manifest error in that hee affirmes that the first Star of Aries at the time of our Saviours Naâ—…ivity was in the very Vernall intersection especially contending to prove it as he doth out of Ptolomies observations out of which it plainly appeares that it was behind it no lesse then 5. degrees In like manner the places of the Solstices are also changed as being alwayes equally distant from the AEquinoctiall points This mâ—…tion is finished upon the Poles of the Ecliptick as is agreed upon both by Hipparchus and Ptolomy and all the rest that have come after them Which is the reaso that the fixed Starrs have alwayes kept the same latitude though they have changed their declination For confirmation whereof many testimonies may be brought out of Ptolomy lib 7. cap. 3 Almag I will onely all dg one more not able then the râ—…st out of Petolomies Georgr lib. 1. cap. 7. The Starr which wee call the Polar Starr and is the last in the taile of the Beare is certainly known in our time to be scarse three degrees distant from the Pole which very Starr in Hipparchus his time was above 12. degrees distant from the Pole as Merinus in Ptolomy affirms I will produce the whole passage which is thus In the Torrid Zone saith hee the whole Zodiack passeth over it and therefore the shadowes are cast both wayes and all Starrrs there are seen to rise and set Onely the little Beare 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 â…– And Hipparchus affirmes that the Starr in the end of the little Beares taile which is the most Southward of that Constellation is distant from the Pole 12. degrees â…– This excellent testimony of his the Interpreters have in their translating the place most strangely corrupted aâ—… 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 Starr is indeed in our time the most Northern But if these testimonies of Marinus and Ptolomy in this point bee substracted Strabo in his lib. 2. Geogr. shall acquit them of this crime And hee writes thus It is affirmed by Hipparchus saith he that those that inhabit under the Parallel that runneth through the Countrey called Cinnamomifera which is distant from Meroë Southward 3000. furlongs and from the AEquinoctiall 8800. are situated almost in the midst betwixt the AEquator and the Summer Tropick which passeth through Syene which is distant from Meroë 5000. Furlongs And these that dwell here are the first that have the Constellation of the little Bear inclosed within their Arctick Circle so that it never sets with them for the bright Starr that is seen in the end of the taile which is also the most Southward of all is so placed in the very Cirele it self that it doth touch the Horizon This is the testimony of Strabo which is the very same that Ptolomy and Merinus affirme saving that both in this place and elsewhere he always assignes 700. Furlongs in the Earth to a degree in the Heavens according to the doctrine of Eratosthenes whereas both Marinus and Ptolomy allow but 500. onely os which wee 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 Ecliptick on each side of the AEquator Of which that which lookes toward the North Pole is called the Tropicke of Cancer and the other bordering on the South the Tropicke of Capricorne For the Sun in his yearly motion through the Ecliptick arriving at these points as his utmost bounds râ—…turneth again toward the AEquator This Retrocession is called by the Greekes 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 and the Parallel Circles drawn through the same points are likewise called Tropickes PONT The use of those tropickes is First to shew when the Sun in an oblique Sphaere is neerest the verticall point of any place and so likewise when the farthest off Secondly they shew when the Sun in his Diurnall motion maketh the longest or shortest dayes in the yeare 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 Tropicks from the AEquator is diversly 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 Tropicke from the AEquator to bee 24. degreeâ—… for these seeme to have handled the matterbut carelessely we may observe the same from the more accurate obseruations of the greatest Artists For Ptolomy found the distance of either Tropicke to be 23. gr 51. min. and â…“ just as great aâ—… Eratosthenes and Hipparchus had found it before him and therefore he conceived it to be immutable Machomethes Aratensis observed this distan to bee 23. degrees 35. minutes right as Almamon King of Arabia had done before him Arzâ—…l the Spaniard found it to be in his time 23. degees 34. minutes Almehon the Son of Albumasar 23 degrees 33. minutes and halfe 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 Suns greatest declination as the Astronomers call it which greatest declination of the Sun hath been at divers times found to be variable For begining as sar backward as possibly we can and so driving it down by the Olympiads and the yeare of Christ even to these present times according to Tychoes calculation wee find it to bee 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 adde 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 Suns greatest declination as also the other Intermediat by the same reason are alter'd as it is testified by the whole current of the most skilfull Artists
by Pliny and Solinus oâ—… 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 then meer fables is acutely and solidly proved by Petrus Noninus out of the veâ—…y principles â—…f Geometry As for that which Eustathius writes that Hercules pillâ—… called by the Greeks Calpe and Abenna are celebrated by Dionysius Perlegetes for their miraculous height is plainly absurd and ridiculous For these aâ—…ise not above an hundred Ells in height which is but a furlong whereas the Pyramids of Egypt are reported by Strabo to equall that height and some trees in India are found to exceed it if wee 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 vaine reports of our modern times And first of all Scaliger writes from other mens relation that Tenariff one of the Canary Islands riseth in height fifteen leagues which amount to above sixtie miles But Patricius not content with this measure stretchth it to seventie miles There are other hills in like manner cryed up for their great height as namely the mountain Andi in Peâ—…u and another in the Isle Pico among the Azores Islands but yet both these fall short of Tenariffe What credit the relations may desâ—…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 affoards not a more eminent place nâ—…t exâ—…pting the mountaine Sloâ—…us it selâ—… which whether ever any other mortall man hath seen besides that Monke of Oxford who by his skill in Magicke conveighed himself into the utmost Northerne regions and tooke a view of all the places about the Pole as the Story hath it is more then I am able to determine Yet that this Isle cannot be so high as Scaliger would have it wee 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 coverd all over with snow all the year long save onely one or at the most two months in the midst of summer as may appear out of the Spanish Writers Now that any sâ—…ow is generated 60 or 70 miles above the plain superficies of the Earth and Water is more then they will ever perswade us seeing that the highest vapourâ—… never rise above 48 miles above the earth according to Eratosthenes his measure but according to Ptolomy they ascend not above 41 miles Notwithstanding Cardan and some other profest Mathematicians are bold to raise them up to 288 miles but with no smaâ—… stain 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 errour 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 thiâ—…gs which are reported of the some mountain and it's height by Herodotus Dionysius Afer and his scholiast Eustathius whence it is called in Authours Coelorum columen the pillar that bears up the Heavens But to let passe these vain prodigious relations let us come to those things that seem to carry a greater shew 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 bottome or vally did not exceed ten furlongs Cleomedes saith that there is no hill found to be above fifteen furlongâ—… 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 booke of his Geography The topps of the Thessalian mountatns are raiscd to a greater height by Solinus then ever it is possible for any hill to reach Yet if wee may believs Pliny Dicaearchus being employed by the Kings command in the same businesse 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 least wee should seem too sparing herein and to restrain them within narrower limits then wee ought we will adde 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 seldome exceeds 80 paseâ—… in most places it is not 20 pases and in many places not above six in few places it reacheth 100. pases and very seldâ—…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 passe the Seâ—…s let us make the depth of the Sea equall to the height of mountains so that suppose the depth thereof to bee ten furlongs which is the measure of the Saâ—…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 deales not fairly with his Author where he makes him assign thirty furlongs to bee 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 roundnesse of the Earth but that this excrescency will bee but like a little knob or dust upon a ball as Cleomedes saith For if wee suppose the circumference of the whole earth to bee 180000 furlongs according to Ptolomies account neither did ever any of the Ancients assigne a lesse measure then this as Strabo witnesseth the Diameter thereof will bee according to the proportion betwixt a circle and it's Diameter found out by Archimedes above 57272. furlâ—…ng If then we grant the highest Hills to bee ten furlongs high according to Eratosthenes and Dicaearchus they will beare the same proportion to the Diameter of the Earth â—…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 topps of the â—…ighest hills to ascend to the perpendicular of â—…ifteene furlongs as Cleomedes would have it â—…he proportion then will be of one to 3818. Or if â—…ouplease let it bee thirtie furlongs of which â—…height is
that 15. Germane miles are as much as 60. Itslian and 60. Italian miles contain 480. furlongs which is lesse then Ptolomies measure by 20. furlongs which make up two Italian miles and an halfe The Spaniards reckon to a degree some of them 16. leagues and two third parts and some seventeen and an halfe But how their measure stands compared with the Grecian furlongs or with the English Italian or Germane miles I have not yet certainly learned Yet Nonius seemeth to equall the Spanish league with the Schoenus or Parasanga which if it be so then those that allow 16. leagues and 2. thirds to a degree have the same measure that Ptolomy hath deliuered 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 Arabick writers since Almamons time do generally account 20400. Miles to be the just measure of the Terrestriall 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 plaine field of Singar and the adjoyning 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 Germane Mile is not so easie to determine Yeâ—… conjecture it cannot be losse than teâ—… Furlongs The Parasanga as Christmannusâ—…ils â—…ils us out of Abilfedea that great Arabian Geographer containeth three Arabian Miles according to the doctrine both of the Ancient and Moderne Writers among them Now a Parasanga as it appeares 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 Greekes there were two kinds of Cubits in use the one the common or ordinary Cubit which contained two foot and an halfe of Grecian measure or twenty foure digitt of which sixteen went to a foot The other was the Kings 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 equall 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 lesse then 30. with which later account if wee should with Herodotus Xenophon and others rest our selves contented neither indeed is it our intention to stand long in disputing whether or no in diverse places the measure of the Parasanga were also different as Strabo seemes to think who observed the very same difference in the Egyptians Schoenus when as being conveighed on the River Nilus from one City to another he obserued that the Egyptians in diverse places used diverse measures of their Schoenus I say if we should rest upon their determination who assigne but 30 furlongs to a Parasanga then one of the Arabian miles will containe tenn furlongs at the least Which conjectures if â—…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 conceruing the true measure of the Earths circumference let it be free for every man to follow whomsoever he please Yet were it not that the later Arabians do countermâ—…nd us by proposing to us their Positions which they averre to have been grounded upon most certain and exact mensurations of the distances of places we should not doubt to preferr Ptolomies opinion I will here propose unto your view a list of all those opinions which carry in them any shew of probability AUTHORS FURLONGS The circuit of the whole earth containeth according to Strabo and Hipperchus 252000. Eratosthenes 250000. Posidonus the Ancient Arabians 240000. Ptolomy and our Englishmen 180000. The modern Arabians 204000 The Italians and Germans 172800. AUTHORS FURLONGS The measure of a Degree according to Strabo and Hipparchus 700. Eratosthenes 694â…˜ Posidomus the Ancient Arabians 666â…” Ptolomy and our English men 500 The later Arabians 566â…” Italians and Germanes 480. MILES FURIONGS The Italian containeth 8. English 8â…“ Arabian 10 Germane 32 PONT For the finding out of the circumference or circuit of the Terrestriall 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 Romane 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 multiplyed by 15. the whole will be 5400. Germane miles and if the number of the degrees be multiplyed by 25. there well arise 9000. French miles All which may be thus expressed A degree containeth 15. Germane Miles each of which containe severally 4000. Paâ—…s 60. Italian 1000. 60. English 1000. 25 French  17. Spanish 2400 In like manner the Circumferance of the Earth mayas easily bee found out by any of the fixed Starrs as the Virgins 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 it's 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 easie 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
a Cubic all and some a Pyramidall forme yet this opinion of it's Roundnesse with greatest consent of reason at length prevailed the rest being all exploded Now wee affirme it to be round yet so as that wee also admit of it's inequalities by reason of those so great eminences of hills and depression of vallies Eratosthenes as hee 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 artificiall Globe is but that it hath certain inequalities The earth cannot be said to be of an exact orbicular forme by reason of somany high hilles and low plaines 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 sphaericall body not of so exact a forme as that of the Heavens although not much unlike it This assertion of the roundnesse 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 Easterne parts foure hours soonner then it doth with those that dwell in Spaine more Westward as Cleomedes affirmes 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 houre of the day or night but the hour of their appearing is later with them that inhabite Eastward then it is with the more Westerne people An Eclipse of the Moon which Ptolomy reports lib. 1 Geogr. cap. 4. To have been seen in Arbela a town in Assyria at the fift houre of the night the same was observed at Carthage at the second houre 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 Coâ—…bulo a Captain in Armenia betwixt 10â—… and 11. as it is related by Pliny Now that it is also of a sphaericall 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 sterne of the Ship Argo and is called by the Greeeks 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 is scarcely to bee seen at all in Rhodes unlesse it bee 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 signe 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 Latine translation are against it Another argument may bee taken from the figure of the shadow in the Eclipse of the Moon caused by the interposition of the Earths opacous body Which shadow being Sphaericall cannot proceed from any other then a round Globous body as it is demonstrated unto us out of Opticall principles But this one reason is beyond all exception that those that make toward the Land at the Sea shal first of all descry the tops of the hilles onely aâ—…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 then the gibbosity of the Earths superficies As for those other opinions of the hollow Cubicall Pyramidall and plaine figure of the Earth you have them all largely examined both in Theon Ptolomies Interpreter Cleomedes and almost in all our ordinary Authours of the Sphaere together with the reasons why they are rejected Yet that old conceit of the plainnesse of the Earths superficies is again now at last tanquam Crambe recocta set forth in a new dresse and thrust upon us by Franciscus Patricius who by some few eold arguments and misunderstood experiments endeavours to confirme his own and consequently to overthrow that other received opinion of the sphaericall figure of the Earth I shall onely lightly touch at his chiefest arguments my present purpose and intention suffering mce not to insist long on the confutation of them And fâ—…rst of all the great beight of Hills and the depression of vallies so much disagreeing from the evennesse of the plain parts of the Earth scem to make very much against the roundnesse of the Earth Who can hear with patience saith hee that those huge high mountains of Norway or the mountaine Slotus which lies under the Pole and is the highest in the world should yet be thought to have the same superficies with â—…he Sealying beneath it This therefore being the chiefest reason that mâ—…y seem to overthrow the opinion of the Earth and Seas making up one sphaericall body let us examine it a little more nearly and consider how great this inequality may bee 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 Solinuâ—… of the unusuall height of Athoâ—… 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 appeare out of Ptolomies Tables no marvail that it casts so large a shadow seeing that wee may observe by dayly experience that as well when the Sunriseth as when it sets the shadowes 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 aire 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 heapes upon the same To this may be added another testimony out of the Excerpts of the seventh booke of Strabo where it is said that those that inhabite the top of this mountain do see the Sun three hours sooner then those that live neare the Sea side The height of the mountâ—…in Caucasus is in like manner celebrated by Arisâ—…otle the top whereof is enlightned by the Suns bâ—…ames the third part of the night both morning and evening No lesle fabulous is that which is reported
that which is comprehended under more then two plaine 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 equall sides but not equall Angles Rhomboides is a Figure having neither equal sides nor equall Angles yet the Opposite sides and Angles are equall A solid Body is that which hath length breadth and thickness as a Cube or Die and the Limits or Extreames of it are superficies The Axis is that Diameter aboue which the Sphaere or Globe is turned The Poles of a Sphaere are the Extreames or ends of the Diameter and are terminated in the superficies of the Sphaere A Sphaere is defined by Euclide to be when the Diameter of a semicircle remaining fixed the Semicircle is turned about till it returne again to the place whence it began to move at first The first Part Of those things which are common both to the Caelestiall and Terrestriall 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 Analogicall representation either of the Heavens or the Earth And we call it Analogicall not only in â—…egard of it's forme expressing the Sphaericall figure as well of the Heavens as also of the Terrâ—…stiall Globe consisting of the Earth it self together with the interflowing Seas but rather because that it representeth unto uâ—… in a just proportion and distance each particular constellation in the Heavens and every severall region and tract of gâ—…ound in the Earth together with certaine circles both greater and lâ—…sser invented by Artificers for the more ready computation of the same The gâ—…eater Circle we call those which divide the whole superficies of the Globe into two equall parts or halfes and those the lesser which divide the same into two unequall parts PONT A Globe is also called a Sphaere onely with this distinction that a Sphere is properly such an one as consists only of circles or little hoopes of brasse or like matter and is not a solid body as is a Globe the Latines 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 meanes of the same the doctrine of the true motions of the Coelestiall bodies might the more easily bee apprehended And what is said of the AEquator Zodiaque Axes and the other Circles is also to bee 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. Schol. Math. touching the facility the ancient AEgyptians had in search ing out the courses of the Stars I think it not amisse to let you see what the Noble Tycho's opinion is herein and what answer hee once upon occasion gave Ramus himselfe proposing the same unto him as wee find it related by himself in his book of Astronomicall Epistles pag. 60. And thus it is Quod celeberrimus ille noltri aevi Philosophus Petus Ramus c. Where as that famous Philosopher of our times Peter Ramus was of opinion that the Science of Astronomy might bee framed by some certain Logicall wayes of computation with Hypotheses this is nothing else but a meere ground-lesse conjecture Which conâ—…eit of his he proposed indeed to mee about sixteen â—…eares since when as wee were together at Auâ—…purge wishing mee withall that when as I had â—…nce reduced the course of the Stars into some â—…xact order by the Hypotheses now in use I â—…ould then try what might be done without them And that this might possibly be effected he brought this for his reason because that hee had read that the AEgyptians had antiently a most easie 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 plaine and compendious way to the knowledge of the course of the Starres and that without them But I opposed him herein shewing withall that it was altogether impossible that the Caelestiall Apparenâ—…es should bee reduced into any certain order or science so as to bee understood without the helpâ—… of Hypotheses And that this facility of the AEgyptians was onely in the AEquators of the Planets whereby they freed themselves from all tedious supputation Whereas the ease and facile use of the Ephemerides was not as yet brought to light But for as much as hee thought otherwise a man of an excellent apprehension and wit and a great lover of the truth seemed not to bee so throughly acquainted with the hidden secrets of this intricate Science and considered not that the course of the Heavenly bodiâ—…s did not keepe 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 noâ—… any thing in this visible world that can be explained or understood Now the office of these Hypotheses is only to shew the measure of the apparent motion of the Heavenly bodies by circles and other figures which are again resolved into numbers by Arithmeticke without which whosoever shal think to attaine to the knowledge of the motion of the Stars he may be said to invoke Fortune as the Proverb is and dreames of some strange incorporeall and more then Seraphicall way above the reach of humane capacity Besides the body of the Globe it self and those â—…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 fabricke of his frame is thus First of all there is a Base or foot to rest upon on which there are raised perpendicularly sixe c Pillars b or a Columnes of equall length and distance upon the top of which there is fastned to a levell and parallel to the Base a round plate or circle of wood of a sufficient breadth and thicknesse which they call the Horizon because that the uppermost superficies thereof performeth the office of the true Horizon For it is so placed that it divideth the whole Globe â—…nto two equall parts Whereof that which 〈◊〉 uppermost representeth unto us the visible â—…emisphaere and the other that which is hid â—…omus So likewise that Circle which diviâ—…es that part of the world which we â—…ee from â—…hat other which we see not is called the Horiâ—…on And that point which is directly over our â—…eads in our Hemisphaere and is
time seeing that it is always divided into 12. intoâ—…4 â—…4 equall parts which are therefore called equall houres because they are alwayes of equall 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 equall hour is the 24th part of the while AEquinoctiall circle In the latitude of 49. degrees the longest day containeth 16 houres Now therefore when it is 10 of the clock before Noon or the sixth hour after Sun-rising on this day 〈◊〉 to know what unequall hour of the day it is I therefore dispose my proportionall tearms thus 16 give 6 therefore 12. which is the number of equall 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 unequall hour we may do it thus namely by dividing the whole number of degrees of the 〈◊〉 〈◊〉 Arch by 12. As if the Artificiall day 〈◊〉 〈◊〉 equall houres in length then the Arch of the Diurnall Parallel will be 240 degrees Which if we divide by 12 the quotient which 〈◊〉 will shew the number of degrees in the AEquator that answer to one unequall â—…ou 〈◊〉 like method also is to be observed in finding out the length of the unequall 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 Starre is an Arch of Eclipticke intercepted betwixt two of the greater Circles which are drawne thorough the Poles of the Eclipticke the one of which passeth through the intersection of the AEquator and Ecliptick and the other through the Center of the star The Latitude of a Starre is the distance of it from the Eccliptick which is also to bee reckoned in that circle which passeth through the Center 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 Ecliptick either Northerne or Southern as the Latitude of the Star shall require Then let it passe through the Center of the Starre to the very Ecliptick and there the other end will shew 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 Starre it selfe and the Eclipticke will also shew the Latitude of the Star PONT The manner how to find the longitude and latitude of Starres may bee shewed by this example First let us propose the head of Medusa which is found in the Tables to bee in the twentie one gr 8. and it hath in Northerne latitude twentie three degrees Now therefore in the superficies of the Globe wee must looke for the signe 8. and reckon 21. gr from the beginning of the same on the Eclipticke And the circle that shall bee drawn from the Pole of the Ecliptick through this degree shall be called the the circle of longitude of the head of Medusa After this reckon the latitude of the Starre also in the same circle among the Parallels of latitude beginning from the Eclipticke and so forward toward the Articke Pole because the latitude of it is Northerne untill you have accounted 23. gr which is the number of the degrees of latitude and sheweth 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 Starres 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 Northerne I apply the end of the Quadrant to the North Pole of the Zodiack otherwise had it been Southern it must have been fitted to the Southern Pole which doâ—…e I seeke in the Eclipticks for the 21 gr of Taurus which is the logitude of the Starre 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 Eclipticke I shall have the true situation of this Starre in the Globe In like manner may we find by a Globe that hath the Starres described on it the longitude and latitude of any Starre in the Heavens For if we fit the Quadrant to the Northern Pole of the Zodiaque if the Starre have Northerne latitude and then let it passe through the center of any Starre the degree of the Ecliptick that the other end of it shall point out will be the longitude of the said Starre and the degrees that are contained betwixt the ECliptick and the Starre will shew you the latitude of the same A for example if the Quadrant being first applied to the Northern Pole of the Zodiaque bee 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 Starre And then if you reckon the number of degrees betwixt the Eclipticke and the same Starre you shall find them to bee 44½ which is the Northern latitude of the same The Declination of a Starre is the distance of it from the AEquator which distance must bee reckoned on a greater circle passing through the Poles of the AEquator And therefore if you but apply any Starre 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 Center of the Star and the AEquator PONT The Declination of Starres 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 AEquinoctiall and the Star proposed And for an example of this let us propose the Great Dog whose right Ascension and Declination wee desire to know First therefore we set the Starre it selfe directly under the Meridian and find the Meridian to cut the AEquinoctiall 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 AEquinoctiall Southward we find them to be 16 degrees which we conclude to bee the Southern latitude of the Starr The same also may be demonstrated
it decreaseth till you are past the Cape of good hope where they will have it to lye in the just situation of the true Meridian neare to a certain river which for this cause is called by the Portugalls Rio de las Agulias And all this deviation is towad the East All this wee have had certain proofe 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 Sphaericall 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 wee have found this to be false And whereas they report that at New-found 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 observatiō 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 appeares to be an idle fancy of theirs who look to find some certai◠point which the Needle should alwayes respect and that either on the earth as namely some certain Magneticall mountains not far distant from the Arcticke 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 sixteene degrees and an halfe 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 performe and indeed it might bee done were there any certaine point that it should alwayes respect But to leave this discourse let us now see how the quantity of this declination of the Needle may bee 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 Suns Azimuth from the situation of a Needle Our Mariners commonly use a Nautical Compasse which is divided into three hundred sixtie degrees having a thread placed crosse-wise over the center of the Instrument to cast the shadows of the Sun upon the center of the same This Instrument is called by our Mariners the Compasse of variation and this seemeth to bee a very convenient Instrument for the same use But yet I could wish that it were made with some more care and accuratenesse then commonly it is With this or the like instrument you must observe the distance of the Suns Azimuth for any time or place from the projection of the Magnetical Needle Now we have before shewed how to find out how much the verticall 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 Compasse Besides we have already shewed 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 shal 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 amisse to set down that which Joseph Scaliger sometime upon occasion offered wrote unto David Rivaldus concerning the declination of the Magneticall 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 workes Anno 1610. Aad because that there is something in the same that concerns the controversie of the Praecession of the AEquinoctiall points I will set down very near the whole Epistle and thus it is Literas tuas cum maxima voluptate c. Your Letters I have receceived and with very great satisfaction and delight wherein I perceived two things chiefely to bee insisted upon which were the Declination of the Magneticall Needle and the Precession of the AEquinoctiall 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 onely made a bare proposall of the matter and no dogmaticall Position that so i◅ the said declination bee to bee examined by the Meridians add the Meridians according to my Hypothesis be moveable that then our Astronomers and Navigators should see whether or no there might not some cause and reason of this so manifest disagreement bee discovered out of this Essay of mine For I would not have proposed it onely 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 Meridians is not sufficient for this matter For wee 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 tearm proposed so many degrees we are next to enquire whence this Uariation proceeds which certainly can be assigned to no other thing then to the Meridians But that wee 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 Physick in London who about three yeares since put forth three large bookes of the same subject wherein hee hath discovered to me his own learning rather then the nature of the Magnet For now I am more in doubt then before The other part of your Letter is concerning the Praecession of the AEquinoctiall points It was observed first of all by Hypparchus out of the observations of the fixed Starres of Aristarchus Saminus Conon and Timocharcis that the AEquinoctiall points were gone gone forward into the precedent parts because that hee had found that the four points AEquinoctiall and Solsticiall were farther off from the Starres assigned for the same then they were in the time of those Astronomers Which when hee saw bee doubted not forthwith to affirme that the AEquinostiall points were immoveable