described in them, but that they might change evermore with the Horizon.  
These and the like inconveniences are easily avoided, by placing the Arctique circle, as usually it is, on the Poles of the Zodiaque. Neither am I any way swayed with the Authority of Joseph Scaliger, adhering to Proclus his Doctrine of the mutability of the Arctique Circle: although I am n●…t ignorant, how rare a thing it is▪ for such Judgement, matched with so great knowledge, to fall into an error. And as for that testimony which they bring out of Strabo, lib. 2. Geogr. that it is sufficient, if there be Arctique circles in the temperate Climes, and that those that have any, have not all the same: this is 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 (to use Straboes own words) nothing to the argument in hand, and concludes nothing. For than they should be of no use at all. I cannot therefore assent to a man, whose Tenent is dissonant both from the nature of the thing, and reason itself.  
But to return at length to Proclus: who, seeing that he acknowledgeth that there are five Zones: two of which are terminated betwixt the Poles, and the Arctique and the Antarctique circles: and other two bordering upon the same, which are the two temperate Zones, and are bounded on one side by the Arctique, and the other, by the Tropickes: betwixt both which lieth the Torrid Zone. he himself seems tacitly to approve these Immoveable Artiques, without which there can be no set constant limits of the Frigid and temperate Zones.  
Thus Scaliger and Pincierus. Now concerning the opinion that the Ancients had of those Zones, namely, that some of them were inhabited through extreme cold, and some through parching heat; notwithstanding these are discovered at length to be but vain dreams, by the late Sea-voyages both of the Portugals and our own Countrymen: yet can it not be denied, but that in each of them there are certain special and peculiar Occurrences. So that, if, but for doctrine sake. it were good that these circles should not be taken away, neither are we to despise it, if by the industry of later times, any thing hath been added to the inventions of the Ancients, which may any whit be useful for the instruction of learners, or may any way conduce so the clearing of things, in themselves obscure and intricate.   

CHAP. III. Of the three Positions of Spheres: Right, Parallel, and Oblique.  
ACcording to the divers habitude of the AEquator to the Horizon, (which is either Parallel to it, or else cutteth it, and that either in Oblique, or else in Right Angles,) there is a threefold Position or situation of Spheres. The first is of those, that have etheir Pole for their Vertical point: for with these, the AEquator and Horizon are Parallel to each other, or indeed rather but one circle betwixt them both. The 2d is of those whose Zenith is under the AEquator. The third agreeth to all other places else. The first of these situations is called, a Parallel Sphere: the second a Right: and the third an Oblique Sphere. Of these several kinds of position, the two first are simple: but the third is manifold and divers, according to the diversity of latitude of places. Each of these have their peculiar properties.  
Those that in habit in a Parallel Sphere, see not the Sun or other Stars, either rising or setting, or higher or lower, in the diurnal revolution. Besides, seeing that the Sun in his yealy motion traverseth the whole Zodiaque, which is divided by the AEquator into 2. equal parts: one whereof lieth toward the North, and the other toward the South: by this means it comes to pass, that while the Sun is in his course through those signs that are nearest their vertical Pole, all this while he never setteth, and so maketh but one continued Artificial day; which is about the space of six months. And so contrariwise, while he runneth over the other remoter signs, lying toward the opposite Pole, he maketh a long continual night of the like space of time, or thereabout. Now at such time as the Sun in his diurnal revolution shall come to touch the very AEquator, he is carried about in ●…uch sort, as that he is not wholly apparent above the Horizon, nor yet wholly hidden under it: but as it were, half cut off.  
The affections of a Right Sphere are these. All the Sarrs are observed to rise and set in an equal space of time: and continue as long above the Horizon, as they do under it. So that the day and night is always here of equal length.  
PONT. That in a right Sphere all the Stars do both rise and set that is, are all generally seen above the Horizon, and in like manner do also all set by turns; so likewise that boath the Poles, both Arctique and Ant●…rctique may be seen at once: hath hitherto been the received opinion both of Geminus. And Proclus, and generally, of all other Writers: whichour Author also here followeth. Yet if we do but examine the matter more nearly, we shall find this to agree not so much with the Sensible, as with the Rational or Intelligible Horizon. For as much as eve●… in a Right Sphere, the fight can hardly reach both the Poles, by reason of the extuberancy of the earth. Which is also confirmed by the Testimony of Johannes Lerius a Burgonian, who in his history of his voyage into the New world, whether thus. Non modo sub AEquinoctiali polus uterque non apparet, etc. Under the Equinoctial (saith he) not only both the Poles are invisible, and do not appear, but neither one nor other can be seen, till a man hath passed on two degrees from the AEquator. But whether this assertion of his, or the contrary of some of our Countrymen, who have also sailed through those parts, be to be accounted the more accurate and trne, I leave to other to determine,  
PONT. The position or siavation of a Sphere is rightly distinguished by our Author, into three ●…inds, to wit, Parallel, Right, and Oblique. Notwithstanding Clavius, with Sacrobosco. acknowledge only two: and they are, Right, and Oblique▪ For if it be demanded, (saith Clavius) what manner of Sphere they may be said to have, that inhabit under the Poles: we must make answer, an Oblique. But both Clavius, and Sacrobosco are herein deceived. For those that have such a position of Sphere, as that they dwell under the Pole, the AEquator with them doth not make Oblique Angles with the Horizon: because the Horizon and AEquator there, make both but one circle. This kind of Sphere therefore may more rightly be called a Parallel, or Neutral Sphere: because that its Vertical point falleth upon the Pole of the Sphere. But Joseph Scaliger hath given it the aptest appellation of all, in his Notes, upon Manilius. Astronom. lib. 3. upon these Verses.  
Stantis erit coeli species, laterúmque meatus Turbinis in morem rectâ vertigine currit.  
Where he saith, that every Sphere may be said, aut jacere, sedere, aut stare, either to lie, sit, or stand. So that the first position of Sphere is, as of lying all along, which is that of a Right Sphere, where the Horizon makes right Angles with the Equinoctial. The seeond is of sitting, 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉. The third is of standing, 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 and is like a Mill. for in this Position, the Equinoctial, supplying the office of the Horizon, and as it were, turned round about, is just like a Hand-mill, both in habit, and manner of turning about, But we cannot so properly call it a Right Sphere because of the right Angles that it makes with the Equinoctial, as passing through its Poles: because that that appellation seems to suit more fitly with a standing Sphere, in which the Equinoctial is the same with the Horizon and Arctique circle. Lastly there is but one Right, or Lying Sphere because there is but one Equinoctial: and there are but two standing Spheres; because there be but two Poles. But there is great variety and diversitis of Oblique; or sitting Spheres, as may manifestly appear to any man; and as our Author hath declared at large,   

CHAP. FOUR Of the Zones.  
THe four lesser Circles, which are Parallel to the AEquator, divide the whole earth into five parts, called by the greeks, Zones. Which appellation hath also been received, and is sti●… in use among all our Latin Writers: notwithstanding they sometimes also use the Latin word, Pl●…ga, in the same signification. But the greeks do sometimes apply the word Zona, to the Orbs of the Planets, (in a different sense than is ever used by our Authors) as may appear by that passage of Theon Alexandrinus, in his Commentaries upon Aratus, 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉. that is: There are also in the heavens seven Zones, whi●…h are not contiguous to the Zodiaque: the first whereof is assigned to Saturn, the second to Jupiter, etc.  
Of these five Zones, three were accounted by the Ancient Philosophers and Geographers to be inhabitable and intemperate. One of them by reason of the Sun's beams continually beating upon the same: and this they called the Torrid Zone, and is terminated by the Tropiques on each side. And the other two by reason of extreme cold, they thought could not be inhabited, as being so remote from the heat of the Sun's beams: whereof one was comprehended within the Arctique circle, and the other within the Anta●…ctique. But the other two were accounted temperate, and therefore habitable, the one of them lying betwixt the Arctique circle and the Tropic of Cancer; and the other betwixt the Antarctique and the Tropic of Capricorn.  
Neither did this opinion, (although in a manner generally received a 'mong the Ancients) concerning the number and bounds of the Zones, even then want its opposition. For Parmenides would have that Zone, which they call the Torrid, to be extended far beyond the Tropiques: so that he made it almost as large again, as it ought to have been: but is withal reprehended for it by Posidonius, because he knew that about half of that space which is contained betwixt our Summer Tropic and the AEquator, was inhabited. So likewise Aristotle terminated the torrid Zone betwixt the Tropiques, and the temperate Zones, with the Tropiques, and the Arctique and Antarctique circle. But he also is taxed by the same Posidonius, in that he appoints the Arctique circles, which the greeks will have to be mutable, to be the limits of the Zones. Polyibus makes six Zones, by dividing the Torrid into two parts, and reckoning one of them from the Winter Tropic to the Equinoctial, and the other from thence to the Summer Tropic. Others following Eratosthenes, would have a certain narrow Zone; which should be temperate and fit for habitation, under the Equinoctial line: o●… which opinion was Avicen the Arabian. And some of our Modern Winters, (Nicolaus Lyranus, Thomas Aquinas, and Campanus) I know not upon what grounds, will have the terrestrial Paradise, spoken of in the beginning of Genesis, to be placed under the Equinoctial line. And so likewise Eratosthenes and Polybius, would have all that which they call the Torrid Zone, to be temperate. In like manner Posidonius contradicted the received opinion of the Ancient Philosophers, because he knew that both Syene, which they place under the Tropic of Cancer, and also AEthiopia, which lieth more inward, and over whose heads the Sun lieth longer, than it doth upon theirs under the AEquator, are notwithstanding inhabited. Whence he concluded, that the parts under the AEqinoctiall were not inhabitable, because he saw ●…at those under the Tropic wanted ●…ot inhabitants. Yet Ptolemy in his 2d book ●…d sixth Chapter of his Almageste, conceiveth ●…hose things, which are prepared of the temperateness under the line, to be rather conjecture then truth of story: and yet in the last Chapter of his fifth book of his Geography, he describes us a Country in AEthiopia, which he calleth Agisymba, and placeth far beyond th●… the Equinoctial: (notwithstanding some of our Modern Geographers stick not to place it Northward from the AEquator, contrary to Ptolemy's mind.) This inconstancy of Ptolemy hath given occasion to some to suspect, that the Almagest, and Cosmography were not the same Authors works.  
Now as concerning these conceits of the Ancients, about the number of the intemperate Zones, if they were not sufficiently proved to be vain and idle, by the authority of Eratosthenes and Polybius: yet certainly it is very evidently demonstrated by the Navigations both of the portugals, and also of our own Countrymen, that not only that tract of land which the Ancients call the Torrid Zone, is fully inhabited; but also that within the Ar●…tique circle, above 70 degrees from the AEquator, all places are full of inhabitants. So that now, no man needs to doubt any further of the truth of this; unless he had rather err with Sacred and Venerable Antiquity, then be better informed by the experience of Modern Ages, though never so strongly backed with undeniable proofs and testimonies.  
PONT. Whereas our Author accuseth Ptolemy of inconstancy, in that in his Almagest. cap. 6. lib. 2. he accounteth it a fahle, rather than any true, history whatsoever is reported of the in hahitants under the AEquator: where as in his Geography lib. 5. cap. ult. he seemeth to contradict the same: I think that Pliny also is not free from the like fault. For whereas in his lib. 6. cap. 22. having discoursed of the M●…gnitude of the Isle Taprobane, (which is now thought to be Sumatra, and lieth directly under the line,) out of Eratosthenes and Megasthenes: he presently adds, that besides the testimony of the Ancients, the Romans had better knowledge of the same, in the time of the Em●…eror Claudiu●…, there being Ambassadors sent from thence to Rome; who among other things, should relate, that with them Gold, & Silver was in high account, and that they had greater wealth than the Romans themselves; but yet that the Romans had greater use of riches, than they. Which words of Pliny, with many other there at large set down by him, if they be but compared with what himself elsewhere writeth, in his 2d book chap. 68 he will be found manifestly to contradict himself. For disputing in this place, and inquireing, how great a part of the earth is inhabited: Tres (saith he) terrae partes abstulisse nobis coelum, etc. Three parts of the world the Heaveus have robbed us of; to wit, the Torrid, or middle Zone, ●…bat is, whatsoever lieth betwixt the two Tropiques: and the two outmost or Frigid Zones: that is to say, whatever ground lieth betwixt either Pole, and the Arctique and Antarctique circles. According to that which the Poet sung of old: 
Quarum quae media est, non est habita bilis aestu.  
Nix tegit alta duos.   
In English thus. 
The midst of these is not inhabited,  
Through heat: and two, with snow are covered.   
For this is that which Pliny meaneth: that those two outwardmost are not habitable, by reason of extremity of ●…old, nor the other, through too violent heat. But that which is more to be wondered at in so great an Author, (who not withstanding indifferently took up aswel the common popular fables, as the extravagant fixions of the Poets also) is that which he very confidently relates out of Corlius Nepos, how that one Eudoxus, taking Ship in the Arabian gulf, came as far as the Gades, two Isles upon the confines of Spain. Which voyage if we should but throughly examine, will be found to be as much, 〈◊〉 that all the Fortugals, and our Countrymen at this day perform in their Sea voyage to the East Ind●…, when as touching upon the Cape of good hope, they twice cross the line, and pass through the whole Torrid Zone. Not to speak any thing of that which he writes in his first book, twenty third Chapter, Namely, that there is never a year, that India doth not suck out of the Roman Empire, at the least 500000. Sesterces, by sending in such commodities, as they sell to the Romans for an hundred times as much as they are worth in India. And that there is yearly Traffic by Ship through the Red Sea, betwixt them and the Romans, who are sane, for their safer passage, to defend themselves from Pirates, by going provided with bands of Archers. And here, all that can be said in Pliny's defence, is, tha●…those things which he relates in this second book, were written by him long before the rest which followeh: and that at that time, these Indian voyages were not so frequently undertaken, or the passages so well known unto the Romans: especially, for that in the books following, as namely the sixth book 17. and 23. Chapters he saith, that the whole course of the voyage from Egypt into India, began but than first to be discovered, when as he was writing the same: and that Seneca having not long before begun a description of India, reckoned up therein 60. great rivers, and 122. Nations, to be contained within the same.  
The principal cause of the habitableness and fortility of the parts under the Torrid Zone, i●…, in that the Sun shineth upon them but 12. hours: so that the nights being always as long as the days, the coldness of the one doth very much attemperate the excessive heat of the other. In like manner, that both the Frigid Zones are habitable, is to be attributed to the Sun, which in his course, through the six Northern signs of the Zodiaque, never sets in six months' space so those that live under 84 degrees of latitude: so that by his continual presene●… the extreme rigidity of the Clime i●… mitigated, and the cold, by this means, dispelled.   

CHAP. V. Of the Amphiseij, Hereroscij, and Periscij.  
THe inhabitants of these Zones, in respect of the diversity of their noonshadowes, are divided into three kinds, Amphis●…ij, Heteroscij, and Periscij. Those that inhabit betwixt the two Tropiqu●…s are called Amphiscij, because that their noon shadows are diversely cast, sometime toward the South, as when the Sun is more Northward than their Vertical point: and sometimes toward the North, as when the Sun declines Southwa●… from their Zenith.  
Those that live betwixt the Tropiques and A●…ct que circles, are called Heteroscij, because the shadows at noon are cast only one way, and that ●…ither North or South. For the Sun never comes farther North, than our Summer Tropic; nor more Southward, than the Winter Tropic. So that those that inhabit Northward of the Summer Tropic, have their shadows cast always toward the North: as in like manner those that dwell more Southward than the Winter Tropic, have their Noon-shadows cast always coward the South. Those that inhabit betwixt the Arctique or Antarctique circles, and the Poles, are called Periscij: because that the Gnomon do cast their shadows circularly: and the reason hereos it, for that the Sun is carried round about, above their Horizon in his whole diurnal Revolution.  
PONT. The Heterosciall Zone is therefore two, fold either Northern or Southern. The Northern is comprehended betwixt the Tropic of Cancer and the Artik circle: and ●…s called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Septentrionalis, because that in it the Sun beams, at noon, are always cast to that part only that byoth toward the ●…ole Arctics  
The Southern Hetorosciall Zone, containeth all that space of ground that lieth betwixt the Tropic of Capricorn, and u●…e Antarctique circle, And it is call●…d 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Meridonalis, because the Noon shadows are proje●…ed toward the South Pole only.  
The properties of these several Zones are these that follow. First, they that inhabit the midst of the Torrid Zone, are in a Right Sphere: for with them, both the Poles of the world lie in their Horizon: and their Zenith or Vertical point falleth in the Equinoctial Circle. So that their peculiar Accidents are these. First, All the S●…arres do rise and set in an equal space of time, except the Arctique and Antarctique Poles: as we have demonstrated out of Lerius, in our notes upon the third Chapter. Secondly, They have a perpetual AEquinoxe. Thirdly, They have the Sun vertical unto them twice in a year, namely, when he entered into ♈ and ♎ Fourthly, In the Sun's periodical motion through the Zodiaque, look how much he goeth Southward from their Zenith, in his return he declines as far northward from the same. Fi●…thly, They have sour Solstices; two when the Sun is in their Zenith and AEquinocti●…ll points: and two Collateral, when he is in the Solsticiall points. Sixthly, They have two summers every year, when the Sun is in the AEquinoctioll points: and two, as it were, Winters, when the Sun declineth to either Tropiqu'. Seventhly, They have five different kinds of shadows: to wit, Eastward, Westward, Northward, Southward, and Perpendicular. And therefore the Inhabitants of this Zone are called Amphiscij, that is to say, having their shadows cast on both sides: The properties os those that inhabit toward the utmost border of the Torrid Zone, and being os the Northern Temperate, whi●…h have an Oblique Sphere, (for the Arctique Pole with them is elevated twenty three degrees and an half, and their Zenith fall th' on the Troqi●…ue of Cancer,) are these following. Fi●…st, All those Stars that are comprehended within the compass of the Arctique Circle, are always above the Horizon: and chose, those within the Circuit of the Acctique always lie hid. But if the intermediate Stars, those that are Northward from the AEqnator, or a longer time above the Horizon, than they are under it: in like manner, as the other that decline more Southward, their Nocturnal Arch is greater than the Diurnal: only those in the line itself, do rise and set in an equal space of time. Secondly, Their Artificial days and nights are unequal. Thirdly, The Sun is in their Zenith but once in the year, and that is in the beginning of Cancer: so that it never ascends more Northward, but at all other times is Southward to them. Fourthly, They have two Solstices: one, when the Sun is in the beginning of Cancer, which is their Vertical point: and the other when the Sun entereth into the beginning of Capricorn, at which time the Sun hath the least elevation. Fifthly, They have also but one Summer and one Winter. They have four differences of shadows, namely, Eastern, Western, Northern, and Perpendicular. And here is the beginning of the Heteroscij.  
They that dwell on the Oblique Sphere, so that the Arctique Pole is elevated with them above 23. degrees, an an half, but less than 66. degrees, and an half: their Zenith or Vertical point always falleth betwixt the Tropic of Cancer, and the Arctique Circle: whence they have these properties. First, Very many Stars with them are never observed to set: for the higher the Pole is elevated, the more Stars there are which always appear; and so, in like manner, there are as many in the opposite Haemisphaere that never rise. Secondly, Their Artificial dates and nights are equal. Thirdly, The Sun is never in their Vertical point: but is always at Noon Southward from them. Fourthly, They have one Summer, and one Winter, and two Solstices. Fifthly, They have also three different kinds of shadows, as namely, Eastward, Westward, and Northward. Whence they are called Heteroscij.  
Those that inhabit about the end of the Northern temperate Zone, have the Pole Arctique elevated with them 66. degrees and an half: so that their Zenith falleth on the Arctique circle: whence they have these properties of Sphere. 1. All the Stars that lie within the Tropic of Cancer, and the Pole Arctique are of perpetual Apparition: and contrariwise, those that are comprehended within the Opposite circle, are never seen to rise. 2. When the Sun is in the beginning of Cancer, the Artificial day is with them twenty four hours in length: and so likewise when the Sun entereth into Capricorn; the nights are as long. 3. The Sun, at noon, is always Southward to them: but when he is in the beginning of Cancer, and is near the very Horizon, he than seems, in a manner, to be Northward. 4. They have two Solstices, and one Summer, and one Winter. 5. They have four differences of shadows: as namely, Eastern, Western, Southern and Northern also, especially when the Sun entereth into the beginning of Cancer▪ About these parts the Heteroscij end, and the Periscij begin.  
Those that inhabit about the middle of the Northern Frigid Zone, have a Parallel or standing Sphere: for the Equinoctial is their Horizon, whence they have consequently these properties 1. No Stars either rise are set at all: but whatsoever are circumscribed within the Equinoctial circle and the very Pole, are carried about in circles Parallel both to the Equinoctial and Horizon. 2. For the space os 6. months they have one continued day, the Sun in this space finishing his course through the Northern signs of the Zodiaque, and so likewise while he is in the opposite meridional signs, they have a night of the same length. 3. They have but one Solstice, and that is, when the Sun entereth into the beginning of Cancer. 4. They have one Winter and one Summer, or rather instead of a Summer they have some certain small remission of the extremity of cold. 5. Their shadows are carried round about them in à circle toward every part of the world: whence they are called Periscij, that is to say, having their shadows carried round about in a circular form.  
These are the properties of the Northern Zones; which if they be referred to the opposite meridional parts also, you have their properties likewise. For whatsoever is said of one Hemisphere, the same is also to be understood of the other opposite Hemisphere, only in a contrary sense. For when these that dwell in the Septentrional Hemisphere, have their longest day, the opposite inhabitants in the meridional part of the world have their shortest: and when they have their Summer, with those it is then winter, etc. And the same is also to be understood of the other Accidents also, concerning their shadows, the rising and setting of the Stars, and the li●…e.   

CHAP. VI Of the Perioeci, Antoeci, and Antipodes:  
THe Inhabitants of the temperate Zones have by the Ancient Geographers been divided, in respect either of the same Meridian, or Parallel, or else equal situation in respect of divers parts of the AEquator, in such sort, as that to every habitation in these several parts, they have added three other different in position, whose inhabitants they called, Perioeci, Antoeci, and Antipodes.  
Perioeci, are those that live under the same Meridian, and the same Parallel also, being equal distant from the AEquator; but in two opposite points of the same Parallel.  
Antoeci, are such as have the same Meridian, but live in divers Parallels, yet equally distant from the AEquator, though in divers parts.  
Antipodes, (which are call●…d Antichthones) are such as inhabit under one Meridian, but under two divers Parallels, which are equally distant from the AEquator, and in opposite points of the same: or else we may define them to be such, as inhabit two places of the earth, which are Diametrically opposite.  
They therefore which are Perioeci in respect of us, are Antoeci to our Antipodes: & those that are Antoeci to us, are Perioeci to our Antipodes: and our Perioeci, are Antipodes to those which are Antoeci to us.  
We have also many accidents common with our Perioeci. For we both inhabit the same temperate Zone; and have Summer, Winter, increase and decrease of days and nights, at the same time. Only this difference is betwixt us, that when it is noon with us, it is midnight with them. Those Authors that have added this differnce also, that when the Sun riseth with us; it setteth with those that are our Perioecij, have betrayed their own ignorance. For if this were so, it would then follow, that when the day is longest with us, it shall be at the shortest with them: but this is most false. They have committed the like error concerning our Antoeci also; when as they will have the Sun to rise with us, and them at the same time. The ground of which their error perhaps may be, in that they conceived us and our Antoeci to have the same Horizon, but that ours was the uppermost Hemisphere, and theirs the lower: the like they conceived of our Perioeci. But this is an error unworthy of those that are but mean●…ly versed in Astronomy. We agree with our Antoeci in this, that we have midday, and midnight both at the same time. But herein we differ, that the seasons of the year are clean contrary. For when we have Summer, they have Winter: and our longest day, is the shortest with them. We also inhabit temperate Zones both of us, though different from each other in the time and seasons.  
But with our Antipodes all things are quite contrary, both days and nights, with their beginnings and end, as also the seasons of the year. For at what time we, through the benefit of the Sun, enjoy our Summer and the longest day: then is it winter with them, and the days at the shortest. So likewise when the Sun riseth with us, it setteth with them; and so contrary wise when it setteth with us, it riseth with them. For we inhabit the upper Hemisphere, and they the lower, divided by the same Horizon.   

CHAP. VII. Of Climates and Parallels.  
ACcording to the different quantity of the longest days, Geographers have divided the whole earth, on each side of the AEquator to the Poles in Climates and Parallels. A Climate they define to be a space of earth comprehended betwixt any two places, whose longest days differ in quantity half an hour. And a Parallel is a space, wherein the days increase in length a quarter of an hour: so that every Climate containeth two Parallels. Those Climates, as also the Parallels themselves are not all of equal quantity. For the fi●…st Clime, (as also the Parallel) beginning at the AEquator, is larger th●…n the second, and the second is likewise greater th●…n the third. Only herein, they all agree, that they differ equally in the quantity of the longest day.  
The Ancients reckoned but 7 Climates at the first; to which number were afterward added two more, so that in the first of these numbers were comprehended 14 Parallels, but in the later. 18. Ptolemy accounting the Parallels by the difference of a quarter of an hour, reckoneth in all 24. by whole hours difference 4 by whole months, 6 So that b●…ides the AEquator, reckoning he whole number of Parallels on each side, they a mount to 38.  
In the Meridian of a Material Globe, there are described nine Climates, differing from each other by the quantity of half an hour. After these, there are, other also set according to the difference of an whole hour: and last of all those that differ in whole month●… are continued to the very Pole, each of them expressed in their several latitudes. The distance of all, both Climates and Parrallel●…, together with, their latitudes from the AEquator, and differences of the quantity of the longest days, are here fully expressed it this Table following.  
Ampihscij. Climates. Parallels. The longest Summers day Hour. Scr. Latitude and Elevation of Pole Hour. Scr. The breadth of the Climates. Deg. Scrup. 0 0 12 0 0 0 4 18 1 12 15 4 18 1 〈◊〉 12 30 8 34 8 25 〈◊〉 12 45 1●… 43 2 4 13 0 16 43 7 50 5 13 15 20 33 3 6 13 30 23 10 7 3 7 13 45 27 36 Heteroscij. 4 8 14 0 30 47 6 9 〈◊〉 14 15 33 45 5 10 14 30 30 30 5 17 11 14 45 39 2 6 12 15 0 41 22 4 30 13 15 15 43 32 7 14 15 30 45 29 3 48 15 15 45 47 20  
Heteroscij. Climates. Parallels. The longest summers day Hour. Scr. Latitude and Elevation of the Pole. Degr. Scr The breadth of the Climates. Degr. Scr. 8 16 16 ●…0 49 1 3 13 17 16 15 50 33 9 18 16 30 51 58 2 44 19 16 45 53 1●… 10 20 17 0 54 29 2 17 21 17 15 55 34 11 22 17 30 56 37 2 0 23 17 45 57 34 12 24 18 0 58 26 1 40 25 18 15 59 14 13 26 18 30 59 5●… 1 26 27 18 45 60 40 14 28 19 0 61 18 1 13 29 19 15 61 53 15 30 19 30 62 25 1 1 31 19 45 62 54 16 32 20 0 63 22 0 52 33 20 15 63 46 17 34 20 30 64 〈◊〉 0 46 35 20 45 64 3●… 18 36 21 0 69 49 0 36 37 21 15 65 6 19 38 21 30 65 21 0 29 39 21 45 65 35 20 40 22 0 65 47 0 22 41 22 1●… 65 57 21 42 22 30 66 6 0 17 43 22 45 66 14 22 44 23 0 66 20 0 11 45 23 15 66 25 23 46 23 30 66 ●…8 0 5 47 23 45 66 ●…0 24 48 24 0 66 31 0 0   Months. Periscij. Here the Climates begin to be accoun●…ted by months, from 66 gr. 3●…. 〈◊〉. where the day is 24 hours' lon●… to the Pole itself, who●…e it is 6. months in length. 1 67 15 2 69 30 3 73 20 4 78 20 5 84 0 6 90 0    

The second Part,  

CHAP. I. Of such things as are proper to the Celestial Globe: and first of the Planets.  
HItherto, hath our discourse been concerning those things which are common to both Globes: We will now descend to speak of those that properly belongs to each of them in particular. And first of those things that only concern the Celestial Globe: as namely the Stars, with their several configurations.  
The whole number of Stars hath been divided, by the Ancient Astronomers, who first applied themselves to the diligent observing of the same, into two kinds. The first is of the Planets, or wandering Stars: the other of the fixed. The first of which, they therefore called Planets or Wanderers because they observe no constant distance or situation, neither in respect of each other, nor in respect of those that are called fixed Stars. And these were so called, because that they were observed always to keep the same situation and distance from one another, as is at large proved Ptolemy, in his Almagest, lib. 7. cap. 1. out of his own observations, diligently compared with those delivered by Hipparchus.  
PONT. The Stars are divided into Planets, or wand'ring Stars, and fixed: not as if these were indeed fixed in one certain place, and altogether without motion, and the other only movable and erratical: but these appellations are only given then comparatively; in which sense also they are to be understood. For seeing that the fixed Stars were observed always to keep the same places in the eighth Sphere, and the same distance from each other: notwithstanding that they are always in continual motion, caused by the virtue of the first Movable, which carrieth them about in the space of twenty four hours. But the Planets, besides this motion, have a proper motion of their own, so that they keep neither their the same distance from the fixed Stars, nor yet the same aspect to each other: for these reasons were the one called Fixed, and the other Planets. For otherwise if the Planets be considered severally, each one by himself, there is nothing more certain than their periodical motion. So that Tully, alluding hereto, would have the Planets to be called Errantes, by Antiphrasis, quam minimè errantes.  
The Planets, (exceeding those two greater lights, the Sun and Moon) are five in number. A●… which, beside the Diurnal motion, by which they are carried about from East to West, by the Rapture of the first Movable, have also a free proper motion of their own, which finish from West to East, according to the succession of the Signs, upon the Poles of the Zodiaque; each of them in a several manner and space of time: Their order in the Heavens, and periods of their motions being such as followeth.  
Saturn, called in Greek 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 or 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, (and by Julius Higinus, Stella Solis the Star of the Sun) is the highest of all the Planets: and 〈◊〉 about the greatest 〈◊〉: but doth not therefore appear to be the least of all the Planets, as Pliny hence conjectured. He finisheth his Periodical course in twenty nine years, five months fifteen days, according to Alfraganus.  
Jupiter, in Greek Zeus and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, moveth through the Zodiaque in the space of eleven years, ten months, and almost 16. days.  
Mars, 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, (which is also cal-called by some, Hercules his Star) finisheth his course in two years.  
Sol, the Sun in Greek 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, performeth his course in a year, that is to say, three hundred sixty five days, and almost six hours.  
Venus, 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, (called by some June's Star, by there's, Isis, and by others, The Mother of the Gods:) when it goeth before the Sun, it is called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, the day Star appearing like another 〈◊〉 Sun, and as it were, matu●…g the day. But when it followeth the Sun, in the Evening, p●…otracting the light, after the Sun is ●…er, and supplying the place of the Moon; it is then called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, the Evening Star. The names of which Star, Pythagoras Samius 〈◊〉 〈◊〉 first to have observed about the thi●… ie 2d. Olympiad, as Pliny relates, lib. 2. cap. 8. It p●…meth its course in a years space, or thereabout: and is never distan●… from the Sun above forty six degrees, according to Timaeus his computation. Notwithstancing, our later Astronomers, herein much more 〈◊〉 than h●…, allow it two whole signs, or 60 degrees, which is the utmost limit of its deviation from the Sun.  
Mercury, in Greek 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, (called by some Apollo's Star) 〈◊〉 his course through the Zodiaque in a year also: And according to the opinion of Timeus and Sosigenes, 〈◊〉 ever distant from the Sun above 25. gr. or, 〈◊〉 our later writers will have it, not above a who●…e, 〈◊〉, or 30. degrees.  
Luna. 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 the Moon, is the lowest of all the Planets, and finisheth her course in twenty seven days, and almost eight hours. The various shapes and appearances of which Planets, (seeming sometimes to be ●…ned, sometimes equally divided into two halves, sometimes finished like an Imperfect circle, and sometimes in a respect circular 〈◊〉) together with the other diversities of this Star, were first of all observed by Endymion; as it is related by Pliny: whence sprung that Poëticall fiction, of his being in love with the M●…on.  
All the●…e Planets are carried in Orbs, which are Eccentrical to the earth: that is, which have not the same centre with the earth. The Semidiameter of which Orbs, compared to the Semidiameter of the earth, have this proportion, as is here set down in this Table.  
Of what parts the ●…emidiameter of the Earth i 1. Of t●…e same the 〈◊〉ter of the Orb of Luna 1. 48. 56 m. Mercury 116. 3 m. Venus' 641. 45. m Sol 1165. 23. m. Mars 5022. 4. m Jupiter 11611. 31. m. Saturn 17225. 16. m  
The Eccentricities of the Orbs, compared to the Orbs themselves, have this proportion.  
Of whatparts the Semidiameter of the Deferent is 60. Of the same the Eccentricity of. Luna 18 12. 28. m. 30 sec Maurolycus, out of Alphons. Mercury 2. 0. m. Venus' 1. 8. m. Sol 2. 16. m 6. sec. Mars 6. 0 m. Jupiter 2. 45 m. Saturn 3. 25 m.  
The Eccentricities of some of the Planets, (especially of the Sun) are found to have decreased and grown less since Ptolomyes●…ime ●…ime. For Ptolemy sets down the Eccentricity of the Moon to be 12. gr. 3●… m. but by Alphonsus it was found to be but 13 gr. 28. m. and an half. Ptolemy assigned Eccentricity to Venus 1 gr 14. m Alphonsus 1. gr 8. m. Ptolemy found, by his own observations. and also by those that Hipparchus had made, that the Eccentricity of the Sun was 2 gr. 30. m. Alphonsus observed it in his time to be but 2 gr. 16. m. and the 10th. part of a minute In the year of ou●… Lord 1312 it was found to be 2. gr. 2. m. 18. sec. Copernicus found it to be less yet then that. and to be but 1 gr. 56 m 11. sec. So, that without just cause, did the Illustrious Julius Scaliger think Copernicus his writings, for this reason, to deserve the Sponge, and the Author himself the Bastinado: he●…ein dealing more hardly with Copernicus, than he deserves.  
PONT. Besides the Eccentricities of the Planets, it is worth our pains also to observe their Magnitudes: And this consists especially in the knowledge of their Diameters, and what proportion they bear to each other. For the Diameter of a Planet, compared to the Diameters, of the Earth, is after this, manner following.  
The Diameter of Saturn Compared ●…o the Diameter of the Earth is as 9 10 2 Jupiter 32 7 Mars 7 6 Sol 11 2 Venus 3 10 Mercury 1 28 Luna 5 17  
The Diameter of the Sun compared to the Diameter of the Moon, beareth the same proportion, that is betwixt 187. and 10.  
And now that which is said may be demonstrated by an example: let us suppose the Diameter of the Sun, in proportion, to the Diameter of the Earth, to be (as is already showed) as 11 to 2. The Cube therefore of the Sun is 11. and the Cube of the Earth. 2. Now these Diameters being multiplied cubically and thaes greater Cube divided by the less, the difference of their severaell Globes will appear. For if you multiply 11. by 11. there ariseth 121. which number being multiplied again by 11. the whole will be 1331. So likewise multiply 2. cubically, that is to say, by itself, and there riseth 4. which being again multiplied by 2- ariseth to 8. Now divide the greater Cube, 1331. by 8. and the product will be 166. which is the difference of the Globes of the Sun and the Earth.  
And thus much may suffice us to have spoken of the Planets: and if any desire a more copious Narration of the same, they may have recourse to Ptolemy, Copernicus, and others, that have written the Theories of the Planets. For a more large description of these things seams not ●…o stand without purpose: especially for that by reason of their Erratical motion, they cannot be expressed in a Globe. Let thus much therefore be spokn of them, as by the way only,   

CHAP. II. Of the fixed Stars, and their Constellations.  
ANd here, in the next place, we intent to speak of the Fixed Stars, and their Asterisms, or Constellations, which Pliny calls Signa and Sidera, signs. Concerning the number of which Constellations, as also of their figure, names, and number of the Stars they consist of, there is diversity of opinion among Authors. For Pliny in his 2d book, 41. chap. reckoneth the whole number of the signs to be 72. But Ptolemy Alfraganus, and those which follow them, acknowledge but 48. for the most part: notwithstanding some have added to this number one, or two more; as Berenice's Hair, and Antinous. Germanicus Caesar, and Festus Avienus Rufus, following Aratus, make the number less. Julius Higinus will have them to be but 42. reckoneing the Serpent: and The man that holdeth it, for one sign: and he omitteth the little Horse: and doth not number Libra among the signs: but he divideth Scorpio into two signs, as many others also do. Neither doth he reckon the Crow, the Wolf, nor the South Crown among his Constellations, but only names them by the way. The Bull also. which was described to appear but half, by Hipparchus, and Ptolemy, and those that follow them: the same is made to be wholly apparent, both by Vitruvius, and Pliny, and also before them, by Nicander, if we may believe Theon, Aratus his Scholiast: who also place the Pleyades in his back.  
Concerning the number also of the Stars, that go to the making up of each Constellation, Authors do very much differ from Ptolemy, as namely, Julius Higinus, the Commentator upon Germanicus, (whether it be Bassus as Philander calls him: or whether those Commentaries were written by Germanicus himself, as some desire to prove out of Lactantius) and sometimes also Theon, in his Commentaries upon Aratus; and Alfraganus very often.  
Now if you desire to know what other reason there is, why these Constellations have been called by these names. save only, that the position of the Stars doth in some sort seem to express the forms of the things signified by the same: you may read Bassus, and Julius Higinus, abundantly discoursing of this argument out of the fables of the greeks. Pliny assures us, (if at least we may believe him) that Hipparchus was the man that first delivered to posterity the Names, Magnitude, and Places of the Stars. But they were called by the same names, before Hipparchus his time, by Timochares, Aratus, and Eudoxus. Neither is Hipparchus ancienter than Aratus, as Theon would have him to be. For the one flourished about the 420. year from the beginning of the Olympiads: as appeareth plainly out of his life written by a Greek Author. But Hipparchus lived above 600. year●…s after the beginning of the Olympiads: as his observations, delivered unto us by Ptolemy, do sufficiently testify. Besides that, there are extant certain Commentaries upon the Phaenomena of Eudoxus and Arratus, which go under Hipparchus his name: unless perhaps they were written by Eratosthenes (as some rather think) who yet was before Hipparchus.  
PONT. That which is written of Hipparchus, is not to be understood any further, then touching the distinction of the Stars of the first, second, and third magnitude. For so Servius in his Commentaries upon the 1. lib. Geogr Hipparchus (inquit) scrip●…it de signis, etc. Hipparchus (saith he) wrote of the Signs, and reckoned up how many bright Stars, how many of the second degree of light, and how many obscure Stars there were in each constellation, For otherwise, that the Stars were known by the same names 1000 years before Hipparchtus, may be proved cut of Seneca, who in his 7. lib. Natural, Quest. chap: 25 saith thus Nondum sunt an●…i, etc. It is not (saith he) 1500. years yet, since Greece first began to number the Stars, and to give them certain Appellations, Now Seneca, we know, was put to death by the command of Nero, in the 65. year after Christ, And Hipparchus lived not above 283. years before Christ, in the time of Ptolemy's Philadelphus. And Job also whom Philo Judaeus reporteth to have married 〈◊〉, Jacob's daughter, mentioneth these names, Arcturus, Pleiades, and Orion, if we may trust St. Hierom's translation in this case, cap. 9 verse. 9 Who maketh (saith he) Arcturus, Orion, and Pleyades, and the Stars in the remo●…st parts of the South. So likewise the Prophet Am 〈◊〉, chap 5 verse 8. Quaerite (inquiet) opificem Pleiadum & Orionis, etc. Seek ye him that made the Pleyades and Orion, etc.  
Now it is probable, that there were two kinds of men, that reduced the Stars into constellations: and these might probably be Husbandmen, and Mariners. The Husbandmen perhaps might make these, to wit: the Ram, the Bull, the E●…e of Corn in the Virgin's hand, the young Kids, the Goat, the Waggoner, the little Goat, the Wagon: all which, are names used also by Homer. Of the Mariners, the Pleyades, the Hyadeses, the Whale, and the like names seem to have been invented, according to that of Virgil, in the first of his Georgickes. 
Nav●…ta tu●… Stellis numeros & nomina fecit:  
〈◊〉 des, Hyades, clarumque Lycaonis Ast●…m.   
Which is thus translated into English Verse by T. May. 
The Sailor's number then, and named▪ 〈◊〉 Star:  
The Pleiads, Hyads, and the Northern Car.   
And now to whom do those other new Constellations above the Antarctic Pole, we their now so well known names but to the Portugals, Hollander, and English Seafaring men? Neither are those men at all to be regarded, that condemn these usual names of the Stars, and Constellations, as unfit to be used by Christian men. For seeing they are now used, without the least show of superstirion, and that there is very great necessity of these Appellations, in as much as without them there could be no agreement or accord in these Arts and cience (for these very names are used all the world over, where ever the same Arts are taught or professed) I see no reason but that we may lawfully use these names, till such time as, the true names, wherewith the great Creator of all things, at the first called every Star as David witnesseth in the 146 Psalms be made known unto us. As concerning the practice of the Arabians, who rejected these humane figures, having substituted in their places the form of Beasts: you may read Joseph Scaliger, in his Commentaries upon Manilius.  
Pliny in his 2. Book, 41. chapter affirmeth, (though I know not upon whose authority or credit) that there are reckoned 1600. fixed Stars, which are of notable effect and virtue. Whereas Ptolemy reckoneth but 1022. in all, accounting in those which they call Sporades, being scattered here and there, and reduced to no Asterisme. All which, according to their degrees of light, he hath divided into 6. orders. So that of the first Magnitude he reckoneth 15. of the second 45. of the third, 208. of of the fourth. 474. of the fifth, 217. of the sixth, 49. to which we must add the 9 obscure ones, and 5. other. which the Latins call Nebulosae, cloudy Stars. All which Stars, expressed in their several Constellations, Magnitudes, and names, both Latin and Greek,) and some also with the names by which they are called in Arabic) you may see pescribed in the Globe.  
PONT. Now as we have already showed, how by comparing the Diameters of the Planets, with the Diameter of the Earth, their magnitude may be known: in like manner also, may the magnitude of the fixed Sttarrs be found out: as may be seen by this scheme.  
The Diameter of a Star of the 1 is to the Earth's Diameter, as 119 to 4 2 269 60 3 25 6 4 19 5 5 19 36 6 21 8  
More over concerning those other fixed Stars about the Southern Pole, which were unknown to Ptolemy and the Ancients, and now of late years discovered by the Portugals and Hollanders; we shall set down their names also in their due place.  
All these Constellations (together with their names in Arabic, as we find them partly set down by Alfraganus, partly by Scaliger in his Commentaries upon Manilius, and Grotius, his Notes upon Aratus his Asterisms, but especially as Jacobus Christmannus hath delivered them unto us out of the Arabic Epitome of the Almagest) we will set down in their order. And if any desire a more copious declination of the same, we must refer him to the 7. and 8. books of Ptolemy's Almagest, and Copernicus his Revolutions, and the Prutenicke Tables digested by Erasmus Reinholt: where every one of these Stars is reckoned up, with his due longitude, latitude, and magnitude annexed.  
PONT. You may also see Christophorus Clavius in his Commentary upon Johan. de Sacrobosco, cap. 1. And above all the rest Tycho Brahe: who in his book of the New Stars that appeared in the year 1572. hath proposed tables of the longitude and latitude of all the fixed Stars that can conveniently be seen in these Climates, according to his own most accurate observations: as you may see in the aforenamed book, pag. 258. and so forward.  
But here you are to observe by the way, Copernicus and Erosmus Reinholt do reckon the longitude of all the Stars, from the first Star in Aries: but Ptolemy from the very Intersection of the Equinoctial and Ecliptic. So that Victorinus Strigelius was in an error. when he said, that Ptolemy also did number the longitude of Stars from the first Star, the head of Aries.   

CHAP. III. Of the Constellations of the Northern Hemisphere.  
THE first is called in Latin Ursa Minor, and in Arabic Dub Alasgar; that is to say, the lesser Bear, and Alrucaba, which signifieth a Wagon or Chariot: yet this name is given also to the hindermost Star in the tail, which, in our time, is called the Pole Starr, because it is the nearest to the Pole of any other. Those other two in the tail, are called by the greeks 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, that it to say, Saltatores, Dancers. The two bright Stars in the fore part of the body, the Arabians call Alferkathan, as Alfraganus writeth: who also reckoneth up seven Stars in this Constellation, and one unformed near unto it. This constellation is said to have been first invented by Thales, who called it the Dog, as Theon upon Aratus affirmeth.  
The second is Vrsa Major, the Great Bear: in Arabic, Dub Alacher. The first Star in in the back of it, which is the 16 in number, is called Dub 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, and that which is in the flank, being the 17 in number, is called Miraë, or rather, as Scaliger would have it, Mizar, which signifieth (saith he) locum praecinctionis, the girthing place. The first in the tail, which is the 25. in number, is called by the Alfonsines, Aliare, and by Scaliger, Aliath. This Asterisme is said to have been first invented by Nauplius, as Theon affirmeth. It hath in all 27. Stars: but as Theon reckoneth them, but 24 Both the Bears are called by the Greeks, according to Aratus, 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, which signifieth a Wagon or Chariot. But this name doth properly appertain to those seven bright Stars in the great Bear, which do something resemble the form of a Wagon. These are called by the Arabians, Beneath As; i. e. Filiae Feretri, as Christmanus testifieth. They are called by some, though corruptly, Benenas, and placed at the end of the tail. some will rather read it Benethasch, which signifies Filium Vrsae. The Grecians in their navigations were wont always to observe the great Bear: whence Homer gives them the Epithet 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 as Theon observes: for the greeks call the great Bear 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉. But the Phoenicians always observe the lesser Bear, as Aratus affirmeth.  
The third is called the Dragon, in Arabic Alanin, and it is often called Aben: but Scaliger readethit Taben; whence he calleth that Star which is in the Dragon's head, and is the 5. in number, Rastaben, though it be vulgarly written Rasaben. In this Constellation there are reckoned 31. Stars.  
The fourth is Cepheus, in Arabic Aluedaf. To this Constellation, besides those two unformed Sarrs, which are hard by his Tiara, they reckon in all, 11. among which, that which is in number the 4. is called in Arabic Alderaimin, which signifieth, the right Arme. This Constellation is called by the Phoenicians Phicares, which is interpreted Flammiger, which appellation, peradventure they have borrowed from the Greek Word 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉.  
The fifth is Booses' 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, which signifieth in Greek an Herdsman, or one that driveth Oxen. But the Arabians mistaking the word, as if it had been written 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 of 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, which signifies a Clamators, Cryer, call it also Alhava, that is to say Vociferator, one that maketh a great noise or clamour: and Alsamech, Alramech, that is the Launce-bearer. Betwixt the legs of this Constellation, there stands an unformed Star of the first magnitude, which is called both in Greek and Latin Arcturus, and in Arabic Alramech, or the ●…ghtest Star, Somech haramach This Star Theon placeth in the midst of Boötes his belt or girdle, The whole Constellation consisteth of 22. Stars.  
PONT. There is mention made of Arcturus also in Job, cap. 9 verse. 9 according both to Hieroms translation, and also the Greek translation of the 70. as we have noted already. But in the Hebrew text itself, it is called Gnasch, or Asch, from the root Gnusch, which signifieth Congregabit. Hesychius in his Onomastic●…n observeth that Boötes is also called sometimes Orion: according to that of Manilius.  
Arctos & Orion adversis frontibus ibant.  
In Which signification H. Grotius in his notes upon Aratus his Asterisms, thinks it is here to be taken. Sometimes also the whole Constellation of Boötes, or Arctophylax, is called Arcturus; from the Greek word 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, a Bear, and 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, which is the same that 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, a Keeper: as Scaliger upon Manilius observes. Now that the Hebrews call Arcturus by a word signifying a congregating, or gathering together, the reason I take to be, because he hath the great Bear joined to him. For this Star standeth behind the tail of the great Bear, whence it seemeth to have its name, quasi 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 the keeper of the Bear, whence Pliny also, lib. 2. cap. 41. Bootes sequitur Septentriones.  
The sixth Constellation is Corona Borea, the North Crown, called by the Arabians, Aclilaschemali, and that bright Star, which is placed where it seemeth to be fastened together, and which is the first in number, is called in Arabic Alpbecca, which signifieth Solutio, an untying or unloosing. It is also called Munic: but this name is common to all bright Stars. The whole Constellation consisteth of eight Stars.  
The seventh is Hercules, in Arabic, Alcheti hale rechabateb, that is one falling upon knees, and sometimes absolutely Alcheti: for it resembleth one that is wearied with labour (as Aratus conceives) whence it is also called in Latin Nisus, or Nixus; (which in Vitruvius is corrupted into Nesses:) and the greeks call it 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 that is to say, One on his knees. The Star which is first in number in the head of this Constellation, is called in Arabic Rasacheti, not Rasaben, as the Alfonsines corruptly have it: and the 4. Star is called, Marsic, or rather Marsic, Reclinatorium, that part of the Arm on which we lean. The eight Star, which is the last of the three, in his Arm, is called Mazim, or Maasim, which signifieth Strength. This Constellation hath eight Stars, besides that which is in the end of his right foot, which is betwixt him and Boötes, and one unformed Star at his right Arme.  
The eight is the Harp, called in Latin Lura, in Arabic Schalias, and Alvakah. i. 〈◊〉 Codens so Vulture, the Falling Vulture. It consisteth of 10. Stars, according to Hipparchus and Ptolemy: but Tymochares attributed to it but 8. as Theon affirmeth: and Alfraganus 11. The bright Star, in this Constellation, being the first in number, Alfonsus calleth Vega.  
The ninth is Gallina, or 〈◊〉, the Hen, or Swan, and is called in Arabic Aldigaga and Altayr, that is the flying Vulture. To this Asterisme they attribute, besides those two, unformed, near the left wing. 17. Stars, the 5. of which is called in Arabic Deneb Adigege, the tale of the Hen; and by a peculiar name, Arided, which they interpret, quasi redolens li●…um, smeiling as it were of Lilies.  
PONT. And here, in this place, it is worth our noting that there was a new Star observed in the breast of the Swan, in the year one 1600 which set many Mathematicians on work and among therest, besides Justus Byrgius Engineer to the Emperor, Johannes Beierus, Maestline, and others: Johan. Kepler also, who had some time been Tychoes Scholar, put forth a Mathematical Tract of it. when it had now continued in the same place of that constellation for the space of 6. years, being a Star about the third Magnitude.  
The 10th is Cassiopeia, in Arbiaque Dha●… Aleursi, the Lady in the Chair: and it consisteth of 13. Stars: among which the 2d in number Alfonsus calleth Scheder, Scaliger Seder, which signifieth a Breast.  
PONT. There was another new Star also appared in Cassiopeia, being as great as a Star of the first Magnitude, in the year 1572. Novem. 11. th' and it lasted 11. Months. Of which Star there were divers opinions amongst Astronomers: yet they all agreed in this, that it was placed in the seat of Cassiopeia in the very Sky, and in Vialactea. and those that had observed it more accurately) & among the rest, the noble Tycho Brahe, who also wrote a large Volume of the same, full of most accurate observations did a●… of them unanmiously confess that they could not perceive that it had any 〈◊〉 at ●…all, nor yet distinguish any difference betwixt its True and Apparent place; and also added, that it always kept the same situation in the Eight Sphere whence they manifestly are refuted, who deny that there hath ever any new Star risen in the heavens since the first Creation: among which is Lambertu●… Danaeus, as may appear in his Physic. Christian. Tract. 4. cap. 10. as●…ny ●…ny testifieth) was observed by Hipparchus to have been generated in the very Sky itself in his time. For where as the same Danaeus thinks, that the Star which appeared at our SAVIOUR'S Nativity, was either some Comet, or else some one of the Ordinary Stars, whichr at that time kept an extraordinary course in its motion: the first of these cannot be granted; because it is expressly called a star: neither is the second of any force becaase, it is not probable, that the Magis, who were so skilful in the knowledge of the Stars, should be so much deceived as to mistake an old star that had only changed its place, for a new one. Neither yet do we believe this to be the same that Hipparchus is said to have observed in his time, or this other, which, as we have said. was seen Anno 1572. but rather that it was a different star from both. For further satisfaction whereof, I refer my reader to Tycho de Nova Stella pag. 3●…9. etc.  
The 11.th is Perseus, Chamil Ras Algol that is to say, Bearing the head of Medus●…: for that Star which is on the top of his left hand, is called in Arabic Ras Algol, and in Hebrew Rosch hassatan, the Devil's head. This constellation hath besides those three unformed, 26 other Stars: of which, that which is 〈◊〉 seventh in number, Alfonsus. alleth Alchcemb, for Alchenib, or Algeneb, according to Scaliger, which signifieth a side.  
The 12th is Auriga, the Waggoner, in Arabic Roha, and Memassich Alhanam, that is, One holding the reins of a bridle in his hand. This Astermisme hath 14. Stars: of which that bright one in the left shoulder, which is also the third in number, is called in Greek, 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Capra, a Goat; and in Arabic Alhaiok or, as Scalig●… saith, Alatod, which signifieth a He Goat: and the two which are in his left head, and are the 8th and 9th are called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, Hoedi Kids; and in A abique, s Alfonsus hath it, Saclateni, but according to Scaliger, Sadateni, the ●…inmost a●…me. This Configuration of these Stars was first observed by Cleostratus Tenedius, as Higixus reporteth.  
The 13th Aquila Alhhakkab, the Eagle: the modern Astronomers call it, the flying Vulture, in Arabic Altayr: but Alfraganus is of a contrary opinion, for he calleth the Swan by this name, as we have already said, they reckon in this Alte●…isme 9 Stars; besides 6. other unformed, which the Emperor Hadrian caused to he call Antinous, in memory of Antinous, his Minion.  
The 14th is the Dolphin, in Arabic Aldelphin, and it hath in it 10. Stars.  
The 15th is called in Latin Sagitta, or Telum, the Arrow or Dart, in Arabic Alsoham: it is also called Istusc, which word Grotius thinks is derived from the Greek ward 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 signisying an arrow. It containeth 5. Stars in all.  
The 16th is Serpentarius the Serpent bearer; in Arabic Alhava, and Hasalangue. It consisteth of 24. Stars. and 5. other unformed. The first Star of these is called in Arabic Rasalangue.  
PONT. There was also discovered a new Star in the foot of the Serpent. bearer, Anno. 1605. which might have been reckoned among the Stars of the third magnitude. It began first to appear about October, in the year aforesaid, and about February, the year following, being 1606▪ it vanished out of fight. Kepler wrote a Book of this Star also, unto whom you may have recourse for further satisfaction.  
The 17th is Serpens, the Serpent, in Arabic 〈◊〉: it con●…sts of 18. Stars.  
The 18th is Equiculus, the little Horse, and in Arabic Kasam Alfar●…, that is in Greek 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, as 〈◊〉 were the sure part of a Horse cut off. it consisteth of 4. obscure Stars.  
The 19th is Pegasus, the great Horse, in Arabic Aifaro●… Alath●…m; and it Hath in it 10. Stars. The Star on the right shoulder, which is called Almenkeb, and is the third in number, is also called Seat Alfras, Br●…hium equi. And that which is in the opening of his month, and is numbered the 17th is called in Arabic Enif Alfaras, he Note of the Horse.  
The 20th is 〈◊〉, in Arabic Almara Al●…sela, that is, the Chained Woman; Alfraganus interpre●… it 〈◊〉, quae non est experi●… 〈◊〉 a Woman that hath not known a man. This Constellation concaineth in it 23. Stars: whereof that which is the 12th in number, and is in the girdling place, is commonly called in Arabic M●…ach, or, according to Scaliger, Mizar: and that which is the 5th is called Alamac, or rather Almaac. which signifieth a sock or bu●…kin.  
The 21th is the Triangle in Arabic 〈◊〉, and 〈◊〉, which signifies Triplici●…. It consisteth of 4. Stars.  
PONT. Among all these constellations in the Northern Hemisphere, which are in all 21. there are but three Stars only of the first Magnitude. The first of which is that in the left shoulder of Erichthonius, or the Waggoner, called in Latin Capella. The second is the bright Star in the Harp: and the third is Arcturus, betwixt the legs of Boötes. Now the whole number of Stars in this part of the Heavens, reckoning in these also which are of the 2d 3d 4th 5th and 6th magnitude, with the obscure and cloudy ones also, ariseth to 360.   

CHAP. VI Of the Northern Signs of the Zodiaque.  
THe first is Aries the Ram, in Arabic Alhamel: this Constellation hath 13. Stars, according to Ptolemy's account; yet Alfraganus reckoneth but 12. besides the other 5 unformed ones, that belong unto it.  
The 2d is Taurus, the Bull, in Arabic Altor, or Ataur: in the eye of this Constellation there is a very bright Star, called by the Ancient Romans Palilicium, and by the Arabians Aldebaram, which is to say, A very bright Star, and also Hain Altor, that is, the Bull's eye. And those five Stars that are in his forehead, and are called in Latin Suculae, the Grecians call 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 because, as Theon, and Hero Mechanicus conceive, they represent the form of the Latin. Y. although perhaps i●… is rather because they usually cause rain and stormy weather. Thales Milesius said that there were two of these Hyadeses, one in the Northern Hemisphere, and the other in the South: Euripides will have them to be 3. Achaeus 4. Hippias & Pherecides 7. Those other 6. or, rather 7 Stars, that appear on the back of the Bull the Greeks call Pletadoes, (perhaps from their multitude) the Latins Vergiliae, the Arabians Atauria, quasi Taurinae, belonging to the Bull. Nicander, and after him Vitruvius, and Pliny place these Stars in the tail of the Bull: and Hipparchus quite out of the Bull, in the left foot of Perseus. These Stars are reported by Pliny and Solius to be never seen at all in the Isle Taprobana: but this is rid culous, and fit to be reported by none, but such as Pliny and Solinus. For those that inhabit that Isle, have them almost over their heads. This Constellation hath 33. Stars in it, besides the unformed Stars belonging to it, which are 11. in number.  
PONT. Pliny's words in that place do not seem to carry any such sense simply, seeing that he adds the same also of the Bear. His words are these in his lib. 6. cap. 22. Where speaking of certain Ambassadors that came from the Isle Taprobana to Rome, he saith; Septentriones, Virgilia sque apud no●…, veluti novo caelo, mirabantur. They wondered to see the Bear. and the seven Stars withus, 〈◊〉 if they had b●… 〈◊〉 in a new world. And ●…tainely if Vap 〈◊〉 be situated under the very Li●…e, this then, for that very reason we alleged before on the 3. 〈◊〉 par. 〈◊〉 of Lerius, had been no such strange ●…ter, is it had been spoken of the Septentriones only. Neither had Pliny written any so absurd ●…on, if he had said thus. Septentriones 〈◊〉 nos, veluti novo ●…lo, mirabantur.  
In the mean time I could wish, that Authors would 〈◊〉 nothing in their books, without 〈◊〉 examination: although I am not ignorant, that it is not strange to find Pliny fa●…ring, 〈◊〉 and then, in these kind of things.  
The third is Gemini, the Twins, in Arabic Algeuze. These some will have to be Castor and Pollux, and others, Ap●… and Her●…: whence with the Arabians, the one is called Apollar, for a Aphella●…; and the other 〈◊〉, for 〈◊〉 〈◊〉 Scaliger 〈◊〉. It containeth in it, (besides the 7. ●…formed,) 18, Stars, amongst which, that which 〈◊〉 their ●…ad, is called in Arabic ●…geazr.  
The fourth is Cancer, the Crab, in Arabic 〈◊〉, consisting of 9 Start, beside 4. ●…formed: of which that cloudy 〈◊〉, which is in the 〈◊〉, and is the 〈◊〉 of all, is called M●…lles in Arabic, which, as Scaliger faith, signifieth thick or well compact.  
The fifth is 〈◊〉, the Lion, in Arabic Alosed; in the breast whereof there is a very bright Star, being the 〈◊〉 in number, and is called in Arabic Cale Alased, the heart of the Lion, in Greek 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, because that these that are borne under this Star, have a Kingly Nativity, saith Proclus. And that which is in the end of the tail, and is the last of all in number, is named Deneb Alased, that is to say, the tail of the Lion: Alfraganus calleth it Asumpha. This Constellation containeth in it 27. Stars besides 8. unformed. Of the unformed Stars which are betwixt the hinder parts of the Lion, and the Great Bear. (according to Ptolemy's account, although Theon following Aratus, reckons the same as belonging to Virgo,) they have made a new Constellation, which Conon the Mathematician, in favour of Ptolemy and Berenice, would have to be called Berentces Hair: which story is also celebrated by the Poet Call●…achus in his Verses.  
The sixth is Virgo, the Virgin, in Arabic Eladari: but it is more frequently called Sunbale, which signifieth an Ear of Corn: and that bright Star which she hath in her left hand, is called in Greek, 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, an Ear of Corn, and in Arabic Hazimeth Al●…acel, which signifieth a handful of Corne. This Star is wrongly placed by Vitruvius and Higinus in her right hand. The whole Constellation consisteth of 26. Stars, beside the 6. unformed.   

CHAP. V. Of the Constellations of the Southern Hemisphere: and first of those in the Zodiaque.  
ANd first of Libra, which is the 7. in order of the Signs. that part of this Constellation which is called the Southern Balance, the Arabians call Mizan Aliemin, that is to say, Libra dextravel meridionalis, the Right-hand or Southern balance. But Libra was not reckoned anciently among the Signs: till that the later Astronomers robbing the Scorpion of his claws, translated the same to Libra, and made up the number of the Signs: whence the Arabians call the Northern ball●… Zubeneschi mali, that is in Greek, 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 the North Claw, and the other part of it that looks Southward, they call Zubenalgenubi 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, the South Claw. This Constellation containeth in it 8. Stars, besides 9 other unformed belonging to it.  
The eight is Scorpio, the Scorpion, in Arabic commonly called Alatrab, but more rightly Alacrab: whence the Star in the breast of it, which is the 8. in number, is called Kelebalacrab, that is, the heart of the Scorpion: and that in the end of his tail, which is the second in number, they call Leschat, but more truly Lesath, which signifieth the sting of any venomous creature, & by this word they understand the Scorpion's sting. It is also called Schomlek, which Scaliger thinks is read by transposition of the letters, for Mosclek, which signifieth the bending of the tail. This Constellation consisteth of 21. Stars, besides 3. unformed.  
The ninth is Sagitarius, the Archer, in Arabic Elcusu, or Elcausu, which signifieth a Bow; it hath in it 31. Stars.  
The tenth is Capricornus, the Goat, in Arabic Algecli. To this Constellation they attribute 28. Stars, among which that which, is in number the 23. is called in Arabic Denob Algedi, the tail of the Goat.  
The eleventh is Aquarius, the Waterman, in Arabic Eldelis, which signifieth a Bucket to draw water. The 10. Star of this Constellation is called in Arabic Seat, which signifieth an Arme. It containeth in all 42. Stars.  
The twelfth is Pisces, the Fishes, in Arabic Alsemcha. It containeth 34. Stars, and 4. unformed.  
PONT. Among all the Constellations reckoed up by the Author in this and the precedent chapters, there are only found 5. Stars of the first Magnitude. The first of which, is Oculus Tauri: the the second, Cor Leonis; the third, Cauda Leonis: the fourth Spica Virgins: and the fifth and last, is a star about the month of the south Fish. The rest are all either of the 2. 3. 4. 5. or 6. Magnitude, beside some certain cloudy ones; which are reckoned in all to be 346.   

CHAP VI Of the Constellations of the Southern Hemisphere, which are without the Zodiac.  
THE first is Cetus, the Whale, called in Arabic Elkaitoes, consisting of 22. Stars. That which is in number the second, is commonly called Menkar, but more rightly; as Scaliger saith, Monkar Elkaitoes, the nose or snout of the Whale: and the 14. Boten's Elkaitoes, the belly of the Whale: and the last of all save one, Deneb Elkaitos, the tail of the Whale.  
The secondis Orion, which the Arabians call sometimes Asugia, the madman; which name is also applied to Hydra: and sometimes Elgeuze. Now Geuze signifieth a Walnut: and perhaps they allude herein to the Latin word Jugula, by which name Festus calleth Orion: because he is greater than any of the other Constellations, as a Walnut is bigger than any other kind of Nut. The name Elgeuze is also given to Gemini. This Constellation is also called in Arabic Algibbar, which signifies a strong man, or Giant. It consisteth of 38. Stars, among which that which is the second, and is placed in his right shoulder, is called jed Algeuze, that is, Orion's●…nda ●…nda, as Christmannus thinketh: but more commonly Bed Elgeuze, and perhaps it should rather be Bet Elgeuze, that is the bright Star in Orion. The third Star is called by the Alfonsines Bellatrix, the Warrior. That which is in his left foot, and is the 35. in number, is called Rigel Algeuze, or Algibbar, that is to say, Orion's foot.  
PONT. In the 9 cap. of Job. vers. 9 there is mention made of Orion, as we said before. Now the word in the Original is Kesil, which signifieth Madness; Rage, and Instability: and it is so called perchance, because that when this Constellation riseth with the Sun, it causeth great store of tempestuous weather in all places: whence it is stled by the Poets, Nimbosus & Aquosus Orion. Now we must note, that this word Kesil in Hebrew, (which is rendered Orion by Hierome and others) doth answer to the Arabic word Asugia, which signifieth likewise a Bold or Furious fellow as our Author saith. In like manner there is mention made of Orion again in the 38. Chapter of Job, verse 13. Nunquid cohibebis delicias Pleiadum, aut lora Orionis dissolves: Canst thou bind the sweet inflences of the Pleyades, or lose the bands of Orion? notwithstanding, Interpreters do not all agree in rendering this plaee. Look also in the Prophet Amos. cap. 5. ver. 8.  
The third is Eridanus, in Arabic Alvahar, that is to say, the River: whence Nar, the name of a River in Hetruria, is conceived, by some, to have been contracted. It hath in it 34. Stars: among which that which is the 19 is commonly called in Arabic Angetener, but Scaliger rather thinks it should be red Anchenetenar, which signifieth the winding or crooking of a River. The 29 Star is also called Beemim, or rather Theemim, which signifieth any two things joined ●…ther: so that it is to be doubted, whether o●… no, this name may not be as well applied to any two Stars standing close by one another. And the the last bright Star in the end of it, is called Acharnahar, as if you should say, Behind the River, or, in the end of the River and it is commonly called Acarnar.  
PONT. Avienus calls this River Nilus, in these verses of his. 
— Pharium pars altera Nilum (amne.  
Commemorat, largo s●…getes quòd nutriat   
In English thus. 
The other part relates of fruitful Nile,  
Whose swelling streams enrich the Pharian I'll.   
And Plautus also hath an elegant Periphrasis of the same in his Trinummus, Scen. Huic ego. where be speaks thus: Ad caput amnis, quod de coelo 〈◊〉 sub solio lovis. relating it, as of a River that should spring out in the Heavens, from under Jupiter's Throne.  
The forth is Lepus the Hare, in Arabic Al●…bet: and it containeth in all 12. Stars.  
The fifth is Canis the Dog, Alcheleb Alachbar in Arabic, the great Dog; and Alsahare aliemalija, that is to say, the right hand or Southern Dog. Which name, Alsabare, which is also sometime written Scera, Scaliger thinks is derived from an Arabic word which signifieth the same that 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 in Greek, a disease that mad Dogs are troubled with, when as they cannot endure to come near any water. Notwithstanding Grotius is in doubt, whether or no it should not rather be Elseiri, and so derived from the Greek word 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, For by this name is that notable bright Star called, which is in the Dog's mouth, and is called in Arabic Gabbir, or Ecber, and by corruption, Habor. This Constellation hath in it 11. Stars.  
The sixth is the little Dog, called in Greek protion, and in Latin Antecanis, because it riseth before the great Dog. The Arabians call it Alcheleb Alasgar, that is to say, the lesser Dog, and Alsahare alsemalija, and commonly, though corruptly, Algomeiza, the left hand or Northern Dog. This asterisme consisteth of two Stars only.  
PONT. There is extant a noble witty Epigram in Ausonius of the Celestial, Terrestrial and Marine Dogs; which may have reference to this place also, if so be that, it be presented in its proper meaning after this manner. 
Trinacrij quondam currentem in littoris ora  
Antecanis seporem coeruleus rapuit. (〈◊〉:  
At Lepus. In me omnis terrae, pelagique ruina,  
Fo●…i an & Doeli; si Canis astra tenet.   
In English thus. 
At once a Hare came lightly tripping o'er  
The sandy banks of the Trinacrian shore:  
A Dog fish caught her. Where at she replies.  
Land, Stars, and all are still mine enemies  
Nor should 〈◊〉 yet be more secure, I fear,  
In heaven itself; if dogs they bar bour there,   
In which place Antecanis Coeruleus, in the second verse, signifieth a Sea-Dog. Yet this place hitherto hath commonly gone thus, Ante canes, lepo●…m, etc. without any sense at all. Now the Poet in this place useth this word Antecanis, in ●…ation of Tully, who first of all Latin Authors, rendered protion, Antecanis: as manifestly appeareth out of his translation of Aratus into Latin verse.  
The seventh is Argo: the Ship in Arabic Alseph●…a; now Seph●…a signifieth ship. It is also called Merk●…b, which signifieth a Chariot: according as the Poet's 〈◊〉 usually call it, 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 if one should say, a Sea-chariot, instead of a Ship. But the Alsonsines give this appellation to that 〈◊〉 which is the 6. in number. The whole Asterisme containeth in it 45. Stars, of all which that which is the last save one, is called in A abique Sohel, or Syhel, which signifieth Ponderous or weighty. Which Appellation they perhaps have given it, for the same reason, that Bassus hath another like it, which is, Terrestris because it always appeareth to them very low, and near the earth. The Greeks 〈◊〉 this Star 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, the Hebrews Chesil, as Christmannus is of opinion. Which if it be so, then Ar●…as Montanus is in an error, in taking it for Orion, in his 〈◊〉 of the Itin●…rary of Benjamin Tudelensis. The Inhabitants, of A●… 〈◊〉 called it an Horse, as Prolomy affirms, in his Geogra. lib. 5. cap. 7.  
The eighth is Hydra, in Arabic Alsugahh, or Asuta, which signifieth Strong, or Furious. The AEgyptinas called it Nilus, as Theon writeth in his Commentaries upon Aratus. It hath in it, 25. Stars, besides two unformed: the 12. of which the Alphonsines call Alphart.  
The ninth is Crater, the Cup, in Arabic Albatina, and Elkis, which signifieth a Goblet or standing cup. It hath in it 7 Stars.  
The tenth is Corvus, the Crow, Algorab in Arabic, consisting of 7. stars.  
The eleventh is Centaurus, the Centaur, called by the same name in Arabic. It containeth 37. Stars: among which, those that are in his hinder feet, are the Stars that make up the Cross, so much celebrated in the Spanish Navigations.  
The twelfth is Fera, the Wild beast, called in Arabic Asida, signifying a Lioness, and Alsubahh, which also is taken for a Wolf; or other ravenous beast. To this Constellation they reckon 19 Stars.  
The thirteenth is Ara, or Thuribulum, the Altar, or Censer, in Arabic Almugamra: Bassus called it Sacrarium. It containeth 7. Stars.  
The foureteenth is Corona Australis, the South Crown, in Arabic Alachil Algenubi: it consisteth of 13. Stars making up a double wreath, according to Alfraganus: yet Theon reckoneth but 12. in it.  
The fifteenth is Piscis Austrinus, the South Fish, Ahaut algenubi in Arabic. It containtaineth in it 12. Stars in Ptolemy's account but 11 only according to Alfraganus. Among which the bright one that is in his mouth, is call●…d Phom Ahut, that is to say, the mouth of the Fish, and commonly by corruption, Fomahant.  
There is also described in the Celestial Globe a certain broad Zone or circle, of the colour of milk, which representeth that which appeare●…h in the Heaven●…, and is commonly called Via Lactea, ●…he milkev way. Which Zone or circle is n●…t drawn regularly or equally, either in respect of latitude, colour or frequency of 〈◊〉 〈◊〉 is differenc and various, b●…th in ●…rm and ●…tion, in ●…ome places appearing but as 〈◊〉 〈◊〉 circle, and again in others seeming as it were dividing in two parts. The delineation whe●…eof, you may see in the Globe, and the d●…scription more largely set down by Ptolemy in his A●…megest. lib. 8. cap. 2.  
PONT. This part of the Heavens hath in it 7, Stars of the first Magnitude, whereof the first is in the right shoulder of Ori●…n: the second, in his left scot: the third, in the end of the River Eridanus; the fourth, in the mouth of the great Dog, which they call Siriu●…: the sifih, in the thigh of the Little Dog, called protion: the sixth, is Canobus, in the ship Argo: and the seventh is in the right foot of the C●…ntaure. To which we may add of the second magnitude. 18. of the third, 60. of the fourth, 168. of the fifth, 53. of the sixth, 9, and one cloudy one. All which are in the general, 316.  
Now the whole Firmament, reckoning in the Northern and Southern Hemi phaeres together with th' Zodiaque, co●…taineth in all 1022. Stars, which make up 48 Aste●…ismes or Constellations. Neither did either Ptolemy, or Hipparchus before him, know any more than these. Notwithstanding Pliny, as our Author hath advertised before in the second Chapter, made the number of Stars and Constellations a great deal larger But of this we shall spe●…k more in the end of the next Chapter. And concerning those Constellations, which have been more lately observed about the South Pole by the Portugals and Hollanders. and by them named, we intent to speak something in the end of t●…o Chapter following.   

CHAP. VII. Of the Stars which are not expressed in the Globe.  
BEsides these Stars which we have here reckoned up out of Ptolemy, there are yet many other to be seen sometime, especially in the winter time, in a clear night, when as there are both many more Stars to be seen, then at other imes, and those that are seen, appear by much, greater. Now if you expect that we should assign the cause of this: we might answer, that it is besides the intention of our present purpose. Yet for your satisfaction, and because that some Au●…hors have very much erred from the right, in setting down the true reason of the same: we do therefore the more willingly make this digression. For some there are, who (out of the extraordinary knowledge they have in Philosophy, and Optickes) would very willingly persuade us, that either we conceive them to be more, than indeed they are, and that our sense only is deceived: or else (which is altogether as ridiculous) that the air being in winter more pure and thin, making them more conspicuous, which otherwise in the Summer, when the air is more gross, do altogetherlye hid. And this is an error which I do not so much blame in others as I wonder at i●…, in Johannes de Benedictis: that so great a Mathematician, as he is held to be, should be led away with so gross an error. For the reason of this is altogether otherwise, and clean contrary. For, for that very cause that the air is more gross and thick, the Stars therefore do appear more, and greater. Which opinion of ours is confirmed, both out of principals of the Opti●…s, and also by the sense of itself, experience, and authority of learned writers.  
For first, that the rays being refracted through a gross Medium, and diffused, as it were, in certain Canales, do represent the image of the object greater than indeed it is, is plainly affirmed (and that accordiong to the doctrine of the Optickes) by Strabo himself out o●… Posidonius. And that through Perspicills o●… Sp●…ctacles, things appear more, and 〈◊〉 ●…hen otherwise they would, is a thing well known to the most Ignorant. Cleomodes also saith, that the Sun being seen by any in the bottom of a deep Well, s●…emes gr●…ater, then when he is seen from above: and ●…hat by reason of ●…he moistness and 〈◊〉 ●…f the air in the bottom of the Well. And if it were possible to see the Sun through stone walls, or other solid bodies, (as the old Poets fabulously report of Lynceus:) he would seem much bigger than he is, as Posidonius rightly teacheth. And hence is it, (saith Strabo) that we see the Sun always gre●…ter at his rising and setting, especially to those that are at Sea. Yet we do not say that he appears ten times greater than he is, as it is reported he doth in India, out of the Excerpts of Etesias his Indian H●…stories: much less, that he seems to be an hundred times greater than he is in other places, as he is feighned by Artemidorus to be at his setting, to those that inhabit a Promontory in the outmost parts of Spain, which he calls Promontorium Sacrum: but is justly taxed for the same by Posidonius. Alsraganus would have the cause of this to be, for that the vapours which are exhaled out of the earth, and elevated into the air, and so interposed be 'twixt our sight and the Sun, at his rising or setting, do make him appear greate●… than he is. The same is the opinion of Strabo and Cleomedes also, out of Posid●…nius: neither doth this differ much from the opinion of the best of our optical writers. But of this enough.  
There are also observed many Stars in the Southern parts of the world: which because they could not be seen by our Artists in these parts of the World, we have therefore no certain knowledge left us concerning the same. So in like manner, among those which we have hitherto spoken of, many of them cannot be seen by those that inhabit any whit near the North Pole. But concerning those Stars that appear about the South Pole of the World, I will here set you down a very admirable story, which Franciscus Patricius Senensis relateth in the end of his Nova Philosophia, out of the Navigations of Americus Vespuccius. And it is thu●…. Coelum decentissimè exornatur, etc. The Heavens (saith he, meaning about the Antarctique Pole) is variously adorned with divers Constellations, which cannot be seen here with us: among which I do verywell remember that I reckoned very near twenty, which were as fair and bright as Venus, and Jupiter here with us, and a little after he saith. I was certain therefore, that these Stars were of greater magnitude, than any man can conceive: and especially three Canobi, which I saw, and observed; two whereof were very bright ones, but the third was somewhat obscure, and noth●…g like the rest.  
And a little after, he proceeds. But the Pole itself is encompassed about with three Stars, which represent the figure of a right-angled Triangle: among which, that which is in the midst, is in circumference, 9 gr. and a half: and when these ●…ise, there appears, on the left hand of them, another bright Canobus of notable magn●…tude.  
And a little after, he saith▪ After these there follow three other very fair Stars, the middlemost of which hath in Diameter 12. degrees and an half; and in the midst among these, there is seen another Canobus. After this there follows 6. other bright Stars which excel all the other Stars, in the eighth Sphere for brightness: the middlemost of them, having 32. gr. in Diameter. These Stars are accompanied by another greater, but darker Canobus: all which Stars are observed in the Milky way.  
To this he addeth, out of Corsalius, his that followeth. Andrea's Corsalius also affirmeth, that there are two clouds, of a reasonable brightness, appearing near the Pole; betwixt which there is a Star distant from the Pole, about a 11 gr. over which, he saith; there is seen a very admirable figure of a Cross, standing in the midst of 5. Stars that compass it about, with some certain others that move round about ●…ith it, being distant from the Pole, about 30. degrees: which are of so great brightness, as that no Sign in the Heavens may be compared with them.  
And now, that you have heard this so strange and admirable relation of the Stars about the Antarctique Pole, Auditum admissi risum teneatis? For Vespuccius hath here forged three Canobi, whereas Ptolemy, and all the Ancient Greeks never knew but one, and that is it which is placed in the stern of the ship Argo, And here it is very well worth our noting, that Patricius (as far as I am able to gather out of his writings) out of Vespuccius his ill expressed language, and by him worse understood, hath very excellently framed to himself a strange kind of Star, that hath in apparent Diameter; 32. degrees: whereas the Diameter of the Sun itself hardly attaineth to 32. minutes.  
But those things which out of our own certain knowledge and experience in above a years voyage on Sea, in the years, 1591. and 1592. we have observed beyond the AEquator, and about the Southern parts of the world, we will here set down.  
Now therefore, there are but three Stars of the first magnitude that I could perceive, in all those parts, which are never seen here in England. All which, notwithstanding, Ptolemy saw, in Alexandria in Egypt. The first of these is that bright Star in the stern of Argo, which they call Canobus. The second is in the end of Eridanus. The third is in the right foot of the Centaur. To which if you will add for a fourth, that which is fixed in the Centaur's left knee, I shall not much stand against it. But other Stars of the first magnitude, than these which I have named, that part of the world cannot show us. Neither is there to be found scarcely two or three at the most, of the second magnitude, but what Ptolemy had seen▪ and indeed there is no part of the whole Heavens, that hath so few Stars in it, and those of so small light, as this near about the Antarctique Pole. We had a sight also of those Clouds Andreas Corsalius speaks of, the one of them being almost twice or thrice as big as the other, and in colour, something like the Via Lactea, and neither of them very far distant from the Pole. Our Mariners use to call them Magellanes Clouds. And we saw also that strange and admirable Cross which he talks of, which the Spaniard call Crusero, and our Countrymen, the Crusiers. And the Stars of which this Cross consists, were not unknown to Ptolemy also: for they are no other, than the bright Stars which are in the Centaur's feet. All which things I did the more diligently and oftener observe, for that I remembered that I had read in Cardan also, strange relations of the wonderful magnitude of the Stars about the South Pole, not unlike the stories he have now alleged out of Patricius.  
PONT. The names of the Constellations of the Southern Hemisphere as they have been now lately observed, and named by the Portugals and others, are these. The South Triangle: the Crane; the Phoenix; the Water Serpent; the Dorado, or Gilthead fish, situated in the very Pole of the Ecliptic; the Chamaeleon with the fly; the Flying Fish; the Bird of Paradise; the Peacock; the naked Indian; bird●…oucan ●…oucan, or Brasilian Pye. All which are accurate●…y portraited in the Globes set fourth by Hondius. Among all these there are no Stars, of the first Magnitude, hut of the 2. seven: of the 3. six: of the 4. thirty five: of the 5. fifty six; of the 6. eleven: with six unsormed, and two cloudy Stars, besides the two clouds themselves. Now, the whole number of the Stats in this Southern part, beside-the cloudy ones, is 121. which being added to 1022. the whole sum will b●…e 1143. Of which, 1022. were reckoned before, by our ●…uthor, out of Ptolemy only there is a scruple cast in our way by those words of Pliny, in his lib. 2. cap. 41. Patrocina●…ur vastitas coeli etc. And this opinion (sa●…th he) is seconded also by the vast n●…sse and immensity of the Heavens which is distinguished into 72. Signs, all which are the resemblances either of living creatures, or other things, according as they have been reduced into method and order by the skilful in those Arts. Among which Constellations. They have observed 1600. Stars, all which are not able either in their effects or magnitude, Where we see that ●…ee accounteth the whole number of the Stars to be 1600 whereas Ptolemy, after him acknawledged only 1022. So likewise he reckoneth the Signs or Ast●…rismes to be be in all 72. which yet in Hipparchus, Eud●…xus, and Ptolemy's account, are but 48.  
Scalig●…r in his Commentaries upon Manilius, pag 67. that he might untie this knot, reads these words of Pliny thus. Patrocinatur vastitas coeli, immensa altitudine, discreta in duo de L: signa, etc. Where, for seventy two, he would have it to be wanting two: which is 48. the j●…st number reckoned by Ptolemy But yet the same doubt still remains in the ensuing words, where he maketh the whole number of the Stars to be 1600.  
I find also two other Signs added to the former Southern Constellati●…ns, which are Noah's Dove, a●…d the Phoenicopter. The first of which containeth in it, 11. Stars: of which there are two in the back of it, of the second magnitude, which they call the Good 〈◊〉, or bri●…gers of good news: and those in the right wing are consecrated to the App●…d Deity, and those in the lest to the Retiring of the Waters in the time of the Deluge.  
The Phoenicopter we may call the ●…ittou. Of this bird, Mar●…iall hath an Epigram, lib. 13. 
Dat mihi penna rubens nomen, sed lingua gu●…osis  
Nostra placet. Quid si garrula lingua foret?   
The Spaniards call it Flamengo: and it is described with the wings spread abroad and as it were striking with his bill at the South Fish, in that part where he boweth himself. This Asterisme consisteth of 13 Stars ●…nf whi●…h that of the second magnitude in his head is called the Phoenic p●…rs Eye: and it hath ●…wo other tars also of the same magnitu●…e, one in his back and the other in his l●…twing. And those two which are in the middle of his neck. Paulus Merula in his first book of his Cosmography, calleth his Collar or Chain.  
Lastly we are to take notice that the Indian●… call the south Pole, Dramasa: for so Pliny testifieth in his lib. 6. cap. 19 Austrinum Polum Indi Drammasa vocant.    

The third Part,  

CHAP. I. Of the Geographical description of the Terrestrial Globe; and the parts of the world yet known.  
DIonysius Afer, in the beginning of his Perigesis, saith, that the whole Earth may be said to be, as it were, a certain vast Island, encompassed about on every side with ●…e Ocean. The same was the opinion of Homer also before him, a●…d of Eratosthenes (whom Dionysius is observed by Eustathius, his Scholiast, to follow in many things) as is witnessed by Strabo. The same is affirmed by Mela also after him This vast Island of the whole Earth they would have to be terminated on the North side, with the frozen Sea, which is called by Dionysius Mare Saturninum, and M●…rtuum: ●…n the East, with the Eastern Sea, which is also called Mare Se●…: on the South, with the Red Sea, (whi●…h Ptolemy calleth the Indian Sea) and The AEthyopian: and on the West, with the Atlantic Ocean. Out of this Ocean also, there are four particular gulfs (as the Ancient Geographers conceived) which embosomed themselves into the main land. Two of which derived their course out of the Erythraean or Red Sea, to wit, the Persian and Arabian gulfs. From the West, there is sent out of the Atlantic Ocean a vast gulf, which is called the Mediterranean Sea. And out of the North, they would have the Scythian Ocean to send in the Caspian Sea, which is shut in, almost on every side, with high craggy rocks; from whence the streams flow with su●…h violence, that when they are come to the very fall, they cast forth their water so far into the Sea, without so much as once touching upon the shore, that the ground is left dry and passable for whole Armies, under the banks: the streams in the mean time being carried over t●…r head●…s; as it is reported by Eudoxus in Strabo. This Sea both Strabo, Pliny, Mela, ●…nd Solinus, will have to come out of the Scythian Ocean, (as we have said) But this e●…rour, of theirs b●…sides the experience of these later times, is manifestly convinced by this one testimony of Antiquity: which is, that the water of this Sea is found to be fre●…h and sweet, as was first observed by Alexander the Great, and afterwards by Pompey, as M. Varro in Solinus t●…stifieth, who at that ●…ime himself served under Ptompey in his Wars. And this is the chiefest reason which Polycletus in Strabo●…lledged ●…lledged, for the proof of the same.  
Now all this tract of land the Ancients divided at first into two parts only, namely, Asia, and Europe: to which, succeeding times a●…ded a third, which they call Africa, and sometimes also Lybia. And of these, Asia is the greatest, Africa the next, but Europe the last of all: according as Ptolemy determines it, in the 7. book of his Geography.  
Europe, is divided on the East from Asia by the AEgaean Sea (which is now called the Archipelago) and the Euxine Sea, which was at first (as Strato in Strabo tho●…ght) encompassed about on all sides in manner of a great lake, till at last by the great accession of other River●… and waters, it so far increased, as that the banks being unable to contain it, it violently made its way into the Propontis and the Hellespont. The Euxine Sea, is now called Mare Maggiore. It is also bounded on the same side, by the like of Maeotis (now called Mare dellezahacche) the River Tanais, (commonly called Don) and the Meridian, which extends itself from thence to the Scythian or Frozen Sea. On all other sides it is encompassed with the Sea. For toward the South it is divided from Africa, by the Straits of Gibraltar, and part of the Mediterranean Sea. (The length of these 〈◊〉 is according to Strabo, and Pliny 120. fu●…longs: and the breadth of it, according to the same Strabo, 70. surlongs. But Mela would have it to be 10. miles, that is to say, 80. Furlongs. T. Livius, and Cornelius Nep●…s, make the latitude of it to be, in the broadest place, 10. miles, or 80. furlongs; and where it is narrowest, 7. miles, or 56. furlongs. But Turannius Graccula, who as Pliny reports, was borne about those parts, accounted it to be from Mellaria, a town in Spain, unto that Premontory in Africa, which is called Promontorium Album, but 5. miles in all, that is, 40. Furlongs. Eratosthenes was of opinion, that Europe was sometime joined to the Continent of Africa. and it is reported by Pliny▪ that the inhabitants of those parts have a Tradition, that the Isthmus, or neck of the land by which Europe and Africa were joined together, was cut through by Hercules.  
Europe, is terminated on the West with the Atlantic Ocean: and on the North with the British, German, and frozen Seas.  
PONT. This Northern part of Europe began first to be discovered and known to the world, in the reign, or rather through the means, and by the direction of Augustus Caesar. For as Pliny saith. lib. 2. cap. 76. Septentrionalis Oceanus, majore ex parte navigatus est, etc. The Northern Ocean for the greatest part was first searched by Augustus Caesar, who sent forth a Navy, which passing all along the Coasts of Germany, came so far as the Promontory of the Cimbrians, and thence passing on through a vast Sea, which they h●…d only heard of, before, they went as far as the Coasts of Scythia. In which place, Pliny meaneth those Sea expeditions, performed by Tiberius, and Drusus Germanicus: but especially that of Drusus, as may appear by those words of Tacitus, where he saith thus. Ipsum quin●…tiam Oceanum illa tentavimu●…, etc. We left not the Ocean unattempted that way also, and it is a common fame, that Hercules Pillars are yet remaining; whether it be true indeed, that H●…rcules ever went so ●…ar, or else, that ●…hat ever Magnificent thing is any where to be found, we all conspire un●…nimusly to honour him therewith. Neither was there wanting courage for the attempt to Drusus Germanicus: only the Ocean would not suffer itself, nor Hercules, to be sarther inquired into. After this no man att●…mpted it: and is was thought a greater point of reverence and religion, to believe the Actions of the gods, then to know 〈◊〉. Thus he.  
Now before this time, all this tract of land lying towards the North, the Romans called Novus Orbis, Ignotus Orbis, the new and unknown world: as I remember I have seen it, in a certain Elegy of Albinovus upon the death of the same 〈◊〉. And the Promontory of the Cimbria●…s, which 〈◊〉 speaks of, is now called Scagen, and is the most northern point of Denmark.  
And as concerning these Pillars of Hercules, mentioned by Tacitus; Hadrianus Junius who sometimes saw these coasts, r●…ferreth the same to that high rock or Promontory in Scandinavia (Junius hath it No●…vegia, but not rightly) which is at this day called Col, bath by the Natives, and our Mariners also. For in this place they have a superstitious custom, that as Strabo reports of the Gad ta'en Pilla●…s, when any ships had arrived there, as if they had attained the end of their labours and travail, they forthwith sacrificed to Hercules: in like manner in this place they have a custom, that if they have fresh men that never sailed tbose Northern Seas before, they have certain Ceremonies with which they use to make them free of the Sea, (as I myself once saw done sailing by this Promontory) for they ta●…k and bind them to the Mast of the ship and then taking the scoop, and filling it with Sea water, they make as it were a Libation, pouring it upon their heads, which done, they are forthwith expiated, and accounted free of the place. But whereas Junius would have the word Col, to be only corrupted from Columna, I much doubt whether he will have any more of his opinion But of this place, as also of all this Northern tract of land, I shall have a more convenient opportunity to speak elsewhere.  
Africa, is divided from Asia, according to Dionysius and Mela by the River Nilus, and a Meridian drawn through it, to the AEthiopian Ocean. But Ptolemy, would rather have its limets on this part to be the Arabian gulf, (which he not so rightly calleth the Red Sea, and a Meridian, which should be drawn from thence to the Mediterranean Sea, over that neck of Land which lieth betwixt the two Se●…s, and which joineth Egypt to the Continent of Arabia and judaea, Neither doth he think it congruous, that Egypt should be divided into two parts, one whereof should be reckoned to Africa, and the other to Asia: which must needs be, if the River Nilus be set for the bounds of the same. Neither doth Strabo conceive this to by any whit improper, since that the length of this Isthmus, which divideth the two Seas, is not above 1000 furlongs. And he seemeth to have said very rightly, that it is not above a 10●…0. furlongs. For however Posidonius reckoneth it to be very near 1500. furlongs: yet Pliny would have it to be no more than 115. miles, that is to say, 920. forlongs. And Strabo also reckoneth the distance betwixt Pelusium and the Hero's City, which is situated close by the highest part of the Arabian Gulf, to be but 900. Furlongs. But if we will give any credit to Plutarch, at the narrowest ●…art of the Isthmus, the two Seas will be found to be distant not above 300. furlongs. And that, (when Anthony was overthrown by Augustus in a Sea fight, and all his forces clean●… broken,) Cleopatra, seeking to avoid the servitude of the Romans, went about to transport her Navy this way over the firm Land, that ●…o she might find some new place of habitation, as far remote from the Romans as she might: as it is reported by the same Author, in the life of Anthony. But what should move Copernicus, In his first Book, 3. Cap. to say that these two Seas are scarcely 15. furlongs distant; I cannot conjecture; unless I should think the place to be corrupted, through the negligence of the Transcribers, or Printers. And yet I could wish, that this, (though it be a very great one,) were all the errors that were to be found in the writings of that most excellent man.  
This Isthmus, as Eratosthenes conceived, was anciently covered all over with waters, till such time as the Altantick Ocean had intercourse with the Mediterranean: and some of the old Grammarian●…▪ Scoliasts on Homer, do affirm, (as Strabo testifieth) that it was this way, that Menelans in Homer, sailed to the AEthiopians. I will therefore here set down some few things, which may seem to make for the confirmation of this relation, (whether you will call it an History, or rather a Fable, or Conjecture) of Erat●…sthenes:  
First therefore that Egypt, (if not all of it) yet atleast that part of it, which is situated beneath Delta, and is called Egyptus Inferior, the lower Egypt, and is accounted to be the gift of Nilus (or rather the Sea) was made by the aggestion and gathering together of mud and sand; was the conjecture of Herodotus, long before Strabo. In like manner, that the Island Pharos, which in Pliny's time was joined to Alexandria by a bridge, as himself testifieth, lib. 5. cap. 31. (and therefore, for this reason may seem to have been called a Peninsula by Strabo) was ancien●…ly distant from Egypt a whole day and night's sail, is re●…orted both by Pliny and Solinus, out of Homer. And this is the reason as Strabo conjectures, that Homer, (whereas h●…e ma●…es often mention of Thebes in Egypt) yet speaks not o●…e word of Memphis: and that either because at that time it was a very small place or else perhaps was not as yet in being, the land being in Homer's time covered all over with water, where Memphis was afterward built. And this seems also to be confirmed by the great depression and lowness of though intermediate shore betwixt the two Stars; which is so great, that when Sesostris fi●…st had an intent of cutting a channel betwixt the two Seas, as was afterward intended also by Darius, and lastly, by Ptolemy; they were all forced, for this reason, to desist from their enterprise. And indeed Strabo reports that himself saw the Egyptian shore, in his time, all overflowed, beyond the Mountain Casius. Besides, the great retireing of the waters at an ebb, as well in the Arabian gulf, as in the Persian, seem somewhat to confirm this conjecture of Eratosthenes. For the tides withdrew themselves so far back in the Arabian gulf: that Julius Scaliger makes mention of some Cavillers, that, for this very reason went about to derogate from the miracu lous passage of the Children of Israel for the space of above 600. miles through the red Sea: as if they had watched their time, when the tide gave way: and that when it returned again, the Egyptians were overtaken therewith and all drowned.  
PONT. This Sea is always rendered by the Septuagint, Erythraeum; and by St. H●…erom, Rubrum: but the Hebrew text itself, unders●…ding this gulf of the Sea (which is called also by Ptolemy, Sinus Arabicus) calleth it Mare Suph; which is as much as to say, Mare algosum, seu caricosum, because it bringeth forth great store of Alga, and Sea weeds. Which is observed also by Pliny lib. 13. cap. 25. where he saith. Naseuntur & in ma●…i frutices, etc. There are also bred shrubs in the Sea, and in our Sea, little trees also. For the Red Sea, and all the Eastern Ocean is full of trees. For no other Language hath a proper word to express that which the Greeks call 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 because that Alga is more usually taken for the name of an herb, but in this place it signifieth a shrub. Thus Pliny. You may also see Strabo, lib. 16. That place which the Author cit●…th out of Scalige●…, is in his 35. Exercitation against Cardan. And I think it not a miss to hear him speakeing in his own words, that so it may appear what his judgement is of that which is objected by those Cavillers. His words are these. In plaga Indica secnndùm Gangis at que Ind●… fauces magnus est aestus, etc. About the coast of India (saith he) where the Rivers Ganges and Indus, disburden themselves into the Sea, there are very high tides: So likewise in the Red Sea, they are so great, as that the contemners of Holy Writers have impiously forged that Moses, when he led the Israelites out of Egypt, took the opportunity of the Waters, retireing after the Tide. Which notwithstanding could not possibly be, because that as far as Sues, which is situated in the innermost corner of the gulf●…, the Sea covereth the very shore; neither, when it ebbeth, doth it ever leave the ground so bare, as that the lower parts, through which the Israelites passed, should be free from passage on foot.  
And it is reported by Pliny, that Numenius, General to Antiochus; sig●…ting ag●…st the Pe●…sians, near the mouth of the Persian gulf, not far from the Promontory called Macavum, got the victory of them twice in one day, first by a Sea combat: and afterward (the waters having left the place dry) on horseback: as it is related by him in his 6. book, 28. cap.  
And thus much concerning Eratosthenes his conjecture. Let us now return to the bounds of Africa. Which is divided (as we have already said) on the East from Asia, by a Meridian drawn through the Arabian gulf to the Mediterranean Sea. On all other sides it is encompassed about with the Sea: as on the West, with the Alantick; on the South with the AEthtopian Ocean; and on the North, by the Mediterranean, which is also the Southern bound of Europe,  
Now as concerning Ptolemy's ignorance of the Southern parts of Africa, making it a continent and contiguous to Asia by a certain unknown Land, which he would have to encompass about the South side of the Indian Sea, and the AEthiopian gulf: if it be not sufficiently evinced out of the relations of the Ancients; as namely of Herodotus, who reporteth, that certain men were sent forth by Darius by Sea, who sailed about all this tract: nor yet of Heraclides Ponticus, who re●…es a story of a certain Magician that came from Gelon, who said that he had compassed about all those coasts: (because Posidonius accounteth not these relations of credit enough to conclude any thing against Polybius: neither doth he approve of that story of one Eudoxus Cyzicenus, reported by Strabo, Pliny, and Mela, out of Cornelius Nepos, an Author of very good esteem, (and that because Strabo thought this relation to deserve no more credit, than those fabulons narrations of Pytheas, Evemerus, and Antiphanes: nor lastly, those traditions of King Ju●…a concerning the same matter, related by Solinus: Howsoever, I say, that those Traditions of the Ancients do not convince Ptolemy of ignorance: yet certainly the later Navigations of the Portugals most evidently demonstrate the same, who touching upon the outmost point of all Africa, which they now call, the Cape of good hope, pass on as far as the East Indies. I shall not, in the mean time, need to speak at all of that other story which Pliny hath: how that at what time C. Caesar, Son to Augustus, was Proconsul in Arabia, there were certain Ensigns found in the Arabian gulf, which were known to be some of those, that were cast away in a shipwreck of the Spanish Navy: and that Carthage at that time being in her height of power, Hanno a Carthaginian sailed about from Gades, as far as Arabia, who also afterward himself wrote the story of that n●…vigation.  
Asia, lieth Eastward both from Europe, and Africa, and is divided from them, by these bounds and limits which we have already set down. On all other parts it is kept in by the Ocean: On the north by the Hyperborean or Frozen Sea: on the East, by the Tartarian and Eastern Ocean: on the South, by the Indian and Red Sea. But Ptolemy would have the Northern parts of Asia, as also of Europe, to be encompassed, not with any Sea, but with a certain unknown Land: which is still the opinion of some of our later writers, who think that Country, which we call Grcënland, to be part of the Indian Continent. But we have very good reason to suspect the truth of this their opinion; since that so many Sea-voyages of our own countrymen, who have gone far within the Arctique Circle, beyond the utmost part, of Norway, and into that cold frozen Channel, that divides Nova Zemla from Russia: do sufficiently testify, that all those parts are encompassed with the Sea. Not to speak any thing of that which Mela allegeth out of Cornelius Nepos, how that when Q. Matellus Cesar was Proconsul in Gallia, there were presented him by the King of Suevia, certain Indians, who having been severed by force of tempests form the Indian shore, had been br●…ught about by the violence of the winds as far as Germany. Neither will I here mention that other relation of Patrocles, in Strabo: who affirmed, that it was possible to sail to India, all along the Sea shore a great Ideal more Northward than the Bactrians, Hyrcania, and the Caspian Sea: now Patrocles was made governor of these place●…. Nor last, that which Pliny himself reporteth, how that all this Eastern coast, from India as far as to the Caspian Sea, was sailed through by the Macedonian Armies, in the reign of Seleuchus and Antiochus.  
Concerning the quantity of the Earth, which was inhabited, there was great diversity of opinions among the ancient. Ptolemy defined the longitude of it to be, from West to East, beginning at the Meridian which passeth through the fortunate Islands, and ending at that which is drawn through the Metropolis of the Sinae, or Chineans country. So that it should contain half the AEquator, which is 180 degrees, and 12. Equinoctial hours, or 90000. furlongs measured by the AEquator. And he determined the bounds of the Latitude to be, toward the South, that Parallel which lieth 16. gr. 25. m. Southward of the AEquator: and the Northern limets he made that Parallel which passeth through Thule or Iseland, being distant from the Equinoctial 63. degrees. So that the whole Latitude of it containeth in all, 79. gr. 25. m. or 80. whole degrees, which is near upon 40000. furlongs. The exent of it therefore from East to West, is longer, than it is from North to South, under the Equinoctial, something than more by half as much, and under the most Northern Parallel, almost by a fiftieth part. Good reason therefore had the Ancient Geographers, as Ptolemy conceiveth in his lib. 1. cap. 6. Geograph. to call the extent of it from West to East, the Longitude of it; and from North to South, the Latitude. Strabo also acknowledgeth the Latitude with Ptolemy, to be 180. degrees in the AEquator, as likewise Hipparchus doth also: notwithstanding there is some difference betwixt them, in the number of the furlongs. For these last have set down the Longitude to be of 126000. surlongs under the AEquator: herein following Eratoshenes, who reckoneth 700. furlongs to a degree. But Strabo maketh a Latitude agreat deal less; that is, something less than 30000. furlongs: and he bounded it on the South with the Parallel, drawn through Cinnamomifera, which is distant. Northward from the AEquator 8800. furlongs: and on the North with that Parallel, which passeth through these parts which are 4000 furlongs, or thereabout, more Northward than Britain. And this Parallel that passeth through the Region called Cinamomifera, Strabo makes to be more Southward than Taprobane, or at least, to pass through the most Southern parts of the same. But herein he betrayeth his own notable ignorance; for as much, as the most Southern part of this Island, is extended far beyond the AEquator; as both Ptolemy affirmeth in his Geography, lib. 7 cap. 4. and is further confirmed by the late Navigations of the Portugals. But Dionysius Afer is much farther out of the way then so: for he placeth Taproba●… under the Tropic of Cancer.  
And these were the bounds where with the Ancient Geographers terminated the then in habited parts of the world. But in these riper times of ours, by the industry at Sea, both of the Spaniards, English, and others, the Maritime coasts of Africa have been more throughly discovered, to above 35. gr. of Southern Latitude: and the Northern limits of Europe have now been searched into, as far as the 73. degree of Northern Latitude, far within the Arctic circle: besides all that which hath at length been discovered in the New World, beyond the hope or opinion of any of the Ancients, the name of it being not so much as known to them.  
America, which for its spaciousness, may well be called, The other World, extending itself beyond 52. gr. of Southern Latitude, is there bounded wi●…h the straits of Mag●…llane: and toward the North it runeth far within the Arctique circle: on which side also that it is bounded by the Sea, the many Navigatiors of our Countrymen into these parts, do give strong arguments of hope I shall not here speak of those Sea coasts, which are beyond that Sea that encompasseth about the most Northern parts of Europe and Asia; as having been but only seen afar off as yet, and not throughly discovered Nor yet those other, which are more Southern, than the Indian and Red Sea: which as yet we have not any experience to the contrary, but that we may believe to be one continent with those other Southern Lands, that lie beyond the Straits of Magellane.  
Europe, (whether so called from Europa Tyria, daughter of Agenor, as some think; or Phoenix, as Herodotus will have it; or else from Europa a Sea Nymph, according to the opinion of Hippias in Eustathius; or else from Europus, as Nicias in the same Eustathius would have it to be; containeth in it these principal regions: to wit, Spain, France, Italy, Germany, Bohemia, Prussia, Rhaetia, Livonia, Sclavonia, Greece, Hungary, Polonia, Moscovia. or Russia, Norway, Sweden, and Denmark. To these we may add the principal Islands, as namely, those of great Britain, the chief of which is England, and Scotland, ennobled chiefly by being united to the English Crown: as also Ireland, which is, in like manner, subject to the same. Besides the Azores, and many other Islands scattered up and down in the Mediterranean Sea, as Sicily, Sardinia, Crete, etc.  
PONT. In Europe these things are chiefly observable. 1. The most famous Monarchies which are in it; as namely the Emperor of Germany, the Kings of Spain, France, Great Britain, Denmark, Swethland, Polonia, and Moscovia. To which we may add the Pope of Rome, who, though he usurp not the title of a King, yet is his power no whit inferior to theirs: a●… also the great Turk, who at this day possesseth a great part of Europe also. 2. The principal hills, which are the Alps, dividing Italy from Germany and France; and also the Pyrenoean Hills, severing Spain s●…om France. 3. The noteable Rivers, as the Da●…ow, the Rhine, the Ell, the Wetsell, Bortsthenes, and Tanais, now called Don. To which we may add the River Tagus in Spain, the Rhine and Guar●…nn: in France, and Thames in England. Lastly, the principal commodities in Europe, are Gold, Silver, Tin, Led, Iron, Oil, all kind of grain, Flax, Wool, Salt, etc.  
Africa, (whether it be so called from Apher, one of Hercules his companions, in his expedition against Geryon; according to Eustathius: or else from one Iphricus, a certain King of the Arabians; whence also it is called in Arabic Iphricia, as Johannes Leo testifieth: or lasty from its scorching heat, as if it should be called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 quasi sine frigore, as some are pleased to derive it:) hath in it these principal regions. First of all, next to the Straits of Gibraltar, (anciently called Fretum Gaditanum) there lieth Barbary. heretofore called Mauritania; which containeth in it the kingdoms of Morocco, Fez. Algiers, and Tunis. Next to Barbary lieth Egypt, which also bordereth upon the Mediterranean Sea. Now within Barbary toward the continent, there lieth Biledulgerid known to the Ancients by the name of Numidia. The 3d is that part which is called by the Greeks and Latins Lybia: but the Arabians name it Sarra. After this follows the country of the Negroes, so called because they border upon the River Niger, or else from their colour, This Country is now usually called Senaga: and it hath in it many petty Kingdoms, as namely, Gualata, Guinea, Melli, Tombutum, Gagos, Gub●…ris, Agades, Canos, Casena, Zegz●…ga, Zanfar●…, Burnum, Gaoga, Nubia, etc. Next othese is the spacious Territory of the King of the AEthtopian, (who is al●…o called Pretegiani, and corruptly Prester John) which Kingdom is famous for the long continuance of the Christian Religion in it, which hath been kept amongst them in a continual succession, ever since the Apostles time. These Christian are commonly called Abyssines, but more rightly Habassines, as Arias Montanus observeth in the Itinerary of Benyamine Tudelersis. I h●… dominion was anciently extended very far through Asia also. These have bordering on the West some few obscure kingdoms, as Manicongo, and D' Angola: and toward the East and South, Melinde, Quiloa, Mozambique, and Benamatapa. The chief Islands that are situate near it, are Madagascur, the Canary Islands, the Isles of Cape Verd; and S. Thomas Island, lying directly under the AEquator.  
PONT. Africa, hath these things in it considerable. 1. It is greater than Europe but less than Asia, and less inhabited, and civiliz●…d then either. 2, It is b●…unded with the Sea on all sides, sa●…e on●…ly where it is is con terminat with Asia, 3. The principali regions of it, are, Mauritania, Numidia, Libya, Cyrenaica, Egypt, and AEthiopia. 4. The mast famous kingdoms are these, Morocco, Fez, Algiers, and also that of Prester John, or AEthiopia 5. The greatest Mountains are, Atlas, and that other whence Nilus, springeth 6. The principal r●…rs of Nigar, and Nilus, which is accounted to be the greatest in the world, and as Diodorus Siculus affirmeth, encompasseth 700. Islands. 7▪ The principal Merchandise of Africa, is Ivory, Civet, Gold Cotton Wool, Jewels, and certain kinds of spices, as also Salt, Lions, Camels, etc.  
Asia (so called from Asia, the mother of Prometheus, as the common received opinion is; or else from a certain Hero of that mane a●… Hippias in Eustathius will have it, at this day wholly in subjection to the great Turk, and the Persian, as far as to the East Indies, the greatest part whereof is under the Kings of China & Pegu. But the more Northern parts of Asia are possessed by the Muscovites, Tartarians, and those that inhabit the region or Cathaia. The principal Islands appertaining unto at, are Cyprus, and Rhodes in the Mediterranean: and on the South side, Sumatra, Zeilam. Java, Major and Minor, the Molucean and Philippine Islands, beside Borneo, and almost an infinite company of others And on the East of it there lie the Japonian Islands.  
PONT. That it ought to be written Sinae, not Chinae, as our Author in this place, and commonly all other writers use to do, appeareth manifestly out of Ptolemy, who always calleth them Sinai. The eighth Table also of Asia in Ptolemy's Geography, placeth the Scythians called Cathae, (which our Author calleth the region of Cathaia.) betw●…xt th●… mountains Imavus and Emodus: and the region of the Siaeans a part of it beyond the same Emodus and Ottoro cara, which are hills in the Country of the Seres, and looking towards the South East. So that I cannot but wonder that Matthaeve Riccius a Jesuit, in his Sinaean expedition should take so much pains to prove, that the Kingdom of Cathaia▪ and of the Sinaeans is all one. But it were easi●…, by other, and those more proper arguments and testimonies, (were this place convenient) to prove the contrary to this his assertion.  
Now as concerning Asia, these things occur n●…it worth our observation. 1. That it is twofold, Asia Minor, and Major. 2. Asia Minor, or the lesser Asia, is bounded on the East by the Euxine Sea; on the South by the river Euphrates; on the West by the Mediterranean, on the North by the AEgean Sea. 3. The principal countries it contained anciently, were these: Cilicia, Pamphilia, Caria, Lycia Jonia, Lydia, AE●…lia, Mysia, Bithynia, Paphlaponia, Cappad▪ cia, Galatia, Lycaonia, and Pisidia. 4. To the greater Asia th●…se Regions appertained: Syria, Armenia, Chaldaea, Arabia, Pe●…a, Tartary, Hircani●…, Parthia, and India. 5. In both of them there are settled at this day these Empires; namely, the Turkish, Persian, Tartarian, Indian, and Sin●…sian or Chinean 6. The chiefe hills of note in it, are Taurus, Caucasus, and Im●…us. 7. The principal Rivers, Euphrates Ganges, and Indus, 8. The chiefest traffic is, Gold, Pearl, Jewels, all kind of Spices, Musk, Frankincense, Balsam, Amber, Silks, Ivory, and Elephants.  
America, (so called from Americus Vespuccius, who first discovering it, gave it both name and bounds,) is terminated on the East side, (on which it looks toward Europe, and Africa) by the Atlantic Ocean: on the West with the Sea, which they call, deal Zur, or the South Sea: on the South it is bounded with the Straits of Magellane. But as for the Northern parts of it, they are not yet throughly discovered, or the Limets thereof known: notwithstanding the many adventures by Sea of our Countrymen, M. Martin Frobisher, and M. John Davis, having given strong arguments o●… hope, that it is on that side ●…ounded by the frozen Sea. It containeth in it these principal regions. First, on the North, that Country which the Spaniards call, Tierra de Labrador: after which followeth that which they call, Baccalearum Regio: then Nova Francia: after this Virginia: then Floride: next to this Nova Hispania, famous especially for the City Mexico and last of all the Kingdoms of Brasilia and Peru, which are the most Southern parts of all. There are also many adjacent Islands: most of which lie in the Bay of Mexico, Eastward from America: the most notable of which are Cuba and Hispaniola, besides many other of les●…e note.  
There are also many other parts of the world, not yet throughly known or discovered, as namely those southern coasts, wherein stands Nova Guinea lying beyond the Indian Sea, which whether it be an Island, or else a part of the m●…ine Continent, i●… not yet discovered: and likewise, that the other tract of the Southern known Continent, which is called Magellanica: as also these Northern parts of Europe, Asia, & America which have bee●… but lately detected by many of our English Navigators, but not as yet fully searched into.   

CHAP II. Of the Circumference of the Earth or of a Greater Circle: and of the Measure of a Degree.  
IT remaineth now that we speak somewhat of the circumference of the Earth, or of the greatest circle in it; the knowledge whereof is very necessary, both for the study of Geography, as also for the easier attaining to the Art of Navigation. And therefore, I hope, I shall not seem impertinent, if I insist something the longer on this argument: especially seeing that there is great diversity of opinion among the most learned Authors that are extant, concerning this matter; in somuch that it is not yet determined, which of them we are to follow.  
Aristotle in the end of his 2d●…ook de Coelo, affirms (and that according to the doctrine of the Mathematicians, as himself saith) that the circumference of the Earsh is 400000. in: longs Cleomedes lib. 1. reckons it to be 300000. for he saith that the Vertical Points of Lysimachia and Syene, were observed by Sciotericall Instruments, to be distant from each other the 15th. part of the same Meridian. Now the distance between these two places he sets down to be 20000. furlongs: So that if 20000. be multiplied b●… 15. the whole will arise to 300000. Eratosthenes (if we may believe Strabo, Vitruvius, Pliny, and Censorinus) would have the whole compass of the Earth to contain 252000. furlongs. To which number Hipparchus, as Pliny testifieth, added very near 25000. more. Yet Strabo as well in the end of his 2d book of his Geography, as else where, affirmeth, that he used the s●…me measure that Eratosthenes did: where he saith, that according to the opinionof Hipparchus, the whole quantity of the Earth containeth 252000. furlongs: which was the measure delivered also by Eratosthenes. Which opinion of Eratosthenes is seconded also by that fabulous relation of Dionysiodorus, recorded by Pliny. lib. 2. cap. ult. Where he saith, that there was found, in the Sepulchre of Dionysiodorus, an Epistle written to the gods; wherein was testified, that the Semediameter of the Earth contained 4200. furlongs. Which number being multiplied by 6. the Product will be 252000.  
Cleomedes relating the observations of Eratosthenes, and Posidonius, making it to be somewhat less, and that according to the doctrine of Eratosthenes: to wit, 250000. furlongs. For he placeth Syene and Alexandria under the same Meridian, Now Syene being situate directly under the Tropic of Cancer, the Sun being then in ●…he Summer Solstice the Gnomon cast no shadow at all. For confirmation of which, the experiment was made, by digging a deep Well, which, at that time of the year, was wholly enlightened on every part: as it is reported both by Pliny and also by Strabo before him. But at Alexandria, when the Sun is in the Summer Tropic, the Gnomon is observed to cast a shadow to the fiftieth part of the circumference, on which it is erected to right angles, so that the top of the same, is the centre of the circumference. Now the distance betwixt Syene and Alexandria is commonly set down by Eratosthenes, Pliny, and Strabo, to be 5000. furlongs. If therefore 5000. be multiplied by 50. the whole will arise to 250000. which is the number of furlongs 〈◊〉 to the circumference of the whole earth by Eratosthenes Posidonius, proceeding after another method, though not unlike this, labours to prove the whole circuit of the Earth to contain 240000. furlongs. And first he taketh for granted (which is also acknowledged by Ptolemy, lib. 5. c●…p. 3. Almagest.) that Rhodes and Alexandria are situate under the same Meridian. Now that bright Star in the stern of Argo, (which they call Canobus, and which never appeareth in Greece, which seems to be the reason why Aratus maketh no mention of it:) first beginneth to appear above the Horizon at Rhodes: but it doth but stringere Horizontem, just touch the Horizon, and so, upon the least circumvolution of the heavens, setting again, or else, as Proclus saith, is very hardly seen, unless it be from some eminent place. But when you are at Alexandria, you may see it very clear above the Horizon. For when it is in the Meridian, that is, at the highest elevation above the Horizon: it is elevated above the Horizon about the fourth part of 〈◊〉 Sign: that is to say, the fortieeighth part of the Meridian that passeth through Rhodes and Alexandria. The same is affirmed alo by Proclus▪ if you read him thus: Canobus in Alexandria consp●…euè cerni, quar●…a 〈◊〉 Signi portione supra Horizontem 〈◊〉 as i●… ought to be; and not as it is corruptly read, in Alexandria prorsus non cerni. It is not seen at all: in stead of it, is seen very plainly: 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 being crept into the text, perhaps in stead of 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Now the distance betwixt Rhodes and Alexandria is set down both by him and Pliny, to be 5000. furlongs: which being multiplied by forty eight, the product will be 240000. the number of furlongs, agreeing to the measure of the Earth's circumterence, according to the opinion of Posidonius.  
Ptolemy, every where in his Geography, as also Marinus Tyrius before him, have allowed but 500 furlongs, to a degree in the greatest circle on the earth, of which the whole circumference containeth 360 〈◊〉 that the wh●…le compass of the Earth, after this account, con●…aineth 180000. furlongs. And yet Strabo affirms in his lib. 2. Geograph. that this measure of the Earth's circumference set down by Ptolemy, was both receiv●…d by the Ancients, and also approved by Posidonius himself.  
So great is the difference of opinions, concerning the compass of the Earth: and yet is every one of these opinions grounded on the authority of great men. In this so great diversity therefore, it is doubtful whom we should follow. And if you should desire to know the cause of all these dissensions; even that also is altogether as uncertain. Nonius, and Peucerus would persuade us, that certainly the furlongs they used were not of the same quantity. Maurolycus, and Philander conceive the difference of furlongs to rise out of the divers measure of Pases. And therefore Maurolycus takes great pains to reconcile them; but in vain: for they seem not capable of any reconcilement. They t●…ll us of divers kinds of Pases in use among the Ancients. It is true: we assent to them herein: but withal desire to hear of some diversity of furlongs also, or at least, of feet. The greeks (as I conceive) measured not their furlongs by Pases: but by feet, or rather 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Now 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 is the measure of the extension of both the hands, together with the breast betwixt, containing six feet, which we commonly call a fathom, and is a measure in familiar use with our Mariners, in sounding the depth of the Sea, or other waters. This word notwithstanding is translated by many, a Pace: but how rightly, I leave it to learned men to judge. Xylander in his translation of Strabo, always rendereth it, an Ell. In like manner a furlong is defined by Herodotus, a very ancient Greek Author, to consist of 600. feet: the same also is affirmed by Suidas, by much later than he. Yet Hero Mechanicus (or at least his Scholiast) one, as I conceive, of the lowest rank of Ancient Writers:) will have a surlong to contain 100 fathoms; a fadam four Cubits: a Cubi a foot and a half, or twenty four digits: But you will say perhaps, that Censorinus proposeth three several kinds of furlongs: the first of which is the Italian, consisting of 625. feet: which he would have us understand to be that which is commonly used in measuring the Earth. The second is the Olympian: containing 600. feet: and the third and last is the Pythean, consisting of 1000 feet. But to let pass this later, if we do but look more nearly into the matter, we shall find the Italian and Olympian furlongs, howsoever they differ in names, yet to be no other but the self same thing. For the Italian furlong, which containeth 625. Roman feet, (according as Pliny testifieth, in his second book and twenty third Chapter) will be found to be equal to the Olympian, consisting of 600. Grecian feet. For 600. Grecian feet, are equal to 625 Roman: for as much as the Grecians foot exceeds the Roman by a twenty fourth part: as much as in the difference betwixt 600. and 625.  
Amongst these so great diversities of opinions, let us give our conjecture ●…iso, both what may be the cause of so great disagreement, and also which of them we may most safely follow. We will therefore pass by Aristotle, whose assertion is only defended by a great name. And for Cleomedes his opinion, of the Earth's being in compass 200000. furlongs, we should scarce vouchsafe to mention it, but that Archimedes also had taken notice of the same, as of a portion not altogether disallowed in his time. Let us therefore examine Eratosthenes, and Posidonius, whose opinions seem to be grounded on more certain foundations. The cause therefore of their disagreement I conceive to be in that neither of them had measured exactly the distance of those places which they laid down to work on, but took them upon trust, from the common reducing received of Travellers: save only, that of the two, Posidonius is the more extravagant. Whereas on the contrary Ptolemy grounded his opinion on the distances of places exactly measured, as himself affirmeth; when he saith: That the latitude of the known parts of the world is 79, degrees, and 45. minutes. Or supposing it to be full 80. degrees; it will then contain 10000 furlongs, allowing for every degree siue hundred furlongs: as by measuring the distance of places exactly, we have found it to be  
But Eratosthenes is much taxed by Hipparchus, for his strange mistakes and gross ignorance in setting down the distance of plac●…s: as Strabo testifieth in his first book. For he reckons betwixt Alexandria and Carthage above 13000. furlongs, whereas (saith Strabo) it is not above 9000. So likewise Posidonius is to be blamed, for setting down the distance betwixt Rhodes and Alexandria to be 5000. furlongs, and that from the relation of Mariners, whereas some of them would have it to be but 4000 and others 5000. as Eratosthenes confesseth in Strabo: but addeth moreover, that he himself had found by Sciotericall instruments, that it was but 3750. And Strabo would have it to be something less than that, namely 3640. furlongs. So that hence, ●…e may safely conclude, that Ptolemy's opinion, being grounded upon the more exact and accurate dimensions of distances, (as bimself professeth (must necessarily come nearer the truth then the rest.  
But Franciscus Maurolycus, Abbot of Messava, whiles he goes about to defend Posidonius against Ptolemy, is overtaken himself in an error, before he is aware. For ●…e suspecteth the truth of Ptolemy's assignment of the latitude of Rhodes, which he sets down to be thirty six degrees▪ And he advertiseth us, that certainly the number in his Geographical tables are corrupted: which, we confess, is most certain. But in the mean time let us see how he proves them to be so, in this Latitude of Rhodes Posidonius (saith he) out of his own observations, setteth down the Latitude of it to be thirty eight degrees, and an half: unless that Ptolemy be out also in designing the Latitude of Alexandria; which Maurolycus thinks cannot possibly be. But we affirm on the contrary side, that Ptolemy himself is against this Latitude, not only in his Geographical books, but also in divers places throughout the Almagest also, and especially in the lib. 2. cap. 6. where he sets down the same latitude for Rhodes, that he hath in this Geography: adding moreover the quantity of the longest day, and also what manner of shadows the Gnomonos cast, both when the Sun is in the Equinoctial, as also in the Tropics: all which do plainly prove the s●…me He also very often hath the same lat●…tude of it in his Planisphaere: unless you will say, that either Masses the Arabian, in translating it into Arabic, or else Rodulphus Brugensis, who translated the some again out of Arabic into Latin, have 〈◊〉 us. Hitherto therefore we stand on equal terms. But he proceeds, and saith, that this opinion of Posidonius is favoured also by Proclus, & the observ●…tions of Eudoxus Cnidius, delivered by Strabo Let us therefore see what all this is. P●…sidonius (saith Strabo) reports, that himself being sometimes in a City distant from the Gaditan Straits 400. furlongs, saw from the top of an high house a certain Star, which he took to be Canobus: and those that went thence more South ward from Spain, confess that they saw it also plainly. Now the Tower Cnidus, out of which Eudoxus is said to have seen Canobus, is not much higher than the other buildings. But Cnidus is in the same Climate with Rhodes, as is also the Gades, with the Sea coasts adjoining. Thus Strabo. But what doth he conclude hence against Ptolemy? That Canobus may be seen in Cnidus? We deny it not. Or that Cnidus is in the Rhodian Climate? Ptolemy acknowledgeth as much: for he makes it to have not above 36. gr. 15. m. of Latitude, in the fifth book of his Geography. But is not Ptolemy out also in assigning the Latitude of Cnidus? That the Latitude of Rhodes is no greater than Ptolemy hath set it, may be proved even out of Proclus himself: for he makes the longest day at Rhodes to be 14. hours and an half. And Ptolemy will have the same to be equal both at Rhodes, and Cnidus. And to this assenteth Strabo likewise, save only that in one place he sets it down to be but 14. hours bare: so that by this reckoning it should have less Latitude. Now Proclus his words are these, In the Horizon of Rhodes (saith he) the Summer tropic is divided by the Horizon in such sort, as that if the whole circle be divided into forty eight parts, twenty nine of the same do appear above the Horizon, and 19 lie hid under the Earth Out of which division it follows, that the longest day at Rhodes must be 14. Equinoctial hours and an half, and the shortest night, 9 and an half, Thus he, I do not deny, but that Posidonius his setting down of the quantity of the portion of the Meridian intercepted betwixt the vertical point o●… Rhodes and Alexandria, might deceive Pliny, Proclus, and others. Yet Alfraganus draweth his second Climate through Cyprus and Rhodes, and maketh it to have the longest day of 14. hours and an half, and in latitude 36. gr. two thirds. So that there is but very small difference betwixt him and Ptolemy. And even Maeurolycus himself. when in his Cosmographical D●…alogues he numbereth up the Parallels, h●… maketh that which passeth through Rhodes to have 36 gr. and a twelfth of Latitude: herein differing, something with the most, ●…om Posidonius. Eratosthenes his observations also do very much contradict Posidonius. For Eratosthenes saith, that he found by Sciotericall Gnomon, that the distance betwixt Rhodes and Alexandria was 3750. furlongs. But let us examine this a little better. The difference of Latitude betwixt these two places he found Scioterically, after his manner, to be something more than 5. degrees. And to this difference, (according to his assumed measure of the compass of the Earth, wherein he allows 700. furlongs to a degree) he attributes 3650. furlongs. Neither is there any other way of working by Sciotericall instruments (that I know) in finding out the distance of furlongs betwixt two places; unless we first know the number of furlongs agreeing either to the whole circumference of the Earth, or else to the part of it assigned. Let us now see if we can prove, out of the observations of Eratosthenes himself, that neither Posidonius his opinion concerning the measure of the Earth's circumference, much less Eratosthenes his own can be defended. And here we shall not examine his observation of the difference of Latitude betwixt Alexandria and Syene, that so we might prove out of his own assumptions, that the whole compass of the Earth cannot be above 241 620. furlongs: as it it demonstrated by Petrus Nonius, in his lib. 2. cap. 18. De Navigatione. Neither do we inquire, how truly he hath set down the distance of these two places to be 5000. furlongs: whereas Solinus reckoneth not from the very Ocean to Meroe above 620. miles, which are but 4960. furlongs. Now Mercë is a a great deal farther than Syene. Neither will we question him at all, concerning the small difference that is betwixt him and Pliny, who reckons from the Island Elephantina (which is 3. miles below the last Cataract, and 16. miles above Syene) to Alexandria but 486. miles so that by this reckoning, betwixt Syene and Alexandria, there will not be above 4560. furlongs. But we will proceed a contrary way to prove our assertion. This one thing therefore we require to be granted us; Which is: that look how great a space the Sun's Diameter taketh up in his Orb; for the like space on the Terrestrial Globe shall the Gnomon be without any shadow at all, while the Sun is in their Zenich. Which if it be granted, (as it is freely confessed by Posidonius in Cleomedes,) we have then gotten the victory.  
Now it is assimed by Eratosthenes, that the Sun being in the beginning of Cancer, and so directly in the Vertical point at Syene; both there, and for 〈◊〉. furlongs round about, the Gnomon cast no shadow at all. Let us now therefore see, how great a part of this Orb the Suns Diameter doth subrend. For by this means, if this position of Eratosthenes, which we have now set down, be true, we may easily find o●…, by it, the whole circuit of the Earth. Firmicus Maternus makes the Diameter both of the Sun and Moon to be, no less than a whole degree. But he is too far from the truth: and assigneth a greater quantity, either than he ought, or we desire. The Egyptians sound by Hydroscopicall instruments, that the Diameter of the Sun takes up the Seven hundred and fifty parts of his Orb. So that if 3●…0. furlongs on Earth answer to the seven hundred and fiftieth part of the whole circumference of the same: the whole circuit of it then will be but 225000. furlongs. The fabric and use of this instrument is set down by Proclus in his cap 3. Designation. Astronomi. And Theon also speaks much of it in his Commentaries upon the 5. lib. Almagest. Ptolemy. as also doth Maurolicus in his third Dialog. Cosmograph. But these kinds of observations are not approved of by Ptolemy And Theon also, and Proclus de●…race them to be obnoxious to much error. And therefore we examine the matter yet a little further.  
Aristarchus Samius, (as he is cited by Archimedes) affirmed that the Sun●… apparent Diameter taketh up the seven hundred and fiftieth part of the Zodiac, that is to say, 30. minutes; and is equal to the apparent Diameter of the Moon: as he hath it (as I remember) in the 7. and 8. Propositions of his book De magnitud, & distant. Solis & Luna. The same was the opinion also of Archimedes himself. But, in the mean time, I cannot free myself of a certain soruple cast in my way▪ by another supposition of the same Aristarchus, in the very same book, where he would have the Diameter of the Moon to be 2. deg●…es. Archimedes also, out of his own observations, by Dioptricall instruments, hath defined the Sun's Diameter to be greater than the 200th part of a right angle, that is to say, 27. minutes: yet less than the 164th part of a right angle, which is 33. minutes. But he himself confesseth, that there is not so great credit to be given to such like observations, as are made by these Dioptricall instruments, as by them to be able exactly to find out the Diameter of the Sun or Moon: seeing that neither the sight, nor the han●…, nor yet the instruments themselves, by which the observations are to be made, can be every way so exact and sure, as not to fail. Ptolemy by the same Dioptricall instruments, as also by the manner of Eclipses, sound the Diameter of the Sun to contain 30. m. 20. sec. and to be equal to the apparent Diameter of the Moon, when she is at the greatest distance from the earth, which is, at the full Moon, and in Conjunction with the Sun. Now whereas he would have this magnitude to be constantly the same, and invariable: Proclus approves not of him herein, as appears in his 3. cap. Designation. Astronom. being hereto induced by the Authority of Sosigenes a Peripatetic: who in those books of his, which he entitleth, Derevolutionibus, hath observed, that in the Eclipses of the Sun, there is sometimes a certain little ring or circle of the Sun to be perceived enlightened, and appearing plainly on all sides round about the body of the Moon. Which if it be true, it is impossible then, that the apparent magnitude of the Sun shall be, at all times, equal to that of the Moon in their Conjunctions and oppositions. And this is the cause perhaps, that those that have come after Ptolemy, have endeavoured to examine these things more accurately. And first of all Albateni found the Diameter of the Sun, when he was in the Apogaeum of his Eccentrick, to be 31. m. 20. sec. which is the same which Ptolemy's observation: but in the Perigaum, to be 33. m. 40. sec. But Copernicus went yet further, and found the Diameter of the Sun, when he was in his greatest distance from the Earth, to be 31. m. 48. sec. and when he is nearest of all, to be 33. m. 54. sec. Now therefore if we work upon this ground here laid before us, and take the Diameter to be 32. in, it will then follow, that if 300 furlongs answer to 32. minutes, the whole circuit of the Earth will be but 202500. furlongs: which falls short of that measure which Posidonius hath set down, but much more of that which Eratosthenes hath delivered. And thus much have woe thought good to say (with all ●…e reverence to the judgements of learned Authors) in examination of ●…hose things, which have been delivered by the Greeks, concerning the measure of the Earth's circumference.  
The way of measuring, used here with us, is by Miles, and Latitudes: of the former whereof 60. and of the later 20. answering to a degree. So that the circumference of the Earth. containeth 21600. English Miles: which also agrees exactly with that of Ptolemy For we find our English foot to be just equal with 〈◊〉 Grecian, by comparing it with the Grecian foot. which Agricola, and others have delivered unto us, out of their monuments of antiquity. Now one of our Miles containeth 5000. feet of our English measure: and a furlong 600. Grecian feet. Now if you multiply th●… 〈◊〉 of a furlong by 500 (for so many furlongs doth Ptolemy allot to a degree) and so likewise the measure of a Mile, which is 5000. feet, by 60. (which is also the number of miles that we reckon for a degree,) they will both produce the same number of feet, viz. 300000. So that from these grounds we may certainly conclude, that the common computation received among our Mariners, doth agree most exactly with that of Ptolemy.  
The Italians also make 60. miles to be the measure of a degree: but their measure is something less than Ptolemy's. The Grecians reckon 15. miles to a degree: one of their miles containing 4. Italian: so that this reckoning of theirs falls ●…ust as much short of Ptolemy's, as the Italian doth. For according to their computation, a degree containeth not above 480. furlongs, every Italian Miles consisting but of 8. furlongs: (unless perhaps you rather approve of Polybius his opinion, who,) as he is cited by Strabo (over and above 8. furlongs, will have 2. Plethra, which is the thid part of a furlong, to be added to every mile: which is the just measure of our English mile.) Yet Appian saith that 15. German miles, are as much, as 60. Itslian: and 60. Italian miles contain 480. furlongs: which is less than Ptolemy's measure by 20. furlongs, which make up two Italian miles, and an half.  
The Spaniards reckon to a degree, some of them 16. leagues and two third parts: and some seventeen and an half. But how their measure stands, compared with the Grecian furlongs, or with the English, Italian, or German miles, I have not yet certainly learned. Yet Nonius seemeth to equal the Spanish league with the Schoenus, or Parasanga: which if it be so, than those that allow 16. leagues and 2. thirds to a degree, have the same measure that Ptolemy hath delivered: but those that allow 17. and an half, make it somewhat too large.  
It only now remaineth to see, what is the doctrine of the Arabians concerning this matter. Of which the most ancient have assigned to the whole circumference of the Earth, 2400. Miles, or 8000. Parasangae: so that after this computation, a Degree must contain 66. Miles, with two third parts. And this measure is used by Alhazenus, in the end of his book, De Crepusclis. Alfraganus, and some of the later Arabic writers, since Almamons' time, do generally account 20400. Miles to be the just measure of the Terrestrial Globe: So that one degree containeth, by this reckoning, 56, Miles and a third part. And it is reported by Abilfedea, in the beginning of his Geography, how that, by the command of Almanon, King of the Arabians. or Caliph of Babylon there were certain men employed, who should observe in the plain field of Singar and the adjoining Sea coasts, (meaning the places in a direct linetoward the Pole, (how many Miles answered to a degree: and that they found, by just computation, that in going the space of one degree, there were spent full 56. Miles without any fractions, and sometime 56. Miles, and a third part which make up 1333. cubits, with two 〈◊〉. But now what proportion the Arabian Mile beareth to ours, or the Italian, or German Mile, is not so easy to determine. Ye●… conjecture it cannot be loss than te●… Furlongs. The Parasanga (as Christmannus●…ils ●…ils us, out of Abilfedea, that great Arabian Geographer) containeth three Arabian Miles, according to the doctrine both of the Ancient, and Modern Writers among them. Now a Parasanga (as it appears plainly out of Herodotus Xenophon, and others) containeth thirty furlongs: so that, by this account, every mile must comprehend ten furlongs. And for confirmation of this, we may observe, that, among the greeks, there were two kinds of Cubits in use; the one, the common or ordinary Cubit, which contained two foot and an half of Grecian measure, or twenty four digitt, of which sixteen went to a foot. The other was the King's Cubit, in use among the Persians: which was greater than the common Cubit by three fingers breadth. Now Alfraganus affirmeth that the Arabian mile contained 4000 Cubits, according to the ordinary measure. So that if this Cubit be equal to the Grecian Cubit, one of their miles will then contain 6000. Grecian feet, which makes up ten furlongs. Now whereas the Parasanga is reckoned by some to contain 40. furlongs, and by others 60. yet no body alloweth to it less than 30. with which later account if we should; with Herodotus, Xenophon, and others, rest ourselves contented (neither indeed is it our intention to stand long in disputing, whether or no in divers places, the measure of the Parasanga were also different, as Strabo seems to think, who observed the very same difference in the Egyptians Schoenus, when as being conveyed on the River Nilus from one City to another, he observed that the Egyptians in divers places, used divers measures of their Schoenus:) I say, if we should rest upon their determination, who assign but 30, furlongs to a Parasanga; then one of the Arabian miles will contain ten furlongs at the least. Which conjectures, if ●…hey be true, we cannot then assent to those learned men, P. Nonius, and Jacobus Christmannus, who will have the Arabian Mile to be all one with the Italian,  
In this so great diversity of opinions, concerning the true measure of the Earth's circumference, let it be free for every man to follow whomsoever he please. Yet were it not that the later Arabians do counterm●…nd us, by proposing to us their Positions, which they aver to have been grounded upon most certain and exact mensurations of the distances of places: we should not doubt to prefer Ptolemy's opinion, I will here propose unto your view a list of all those opinions, which carry in them any show of probability.  
AUTHOR'S FURLONGS The circuit of the whole earth containeth according to Strabo, and Hipperchus, 252000. Eratosthenes 250000. Posidonus & the Ancient Arabians, 240000. Ptolemy and our Englishmen. 180000. The modern Arabians, 204000 The Italians and Germans, 172800.  
AUTHOR'S FURLONGS. The measure of a Degree according to Strabo, and Hipparchus 700. Eratosthenes 694⅘ Posidomus & the Ancient Arabians, 666⅔ Ptolemy and our English men. 500 The later Arabians, 566⅔ Italians and Germans. 480.  
MILES. FURIONGS. The Italian containeth 8. English 8⅓ Arabian 10 German 32  
PONT. For the finding out of the circumference or circuit of the Terrestrial Globe, these Hypotheses are first to be laid down for a ground 〈◊〉 That the greatest circle in the Earth, as well as in the Heavens, is to be divided into 360. parts, or degrees, 2. That one of these degrees doth contain 500 furlongs or 62500 Roman pases, and 60. English miles 3. That 8. furlong, and a third part make an English Mile.  
These things being presupposed, we must multiply 360. degrees by 60 miles, which done, the product will be 21 600. English miles. Or if you multiply 360. degrees, by 500 furlongs; the whole will be 180000 furlongs, which is the measure of the circumference of the Earth.  
So likewise if 360. be multiplied by 15. the whole will be 5400. German miles: and if the number of the degrees be multiplied by 25. there well arise 9000. French miles. All which may be thus expressed.  
A degree containeth. 15. German Miles, each of which contain severally. 4000 Pa●…s. 60. Italian 1000 60. English 1000 25 French  17. Spanish 2400  
In like manner the Circumferance of the Earth maia's easily be found out by any of the fixed Stars, as the Virgin's Spike, or the like. For if we take any two places which are situated under the same Meridian, and the distances in a right line exactly known, so that in both places the Meridian Altitude of the same Star be certainly known also: the difference of its Altitude will be the number of degrees of distance betwixt the same places, Wherefore seeing it is certainly known, as we have already said, how many miles answer to a degree, it is very easy then to gather how many miles the circumference of the whole Earth is also As for example: suppose London and Edenburg in Scotland to be under the same Meridian, and the Elevation of the Pole at London to be 52. degrees, and at Edinburgh 56. gr. 20. m. Now if you subtract the lesser number, which is 52. from the greater, 56. gr. 20. m. the difference will be, 4. gr. 20. m. which being resolved into minutes, it will be found to be the 260. distance of miles betwixt London and Edinburgh. Therefore we must now say, that as 4. gr. 20. m. is to 260. miles: so is 360. degrees to 21600. English miles.    

The fourth Part,  

CHAP. I. Of the Use of Globes.  
HItherto we have spoken of the Globe itself, together with its dimensions, circles, and other instruments necessarily belonging there to. It remaineth now that we come to the practice of it, and declare its several uses And first of all, it is very necessary for the practice both of Astronomy, Geography, and also the Art of Navigation. For by it there is an easy and ready way laid down, for the finding out both of the place of the Sun, the Longitudes, Latitudes, and Positions of places, the length of days and hours; as also for the finding of the Longest Latitude, Declination, Ascension both Right and Oblique, the Amplitude of the rising and setting of the Sun and Stars, together with almost an infinite number of the like things. Of the chief of all which we indeed here briefly to discourse, omitting the enumeration of them all, as being tedious and not suitable to the brevity we intent Now that all these things may be performed far more accurately, by the help of numbers, and the doctrines of Triangles, Plains, and Spherical bodies, is a thing very well known to those that are acquainted with the Mathematics, But this way of proceeding, besides that it is very tedious and prolix, so likewise doth it require great practice in the Mathematics. But the same things may be found out readily and easily, by the help of the Globe, with little or no knowledge of the Mathematics at all.  
PONT. For the better understanding of those things which shall be spoken hereafter, there are two things especially to be promised: the first whereof is, concerning the position of the Globe, and the other Climates. Now touching the position of the Globe, you are, first of all, to take care that it be pla●… perpendicularly to the true Horizon: 2. That the distinction of the winds answer directly to the winds of the real Horizon, that so the East on your material Globe, may look directly toward the true East of the World. For which purpose especially there is usually placed a Nautical Compass in the bottom of the frame. When you have thus placed your Globe, so that it may be turned about any way at pleasure, yet so that the base or foot be not moved out of its place, the next thing that is to be enquired after, is the Latitude of the place Wherein you live: which according as it is greater, or lesser, you must elevate the Pole of your Globe above the Horizon proportionally. As for example, if the Latitude be 50. 51. or 52. grad. or less Northward, then must you elevate the Arctic Pole just so many degrees above the Horizon. And so likewise if the latitude be Southern, you must do●… the like by the Antarctic or South Pole. But under the AEquator, where there is no latitude at all, both the Poles must be placed in the very Horizon, at opposite points.  
2. A Climate is a space of the habitable parts of the Earth, comprehended betwixt two circles Parallel to the AEquator, in which space there is half an hours difference in the longest day. Now those that inhabit under the AEquator have a perpetual AEquinoxe, for the day with them is always twelve hours longer, and the night as much. But as their situation is removed from the Equinoctial nearer to either Pole, the further they are from the Equinoctial, the greater is the the inequality of the Artificial day and night: out of which variation of Artificial days, the diversity of Climates also is takon and distiuguished. For wheresoever this difference amounteth to half an hour, there presently begins another Climate. Now the ancient Geographers constitutede in every Clime, three Parallels, 〈◊〉 which the two outwardmost, namely the first and the third, do comprehend and terminate every Climate: and the second divideth it in the midst. So that the proportion betwixt the Clime and the Parallels was Duple; for the Climes, as we have said, were distant from each other half an hour's space in the length of the day, but the Parallols were distinguished by quarters of an hour.  
Now as concerning the number of Climates, The Ancients, at first, reckoned but seven, but Ptolemy in his Tables of Ascensions, in the 2. lib. May. Construction. acknowledgeth nine: all of which derived their names from some eminent place, either hill or river, situate in the midst of the said Climate. The first Clime to ward the Arctic Pole, beginning from the AEquator, they called Diameroës, because the midst of this Clime runneth through Meroe, which is an Island in Africa encompassed about with the river Nilus, where the longest day is thirteen hours: in the beginning therefore of this Clime it must be 12½ hours long. On the opposite part of the AEquator the first Southern Climate may in●… manner be called, Antidiameroës. But these other Climes were not constituted neither by Prolomy, nor any of the ancient Geographers. Yet by the like reason that part of the world also may as well be described into Climate, reserving the same names that the Northern Climes are known by, and only adding to them the preposition 〈◊〉 which signifies as much as, Opposite, or over against. And the●… the Scheme, of them all will be thus, Northern Climates. Southern Climates. 1. Diameroës'. 1. Antidiameroës'. 2. Diasyenes. 2. Antidiasyenes. 3. Dialexandrias. 3. Antidialexandrias. 4. Diarhodu. 4. Antidiarhodu. 5. Diarhomes. 5. Anididiarhomes. 6. Diapontu. 6. Antidiapontu. 7. Diaboristhenes. 7. Antidiaboristhenes. 8. Diabritanias. 8. Antidiabritanias. 9 Diatanaidos. 9 Antidiatanaidos.  
Yet some there are that do not approve of this distinction of Climates, among whom is John Gigas. in his lib. 24 System. Geograph. cap. 2. probls. 12. And the reasons they allege are these. 1. Because of their great in equality, in so much that the latitude of the first is above 570. English miles, whereas the last of all is scarce a mile. 2. Because that the increase of hours is but a weak ground to build upon, and of no great use: seeing it is as easy to inquire out the length of the day, as the number of the Climate. And therefore he thinks, it were far better, that every Hemisphere were equally distinguished by ten degrees into nine Climates. So that the first Climate should begin at the Equinoctial, and end where the Elevation of the Pole is ten gr. which might be called the AEthiopian Climate. The second should reach to the 20. gr. and should be named the Arabian Clime: because that part of Arabia Foelix is situated therein. The third should reach to the 30 gr. and be called the Egyptian. The fourth the Syrian, ending at the 40. gr. The fifth the Italian, to the 50. gr. The 6. the English, or German, extending to the 60. gr. The seventh the Suecian, or Lapland Climate, reaching to the 70. gr. The eighth, the Frozen Climate, ending at the 80. gr. And the Ninth and last, the Polar Climate, reaching to the Pole itself.  
So likewise the same Method might be observed on the oaths side of the Equinoctial: and then by this means each Hemisphere should have nine Climates: whereof seven would be convenient for habitation, and the Parallels might pass through every fifth degree. And the situation of any place might be known by the number of degrees of the Poles elevation. So Rome, because it hath above 40. gr. of latitude, is in the fourth; Westphalia in the fifth; Sicily in the third; Calecur, the chief City in India, in the second; Zeilan in the first; and so of the rest.   

CHAP. I. How to find the Longitude, Latitude, Distance, and Angle of Position, or situation of any place expressed in the Terrestrial Globe.  
THe Ancient Geographers from Ptolemy's time downward, reckon the longitude of places from the Meridian which passeth through the Fortunate Islands: which are the same that are now called the Canary Islands. as the most men do generally believe, but how ●…ightly? I will not here stand to examine. I shall ●…nely here advertise the reader, by the way, that the latitude assigned by Ptolemy to the Fortunate Islands falleth something of the widest of the Canary Islands, and agreeth a great deal nearer with the Latitude of those islands which are known by the name of Cabo Verde For Ptolemy placed all the Fortunate Islands within the 10 gr. 30. m. and the 16. gr. of Northern latitude. But the Canary Islands are found to be distant from the AEquator at the least 27 degrees. The Arabians began to reckon their Longitude, at that place where the Atlantic Ocean driveth farthest into the main land: which place is ten degrees distant Eastward from the Fortunate Islands: as Jacobus Christmannus, hath observed out of Abilfedea. Our Modern Geographers, for the most part, begin to reckon the Longitude of places from these Canary Islands: yet some begin at those Islands which they call Azores: and from these bounds, are the Longitude of places to be reckoned in these Globes whereof we speak.  
Now the Longitude of any place, is defined to be, an Arch, or portion of the AEquator intercepted betwixt the Meridian of any place assigned, and the Meridian that passeth through Saint Michales Island (which is one of the Azores) or of any other place, from whence the Longitude of places is wont to be determined.  
Now if you desire to know the Longitude of any place expressed in the Globe: you must apply the same place to the Meridian and observe at what place the Meridian cutteth the AEquator, reckon the degree of the AEquator from the Meridian of Saint Michael's Island to that place: for so many are the degrees of longitude of the place you look for.  
In the same manner may you measure the distance of longitude betwixt any other two places that are described in the Globe. For the difference of Longitude is nothing else, but an Arch of the AEquator intercepted betwixt the Meridian of the same places. Which difference of Longitude, many have endeavoured to set down diverss ways how to find by observation. But the most certain way of all for this purpose, is confessed by all learned Writers to be, by the Eclipses of the Moon. But now these Eclipses happen but seldom, but are more seldom seen, yet most seldom and, in very few places, observed by the skilful Artists in this Science, So that there are but few Longitudes of places designed out by this means. Oro●…us Fin●…us, and Johannes Wernerus before him, conceived that the difference of Longitude might be assigned, by the known (as they presuppose it) motion of the Moon, and the passing of the same through the Meridian of any place. But this is an uncertain and ticklish way, and subject to many difficulties. Others have gone other ways to work: as namely, by observing the space of the Equinoctial hours betwixt the Meridian's of two places: which they conceive may be taken by the help of Sun Dial's, or Clocks, or Hourglasses either with water or sand, or the like. But all these conceits, long since de●…ed, having been more strictly and accurately examined, have been disallowed and rejected by all learned men, (at least those of riper judgements) as being altogether unable to perform that which is required of them. But yet for all this, there are a kind of trifling Impostors, that make public sale of these toys or worse, and that with great ostentation and boasting; to the great abuse and expense of some men of good note and quality, who are perhaps better stored with money, than either learning or judgement. But I shall not stand here to discover the errors and uncertainties of these instruments. Only I admonish these men by the way, that they beware of these fellows; lest when their noses are wiped as we say) of their money, they too jate repent them of their ill-bought bargains. Away with all such trisling cheating rascals.  
PONT. If you would know how to find out the longitude of any place by the Eclipse of the Moon, you must first go to some Ephemerideses, as the 〈◊〉 Tables, or of any other learned Mathematicians calculation; and see, what hour such an Eclipse of the Moon shall happen at that place, for which the said Tables or Ephemerideses were made. Then afterward you must observe the same Eclipse in that place, whose longitude you desire to know, Now if the time of the Eclipse agree with that other, for which the Tables were made, than you may conclude that both places have the same latitude, and are situate under the same Meridian. But is the number of the hours be more, than the place you are in, is swate more Eastward, you must therefore subtract the less number out of the greater, and the remainder must be converted into degrees and minutes, multiplying the hours by fifteen and deviding the minutes of hours (if there be any) by four; for so will the number of degrees arise: and if there remain any minutes after the division, they must be multiplied again by fifteen, and so will the number of the minutes of degrees arise, by which these places are distant from each other: which distance is called the difference of longitude. This difference must be added to the Longitude of that place for which the Tables were calculated, if the other place be more Eastward: otherwise if it be more Westward, it is to be substracted from the longitude of the other. An example hereof is thus proposed by Adrianus Metius in his Doctrina Sphaerica. I find (saith he) out of the Prutenick Tables, by exact calculation, that there will be an Eclipse of the Moon in the year 1598. upon the eleventh day of February, at four of the Clock and sixteen minutes, in the morning, and that at Regiomont, a City in Borussia, whose longitude or distance from the Canary Islands, is 41. gr. 16. m. For this Longitude where these Tables calculated. Now I set myself to observe this same Eclipse at Marpurg, and find it to happen at three of the Clock and twelve minutes, on the same day of February. Now because the number of hours here is less, it appears that Marpurg is more Westward than Regiomont. Therefore I take away a less number from the greater, that is. 3. h. 12. m. from 4. h. 16. m. and the remainder is 1 h. 4. minutes: which showeth the difference of longitude in hours, which makes up sixteen degrees. Therefore I again subtract these degrees of difference from the longitude of Regiomont, as being more Eastward than Marpurge; and so I find the Latitude of Marpurge from the Canary Island, to be 25. gr. 16. minutes.   

CHAP II. How to find the Latitude of any place.  
THe latitude of a place, is the distance of the Zenith, or the vertical point thereof from the AEquator. Now if you desire to find out the latitude of any place expressed in the Globe, you must apply the same to the Meridian, and reckon the number of the degrees that it is distant from the AEquator: For so much is the Latitude of that place. And this also you may observe, that the Latitude of every place is always equal to the elevation of the same place. For look how many degrees the vertical point of any place is distant from the AEquator, just so many is the Pole elevated above the Horizon: as you may prove by the Globe, if you so order it, as that the Zenith of the place be 90. degrees distant every way from the Horizon,  
PONT. Seeing that the Latitude of every place is always equal to the elevation of the Pole: It will not be amiss to show, how the elevation of the Pole, or the Latitude of any region may be found out, by the observing of the same fixed Star in the Heavens, which is so near the Pole, a●… that it never sets in that region: which to do you must work thus. You must observe both the least and also the greatest altitude of the sad Star; both which must necessarily happen in the Meridian: the least whereof will be beneath the Pole, and the greatest above it. Which done, you must add the least altitude of it to the greatest; and so the half of the degrees thus numbered together, will be the latitude of the Pole, and latitude of that plaee. An example whereof may be this. The first Star of the three in the tail of the great Bear is in his least altitude observed at London to be about 11. gr. and the greatest altitude of the same, when it is above the Pole, is found to be near upon 92. degrees. Both which numbers being added together, do make up 103. half of which Sum, namely 51⅓. is the true elevation and Latitude of London.   

CHAP. III. How to find the distance of two places, and angle of position, or situation.  
IF you set your Globe in such sort, as that the Zenith of one of the places be 90. gr. distant every way from the Horizon, and then fasten the Quadrant of Altitude to the Vertical point, and so move it up and down, until it pass through the Vertex of the other place: the number of degrees intercepted in the Quadrant betwixt the two places, being resolved into furlongs, miles, or leagues, (as you please) will show the true distance of the places assigned. And the other end of the Quadrant, that toucheth upon the Horizon, will show on what wind or quarter of the World the one place is, in respect of the other, and what Angle of Position (as they call it) it hath. For the Angle of Position is that, which is comprehended betwixt the Meridian of any place, and a greater circle passing through the Zeniths of any two places assigned: and the quantity of it, is to be numbered in the Horizon.  
As for example. The Longitude of London is twenty six degrees, and it hath in Northern latitude 51. degrees, and an half. Now if it be demanded, what distance and angle of position it beareth to Saint Michael's Island, which is one of the Azores: we must proceed thus to find it. First, let the Northern Pole be elevated 51½, degrees: which is the latitude of London. Then fastening the Quadrant of Altitude to the Zenith of it, that is to say, fifty one degrees and an half Northward from the AEquator, we must turn it about, till it pass through Saint Michael's Island: and we shall find the distance intercepted betwixt these two places to be 11. gr. 40. m. or thereabout: which is 280, of our leagues. And if we observe, in what part of the Horizon the end of the Quadrant 〈◊〉, we shall find the Angle of Position ●…o shall near upon 50. gr. betwixt South-west and by-west, And this is the situation of this 〈◊〉 in respect of London  
PONT. The 〈◊〉 of places ●…ring only in latitude may be found after this manner First you must subtract the lesser Latitude from the greater, resolving a degree in minutes, if the substraction cannot be done otherwise conveniently. Then multiply the degrees by 15. and divide the minutes by 4. and the sum produced will be the distance of those two places in common German miles, one whereof containeth four of our English miles. As for example: Basile in Germany and Geneva have both the same longitude. but differ in Latitude, which at Basile is 47. gr. 30. m. and at Geneva 45. gr. 45. m. Therefore substracting the lesser from the greater, the remainder will be 1. gr. 45. m. which being reduced into German miles, will amount to 26. and a quarter or a mile. which is the distance of these two places assigned.  
Now if the place proposed be in divers Hemispheres, than the degrees and minutes of Latitude must first be added together, and so the whole resolved into miles, as formerly hath been said. As for example: The Cape of good hope in Africa, and Constantinople are almost situate under the same meridian, but in divers Hemisphaeres. Now the elevation of the Pole Arctic at Constantinople is 43. gr. or thereabout: and at the Cape of good hope, the Antarctick Pole is elovated above 35. gr. the whole sum therefore is 73. degrees. that is to say 1170. German miles.  
The distance of places differing only in longitude, is found thus. First subtract the less number from the greater: then look in the Table here under written, how many miles answer to a degree 〈◊〉 every Parallel, seeking for the degree of Latitude in the first column descending, and the number of miles over against it. Then lastly let the difference of longitude be multiplied into miles and minutes: and you have your desire. As for example; Naples and Ilium or Troy, are in the same latitude of forty one gr. where eleven German miles, and nineteen minutes answer to a degree of that Parallel: but these places differ in longitude, which at Naples is 39 gr. 30 m but at Troy. 55. gr. 50. m. Naw the difference betwixt them is 16 gr. 20. m. which is as much as 184. German miles, and fifty scruples: the just distance betwixt these two places.  

A Table of Miles answering to a Degree in each several Latitude.  Miles. Degrees. German. Scrup. English. Scrup. 1 41 59 59 59 2 14 59 59 58 3 14 58 59 51 4 14 58 59 51 5 14 56 59 46 6 14 55 59 40 7 14 53 59 33 8 14 51 59 25 9 14 48 59 16 10 14 16 19 5 11 14 43 58 54 12 14 40 58 41 13 14 37 58 8 14 14 33 58 13 15 14 29 57 57 16 14 25 57 41 17 14 21 57 23 18 14 16 57 4 19 14 11 56 44 20 14 6 56 23 21 14 0 56 1 22 14 54 55 38 23 13 48 55 14 24 13 42 54 49 25 13 36 54 23 26 13 29 54 56 27 13 22 53 28 28 13 ●…5 52 59 29 13 〈◊〉 52 29 30 1●… ●…9 51 18 31 1●… ●…2 51 26 3 12 43 50 53 33 12 35 50 19 3●… 1●… 2●… 49 45 3●… 1●… 17 49 9 36 12 3●… ●…8 32 3●… 11 59 47 55 38 11 49 47 1●… 39 11 39 46 38 40 11 29 45 5●… 41 ●…1 19 45 1●… 42 11 9 44 35 41 10 5 43 53 44 10 47 43 10 45 10 36 42 26 4●… 10 ●…5 41 41 47 10 14 40 55 48 10 2 40 9 49 9 50 39 22 50 9 38 38 34 51 9 36 37 46 52 9 14 36 56 53 9 2 36 7 54 8 49 35 16 55 8 36 34 25 56 8 23 3●… 33 57 8 10 32 41 58 〈◊〉 57 31 48 59 7 43 3●… 54 60 7 30 30 0 61 7 16 29 5 6●… 〈◊〉 2 28 10 6●… 6 48 27 ●…4 64 6 34 2●… ●…8 65 6 ●…0 2●… 21 6●… 5 6 24 24 6●… 5 52 23 27 68 〈◊〉 37 2●… 29 6●… 5 23 21 ●…0 70 5 8 20 31 71 4 53 19 ●…2 72 4 38 18 32 73 4 23 17 33 74 4 8 16 32 75 3 ●…3 15 32 76 3 38 14 31 77 3 22 13 30 78 3 7 12 28 79 2 52 11 27 80 2 36 10 25 81 2 ●…1 9 23 82 2 5 8 21 83 1 50 7 19 84 1 34 6 16 85 1 18 5 14 86 1 3 4 11 87 0 47 31 8 88 0 31 2 5 89 0 10 1 3 90 0 0 0 0  
The Longitude or Latitude, of any place or City being known, either by observation, as hath already been showed, or else out of some Geographical Table, the situation os the same in the Globe may also be found out by this same means. You must first reckon the Longitude of your place, among the circles of Longitude which are described upon the Globe beginning at that which is drawn through the Fortunate Islands: and observe the circle where you end your reckoning. Then if the Latitude of your place be Northern: you must reckon that also among the Parallels toward the Arctic Pole, begnining from the AEquator: but if it have Southern Latitude you must then proceed in like manner, but reckon toward the Antarctique▪ And the intersection, or point where these two circles cut each other, sheweth the situation of your place. But if these circles of Long●…ude be expressed in your Globe, then must you place that degree of the Equinoctial, that answereth to the Longitude of your place, under the Meridian, and so reckon the Latitude of your place among the degrees of the Meridian, toward either Pole: and you have the situation of the place you look after.  

A Table of Longitudes and Latitudes of some certain Cities of note.   Longit. Latti. Alexandria 60 30 13. 42. Amsterdam ●…1. 43 ●…2 30. Antw●…rp 20. 16. 51. ●…8. Athens 52. 45 ●…7. 15 Brussels 20. 4●… 51. 0 Bremen 35. 16 53. 40 Bamberg 28. 10. 4●…. 56. B●…sell 24. 22. 4●…. 〈◊〉. Bononia 32. 5 43. 54. Constantin. 56. 0 42. 5 cassel 26. 36. 51. 43. Colen 33. 20. 51 0 Corinth 31. 15. 3●…. 5●…. D●…sden 38. 5 51. 6 Dover 28. 10. 51. 0 D●…ntzik 39 2 5●…. 〈◊〉. Dublin 16. 40 53. 10. Erf●…d 28. 40. 51. 10 Estinga 26. 36 48. 39 Francford ad M●…n. 25. 38 50. 12. Jer●…acia ●…2 1●…. 44. 23 Gen●…a 〈◊〉. 〈◊〉 13. 50. Gant 19 8 51. 24 Graeningen 22. 54. 53. 16 Heidelberg 25. 38. 49. 35 Jena 29. 2 51. 8 Lub●…k 28. ●…0 54. 48 Leiden 20. 47. 52. 10 Regius Mos 46. 45 54. 21 Boruss.   London 25. 〈◊〉. 51. 3●… Marpurg 25. 16. 5●…. 0 Milan 38. 20 45. 〈◊〉 Norimberg 20. 20 49. 24 Naples 30 10. 41 0 Orleans 15 3●… 47. 16 Oxford 24. 0 52. 0 Prage 32. 0. ●…0 6 Paris 29 25. 48 30 Ratisbane 29. 50. 4●…. 56 Rostock 30. 14 54. 36 Spier 35. 29. 49. 20 ●…ubing 20. 23. 48. 38 ●…ienna 34 36. 47 44 ●…orke 23. 30. 54. 30   

CHAP. IV. To find the Altitude of the Sun, or other Stars.  
THe Altitude of the Sun, or other Star, is the distance of the same, reckoned in a greater Circle, passing the Zenith of any place and the body of the Sun, or Star. Now that the manner of observing the same is to be performed either by the Cross Staff, Quadrant, or other like Instrument, is a thing so well known, as that it were vain to report it. Gemma Frisius teacheth a way, how to observe the Altitude of the Sun by a Spherical Gnomon. But this way of proceeding is not so well liked, as being subject to many difficulties and errors: as, whosoever proves it shall easily find.   

CHAP. V. To find the place and Declination of the Sun, for any day given.  
HAving first learned the day of the Month, you must look for the same in the Calendar described in the Horizon of your Globe. Over against which in the same Horizon, you shall find the Sign of the Zodiaque, and the degree of the same, that the Sun is in, at that time. But if it be Leap-yeare, then for the next day after the 28th of February you must take that degree of the sign, which is a scribed to the day follwing it. As for example, if you desire to know, what degree of the Zodiac the Sun is in, 29th of February, you must take that degree which is assigned for the first of March and for the first of March, take the degree of the second; and so forward. Yet I should rather counsel, if the piace of the Sun be accurately to be known, that you would have recourse to some Ephemrides, where you may have the place of the Sun exactly calculated for every day of the year. Neither indeed can the practice by the Globe, in this case be so accurate, as often times it is required to be.  
Now when you have found the place of the Sun, apply the same to the Meridian, and reckon thereon how many degrees the Sun is distant from the AEquator, for somany will the degrees be to the Sun's declination for the day assigned. For the Declination of the Sun, or of any other Star, is nothing else but the distance of the same from the AEquator, reckoned on the Meridian. But the Sun's Declination may be much more exactly found, out of those Tables which Mariners use, in which the Meridian Altitude, or Declination of the Sun for every day in the year, and the quantity of it is expressed. One thing I shall give you notice of by the way; and that is that you make use of those that are latest made, as ne'er as you can. For all of them, after some certain spaces of time, will have their errors. And I give this advertisement the rather, for that I have seen some, that having some of these Tables, that were very ancient, and written out with great care and diligence, (which notwithstanding would differ from the later Tables, and indeed from the truth itself, often times at least 10. m. and sometimes more) yet would they always use them very constantly and with a kind of religion. But these men take a great deal of pains and care to bring upon themselves no small errors.  
PONT You also find out the Sun's greatest Declination, by his greatest and least Altitude both in Summer and Winter, by substracting the least out of the greatest. For than half that which remaineth, will be the declination you seek for So Regiomontanus at Vienna found the Meridian Altitude of the Sun, at the Summer Solstice to be 65. gr. 30. m. and the least Altitude of it, on the Winter Solstice, to be 18. gr. 30. m. when therefore; he had deducted the least number, 18. gr. 30. m. out of 65. gr. 30. m. be found the remainder to be 47. gr. 0. m. the half of which was the Sun's greatest declination, namely 23. gr. 30. m. which is the number of degrees now commonly received: notwithstanding it hath been since observed by some in our time to be somewhat less.  
Now to know the Longitude of the Sun for any time, that is to say, in what degree of the Zodiaque he is, you must do thus. Seek in the limb of the Horizon for the day of the Month, for which you would know the Longitude of the Sun: which found, you shall see, over against it, among the Signs of the Zodiaque, described also upon the Horizon, the degree of the Sign that exactly answereth to it, and which is the place of the Sun for that day and Month. But if it be Leap year, you must remember after the 28th. of February, to add one day more still as you go, as if you should look for the place of the Sun on the 13th. March, you must take that degree which is set for the 14th of March: which is the 3 gr. of V.   

CHAP. VI How to find the Latitude of any place, by observing the Meridian Altitude of the Sun, or other Star.  
OBserve the Meridian Altitude of the Sun with the Cross staff, Quadrant, or other like instrument, & having also found the place of the Sun in the Ecliptic, apply the same to the Meridian, and so move the Meridian up and down through the notches it stands in, until the place of the Sun be elevated so many degrees above the Horizon, as the Sun's Altititude is. And the Globe standing in this position, the Elevation of either of the Poles, will show the Latitude of the place wherein you are. An example whereof may be this.  
On the 12th of June, according to the old Julian account, the Sun is in the first degree of Cancer, and hath his greatest declination 23●… degrees. And on the same day, suppose the Meridian Altitude of the Sun to be 50. degrees. We inquire therefore now, what is the Latitude of the place where this observation was made. And this we find out, after this manner. We apply the first degree of Cancer to the Meridian, which w●… move up and down, till the same degree be elevated above the Horizon 50 degrees: which is the Meridian Altitude of the Sun observed. Now in this position of the Globe, we find the North Pole to be elevated 63 gr. and an half: So that we conclude this to be the Latitude of the place, where our observation was made.  
The like way of proceeding do Mariners also use, for the finding out of the Latitude of places by the Meridian Altitude of the Sun, and their Tables of Declinations: But I shall not here speak any further of this, as well for that, the explication hereof doth not so properly concern our present intention: as also because it is so well known to every body, as that the handling of it in this place would be needless and superfluous.  
The like effect may bewrought in observing the Meridian altitude of any other Star expressed in the Globe. For if you set your Globe so, as that the Star you mean to observe, be so much elevated above the Horizon, as the Meridian Altitude of it is observed to be: the elevation of the Pole above the Horizon will show the latitude of the place. But here I should advise, that the latitude of places be rather enquired after, by the Meridian Altitude of the Sun, then of the fixed Stars: because the declinations, as we have already showed, are very much changed, unless they be restored to their proper places by later observations.  
Some there are that undertake to perform the same, not only by the Meridian Altitude of the Sun or Star, but also by observing it at two several times, and knowing the space of time or horizontal distance betwixt the two observations. But the practice hereof is prolix and doubtful: besides that by reason of the multitude of observations that must be made, it is also subject to many errors and difficulties. Notwithstanding the easiest way of proceeding, that I know, in this kind, is this that followeth.  

To find out the Latitude of any place, by knowing the place of the Sun, or other Star, and observing the Altitude of it two several times with the space of time betwixt the two Observations.  
FIrst having taken with your Compasses the compliment of the Altitude of your first Observation, (now the compliment of the Altitude is nothing else, but the difference of degrees by which the altitude is found to be less than 90 degrees,) you must set one of the fee●… of your Compasses in that degree of the Ecliptic that the Sun is in, at that time: and with the other describe a circle upon the superficies of the Globe, tending somewhat toward the West, if the observation be taken before noon, but toward the East, if ibe made in the afternoon. Then having made your second observation, and observed the space of time betwixt it and the former, apply the place of the Sun to the Meridian, turning the Globe toward the East, until that so many degrees of the AEquator have passed by the Meridian, a●…answer to the space of time that passed betwixt your observations, allowing for every hour fifteen degrees in the AEquator, and marking the place in the Parallel of the Sun's declination that the Meridian crosseth after this turning about of the Globe. And then setting he foot of your Compasses in the very Intersection, describe an Arch of a circle with the other foot of the Compass extended to the compliment of the second observation, which Arch must cut the former circle. And the common Intersection of these two circles, will show the vertical point of the place wherein you are: so that having reckoned the distance of it from the AEquator, you shall presently have the latitude of the same.  
The same may be effected, if you take any Star, and work by it, after the same manner: or it you describe two circles mutually crossing each other, to the compliments of any two Stars.  
PONT. The Meridian altitude of the Sun, being found by the help of of the Meridian circle, it will be very easy to find out the latitude of the place or elevation of the Pole, in any region whatsoever. For seeing the Zenith or Vertex of every place is distant aquarter of a circle that is 90. degrees from the Horizon: if then, the Sun being in either of the Equinoctial points, the Meridian altitude be substracted from 90 degrees; the remainder will be the distance betwixt the Zenith of the place and the Equinoctial circle: which will be the latitude of the same place. And the reason also of this deduction is manifest, because that the Equinoctial Altitude of the Sun, is nothing else, but the Elevation of the AEquator, the compliment whereof is always equali to the elevation of the Pole. But this will appear more plain by an example, which shall be thus. The Equinoctial altitude of the Sun at Rome is 40. degrees: which being substracted from 90 gr. the remainder, which is 42. gr. is the elevation of the Pole, and the latitude of Rome. So likewise here at London in the Meridian altitude of the Sun, when he is in the Equinoctial, is found to be 38 degrees and an half: which being deducted out of 90 gr. which is the Quadrant of a circle, there w●…ll remain 15½ gr. which is the latitude of London, and the elevation of the Pole.  
The same also may be done, by observing any one of the fixed Sarres, which is is so near the Pole, as that it never sets in that Country, whose latitude you seek. For you must observe both the greatest and least altitude of the same Star; both which will happen in the Meridian: the least of them beneath the Pole, and the greatest above it. Which done, you must add the least altitude to the greatest, and so dividing the whole into two parts, the half will be the altitude of the Pole. As hath been showed before.    

CHAP. VII. How to find the Right and Oblique Ascension of the Sun and Stars, for any Latitude of place, and time assigned.  
THe Ascension of the Sun or Stars, is the degree of the AEquator that riseth with the same above the Horizon. And the Descension of of it, is the degree of the AEquator, that goes under the Horizon with the same. Both these is either Right, or Oblique. The Right Ascension or Descension is the degree of the AEquator that ascendeth or descendeth with the Sun, or other Star in a Right Sphere: and the Oblique is the degree that ascendeth, or descendeth with the same in an Oblique. The forms of these is simple and of one kind only: because there can be but one position of a Right Sphere. But the later is various and manifold, according to the divers Inclination of the same.  
Now if you desire to know the Right Ascension or Descension of any Star, for any time and place assigned apply the same star to the Meridian of your Globe: and that degree of the AEquator that the Meridian crosseth at that situation of the Globe, will show the Right Ascension and Descension of the same, and also divideth each Hemisphere in the midst at the same time with it.  
And if you would know the Oblique Ascension or Descension of any Star, you must first set the Globe to the latitude of the place, and then place the Star at the Eastern part of the Horizon: and the Horizon will show in the AEquator the degree of Oblique Ascension. And if you turn it about to the Well side of the Horizon, the same will also show in the AEquator the Oblique Descension of that Star. In like manner you may find out the Oblique Ascension of the Sun●… or any degree of the Ecliptic, having first found ou, in the manner we have formerly showed the place of the Sun. And hence also may be found the difference of the Right and Oblique Ascension, whence ariseth the divers length of days.  
As for example. The Sun entereth into Capricorn on the eleventh day of December, according to the old account. I would now therefore know the Right and Oblique Ascension of this degree of the Ecliptic, for the latitude of fifty two degrees. First therefore, I apply the first degree of Capricorn to the Meridian: where I find the same to cut the AEquator at 270. gr. which is the degree of the Right Ascension. But if you set the Globe to the Latitude of fifty two degrees, and apply the same degree of Capricorn to the Horizon; you shall find the 303 gr. 50. m. to rise with the same. So that the difference of the Right Ascension 270. and the Oblique 303. gr. 50. m. will be found to be 33. gr. 50. minutes.  
PONT. This Ascension and descension is also called the Astro nomicall rising and setting of the Stars: and that in respect of the Arches and parts of the Ecl ptick, or Stars, either above or beneath the Horizon. Now an Arch of the Ecliptic or Zodiac is tobe understood two manner of ways namely Continued, or Discrete. A continued Arch, is when it is reckoned in the AEquator in a continued Series from the beginning of Aries, and so forward into the consequent signs. A Discrete Arch is so called because it is not reckoned from the first degree of Aries, but from any other point in the AEquator: as if you should say, an Arch from the 14. gr. of Gemini to the 14. gr. of Taurus.  
Beside, this Right Ascension is called also the greater Ascension, because that in it, a greater Arch of the AEquator riseth above the Horizon, then of the Zodiac: & it is called Right, because that in this, the Angle which is made by the Horizon and Ecliptic, is nearer to a Right Angle, then that that is made by any other part of the Ecliptic with the same. And that is said to be a greater Arch or portion of the AEquator, which is more than 30. degrees in the Ascension or Descension: and that is called a lesser Arch, which falls short of thirty, degrees in rising or setting.  
In a Right Sphere four signs only ascend Rightly, which are Gemini, Cancer, Sagittarius and Capricornus: all the rest ascend Obliquely.  
In an Oblique Sphere six signs rise Rightly and the other six Obliquely. The right are these, Cancer, Leo, Virgo, Libra, Scorpius, Sagittarius: and all the rest Obliquely.  
Oblique ascension, is when a less Arch or portion of the AEquator riseth, then of the Zodiaque: or else, that Star may be said to rise Obliquely, with whom a less portion of the AEquator ascendeth above the Horizon. And so the Oblique descension or setting of a Star is, where a less portion of the AEquator descendeth with it. As for example. At Rome with the Arch of Libra, which containeth 30. gr. in the Zodiaque, there riseth an arch of the Equinoctial of 37 gr So that this sign is said there to rise rightly: Because that a greater Arch of the AEquator ascendeth with it, then of the Zodiaque, But then, at the same place, with the Arch of Aries, there arise only 17. gr. of the AEquator. Whence it followeth that Aries riseth Obliquely at Rome. In our position of Sphere also here at London, which is Oblique, like as that at Rome with Libra there ariseth an Arch of the AEquinoctial concoutaining about 41. gr. but with the Arch of Aries there ariseth not above 13 degrees. Therefore in our Sphere Libra ascendeth or riseth rightly, but Aries Obliquely.  

Certain Rules, for the Astronomical rising in a right Sphere.  
THe Rules of Astronomical rising in a right Sphere are these. 1. The whole Quadrants or quarters of the Zodiaque and Equinoctial rise and set in an equal space of time. 2. But the the parts of the Quadrants rise and set unequally. 3. Those signs that are equally distant from any of those points, have also equal ascensions: as Gemini and Cancer. 4. The Ascension of a sign is always equal to the Descension of the same. 5. Four signs only rise rightly, namely Gemini, Cancer, Sagittarius, and Capricornus: and all the rest Obliquely.   

Rules for the Astronomical rising in an Oblique Sphere.  
IN an Oblique Sphere, the two halves that begin at the two Equinoctial points, do rise together. 2. The parts of these halves do rise unequally. 3. Those signs that rise rightly, descend Obliquely, and so contrarily. 4. The Ascension of any sign is equal to the Descension of the same. 5. The ascensional Arches of the Northern signs are less in a right sphere, but in the Southern signs they are greater. 6. The Ascension of Opposite signs in an Oblique Sphere, taken together, are equal to the Ascension of the same in a right Sphere. 7. Those signs that are equidistant from either of the Equinoctial points, have equal Ascensions, because they decline equally from the AEquator.    

CHAP. VIII. How to finde out the horizontal difference betwixt the Meridian and the Vertical circle of the Sun, or any otheh Star, (which they call the Azimuth,) for any time or place assigned.  
HAving first observed the Altitude of the Sun or Star that you desire to know, set your Globe to the Latitude of the place you are in: which done, turn it about, till the place of the Sun, or Star which you have observed, be elevated so much above the Horizon, as the Altitude of the same you before observed. Now you shall find that you desire, if you take the Quadrant of altitude, and fasten it to the Vertical point of the place you are in, and so move it together with the place of the Sun or Star up and down, until it fall upon that which you have set down in your instrument at your observation. Now in this situation of the Quadrant, that end of it that toucheth the Horizon, will show the distance of the Vertical circle, in which you have observed the Sun or Star to be, from the Meridian. As for example.  
In the Northern latitude of 51. gr. on the 11th. of March after the old account, at what time the Sun entereth into Arts, suppose the altitude of the Sun before noon to be observed to be th●…rtiegr above the Horizon. And it is demanded, what is the Azamuth, or distance of the Sun from the Meridian. First therefore having 〈◊〉 the Globe to the Latitude of 51. gr. and fastening the Quadrant of Altitude to the Zenith, I turn the Globe about, till I find the first degree of Aries to be 30 gr. above the Horizon And then the Quadrant of Altitude being also applied to the same degree of Aries, will show upon the Horizon, the Azimuth of the Sun, or distance of it from the Meridian, to be about forty five degrees.   

CHAP. IX. How to find the hour of the day, as also the Amplitude of rising and setting of the Sun and Stars, for any time or Latitude of place.  
THe Sun, we see, doth rise and set at several seasons of the year, in divers parts of the Horizon. But among the rest it hath three more notable places of rising and setting. The first whereof is in the AEquator, and this is called his Equinoctial rising and setting. The second is in the Summer Solstice, when he is in the Tropic of Cancer: and the third is in the Winter solstice, when he is in the Tropic of Capricorn. Now the Equinoctial rising of the Sun is one and the same in every Climate. For the AEquator always cutteth the Horizon in the same points, which are always just 90 gr. distant on each side from the Meridian. But the rest are variable and change according to the divers inclination of the sphere: and therefore the hours are unequal also.  
PONT. And here you are to understand, that the Amplitude of the Sun's rising and setting, is an Arch of the Horizon intercepted betwixt the AEquator, and the place of the rising and setting of the Sun. And it is either Northern or Southern. The Northern Amplitude, is when he sets and riseth on this side of the AEquator, toward the North Pole: and the Southern when he sets or riseth on the contrary side. Now when the Sun is in the AEquator, he hath no amplitude at all: but when he is in the Solsticall points, he hath then the greatest amplitude of all: of which that in the Tropic of Cancer is called the aestival, or summer solsticiall amplitude; and the other the Brumal or Winter solsticiall amplitude.  
And here it is to be noted that in all places the Ortive amplitude of any Star is equal to the Occidental amplitude of the same. And likewise, that two stars being equally distant from the AEquator the one Northward, and the other Southward, or both of them Northward or Southward, have equal amplitude of rising and setting.  
Now if you desire to know the hour, or distance of time, betwixt the rising and setting of the Sun, when he is in either of the Solstices, or in any other intermediate place, and that for any time or latitude of place: you shall work thus. First, set your Globe to the latitude of your place; then having found the place of of the sun, for the time assigned, apply the same to the Meridian, and withal you must set the point of the Houre-Index at the figure twelve in the Houre-circle. And having thus done, you must turn about the Globe toward the East part, till the place of the sun touch the Horizon: which done, you shall have the Amplitude of the suns rising also in the AEquator, which you mustr eckon, as we have said, from the East point, or place of intersection betwixt the AEquator and Horizon. And then if you but turn the Globe about to the West side of the Horizon, you shall in like manner have the hour of his setting, and Occidental Amplitude.  
And if at the same time, and for the same latitude of place, you desire to know the hour and Amplitude of rising and setting, or the greatest elevation of any other star expressed in the Globe: you must turn about the Globe, (the Index remaning still in the same position, and situation of the Index as before) till the said star come to the Horizon, either on the East or West: and so shall you plainly have the hour and latitude that the star riseth or seateth in, in like manner as you had in the sun. And then if you apply the same to the Meridian, you shall also have the Meridian Altitude of the same star. An example of the Amplitude of the Suns rising and setting may be this.  
When the Sun enters in to Taurus (which in our time happen●… about the eleventh of April according to the Julian account) I desire to know, the hour and Amplitude of the Suns rising, for the Northernlatitude fifty one degrees. Now to find out this, I set my Globe so, that the North Pole is elevated above the Horizon fifty one degrees. Then I apply the first degree of Taurus to the Meridian, and the Hour-Index to the twelfth hour in the Hour-circle. Which done, I turn about the Globe toward the East, till that the first degree of Taurus touch the Horizon: and then I find that this point toucheth the Horizon about the twenty fifth degree Northward from the East point. Therefore I conclude that to be the Amplitude of the Sun for that day. In the mean time, the Index strikes upon half an hour after four: which I take to be the ●…me of the Sun's rising.   

CHAP. X. Of the threefold rising and setting of Stars.  
BEsides the ordinary Emersion and Depression of the Stars in regard of the Horizon, by reason of the circumvolution of the Heaven: there is also observed a threefold rising & setting of the Stars. The first of these is called in Latin, Ortus Matutinus, sive Cosmicus, the Morning, or Cosmical rising, the second Vespertinus, sive Achronicus, the Evening, or Acronical: and the last Heliachus, vel solaris, heliacal or Solar. The Cosmical or morning rising of a Star is, when as it riseth above the Horizon together with the Sun. And the Cosmical or morning setting of a Star is, when it setteth at the Opposite part of heaven; wh●…n the Sun riseth. The Acronychal or Evening rising of a Star is, when it riseth on the Opposite part, when the Sun setteth. And the Acronychall setting of a Star, is when it setteth at the same time with the Sun. The heliacal rising of a star (which you may properly call the Emersion of it) is, when a star that was bid before by the Sun beams beginneth now to have recovered itself out of the same, and to appear. And so likewise the setting of such a star (which mav also fitly be called the occultation of the same) is, when the Sun by his own proper motion overtaketh any Star, so that by reason of the brightness of his beams it can no more be seen.  
PONT. Concerning the rising and setting of the Stars, which is considered in respect of the Horizon and AEquator, hath been spoken already in the seventh Chapter: where we also showed, that that kind of rising and setting of the Stars was called astronomical. But in this place the rising of the Stars is considered in relation only to the Horizon and Sun's aspect, but not of the AEquator; and therefore it is also commonly called, the Poëtioall rising and setting of the Stars.  
Now as touching the last of these kinds, many Authors are of opinion that the fixed Stars of the first magnitude do begin to show themselves after their Emersion out of the Sunbeams, when as they are yet in the upper Hemisphere, and the Sun is gone down twelve degrees under the Horizon. But these of the second magnitude require that the Sun is depressed 13, gr. and those of the third, require fourteen; and of the fourth, fifteen; of the fifth, sixteen; of the sixth, seventeen, and the cloudy and obscure Stars require eighteen degrees of the Sun's depression. But Ptolemy hath determined nothing at all in this case: and withal very rightly gives this admonishment, and lib. 8. cap ult Almag. that is a very hard matter to set down any determination thereof. For as he there well noteth, by reason of the unequal disposition of the air, this distance also of the Sun, for the Occultation and Emersion of the Stars, must needs be unequal. And one thing more we have to increase our suspicion of the incertain●…y of this received opinion, and that is, that Vitellio requireth nineteen degrees of the Sun's depression under the Horizon, before the Evening twilight be ended. Now that the obscure and cloudy Star, should appear ever, before the twilight be down, I shall very hardly be persuaded to believe. Notwithstanding however the truth of the matter be, we will follow the common opinion.  
Now therefore if you desire to know at what time of the year any Star riseth or 〈◊〉 in the morning or the evening in any Climate whatsoever: you may find it out thus. First, set your Globe to the latitude of the place you are in, and then apply the Star you inquire after, to the Eastern part of the Horizon and you shall have that degree of the Ecliptic; with which the said Star riseth Cosmically, and setteth Acronychally: and on the opposite side, on the West, the Horizon will show the degree of the Ecliptic, with which the same Star riseth Acronychally, and setteth Cosmically. For the Cosmical rising, and Achronicall setting and so likewise the Acronycall rising, and Cosmical setting of a Star are all one: according to those old verses, 
Cosmicè deseendit signum, quòd Acronychè surgit.  
Chronychè descendit signum, quod Cosmici surgit.   
But these things are to be explained more fully. For a Star doth not always rise and set with the same degree of the Ecliptic. For the Southern Stars do anticipate the degree with which they rise, at their setting: but the Northern Stars come after it: that is, if the elevation be of the Arctic ●…ole. Otherwise it is quite contrary, if the South Pole be elevated. Now having found the degree of the Ecliptic with which the Star you inquire after, doth rise and set; if you seek for the same degree of the sign in the Horizon of your Globe, you shall presently have the month and day expressed, wherein the Sun cometh to the same degree and sign.  
And as for the heliacal rising and setting of a star, you may find it thus. Having set your Globe to the Latitude of your place, you must turn about the star proposed to the West side of the Horizon, and withal on the opposite East part observe what degree of the Ecliptic is elevated above the Horizon 12, 13, 14. or any other number of degrees, that the magnitude of your Star shall require for distance from the Sun. And when the Sun shall be in the Opposite degree to this, than that star will set Heliacally, that is to say, it will be quite taken out of our sight by the brightness of the Sun beams. Now, if on the other side, you apply the same star to the East, and find out the Opposite degree in the Ecliptic on the West part; that is, the same number of degrees above the Horizon: when the sun cometh to this place, the same star will rise Heliacally, or recover itself out of the sun's beams. And so, if you but find the same degrees of the Ecliptic among the signs on the Horizon of your Globe, you have the Month and the day when the Sun will be in those degrees. And the same also is the time of the Emersion and Occultation of the Star you inquire after. But we will here propose an example of the Occultation of some fixed Star of the first magnitude: which done, the Emersion of the same is also found by the contrary way of working.  
And the Star we propose, shall be, that bright Star in the mouth of the Great Dog, which is called Sirius: whose Occultation we desire to know for the Latitude of 51. gr. Northward. Now this Star, being of the first magnitude, begins to be hid, whenas it toucheth the Horizon in the upper Hemisphere, and the Sun is at the same time depressed under the Horizon but 12. degrees. If therefore you apply this Star to the West part of the Horizon (having first set your Globe to the latitude of 51 degrees) and on the Opposite East side, observe what degree of the Ecclipticke is just 12 degrees above the Horizon (now this degree is very near the 11. gr. of Scorpius) when the Sun shall come to the Opposite: degree in the Ecliptic, which is the 11. of Taurus, that Star will set Heliacally, and be hid by the Sunbeams. But the Sun comes to this degree of Taurus about the 22. of April: therefore we conclude that the Dog Star sets Heliacally about that time. And if you work in the same manner, applying the Star to the East part of the Horizon, you shall have the time of it●… Heliacal rising or Emersion out o●… the Sun's be●….  
N●…t unlike this, is the manner of proceeding al●…o in finding the b●…ginning and ending of the twilights: of which we shall speak in the next Chapter.  
PONT. The use and benefit of this discourse concerning these kinds of rising and setting of the Stars is principally seen, in reading of the ancient Authors and Poets, especially those that have written of Husbandry, and the several seasons of the year. For so Virgil. lib. 1. Georg. makes mention of the Cosmical rising of the Stars in these verses. 
Candidus auratis aperit cum cornibus annum.  
Taurus, & adverso cadens Canis occidit astro.   
Which is thus Englished by T. May. 
When, with his golden horns bright, Taurus opes,  
The year: and downward the cross Dog-star stoope●….   
In which place he meaneth to intimate the month of April, when as the sun is in the sign T●…us and riseth with it. And we have an example also of the Cosmical setting in the same place, where he saith, 
At si triticeam in messem, robustaque farra  
Exercebi●… humum solisque instabis aristis.  
An ●…ibi Eoae Atlant●…des abscondantur,  
Gno●…áque ardentis dec●…dat stella coron●…,  
Deb●…ta quam●…ulcis cōmi●…tas s●…ina, quamque  
Invitae properes anni spem credere terrae.  
Mult 〈…〉 pere; sed illos  
Expectata 〈◊〉 vanis 〈◊〉 venis.   
Thus rendered by T. May. 
But if thou plough, to sow more solid grain,  
A wheat or barley harvest to obtain:  
First let the morning Pleiades be set,  
And Ariadne's shining Coronet,  
Ere thou commit thy seed to ground, and there  
Dare trust the hope of all the following year.  
Some that before the fall o'th' Pleyades  
Began to sow, deceived in the increase,  
Have reaped wild oats for wheat, etc.   
Where he would have them to expect their sowing time, till that the Alta●●ide, that is, the Pleyades, ere seven Stars be hid in the East, that is, in the Morning by the approach of the Sun, which is also called Occa●us Cosmicus. At which time also the bright Star in the Northern Crown sets in the Evening with the Sun, or Heliacally. and so the Poet, by a twofold kind of setting of the Stars, describes the 28. and 29. of October.  
An example of the Achronycall rising you have in Ovid. lib. 1; de Ponto Eleg. 9 where he decribeth the tediousness of his exile, from the Autumnal or Vespertine rising of the Pleyades, in words. 
Ut careo vobis Sythicas detrusus in oras:  
Quatuor Autumnos Plë●as orta facit.   
In English thus. 
Since of your joyful sight cold Scythia me deprived  
The rising Pleiades four Autumn's have revived.   
And he also mentioneth the Achronicall setting, lib. 2. Faster: where speaking of the third of February, he doth it by this Periphrasis, 
Quem modo celatum stellis Delphina videbas,  
Is fugiet visus no●…te sequente tuos.   
That is to say. 
The Dolphin erst with Stars you saw bedight,  
The next night vanisheth out of your sight.   
An example of the heliacal rising in February you have in the same Author, in these words. 
Tertia nox veniet, custodem protinus ursae,  
Aspicies geminos exeruisse pedes.   
Which may be Englished thus. 
When now the third night comes, you shall perceive  
Arctophylax will both his feet up heave.   
And for the heliacal setting, you had an instance above, out of Virgil. Georg. 1. 
— Et adverso cadens canis occidit astro.   
In which place the Poet speaketh of sowing millet and beans in the spring time. To these we may also add these several kinds of Poetical rising and setting of Stars expressed. 
Cosmicus est ortus, cum sol emergere quaerit.  
Ipsius oppositum lapsus, ad ima gerit.  
Chronicus est lapsus, cum sol in vespere tabet.  
Ipsius oppositum Chronicus ortus habet.  
Heliacus signo datur ortus sole remoto.  
Illius occasum proximitate noto.    

CHAP. XI. How to find the beginning and end of the Twilight, for any time and Latitude of place.  
THe Twilight is defined to be a kind of imperfect light betwixt the Day and the Night, both after the setting; and before the rising of the Sun. Of which the first is called the Evening Twilight, and the other the Morning. Now the beginning of the one, and the ending of the other are perceived at the same equal space of time from the rising and setting of the Sun: notwithstanding the continuance of each of them is sometimes greater, and sometimes less. For in Summer the Twilights are much longer then in the Winter. The measure of them they commonly make to be, whenas the Sun is depressed 18 degrees under the Horizon. But, as P. Nonius rightly observeth, there cannot be any certain Measure or Term assigned them by reason of the various disposition of the air, and the elevation of the vapours that are exhaled out of the earth; which the same Author saith, he finds to be also divers, sometimes higher, and sometimes lower. Vitelio, and Alhazenus before him, would have it to be when the Sun is depressed under the Horizon nineteen degrees. But how ever the truth be, we shall follow the common rceived opinion herein. Now therefore, if you desire to know upon these grounds here laid down, at what hour the Twilight begins and endeth, at any time or latitude of place; you must do thus. First, set your Globe to the latitude of that place, and apply that degree of the Ecliptic, wherein the Sun is at that time, to the Meridian, and withal direct the point of the Index to twelve in the Hour-circle: Then marking the degree of the Ecliptic, that is directly opposite to the place of the Sun, turn about your Globe, till such time as the opposite degree of the Sun be elevated eighteen gr. above the Horizon toward the West part of it: and forthwith the Index will show in the Houre-circle the beginning of the Morning Twilight. And if you turn about your Globe, in like manner, to the East, you shall also have the hour when the Evening Twilight endeth.  
PONT. Our Northern regions have their 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, or Twilight, of above an hour long. But those Countries, where the Tropickes are very far beneath their Horizon, have in a manner no 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, no Twilight or break of day. And therefore those that inhabit near the AEquator, have not the beginning nor later part of the night enlightened at all, neither is there any appearance of light, before the Sun be risen. Whereas, on the contrary side, those that have the Tropic very near their Horizon, must necessarily have Twilight almost all the night long in Summer. And therefore when the Romans came into Britain, and perceived that, at the Summer Sostice, their nights were light almost all the night long: they did not ac ount this Twilight to be night, but said, Minimâ nocte contentos Britannos, that the Britain's were contented with a very short night.  
Now this. 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, as it is defined by Joseph Scaliger upon Manilius, is nothing else but 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, a kind of Antiperistasis, or Circumstipation (as we may call it) of the light: which can be none at all, in those places, where the Tropic and Horizon, are far distant. For this 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, as Scaliger in that place accurately observeth, is only found under those signs which are near the Solsticiall point, as Gemini and Cancer; and that in those Countries too, where the night is somewhat larger, than it is under the Pole of the Ecliptic: as for example. (to use Scaligers own words) those that have not the Tropic for their Arctic circle, nor where it toucheth the North point of the Horizou; with them the night is so long dark, as while the Tropic cometh to strike upon the North point of the Horizon. As we know it happeneth an Scotland where our Country men that were Soldiers there, could see to play at dice all night long without any Candle, about the time that the days were at the longest. Now the Tropic is distant from the Horzizon at Edenburge 9 gr. 17. m. or thereabout. And therefore so much is the distance betwixt the Sun and their Horizon at midnight in the Summer Solstice: so that necessarily the rest of the night must be Twilight, and of 6. hours, 23. minutes, which is the length of their night, not above 37 m. which is not much above half an hour, are quite dark: and all the rest of the night is light. Whence you may perceive the reason of the long continuance of the day in those regions, that have the Tropic near bordering on their Horizon. And therefore the Romans being not well acquainted with this Antiperistasis of the light, thought that in those parts they had had scarce any night at all. And hence it necessarily follows, that by how much the Tropic is more remote from the Horizon, by so much are the nights less enlightened: and those that inhabit near the Equinoctial are so far from having their day extended farther, either before the Sun rises, or after it sets, as that with them there is no appearance of light at all, before the Sun is up. And there is scarcely any Twilight or dawning of the Day at all in those regions that lie within ten, degrees of the Equinoctial: for which there can b●… no other reason given, but only the distance betwixt the Tropic and their Horizon. And if they have no Twilight in the Summer, how much less will there be any when the Sun is in the other Tropic. So that we have no reason to give any credit to Alosiyus Cadamustus, who when he had occasion to write of this argument, gave this to be the reason of it, because there are no mountains there to hinder, but that the Sun may be seen at the instant of his rising. But this is a ridiculous reason, and not worthy a consutation. Thus Scaliger.   

CHAP. XII. How to find the length of the Artificial Day or Night, or quantity of the Sun's Parallel that remains above the Horizon, and that is hid beneath it, for any Latitude of place and time assigned. As also to find the same of any other Star.  
THe Day we have already showed to to be twofold; either Natural, or Artificial. The Natural Day is defined by the whole revolution of the AEquator, with that portion also of the same that answereth to such an Arch of the Ecliptic, which the Sun passeth over in one day. Now the whole revolution of the AEquator (besides that portion which answereth to the Sun's proper motion) is divided into twenty four equal parts, which they call equal hours: because they are all of equal length, fifteen degrees of the AEquator rising, and as many setting every hour's space. Now the beginning of this Day being divers, according to the diversity of Countries, (some beginning i●… at Sunset, as the Athenians and Jews: so●…e at midnight, as the Egyptians and Romans; others at Sunrising, as the Chaldeans; or at Noon, as the Umbrians, and commonly our Astronomers do at this day:) this being not a thing suitable to our present purpose, I shall not proceed any further in the explanation of the same.  
The Artificial day is defined to be, that space of time that the Sun is in our upper Hemisphere: to which is opposed the Artificial Night, while the Sun remaineth in the lower Hemisphere. The Artificial day, as also the Night, are divided each of them into 1●…. parts, which they call unequal hours: because that according to the different seasons of the year, they are greater or less, and are never always of the same length.  
The length of the Artificial day is thus sound out. The Globe being set to the latitude of the place, you must find out the degree of the Ecliptic that the Sun i●… in at that time, and apply the same to the Meridian, and direct the Houre-Index to the number of 12. in the Circle. And then turning about the Globe, till that the place of the Sun touch the Horizon at the Eastern part, the Index will show the hour in the Circle of the rising of the Sun: and if you but turn it about again to the West, you shall, in like manner, have the hour of his setting, and so by this means find out the length of the Artificial day. Now if you multiply the number of the hours by 15. (for so many degrees, (as we have already often said) are allowed to one equal Equinoctial hour) you shall presently have the number of degrees of the Sun's Parallel that appears above the Horizon: which if you subtract out of 360. the remainder will be the quantity of that part of the same Parallel, that always is hid under the Horizon. Or else you may proceed the contrary way, and first find out the quantity of the Diurnal Arch, and afterward by the same, you may gather the number of the hours also. For the Globe being set to the latitude of the place, and the degree of the Ecliptic that the Sun is in, being known, you may find out, in the manner now set down, the difference of the Right and Oblique Ascensions of the same degree of the Ecliptic, for the Latitude of that place. For this difference will be the half of that, wherein the Artificial day, for that time and place, is either deficient, or exceeds the length of our Equinoctial day. And therefore you must add it, when the days are longer than the nights, (which is from the 11th. of March, to the 12th. of September:) but subtract all other times of the year, when as the nights are longer than the days.  
As for example. On the 12 day of June, according to the old account, the Sun enters into Cancer: the Right Ascension of which degree of the Ecliptic is 90. degrees. But if in the latitude of 52 gr. the first degree of Cancer be applied to the Horizon, we shall find the Oblique Ascension of it to be fifty six gr. and about ten m So that the difference betwixt them is 33. gr. 5●…. m which if you add to ninety gr. the half of the Equinoctial day, the length of the Artificial day will then be 123. gr. fifty m. and the whole Diurnal Arch 247. gr. 40. m. which if you divide by fifteen, the quotient will be sixteen and almost an half: which is the number of hours in the Artificial day on the twelfth of June, for the latitude of fifty two degrees:  
And by this means, may you also find out the quantity of the longest, or shortest, or any other intermediate day, together with the increase and decrease of the same, for any time or latitude of place.  
Cleomedes would have the quantity of the days to increase and diminish after this manner: that the month immediately before and also after the AEquinox, the days should increase and decrease the fourth part of the whole difference betwixt the length of the longest and the shortest days of the whole year: and the second month they should differ a sixth part; and the third a twelfth part: that is, if the whole difference betwixt the longest and the shortest day be six hours. So that the month going immediately before, and after the AEquinoxe, the day's increase and decrease an hour, and an half, that is to say, the four 〈◊〉 part of 6. hours: the second month an whole hour; and the third month half an hour. But suppose we this to be exactly agreeable to some certain determinate latitude; yet it is not generally so in all places. For according to the divers Inclination of the Sphere, the days also are observed to increase and decrease diversely. For seeing that the Parallels in every several Latitude are cut by the AEquator in a different manner, it must needs follow, that the proportion of the increase and decrease of the days must be also different.  
I shall not here need to set down the manner, how to find the apparent Arch of the Parallel of any Star: seeing that it is found out in the same manner, as the Diurnal Arch of the Sun's Parallel is.   

CHAP. XIII. How to find out the hour of the Day and Night, both equal and unequal, for any t●…me and Latitude of place.  
IF you desire to find out the equal hour of the Day, first set your Globe to the latitude of the place you are in: and also observe the latitude of the Sun. Which done, apply the place of the Sun, to the Meridian, and set the Index to the twelfth hour in the Circle▪ and then turn about the Globe either to the East, or West, as your observation shall require, until that the place of the Sun be elevated so many degrees above the Horizon, as shall agree with your observation: as hath been already showed, in declaring how to find the Azimuth. And the Globe standing in this situation, the Index will point out in the Hour-circle the hour of the day, wherein your observation was made. After the same manner also you may find the hour of the night, by observing the Altitude of any known Star, that is expressed in the Globe. For the Index must stand ●…il, as it did before, when it was fitted to the place of the Sun: and the Globe must be turned about, till the Star be observed to have the same Elevation above the Horizon of the Globe, as it had in the Heavens, and then the Index will show the hour of the Night.  
Now the manner how to find out the unequal hour of the day, is this. First you are to find out, as we have already showed, the quantity or number of the hours of the Artificial day, and also the equal hour of the same: whence by the Rule of Proportion, you may also come to the knowledge of the unequal hour.  
PONT. The unequal hours do answer to the Artificial day, which, as you have heard before,) is defined to be the space of time that the Sun remains in the uppper Hemisphoere: to which is opposed the Artificial night, comprehending all that time, while the sun is hid from us. Which space of time, seeing that it is always divided into 12. into●…4 ●…4. equal parts, which are therefore called equal hours, because they are always of equal length, fifteen degrees of the AEquator rising & setting every hour. For the whole AEquator being divided into 24. parts, there are contained in the revolution of it 15. parts of time, which is the measure of an hour so that an equal hour is the 24th. part of the while Equinoctial circle.  
In the latitude of 49. degrees, the longest day containeth 16 hours, Now therefore when it is 10 of the clock before Noon; or the sixth hour after Sunrising on this day, 〈◊〉 to know, what unequal hour of the day it is. I therefore dispose my proportional terms thus, 16 give 6 therefore 12. (which is the number of equal hours in every day or nigh.) give 4. and and an half.  
And if we desire to know, how many degrees of the AEquator do answer to one unequal hour; we may do it thus: namely by dividing the whole number of degrees of the 〈◊〉 〈◊〉 Arch by 12. As if the Artificial day 〈◊〉 〈◊〉 equal hours in length, than the Arch of the Diurnal Parallel will be 240 degrees. Which if we divide by 12 the quotient, which 〈◊〉 will show the number of degrees in the AEquator, that answer to one unequal ●…ou 〈◊〉 like method also is to be observed, in finding out the length of the unequal hour of the Night   

CHAP. XIV. To find out the Longitude, Latitude, and Declination of any fixed Star, as it is expressed in the Globe.  
THe Longitude of a Star, is an Arch of Ecliptic intercepted betwixt two of the greater Circles, which are drawn through the Poles of the Ecliptic, the one of which passeth through the intersection of the AEquator and Ecliptic, and the other through the Centre of the star.  
The Latitude of a Star, is the distance of it from the Eccliptick; which is also to be reckoned in that circle which passeth through the Centre thereof.  
Now if you desire to find out either of these you must take the Quadrant of altitude, or any other Quadrant of a circle, that is but exactly divided into 90 parts: and lay one end of it on either Pole of the Ecliptic, either Northern or Southern, as the Latitude of the Star shall require. Then let it pass through the Centre of the Star to the very Ecliptic, and there the other end will show the degree of Longitude of the same, which you must reckon from the beginning of Aries; and so that portion of the Quadrant that is contained betwixt the Star itself and the Ecliptic, will also show the Latitude of the Star.  
PONT. The manner how to find the longitude and latitude of Stars, may be showed by this example. First, let us propose the head of Medusa. which is found in the Tables to be in the twenty one gr. 8. and it hath in Northern latitude twenty three degrees. Now therefore in the superficies of the Globe we must look for the sign 8. and reckon 21. gr. from the beginning of the same on the Ecliptic: And the circle that shall be drawn from the Pole of the Ecliptic, through this degree, shall be called the the circle of longitude of the head of Medusa. After this, reckon the latitude of the Star also in the same circle among the Parallels of latitude, beginning from the Ecliptic, and so forward toward the Arctic Pole, (because the latitude of it is Northern.) until you have accounted 23. gr. which is the number of the degrees of latitude, and showeth the place of that Star.  
Now because that all the circles of Longitude, and latitudes neither are, nor indeed can conveniently be expressed on the Globe: therefore the Quadrant of altitude is to serve in stead of the same, for the finding out of the longitudes and situations of the Stars that are set in the Globe: and that after this manner. Let us take our former example of Medusa 's head: the latitude of which being Northern, I apply the end of the Quadrant to the North Pole of the Zodiac: (otherwise, had it been Southern, it must have been fitted to the Southern Pole:) which do●…e, I seek in the ecliptics for the 21 gr. of Taurus, which is the logitude of the Star; and having found it, I lay the other end of my Quadrant over it. For by this means the Quadrant shall supply the office of the circle of Longitude of Medusa's head. 〈◊〉 therefore if I reckon 23 degrees on the said Quadrant beginning from the Ecliptic, I shall have the true situation of this Star in the Globe.  
In like manner, may we find, by a Globe that hath the Stars described on it, the longitude and latitude of any Star in the Heavens. For if we fit the Quadrant to the Northern Pole of the Zodiaque (if the Star have Northern latitude) and then let it pass through the centre of any Star: the degree of the Ecliptic that the other end of it shall point out, will be the longitude of the said Star: and the degrees that are contained betwixt the Ecliptic and the Star, will show you the latitude of the same. A for example if the Quadrant being first applied to the Northern Pole of the Zodiaque, be afterward laid along over the the bright Star in the Crown; the other end of it will fall on the 6. gr. m. which is the longitude of this Star. And then if you reckon the number of degrees betwixt the Ecliptic and the same Star, you shall find them to be 44½. which is the Northern latitude of the same.  
The Declination of a Star, is the distance of it from the AEquator: which distance must be reckoned on a greater circle, passing through the Poles of the AEquator. And therefore if you but apply any Star to the Meridian, you shall presently have the Declination of it, if you account the degrees and minutes of the Meridian (if there be any) that are contained betwixt the Centre of the Star and the AEquator.  
PONT. The Declination of Stars, as also their Right Ascension, may be known by the Globe in this manner. The Star proposed must be applied to the Meridian, and forthwith the same Meridian will discover, among the degrees of the AEquator, the Right Ascension of the same: and it will also give you the Declination, if you reckon upon it the number of degrees that are comprehended betwixt the Equinoctial and the Star proposed. And for an example of this, let us propose the Great Dog, whose right Ascension and Declination we desire to know. First, therefore we set the Star itself directly under the Meridian, and find the Meridian to cut the Equinoctial at 97. gr. 15. min. And this is the right Ascension of this Star. And then reckoning the number of the degrees comprehended betwixt it and the Equinoctial Southward, we find them to be 16 degrees, which we conclude to be the Southern latitude of the Star.  
The same also may be demonstrated by the Sun, For when the Sun is in the 3. gr. of Gemini, he is carried under the Meridian, which crosseth the Equinoctial about the 63. gr. reckoning from the first degree of Aries in the AEquator. And this is the Ascension of the Sun when he is in the 〈◊〉. degree of Gemini. Now the number of the degrees that are comprehended betwixt the place the Sun and the AEquator, being reckoned in the Meridian, are found to be 21 which is also the Sun's Declination, and that Northward, because it falleth among the Northern signs.  
The same may be performed also after another manner, as thus for example. The right Ascension of the bright Star in the Crown is found in the Astronomical Tables to be 275. gr 31. m. and the declination of it Northward 38. gr. 26. minutes. First therefore I reckon the degrees of Right Ascension in the Equinoctial, beginning at the first degree of Aries; and having found the degree I apply it to the Meridian, in which I afterward reckon the Declination assigned, beginning from Equinoctial, and proceeding toward the Arctic Pole, if the Declination of the Star be Northern, if otherwise, toward the Antarctic.  

A Table representing the Longitude, Latitude, Right Ascension, and declination of some certain Notable STARS.  The names of the Stars  Longitude Deg. Min. Latitude D. M. Nor. Sou. Right Ascen. D. M. Declina. Dr M. Nor. Sou. The 1 Star in the Rams Horn. ♈ 28 0 7 20 Nor. 20 0 18 0 Nor. The 1 horse in the wain The 3 horse ♍ 3 30 53 30 Nor. 188 10 57 27 Nor. ♍ 21 10 54 0 Nor. 202 2●… 51 5 Nor. The head of the Dragon. ♐ 21 0 75 ●…0 Nor. 226 8 52 8 Nor Boots left shoulder Arcturus. ♎ 11 0 49 0 Nor. 212 50 40 0 Nor. ♎ 18 20 31 30 Nor. 109 17 2●… 53 Nor. The bright Star in the Crown. ♏ 6 0 44 3●… Nor. 229 0 38 25 Nor. The head of Hercules. ♐ 9 0 37 30 Nor. 252 51 1●… 36 Nor The bright Star of Lybra. ♑ 8 40 62 0 Nor. 275 31 38 26 Nor. The tail of the Swan. ♓ 0 30 60 0 Nor. 307 30 44 15 Nor The Swans bill. ♑ 25 50 49 20 Nor. 288 40 27 3●… Nor. Cassiopeia's b east. ♉ 2 10 46 45 Nor. 4 23 54 5●… Nor. The Goat. ♊ 16 20 22 30 Nor. 71 58 45 7 Nor. The right side of Perseus. ♉ 25 0 30 0 Nor. 43 0 18 0 Nor. Medusa's head. ♉ 21 0 23 0 Nor. 41 0 30 0 Nor  
The names of the Stars  Longitude Deg. Min. Latitude D. M. Nor. Sou. Right Ascen. D. M. Declina. Dr M. Nor. Sou. Andro●…das head. ♈ 16 40 24 30 Nor. 〈◊〉 〈◊〉 〈◊〉 Nor The Star in the end o●… Pegasus wing ♒ 9 0 34 1●… Nor. 358 〈◊〉 13 0 Nor. Pegasus shoulder. ♒ ●…5 0 41 10 Nor. 341 〈◊〉 〈◊〉 0 Nor. The Eagle ● 〈◊〉 〈◊〉 29 10 Nor. ●…2 〈◊〉 〈◊〉 57 Nor. The head of the Serpent-bearer. ♊ ●…6 10 38 0 Nor. 288 3 ●…3 5 Nor. The bu●… 〈◊〉 ♊ 〈◊〉 0 〈◊〉 10 Nor. 6●… 〈◊〉 5 54 Nor. Castor Pollux. ♋ 14 40 9 40 Nor. ●…07 0 ●…2 30 Nor. ♋ 18 0 6 15 Nor. 110 20 ●…8 30 Nor. The Lion's Heart ♌ 〈◊〉 50 0 10 Nor. 146 13 13 45 Nor. Spica Virgins. ♎ 1●… 0 2 0 South 195 46 〈◊〉 55 South The South balance of 〈◊〉. ♏ 〈◊〉 20 0 40 South 217 8 4 0 South The heart of the Scorpion ♐ 〈◊〉 34 4 38 South 241 41 25 30 South The tail of Capricorn. ♒ 〈◊〉 0 4 20 South 〈◊〉 1●… 8 5 South Aquarius Thigh. ♓ 3 0 7 30 South 337 47 ●…7 24 South The Whale's Tail. ♓ 27 0 20 20 South 5 4 19 46 South The Whale's Nostrils. ♉ 9 0 7 45 South 40 3 〈◊〉 4●… South The Right shouldrer of Orion. ♊ 〈◊〉 20 17 0 South 83 34 〈◊〉 16 South The left foot of Orion. ♊ ●…0 30 31 ●…0 South 73 1 〈◊〉 10 South The less Dog. ♋ 20 30 16 0 South 109 4●… 〈◊〉 53 South The great Dog. ♋ 〈◊〉 0 9 0 South 9●… 〈◊〉 5 59 South   

CHAP. XV. To find the variation of the Compass, for any Latitude of place.  
THat the Needle touched with the Loadstone, doth decline in divers places from the intersection of the Meridian and Horizon, is a thing most certain, and confirmed by daily experience. Neither is this a mere forgery of Mariners, intended by them for a cloak of their own errors: as P. De Medina, Grand Pilot to the King of Spain was of opinion. Neither yet doth it so come to pass, by reason that the virtue of the Magnet, by long use and exercise is weakened; as P. Nonius conceived: or else because it was not originally endued with sufficient virtue: as some others coldly conjecture: but this motion proceeds from its own natural inclination. The cause of this deflection, although hitherto, in vain sought after by many, hath yet been found by none. In this as in all other of Nature's hidden and abstruse mysteries, we are quite 〈◊〉. There have been some that have endeavoured to prescribe some certain Canon, or rule for this Deflection, as if it had been regular and governed by some certain order: but all in vain. For that it is inordinate and irregular, is testified by daily experience, not only such as is taken from the dull conjecture of the common sort of Mariners, which ofttimes falls far wide of the truth: but from the far more accurate observations of skilful Navigators.  
At the Isles, which they call Azores, it declineth not at all from the true Meridian: as the common opinion of Mariners is. And I dare be bold to affirm, that at those more Western Islands also, it varieth very little or nothing at all. But if you sail Eastward from those Islands, you shall observe that point of the Needle that respects the North, to incline somewhat towards the East. At An●…werpe in Brabant it varieth about nine degrees: and near London it declineth from, the true Meridian above eleven degrees. And if you sail Westward from those Islands, the Needle also will incline toward the West. About the Sea Coasts of America, in the Latitude of thirty five, or thirty six degrees, it declineth above eleven gr. from the true Meridian. Beyond the AEquatour it happens clean otherwise. Near the outwardmost Promontory of Brasile, looking Eastward, which is commonly called, C. Frio, it varieth from the true Meridian above twelve degrees. Within the most Eastward parts of the straits of Magellane it declineth five or six gr. And if you sail from that Promontory, we now spoke of, toward Africa eastward, the variation still increaseth, as far as to 17, or 18. degrees: which (as far as we can conjecture) happen in a Meridian not far from that which passeth through the Azores. From thence the deflection decreaseth to nine or ten gr. which happeneth near the Isle of Saint Helen, bearing somewhat toward the West. And from hence they say it decreaseth, till you are passed the Cape of good hope, where they will have it to lie in the just situation of the true Meridian, near to a certain river, which for this cause is called by the portugals, Rio de las Agulias. And all this deviation is towad the East.  
All this we have had certain proof and experience of, and that by as accurate observations as those instruments, which are used in Navigation, would afford, and the same examined and caculated according to the doctrine of Spherical Triangles. So that we have just cause to suspect the truth of many of these traditions, which are commonly delivered, concerning the deflection of the Needle. And namely whereas they report, that under that Meridian which passeth through the Azores, it exactly respects the true Meridian: and that about the Sea coasts of Brasilia the North point of the Needle declineth toward the West, (as some affirm) we have found this to be false. And whereas they report that at Newfound land it declineth toward the West above 22 degrees: we very much suspect the truth hereof: because that this seems not at all to agree with the observation we have made concerning the variation about 11. degrees, near upon the coasts of America: of the truth of which I am so confident, as of nothing more. It therefore appears to be an idle fancy of theirs, who look to find some certain point which the Needle should always respect: and that either on the earth, (as namely some certain Magnetical mountains, not far distant from the Arctic Pole,) or else in the Heavens, as (namely the tail of the little Bear, as Cardan thought:) or else that it is situate in that very Meridian that passeth through the Azores, and about sixteen degrees and an half beyond the North Pole: as Mercator would have it. And therefore, there it no heed to be taken to them, neither, who conceive that there might be some certain way found out of calculating the longitudes of places by means of this deflection of the Needle: which I could wish they were able to perform: and indeed it might be done, were there any certain point that it should always respect.  
But to leave this discourse, let us now see, how the quantity of this declination of the Needle may be found out by the use of the Globe, for any place of known latitude, And first you must provide you of some instrument by which you may observe the distance of the Sun's Azimuth from the situation of a Needle, Our Mariners commonly use a Nautical Compass, which is divided into three hundred sixty degrees, having a thread placed crosse-wise over the centre of the Instrument to cast the shadows of the Sun upon the centre of the same. This Instrument is called by our Mariners, the Compass of variation: and this seemeth to be a very convenient Instrument for the same use. But yet I could wish that it were made with some more care and accurateness, then commonly it is.  
With this, or the like instrument, you must observe the distance of the Sun's Azimuth, for any time or place, from the projection of the Magnetical Needle. Now we have before showed, how to find out, how much the vertical circle of the Sun is distant from the Meridian. And the difference that there is betwixt the distance of the Sun from the true Meridian, and from the situation of the Needle, is the variation of the Compass. Besides, we have already showed how the Amplitude of the rising and setting of the Sun may be found If therefore by the help of this, or the like instrument, it be observed, (as we have said) how many degrees the Sun riseth or setteth from those points in the Compass, that answer to the East or West: you shall in like manner have the deviation of the Needle from the true Meridian, if it have any at all.  
PONT. At the end of this Chapter, I think it not amiss to set down, that which Joseph Scaliger. sometime upon occasion offered, wrote unto David Rivaldus, concerning the declination of the Magnetical Needle from the true Meridian. This Epistle of his is extant among those Epistles that were set forth at Paris with some other of his works, Anno 1610. And because that there is something in the same that concerns the controversy of the Praecession of the Equinoctial points; I will set down very near the whole Epistle: and thus it is. Literas tuas cum maxima voluptate etc.  
Your Letters I have receceived, and with very great satisfaction and delight: wherein I perceived two things chiefly to be insisted upon: which were, the Declination of the Magnetical Needle; and the Precession of the Equinoctial points. In my former Letters I made mention indeed of the same, but with an intention rather to discover the opinion of others, then to proclaim mine own. For I only made a bare proposal of the matter, and no dogmatic Position: that so, i●… the said declination be to be examined by the Meridian's, add the Meridian's, according to my Hypothesis, be movable; that then our Astronomers and Navigators should see, whether or no, there might not some cause and reason of this so manifest disagreement be discovered, out of this Essay of mine. For I would not have proposed it only, had I been certainly assured of it: but would rather have endeavoured to make it appear by demonstration. Whether therefore, that be the cause of it, which I desire should be searched for out of my Hypothesis; or whether it be some other it shall be all one to me. But the investigation of the Meridian's is not sufficient for this matter. For we must first dispute concerning the nature of the Magnet, whether or no it be the property of it, always to respect the North point: and if so, yet seeing that it declines from the term proposed, so many degrees, we are next to inquire, whence this Uariation proceeds: which certainly can be assigned to no other thing, then to the Meridian's. But that we may not urge this question any farther: we must consult with those Authors that have written of the Magnet; and especially with William Gilbert of Colchester, a Philosopher and Practitioner of Physic in London, who about three years since put forth three large books of the same subject: wherein he hath discovered to me his own learning rather, than the nature of the Magnet. For now I am more in doubt, than before. The other part of your Letter is, concerning the Praecession of the Equinoctial points. It was observed first of all by Hypparchus, out of the observations of the fixed Stars of Aristarchus Saminus, Conon, and Timocharcis, that the Equinoctial points were gone gone forward into the precedent parts; because that he had found that the four points (Equinoctial and Solsticiall) were farther off from the Stars assigned for the same, than they were in the time of those Astronomers. Which when he saw, be doubted not forthwith to affirm, that the AEquinostiall points were immovable, and that the Sphere of the fixed Stars was gone back into the sacceeding parts. And he did not perswad●… himself only to this, but even Ptolemy also; and Ptolemy, all that came after him, so great is the power of Prejudicated Authority. And he also rectified the Globe, and made the tail of the little Bear to be distant from the Pole twelve gr. twenty four min. choosing rather to believe it to be so, then to consult with the Stars to see whether it were so indeed, or no. Which thing I cannot sufficiently wonder at in him; seeing, that not only in his time, but also two hunared and eighteen years before him, the tail of the lesser Bear was no farther from the Pole of the world, than it is at this day: as Eudoxus observed, Which I have most plainly demonstrated in my book of the Praecession of the Equinoctial poin●…. Besides, Eratosthenes also, who wrote one hundred twenty eight years after Fudoxus, affirmed the same of the same Star: and so did those that wrote in Augustus his time. If therefore two hundred and eighteen years before Hipparchus time, that Star was where it is now; how then can that position of Hipparchus stand, who placed it 12. gr. 24 min. of the Pole of the world? For if the Sphere of the fixed Stars laid more backward into the succeeding parts, (as he would have it) and that in his time the Tail of the Cynosure was 12. gr. 24. min. distant from the Pole: it necessarily follows, that in Eudoxus time it must have been farther distant from the Pole, by 13. or 14. gr. For this is the proportion of degrees required for that motion. But it was then no farther distant, than it is at this day: and therefore Hipparchus hath abused both himself, and all that have come after him. And indeed I myself have made a collection out of him, of all the risings and settings of the Stars; which no man shall ever be able to understand, except he first make such a Globe, wherein the tail of the Cynosure shall be 12. gr. 24. min. distant from the Pole. which thing when I imparted to that great Astronomer Tycho Brahe, he was amused, and wondered very much at the novelty and strangeness of the thing: and indeed not without cause. For I did not speak a word to him of the construction of Hipparchus his Globe, and the distance of the Cynosure from the Pole of it. And therefore we plainly see, that for as much as this Star keeps the same distance from the Pole at this day, that it did 1967. years since, there is no motion at all of the eighth Sphere into the succeeding parts, but of the Equinoctial points into the precedent. For of the motion there is no doubt at all to be made, for at this time the AEquinoxe falleth before the first Star in Aries above 28. gr. which notwithstanding in Eudoxus his time happened at the very Star.  
But now whether the Star hath left the Sun behind it, or the Sun the Star, is the principal matter in question. For it must be, that one of them must stand still, and the other move: but we have already showed that the Stars are immovable: and therefore the Sun and Equinoctial points are movable. And indeed they have manifestly gone forward since Eudox's time 28. degrees.  
This Copernicus (that great Scholar, and second Ptolemy of our age) perceived, when he spoke these words. Vos putatis, etc. You think (saith he) that the eighth Sphere moveth into the consequent parts: but consider whether the Equinoctial points do not rather move forward. Whence it appears, that this never suffioiently commended man, concluded, that there was a praecession of the Equinoctial points, and not a motion of the eighth Sphere into the subs●…quent paerts. For one of these being granted, the other must necessarily be taken away: for if the eighth Sphere doth not move backward, the Equinoctial points must necessarily move forward. And therefore herein Copernicus conjectured aright. But he omitted the chiefest matter of all, either because perhaps he perceived it not, or else despaired of ever being able to demonstrate it. For seeing that the Equinoctial points are Movable, it must needs follow, that a greater Circle described by the same must be Movable also, by the twenty Sphaeric. Element. And if the Circle be Movable, the Pole must also be Movable. And therefore the Pole of the Equinoctial is not the same with the Pole of the world: for this is immovable, but the other Movable: for so consequently all the greater Circles passing through these Poles, which are the Meridian's, are also Movable. So that Sunne-Dialls, and all Sciotericall instruments, that are placed upon a Meridian Line, after some certain term of years, must necessarily be defective: because the line itself is removed from its former situation. Of which variableness we have obse ved notable arguments in monuments of Antiquity. These things, it did concern Copernicus' either to have seen, or demonstrated, who was the first man that ever rejected that fabulous and ridiculousmotionof the eighth Sphere, and withal proposed this opinion of the Praecession of the Equinoctial points: who, had he but seen seen those things, which we have observed historically out of the writings of the Ancient Astronomers, so great was the ingenuity of the man, that he would have instantly consented, and demonstrated the matter Mathematically; which certainly is no hard matter to do. For, is there any man so void of all reason and judgement, as having granted the Equinoctial points to be Movable, to deny that a great Circle described by the same, must necessarily be movable also: and if so, that the Poles are also Movable: and again this 〈◊〉 granted, that the Meridian's are so too? He that shall deny this, I cannot see, what it hath profited him to have studied the Mathematics.  
But you will object, that the Meridian's are not changed, because they pass through the Poles of the world, which are Immutable.  
But than you have forgotten our Hypothesis, which is, that the Poles of the Equinoctial are not the same with the Poles of the world. For these are immutable, but those other Mutable. And therefore we see the necessity of this Argument; and withal, that these things being so, we are yet very far to seek in many things necessary for the situation and construction of the Sphere. For by this reckoning it followeth necessarily, that the Equinoctial Circle should not be described directly Parallel to the Pole of the world: and many other things of this nature, which might hence be concluded, I might willingly omit, because I speak to a Mathematician, who might better teach in these things. Wherefore I think I may boldly say, that none can be so impudent as to deny these things which are so manifest, as that we can prove them not only Historically, but also Apodictically, by certain demonstrations. And it behoves you to see and examine more narrowly whatsoever hath been written by Mathematicians concerning this matter. For there is now no place left of deny all, but rather to see, how these things may be better demonstrated, and this done, the construction and position of the Sphere corrected. But I do not speak this to the common sort of Astrologers, who never have read any thing but the Theories of the Planets, and never so much as saw any of the ancient Writers: unto whom, although they should perhaps have recourse, they could not understand.  
Now as concerning the motion of Trepidation, it is long since exploded: and for Copernicus his motion of Libration, which is also a very vain conceit, and I shall speak more of it here, and show whence this so idle a dream should possess so worthy a man: for it differeth not much from that imposture of Trepidation. And as the truth hath at length got place, and removed that fabulous motion of Trepidation, so we doubt not but necessity will at the last send after it this motion of the eighth Sphere also.  
This therefore is the sum of our answer: that we desire, that the skilful Artists would consider, whether the knowledge of the variation of the Magnetical Needle may be illustrated by those things which we have delivered concerning the Mutability of the Meridian's: That there is no motion of the eighth Sphere into the consequent parts: That we are the first that have demonstrated the same: And that from thence must necessarily follow the praecession of of the Equinoctial points. And this being granted, that then the Equinoctial points, AEquinoctia Circles, and their Poles, and Meridian's, passing through them are also movable: and their Poles also different from the Poles of the world. And that the situation of Sun dials doth vary after s●…me term of years: and that we are the first that observed the History of this not able piece of Antiquity; which also may be demonstrated out of the Mathematics. This is my opinion, which I will ever defend. But do you consider better of it: and in the mean time Farewell. Lug. Bat. 16. Kal. Mai. An. 1604.  
And this is Scaliger's Epistle, in which whereas he speaketh of three Books of the Magnet, written by W. Gilbert, it seems to be a slip of his memory: for the same Author wrote not three, but six Books de Magnete, which were Printed at London by Peter Short, Anno 1600. the fourth and sifth books whereof do especially handle the doctrine of the variation of the Compass. And whereas he addeth, that himself had plainly demonstrated in a certain book of his, that the Tail of the Cynosure had the same situation anciently, that it bathe at this day; he meaneth that book which beareth title, Diatriba de AEquinoctiorum Anticipatione, and was printed at Paris, Anno 1613. Which Book I understand since, that Johannes Maginus a Paduan, and professor of the Mathematics in Bononia, hath undertaken to confute: as appears by the Catalogue of Books in the year 1617. where there is mention made of the same confutation printed at Rome, by Andrew 〈◊〉; and at Colen, by Anthony Hierat, in quarto. In which book the Author takes upon him to impugn certain new Tenets, concerning the Polar Star, and the mutation of the Equinoctial points, and immobility of the fixed Stars: with divers Astronomical matters, which the title promiseth: notwithstanding it hath not yet been my good hap, though I have made very diligent enquiry, to meet with any of these books.   

CHAP. XVI. How to make a Sun Dial by the Globe, for any Latitude of place.  
WE do not here promise the whole Art of Dialling: as being a matter too prolix to be handled in this place, and not so properly concerning our present business in hand. And therefore it shall suffice us to have touched lightly, and as it were, pointed out only some few grounds of this Art: being such as may very easily be understood by the use of the Globe.  
And here in this place we shall show you only 2 the most common sorts of Dial's: one whereof is called an horizontal Dial, because it is described on a plain or flat, which is Parallel to the Horizon: and the other is called a Mural, as being erected, for the most part, on a wall, perpendicular to the Horizon, and looking directly either toward the North, or South. But both these may not unfitly be called Horizontal; not in respect of the same place indeed, but of divers. And therefore whether it be a Flat horizontal, or Erect, or else inclining any way: there will be but one kind of artifice in making of the same.  
Let us therefore now see in what manner a plain horizontal Dial may be made for any place. Having therefore first prepared your flat Dial Ground, Parallel to the Horizon, draw a Meridian on it, as exactly North, and South as possibly you can. Which done, draw another East and West, which must cross it at right angles. The first of which lines will show twelve, and the other six of the Clock, both morning and evening. Then making a Centre in the intersection of these two Lines, describe a circle on your Dial Ground, to what distance you please: and then divide it, (as all other circles usually are) into 360. parts. And it will not be amiss to subdivide each of these into lesser parts, if it may conveniently be done. And now it only remains to find out the distances of the hour lines in this circle, for any latitude of place. Which that we may do by the use of the Globe, let it first be set to the latitude of the place assigned. And then make choice of some of the greater circles in the Globe, that pass through the Poles of the world; (as for example, the Equinoctial Colour, if you please:) and apply the same to the Meridian: in which situation it showeth midday, or twelve of the Clock. Then turning about the Globe toward the West, (if you will) till that fifteen degrees of the AEquator have passed through the Meridian: you must mark the degree of the Horizon that the same Colour crosseth in the Horizon. For that point will show the distance of the first and eleventh hours from the Meridian. Both of which are distant an hours space from the Meridian, or line of midday. Then turning again the Globe forward, till other fifteen degrees are passed the Meridian: the same Colour will point out the distance of the tenth hour, which is two hours before Noon, and of the second hour after noon. And in the same manner you may find out the distances of all the rest in the Horizon, allotting to each of them fifteen degrees in the AEquator crossing the Meridian. But here you must take notice by the way, that the beginning of this account of the distances, must be taken from that part of the Horizon, on which the Pole is elevated: to wit, from the North part of the Horizon, if the Arctic Pole be elevate; and so likewise from the South part, if the Antarctick be elevated.  
These distances of the hours being thus noted in the Horizon of the Globe, you must afterward translate them into your Plain, allotted for your Dial Ground, reckoning in the circumference of it so many degrees to each hour, as are answerable to those, pointed out by the Colour in the Horizon.  
And lastly, having thus done, the Gnomon or Stile must be erected. Where you are to observe this one thing (which is indeed in a manner the chief and only thing in this Art to be carefully looked unto) namely, that that edge or line of the Gnomon, which is to show the hours by its shadow, in all kinds of Dial's must be set Parallel to the Axis of the world: that so it may make an Angle of inclination with its plain ground, equal ●…o that which the Axis of the world makes with the Horizon. Now that the Style is to stand directly to the North and South, or in the Meridian line, is a thing so commonly known, that it were to no purpose to mention it. And this is the manner of making a Dial on a plain horizontal Ground.  
Now if you would make a plain Erect Dial perpendicular to the Horizon (which is commonly called a Mural) and respecting either the North or South: you must remember this one thing: (the ignorance whereof hath driven those that commonly profess the Art of Dialling into many troubles and difficulties:) this one thing, I say, is to be observed: that that which is an erect Dial in one place, will be an horizontal in another place, whose Zenith is distant from that place 90. degrees, either Northward or Southward.  
As for example: Let there be an Erect Dial made for any place whose latitude is 25. gr. this is nothing else, but to make an horizontal Dial for the latitude of 38 degrees. And if there be an Erect Dial made for the latitude of 27. gr. the same will be an Horizontal Dial for the latitude of 63 degrees. The same proportion is to be observed in the rest▪ And hence it manifestly appears, that an Horizontal Dial and a Vertical are the same, at the latitudes of 45 degrees.  
And so likewise by this rule may be made any manner of inclining Dial, if so be, that the quantity of the inclination be but known. As for example, if a Dial be to be made on a plain ground, whose inclination is 10. degrees from the Horizon Southward, and for a place whose latitude is 52. gr. Northward: you must describe in that plain horizontal Dial for the Latitude of 62. degrees Northward. And if in the same latitude the Dial ground do incline toward the North 16. gr. you must make an horizontal Dial for the Northern latitude of 36. gr:  
And thus much shall suffice to have been spoken of the making of dials by the Globe.    

The fifth and last Part. Of the Rumbes that are described in the Terrestrial Globe, and their use.  
THose lines which a Ship, following the direction of the Magnetical Needle, describeth on the surface of the Sea, Petrus Nonius calleth in Latin, Rumbos, borrowing the Apellation of his Countrymen the Portugals. Which word, since it is now generally received by learned writers to express them by: we also will use the same.  
These Rumbes are described in the Globe, either by greater or lesser circles, or by certain crooked winding liines. But Seamen are wont to express the same in their Nautical Charts by rights Lines. But this practice of theirs is clean repugnant to the truth of the thing, neither can by any means be defended from errors. The invention of Rumbes, and practise of describing the same upon the Globe, is somewhat ancient. Petrus Nonius hath written much concerning the use of them, in two Books which he entitleth, de Navigand●… ratione. And Mercator hath also expressed them in his Globes. But the use of them is not, as yet, so well known to every body: and therefore I think it not unfit, to be the more large in the explication of the same.  
Beginning therefore with the nature and original of them, we shall afterward descend to the use, there is to be made of them in the Art of Navigation. And first, we will begin with the original, and nature of the Nautical Index, or Compass: which is very well known to be of the fashion of a plain round Box, the Circumference whereof is divided into 32. equal parts, distinguished by certain right lines passing through the centre thereof. One point of it, which that end of the needle that is touched with the Magnet, always respects, is directed toward the North; so that consequently the opposite point must necessarily respect the South. And so likewise all the other parts in it have respect unto some certain fixed points in the Horizon: (for the Compass must always be placed Parallel to the Horizon.) Now I call these points fixed, only for doctrine sake, not forgetting, in the mean time that the Magnetical Needle, (besides that it doth of it own nature decline in divers places from the situation of the true Meridian, (which is commonly called the variation of the Compass) according to the custom of divers Countries, is also placed after a divers manner in the Compass. For some there are that place it 5. gr. 37. m. more Eastward then that point that answereth to the North quarter of the world: as do the Spaniards, and our Englishmen. Some place it 3. gr. and almost 18. m. declining from the North: and some set it at 11. gr. 15. minutes distance from that point. all which notwithstanding, let us suppose the Needle always to look directly North and South. Now these lines thus expressed in the Mariner's Compass, as the common intersections of the Horizon, and Vertical Circles, or rather Parallel to these. Among which, that wherein the Needle is situate, is the common intersection of the Horizon & Meridian. And that which crosseth this at right Angles, is the common section of the Horizon, and a vertical circle drawn through the Equinoctial East and West. And thus we have the 4 Cardinal winds or quarters of the World, and the whole Horizon divided into 4 equal parts, each of them containing 90. degrees. Now if you divide again each of these into 8. parts, by 7. vertical circles, drawn on each side of the Meridian, through the Zenith: the whole Horizon will be parted into 32 equal sections: each of which shall contain 11. gr. 15. m. These are the several quarters of the world observed by Mariners in their voyages: but as for any lesser parts or divisions then these, they look not after them. And this is the original of the Nautical Compass, by which Seamen are guided in their voyages.  
Let us now in the next place consider, what manner of lines a Ship, following the direction of the Compass, doth describe in her course For the better understanding whereof, I think it fit to praemise these few Propositions: which being rightly and thoroughly considered, will make the whole business facile and perspicuous.  
1. All Meridian's of all places do pass through both the Poles: and therefore they cross the AEquator, and all Circles Parallel to it, at right angles.  
2 If we direct our course any other way then toward one of the Poles: we change ever and anon both our Horizon and Meridian.  
3. The needle being touched with the Loadstone, pointeth out the common Intersection of the Horizon and Meridian: and one end of it always respecteth the North, in a manner, and the other, the South. And here I cannot but take notice of a great error of Gemma Frisius, who in his Corollary to the fifteenth Chapter of P. Appians Cosmography, affirms, that the Magnetical Needle respects the North Pole on this side of the Equinoctial line, but on the other side of the Equinoctial, it pointeth to the South Pole. Which opinion of his is contradicted, by the experience both of myself and others. And therefore, I believe, his too much credulity deceived him, giving credit perhaps to the fabulous relations of some vain heads. But howsoever it be, the error is a ●owle one, and unworthy so great an Author. This frivolous conceit hath also been justly condemned before, by the Illustrious Jul, Scaliger, instructed hereto out of the Navigations of Ludovicus Vertomannus, and Ferdinand Magellane.  
4 The same Rumbe cutteth all the Meridian's of all places at equal Angles, and respecteth the same quarters of the world in every Horizon.  
5 A greater Circle drawn through the vertex of any place, that is any whit distant from the AEquator, cannot cut divers Meridian's at equal Angles. And therefore I cannot assent to Pet. Nonius, who would have the Rumbes to consist of portions of greater Circles. For seeing that the portion of a greater Circle, being intercepted betwixt divers Meridian's, though never so little distant from each other, maketh unequal Angles with the same, a Rumbe cannot consist of them, by the precedent proposition. but this in-equality of Angles is not perceived (saith he) by the sense, unless it be in Meridian's somewhat far remote from one another. Be it so. Notwithstanding the error of this Position is discoverable by Art and demonstration. Neither doth it become so great a Mathematician, to examine rules of Art by the judgement of the sense.  
6 A greater Circle drawn through the Vertical point of any place, and inclining to the Meridian, maketh greater Angles with all other Meridian's, than it doth, with that from whence it was first drawn. It therefore behooveth, that a line, which maketh equal angles, with divers Meridian's, (as the Rumbes do) be bowed and turn in, toward the Meridian. And hence it is, that when a Ship saileth according to one and the same Rumbe, (except it be one of the four Principal and Cardinal Rumbes) it maketh a crooked Spiral Line, such as we see expressed in the Terrestrial Globe.  
7 The portions of the same Rumbe, intercepted betwixt any two Parallels, whose difference of Latitude is the same, are also equal to each other. Therefore an equal segment of the same Rumbe, equally changeth the difference of Latitude in all places. And therefore that common rule of Seamen is true: that in an equal space passed in one & the same Rumb one of the Poles is equally elevated, and the other depressed, So that Michael Coignet is found to be in an error, who out of some certain ill grounded positions endeavoured to prove the contrary.  
Out of the 4 Proposition there arise h this Consectary; namely, That Rumbes, though continued never so far, do not pass through the Poles. For seeing that the same Rumbe is equally inclined to all Meridian's; and all Meridian's do pass through the Poles: it would then follow, that if a Rumbe should pass through the Poles, the same line in the same point would cross infinite other lines: which is impossible, because that a part of any Angle, cannot be equal to the whole. Neither doth that, which we delivered in the last Proposition make any thing against this Consectary: to wit, that betwixt any two Parallels of equal distance, equal portions of the same Rumbe may be intercepted; that so it should thence follow, that the segment of any Rumbe intercepted betwixt the Parallel of 80. gr. of Latitude and the Pole, is equal to a segment of the same Rumbe intercepted betwixt the AEquator and the Parallel of ten gr. of Latitude: and the reason is, because the Pole is no Parallel. And therefore it was a true Position of Nonius, That the Rumbes do not enter the Poles: although it was not demonstrated with the like happy success. For he assumes foundations contrary to the truth: as we said before. And Gemma Frisius also was mistaken, when he affirmed, in his Appedix ad 15. Cap. Appian Cosmography. that the Rumbes do concur in the Poles: which was the opinion also of some others who are therefore justly taxed by Michael Coignet.  
These things being well considered, it will be easy to understand, what manner of lines a Ship, following the direction of the Magnet, doth describe in the Sea If the forepart of the Ship, be directed toward the North or South, which are the quarters that the Magnetical Needle always pointeth at: your course will be always under the same Meridian: because, as we showed in our third Proposition, the Needle always respecteth the Intersections of the Horizon and Meridian, and is situate in the plain of the same Meridian. If the fore part of the Ship be directed to that quarter that Fast and West Rumbo pointeth out: in your course you will then describe either the AEquator, or a Circle Parallel to it. For if at the beginning of your setting forth, your Zenith be under the AEquator, your ship will describe an Arch or segment of the AEquator. But if your Vertical point be distant from the AEquator either Northward or Southward; your course will then describe a Parallel, as far distant from the AEquator, as the Latitude of the place is whence you set forward at first. As suppose our intended course to be from some place lying under the AEquator, by the Rumbe of the East and West: we shall go forward still under the AEquator. For by this means, as we go on, we always meet with a new Meridian, which the Line of our course crosseth at right Angles. Now no other Line, besides the AEquator, can do this: as appears manifestly out of the Corollary of the first proposition. And therefore in this course our Ship must describe a portion of the AEquator. But if we steer our course, by the East and West Rumbe, from any place that lieth besides the AEquator: we shall be always under the same Parallel. For all Circles Parallel to the AEquator, do cut all the Meridian's at right Angles, by the Corollary of the first Proposition. And although the fore part of the Ship always respecteth the Equinoctial East or West, or intersection of the AEquator and Horizon; yet in our progress we shall never come near the AEquator, but shall keep always an equal distance from it. Neither shall we come at all thither, whither the fore part of our ship looketh, but shall keep such a course, wherein we shall have, ever and 〈◊〉, a new Meridian arising, which we shall cross at equal Angles, & so necessarily describe a Parallel. But if our voyage be to be made under the Rumbe which inclineth to the Meridian: our course will then be neither in a greater nor lesser Circle, but we shall describe a kind of crooked spiral Line. For if you draw any greater Circle through the Vertex of any place, inclining to the Meridian, the same Circle will cross the next Meridian, at a greater Angle, than it did the former: by the sixth proposition, And therefore it cannot make my Rumbe: because the same Rumbe cut●…h all Meridian's at equal Angles, by the fourth proposition. And all the Parallels, ●…r lesser Circles, do cross the Meridian's 〈◊〉 right Angles, by the Corollary of the first proposition: and therefore they do not incline to the Meridian.  
Concerning those lines which are made in Sea voyages by the direction of the Compass and Magnetical Needle; Gemma Frisius in his appendix to the fifteen Chapter of Appians Cosmography, part first, speaks thus. Verbum hoc obi●…er annotandum, etc. And (saith he) I think it not amiss to note this by the way, that the voyages on land do differ very much from those that are performed at Sea, For those are understood to be performed by the greater circles of the Sphere, as it is rightly demonstrated by Wernerus, in his Commenearies upon Ptolemy But the voyages by Sea, are for the most part crooked: because they are seldom taken in a great circle, but sometimes under one of the Parallels; when the Ship steers her course toward East or West: and sometime also in a greater circle: as when it saileth from North to South, or chose: or else under the AEquator, either direct East or West. But in all other kinds of Navigation, the journeys are Crooked, although guided by the Magnet, and are neither like to greater circles, nor yet to Parallels: nor indeed are circles at all, but only a kind of crooked lines, all of them at length concurring in one of the Poles. Thus he, and indeed very rightly in all the rest, save only that he will have these lines to meet in the Pole: which as we have already proved, is altogether repugnant to the nature of Rumbes.  
Hitherto have we spoken of the original and nature of Rumbes: let us now see what use there is of them in the Terrestrial Globe.  

Of the use if Rumbes in the Terrestrial Globe.  
IN the Art of Navigation, which teacheth the way and manner how a Ship is to be directed in sailing from one place to another, there are four things especially to be considered. And these are the Longitudes of the places, the Latitudes; or differences of the same Rumbe, and the space or distance betwixt any two places, measured according to the practice used in Sea-voyages. For the distances of the places are measured by the Geographer one way, and by the Mariner another. For the former measureth the distances of places always by greater circles; as after Wernerus, Peucerus hath also demonstrated in his book, De Dimensione Terrae. But the Mariner's course being made up sometimes of portions of greater circles; and sometimes of lesser, but for the most part of crooked lines: it is good reason that he should measure the distances also of places by the same. Which, and how many of these are to be known before hand, that the rest may be found out, come in the next place to be considered. Now the places betwixt which our voyage is to be performed, do differ either in Longitude only, or in Latitude only, or in both.  
If they differ only in Latitude, they are both under the same Meridian: and therefore it is the North or South Rumbe, that the course is to be directed by. And there only then remaineth to know the difference of Latitude, and distance betwixt these two places: One of which being known, the other is easily found out. For if the difference of Latitude be given in degrees and minutes; as Seamen are wont to do, the number of degrees and minutes, being multiplied by 60. (which is the number of English miles that we commonly allow to a degree, and that according to Ptolemy's opinion, as we have already demonstrated:) the whole number of miles, made in the voyage betwixt these places, will appear. And if you multiply the same number of degrees by seventeen and a half, you have the same distance in Spanish leagues. And so chose, if the distance in miles or leagues be known, and you divide the same by 60 or seventeen and an half, the quotient will show the number of degrees and minutes, that answer to the difference of Latitude betwixt the two places assigned. As for example. If a man were to sail from the Lizard (which is the outmost point of land in Corn-wall) Southward, till he come to the promontory of Spain, which is called C. Ortegall; the difference of Latitude of which places is 60 gr. 10. min. If you desire to know the distance of miles betwixt these places, multiply six gr. ten m. by 60. and the product will be 370. the number of English miles betwixt the two places assigned. And this account may be much more truly and readily made by our English miles, in as much as 60. of them are equivalent to a degree, so that one mile answereth to one minute: by which means, all tedious and prolix computation by fractions is avoided.  
In the next place, let us consider those places that differ only in Longitude: which if they lie directly under the Equinoctial, the distance betwixt them being known, the difference of Longitude will also be found: or chose, by multiplication or division, in like manner as the difference of Latitude is found. But if they be situate without the AEquator; we must then go another way to work. For seeing that the Parallels are all of them less than the AEquator, all of them decreasing in quantity proportionably, till you come to the Pole, where they are least of all: hence it comes to pass, that there can be no one certain determinate measure assigned to all the Parallels. And therefore the common sort of Mariners do greatly err, in attributing to each degree of every Parallel, and equal measure with a degree of the AEquator. By which means, there have been very many errors committed in Navigation, and many whole Countries also removed out of their own proper situation, and translated into the places of others.  
That therefore there might be provision made in this behalf, for those that are not so well acquainted with the Mathematics: I have added a Table, which showeth, what proportion a degree in every Parallel beareth to a degree in the AEquator: whence the proper measure of every Parallel may be found. In which Table the first Collume proposeth the several Parallels, each of them differing from other one degree of Latitude. The second showeth the minutes and seconds of the AEquator, that answer to a degree in each Parallel: which if you convert into two miles, you shall know how many miles answer to a degree in every Parallel.  
 M. S. 1 59 59 2 59 57 3 59 55 4 59 51 5 59 4●… 6 59 4●… 7 59 3●… 8 59 25 9 59 15 10 59 ●…5 11 58 53 12 58 41 13 58 27 14 58 1●… 15 57 57 16 57 40 17 57 22 18 57 3 19 56 43 20 56 20 21 56 0 22 55 37 23 55 13 24 54 48 25 54 22 26 53 55 27 53 27 28 52 58 29 52 28 30 51 57 31 51 25 32 50 52 33 50 18 34 49 44 35 49 8 36 48 32 37 47 55 38 47 17 39 46 38 40 ●…5 58 41 45 17 42 44 35 43 43 52 4●… 43 8 45 42 24 46 41 40 47 40 55 48 0 9 49 39 22 50 38 34 51 37 46 52 36 56 53 36 6 54 35 16 55 34 24 56 33 31 57 32 40 58 31 47 59 30 53 60 29 59 61 9 5 62 8 10 63 27 14 64 26 18 65 25 22 66 24 24 67 23 26 68 22 28 69 21 3●… 70 20 31 71 19 31 72 18 31 73 17 31 74 16 31 75 15 30 76 14 28 77 13 26 78 12 24 79 11 22 80 10 20 81 9 18 82 8 16 83 7 14 84 6 12 85 5 10 86 4 8 87 3 6 88 2 4 89 1 2 90 0 0  
By the use of this Table, if a Ship have sailed under any Parallel, and the space be known how far this Ship hath gone, the difference of Longitude may be found by the rule of proportion: and so contrariwise, if the difference of Longitude be given, the distance will in like manner be known. As for example. Suppose a Ship to have set forth from C. Dalguer, (which is a Promontory on the West part of afric) and failed Westward, 200. English Leagues, that is to say, 600 mile. We desire now to know the difference of Longitude betwixt these two places. That promontory hath in Northern Latitude 30. degrees. Now to one degree in that Parallel answer. 51. m. 57 sec. that is to say, 51 miles, and fifty seven sixtieth parts of a mile. Thus therefore we dispose our proportional terms, for the finding of the difference of Longitude. 51. miles, 57 min. (or suppose 52. full miles, because the difference is so small) give one degree: therefore 600. give 11 28/51 gr. which is the difference of Longitude betwixt the place whence the Ship set for●…h, and that where it arrived But the terms are to be invert●…d, if the difference of Longitude be given, and the distance be to be sought. But this is not so congruous. For we never use by the known Longitude to seek the distance: but the contrary. Neither indeed have we as yet any certain way of observing the difference of Longitudes: however some great boasters make us large promises of the same. But, 
Expectata seges vanis deludet avenis.   
It remaineth now to speak of those places that differ both in Longitude and Latitude: wherein there is great variety, and many kinds of differences. Of all which there are four (as we have already said) especially to be considered: and these are the differences of Longitude, and of Latitude, & the distance, & Rumbe, by which the voyage is performed. Two of which being known, the rest may readily be found out. Now the transmutation of the things to be granted for known; and to be enquired after in these four terms, may be proposed six manner of ways, as followeth,  
The diffe rinse of Longitude and Latitude being known: The Rumbe and Distance may also be found. The difference of Longitude and the Rumbe being known: The Difference of Latitude and Distance may be found. The difference of Longitude and Distance being known: The Difference of Latitude and Rumbe may be found The difference of Latitude and Rumbe being known: The Difference of Longitude and Distance may be found The difference of Latitude and Distance being known: The Rumbe & Difference of Longitude. may be found. The Rumbe and Distance being known: the difference of Longitude and Latitude may be found  
Thus you see that any two of these being known, the other two may also be found out. Now most of these (yea all of them, that are of any useat all) may be performed by the Globe And let it suffice to have here given this general advertisement once for all.  
Now besides these things here already to be known: it is also necessary that we know the Latitude of the place whence we set forth, and the quarter of the world that our course is directed unto: for otherwise we shall never be able rightly to satisfy these demands. And the reason is, because that the difference of Longitude and Latitude always wont to be reckoned unto the two parts of the world: some of them to the North and South, and the rest to the East and West. And especially, because that from all parts of the Meridian, and from each side thereof, there are Rumbes drawn that are all of equal angles or inclinations. So that unless the quarter of the world be known, whereto our course tendeth, there can be no certainty at all in our conclusions. As if the difference of Latitude be to be enquired after: the same may indeed be found out; but yet we cannot determine, to which quarter of the world it is to be reckoned, whether North or South. And if we seek for the difference of Longitude: this may be found: but in the mean time we shall not know, whether it be to be reckoned towards the East or West. And so likewise when the Rumbe is sought for, we may perhaps find what declination it hath to this Meridian: but yet we cannot give it its true denomination, except we know toward what quarter of the world one place is distant from the other. For from each particular part of the Meridian, the Rumbs have equal inclinations. These grounds being thus laid, let us now proceed to the examination of each particular.   

I. The difference of Longitude and Latitude of two places being known, how to find out the Rumbe and Distance of the same.  
TUrn about the Globe until that some Rumbe or other do cross the Meridian, at the Latitude of the place whence you set forth. Then again turn about either toward the East or West, as the matter shall require, until that an equal number of degrees in the AEquator to the difference of Longitude of the two places do pass the Meridian. Then afterward look whether or no the aforefaid Rumb do cross the Meridian at the Latitude of the place, where you are: for if it do so, you may then conclude, that it is the Rumbe you have gone by: but if otherwise, you must take another, and try it in like manner, till you light upon one that will do it.  
As for example. Serra Liona is a Promontory of afric, having in Latitude 15. gr. 20. m. and in Northern Latitude 7. gr. 30. m. suppose that we are to sail to the Isle of Saint Helen, which hath in Longitude 24 gr. 30 and in Southern Latitude 15. gr. 30. m. I now demand what Rumbe we are to sail by: and this we find in this manner. I first apply to the Meridian the 356 gr. 40 m. of Longitude: and withal observe what Rumbe the Meridian doth cross at the Latitude Northern of 7 gr. 30. m. (which is the Latitude of the place whence we are to set forth:) and I find it to be the North norwest, and South southeast Rumbe. Then I turn about the Globe toward the West, (because Saint Helen's is more Eastward than Serra Liona) until that 9 gr. 10. m. in the AEquator (which is the difference of Longitude betwixt these two places) do cross the Meridian. And in this position of the Globe, I find that the same Rumbe is crossed by the Meridian in the Southern Latitude of 15. gr. 30. m. which is the Latitude of Saint Helen's Isle. Therefore I conclude, that this is the Rumbe that we are to go by, from Serra Liona to Saint Helen's. And in this manner you may find the Rumbe betwixt any two places, either expressed in the Globe, or otherwise: so that the difference of Longitude and Latitude be but known.  
If the places be expressed in the Globe, betwixt which you seek the Rumbe; you must then with your Compasses take the distance betwixt the two places assigned, and apply the same to any Rumbe that you please (but only in those places where they cross the parallels of Latitude of the said places,) till you find a Rumbe, whose portion intercepted betwixt the Parallels of the two places, shall agree to the distance intercepted by the Compasses. As for example. If you would know what a Rumbe leadeth us from C. Cantin, a Promontony in the West part of afric; having in Latitude 32. gr. 20. m. to the Canary Islands, which are in the 28. gr. of Latitude. First, you must apply the distance intercepted betwixt the two places to any Rumbe, that lieth betwixt the 28 and 32. gr. 30. m. of Latitude, which are the Latitudes of the places assigned: and you shall find that this distance being applied to the South South-west Rumbe, so that one foot of the Compasses be set in the latitude of 32 gr. 20. m. the other will fall on the 28 gr. of Latitude in the same Rumbe. Whence you may conclude, that you must sail from C. Cantin to the Canary Islands by the South South-west Rumbe. There are some that affirm, that if this distance intercepted betwixt two places, be applied to any Rumbe where they all m●…t together at the AEquator, the same may be performed. But these men have delivered unto us their own errors, in stead of certain rules. For suppose it be granted, that the portions of the same Rumbe intercepted betwixt two Parallels equidistant from each other, are also equal in any part of the Globe; yet notwithstanding they are not to be measured by such a manner of extension For the Rumbes that lie near the AEquator, differ but little from greater circles: but as they are farther distant from it, so they are still more crooked, and inclining to the Meridian.  
The Rumbe being found, we are next to seek the distance betwixt the two places. Nomus teacheth a way to do this, in any Rumbe, by taking with your Compasses the space of 10 leagues, or half a degree. Others take 20. leagues, or an whole degree. But I approve of neither of these, nor yet reject either. Only I g●…ve this advertisement by the way: that according to the greater or less distance of the places from the AEquator, a greater or less measure may be taken. For near the AEquator, where (as we have said) the Rumbes are little different from greater circles; you may take a greater measure to go by. But when you are far from the AEquator you must then take as small a distance as you can: because that here the Rumbes are very crooked. And yet the distance of places may be much more accurately measured, so that the Rumbe and difference of Latitude of the same be but known) by this Table here set down: which is thus.  
 Rumbes Degr. Min. Sec.  In the First 1 1 10 Answer to a degree in the AEquator, or Meridian. Second 1 4 56 Third 1 12 9 Fourth 1 24 51 Fifth 1 47 59 Sixth 2 36 47 Seventh 5 7 33  
In this Table you have here ●…et down how many degrees, minutes, and seconds in every Rumbe, do answer to a degree in the Meridian or ●…qinoctiall. Now a degree (as we have often said,) containeth 60 Miles: so that each Mile answereth to a minute, and the sixtieth part of a mile, or seventeen paces, to every second. So that by the help of this Table, and the rule of proportion, the distance of any two places in any Rumbe assigned (if so be that their Latitudes be known) may easily be measured: and so on the contrary, if the distance be known, the difference of Latitude may be found. As for example. If a Ship have sailed from C. Verde in afric, lying in the 14 gr. 30. m. of Northern latitude, to C. Saint Augustine in Brasile, having in Southern Latitude 8. gr. 30 m. by the Rumbe of South-west and by South: and if it be demanded what is the distance or space betwixt these two places. For the finding of this, we dispose our terms of proportion after this manner. 1. gr. of Latitude in this Rumbe, (which is the third from the Meridian) hath 1. gr. 12. m. 9 sec. that is to say, 72 9/80 miles: therefore 23 gr. (which is the difference of Latitude betwixt C. Verde and C. Saint Augustine) require 1659. miles and almost an half, or something more than 553. English leagues. So that this is the distance betwixt C. Verde and C. Saint Augustine, being measured in the third Rumbe from the Meridian.   

II. The Rumbe being known, and difference of Longitude; how to find the difference of Latitude and distance.  
TO find out this, you must turn the Globe, till you meet with some places, where the said Rumbe crosseth the Meridian at the same Latitude that the place is of, where you set forth. And then turning the Globe either Eastward or Westward, as you see cause, until that so many degrees of the AEquator have passed the Meridian, as are answerable to the difference of Longitude betwixt the two places; you must mark what degree in the Meridian the same Rumbe c●…tteth. For that degree showeth the Latitude of the place, you are arrived.  
As for example. The Isle of Saint Helen hath in Longitude 24. gr. 20. m. and in Southern Latitude 15. gr 30. m. Suppose therefore a Ship to have sailed West Northwest, to some place that lieth West from it 24 degrees. We demand what is the Latitude of this place. First, therefore we set the Globe in such soit, as that this Rumbe may cr●…ss the Meridian at the 50. gr. 30. m. of Southern Latitude, which is the Latitude of Saint Helen's: and this will happen to be so, if you apply the 37. gr. of the Longitude to the Meridian. Then we turn about the Globe Eastward, till that 24 gr. of AEquator have passed under the Meridian. And then marking the degree of the Meridian, that the same Rumbe crosseth, we find it to be about the 5. gr. 30. m. of Southern Latitude. This therefore we conclude to be the Latitude of the place where we are arrived.  
And by this means also the distance may easily be found, if the Rumbe and difference of Latitude be first known.   

III. The difference of Longitude and distance being given; how to find the Rumbe, and difference of Latitude.  
THere is not any thing in all this Art more difficult and hard to be found, than the Rumbe, out of the distance and difference of Longitude given. Neither can it be done upon the Globe, without long and tedious practice, and many repetitions and mensurations. The practice hereof being therefore so prolix, and requiring so much labour: it is the less necessary, or indeed rather of no use at all. And the reason is, because the difference of Longitude, as we have already showed, is so hard to be found out. The invention whereof I could wish our great boasters would at length perform: that so we might expect from them something else, besides bare words, vain promises, and empty hope.  
Some of these conclusions also which we have here set down, are, I confess, of no great use or necessity, out of the like supposition of the difference of Latitude. Notwithstanding, for as much as the practice of them is easy and facile, I have willingly taken the pains, for exercise sake onelv, to propose them.   

IV The difference of Latitude and Rumbe being given, how to find the difference of Longitude and distance.  
FIrst set your Globe so, as that the Rumbe assigned may cross the Meridian at the same Latitude that the place is of, whence you set forth. And then turn about the Globe toward the East or west, as need shall require, till that the same Rumbe shall cross the Meridian at the equal Latitude of that place whither you have come. And so marking both places, reckon the number of degrees in the AEquator, intercepted betwixt both their Meridian's. And this shall be the difference of Longitude betwixt the same places. As for example. C. D'alguer in afric hath about 30 gr. of Northern Latitude. From whence suppose a Ship to have sailed Northwest and by West, to the thirty eight gr. of Northern Latitude also. Now we demand, what is the difference of Longitude betwixt these two places? Turning therefore the Globe till the Meridian cross the said Rumbe at the thirtieth gr. of Northern Latitude, (which will be, when the seventh gr. of Longitude toucheth the Meridian,) I turn it again toward the East, until such time as the Meridian crosseth the same Rumbe in the thirty eight gr. of Northern latitude: which will happen, when the three hundred fifty second gr. of Longitude cometh to the Meridian. Whence we conclude, that the place where the Ship is arrived, is Westward from C. D'alguer about fifteen degrees. And the Meridian of that place passeth through the Eastern part of Saint Michael's Island, one of the Azores. Now, how the distance may be found, the Rumbe and difference of Latitude being known, hath been declared already in the first proposition.   

V. The difference of Latitude, and distance being given, the Rumbe and difference of Longitude may be found.  
THe Rumbe may easily be found out, by the Table which we have before set down. But an example will make the matter more clear. If a Ship have sailed from the most Western point of afric, commonly called C. Blanco, (which lieth in the 10. gr. 30. m. of Northern Latitude) betwixt North and West, for the space of 1080. miles, and to the 20. gr. 30 m. of Northern Latitude also: and it be demandid, by what Rumbe this course was directed: for answer hereof, we proceed thus. The difference of Latitude is 10. gr. and the distance betwixt these places 1080. miles. We therefore dispose our terms thus, 10. gr. contain 1080. miles: therefore 1. gr. containeth 108. miles. Which if we divide by 60. we shall find in the quotient 1. gr. 48. m, which number if you seek in the Table, you shall find it answering the fifth Rumbe. Neither is the difference betwixt that number in the Table, and this here of ours above one second scruple. So that we may safely pronounce, that this voyage was performed by the fifth Rumbe from the Meridian, which is Northwest and by west. Now the Rumbe being found, and the difference of Latitude known, you may find out the difference of Longitude by the second proposition.   

VI The Rumbe and distance being given, the difference of Longitude and Latitude may also be found.  
THis also may easily be performed, by the help of the former Table. And therefore we will only show an example how it is to be done. From the Cape of good Hope, which is the most Southernly point of Africa, and hath in Southern Latitud about 35. degrees, a Ship is supposed to have sailed North, Northwest, (which is the second Rumbe from the Meridian) above 64●…. miles, or if you will, let it be full 650. Now we demand the difference of Latitude betwixt these two places: and this is found ●…ter this manner. First, we take the degree and minutes that answer to a degree of Latitude in the second Rumbe, and turn them into miles. And then we find the number of these to be 64 miles, 56 minutes, for which let us take full 65 miles. Now therefore our terms are thus to be disposed: 65. miles' answer to 1. degree of Latitude: therefore 650. will be equivalent to ten degrees of Latitude. Which if you subtract from 34. which is the Latitude of the place, whence the Ship set forth) because the course tends toward the AEquator: the remainder will be 25. gr. of Southern Latitude: which is the Latitude of the place, where the Ship is arrived.  
Now the Rumbe being known, and the difference of Latitude also found; the difference of Longitude must be found out by the second proposition.   
FINIS.   

Imprimatur.  
Tho. Wykes R. P. Epis.  
Lond. Capel. Domest.  
Maii. 110 1638.