most sincere Judges Yet this Opinion found but few Abettors insomuch that many Ages it was as it were buried in oblivion so that there was no mention in Schools made thereof until such time that eminent Astronomer Copernicus some two or three Ages past made it famous and so prevailed therein The opinion of Copernicus therein that very many excellent Astronomers imbraced this Opinion and confirmed it with sundry Arguments and Reasons among whom not long since flourished Kepler the Emperour's profest Mathematician and Galilaeus of Galilee the Italian Mathematician to the grand Duke of Tuscany or Florence and Lanthergius Belga And because there is a twofold motion of the heavenly Bodies perceived by us the first whereof is whereby all the Stars as well fixed â—s Planets seem with equal time to wit in 24 hours to be carried round aboâ—t the Earth and to rise and keep their southing and setting The second motion is that which is called proper whereby the Planets are observed with a different or diverse motion as also are the fixed Stars to be carried from West to East The Ptolomaians aâ—â—irm that both these motions are in the Stars themselves or their Orbs But the Copernicans ascribe that first motion not to the carrying about of the Earth only from one place to another but to the wheeling and turning about of it remaining in her own place about her own Axil from West to East such as is seen to be implanted in all the Stars yet they acquit the fixed Stars as also the Sun from the aforesaid second motion and attribute the apparent motion of these to the carrying of the Earth about the Sun and to the inclination of the Axil notwithstanding they leave the said second motion to the rest of the Planets Forsooth they deny the Sun to be a Planet but place the Earth in his stead and they prefer the Sun into the Ptolomaian place of the Earth to wit the Center of the whole World forasmuch as that is the cause which maketh the Earth Saturn Jupiter Mars Venus and Mercury to turn round about These are the Reasons of this Opinion Of the great number of the Stars which seem to perform their circuit in 24 hours 1. Because so great is the number of the Stars which seem to perform their Circuit in 24 hours about the Earth and this appearance may be declared by the motion of the Earth only remaining in her place therefore it is more agreeable to reason to determine this motion rather then that insomuch as when we sit in a Ship and sayling nearer to a Station or Harbour of many Ships which in the mean while seem as it were to approach or sayl to us yet we do not ascribe a motion or sayling to them And seeing nature doth in no case work by many things that which she can perform with a few it is likely in this business also that that is so observed and kept by her Of the swift motion of the Stars c. 2. Because the swiftness of that motion of the Stars would be incredible and such as would surpass all our imagination for seeing that they are distant from the Earth almost an infinite space and that most vast circuit ought to be run in one minute of an hour at least that they should be carried through 100000 miles Contrariwise if this motion should be ascribed to the Earth she remains still in her place neither need we to fear the least swiftness because she is turned about her own Axil as a Wheel The vastness of the Celestial Bodies compared with the body of the Earth 3. There accrues a greater force to this Argument if we compare the huge vastness of the Celestial Bodies with the Body of the Earth for seeing that the Sun at least is 200 times bigger then the Earth but the fixed Stars are in a manner 1000 times bigger to what man can it not be made more probable that the Earth is turned about its own Axil by a natural motion than that so huge Celestial Bodies should be moved from place to place Of the solidity of the Celestial Orbs according to Tycho Brahe 4. Because all the most famous Astronomers being compelled with Tycho Brahe by the appearances of the Stars c. do now deny that the Celestial Orbs are solid and hard which appearances the ancients used for proving the more easie supposition of the motion of the Stars therefore the carrying or wheeling of them about the Earth seemeth more incredible Yea they deny the Orbs to be solid because if these were so a mutual penetration of the Orbs must needs be granted seeing that some Planets are found frequently in the Sphere of some other No reason for the motion of the Stars about the Earth 5. No reason can be given why the Stars can be moved about the Earth when as contrariwise there may some reason be given why the Earth and the rest of the Planets may be moved about the Sun Of the Pole and Axil 6. Neither is the Pole nor Axil real about which the Stars are determined to be moved contrariwise in the Earth there is both Pole and Axil The sayling of Ships from West to East more easie than from East to West 7. Because the sayling of Ships from West to East is more easie than from East to West For out of Europe into the Indies they sayl in about four months when as in their return home it is about six months And this is because in their Voyage thither they are carried or moved into the same point with the Earth but in their return they are moved or carried into the contrary From the moving of the Earth the Celestial appearances c. may be declared 8. Because all the Celestial appearances the rising and setting of the Stars the increase or lengthning of the days c. may be evidently declared if we maintain the Earth to be moved But most especially the commodiousness and necessity of this Hypothesis is seen in those admirable properties of the Planets to explicate which the Ptolomaicks are compelled to invent many Circles Epicycles and Eccentricks without any reason But the Copernicans do so derive them from the second motion of the Earth about the Sun with easie labour insomuch that thereby they can make the cause of them manifest and so easie that the very unlearned may understand them to wit first why the Planets may seem sometimes to be retrograde or go backwards and indeed Saturn oftner and longer than Jupiter Jupiter than Mars c. sometimes to be carried with a swifter motion and sometimes to be stationary 2ly Why Venus and Mercury can never the whole night long be seen 3ly Why Venus can never depart any greater distance from the Sun than â—0 degrees but Mercury no greater then thirty degrees and therefore those two Planets can never be seen to be opposite to the Sun Fourthly why Venus in the evening
places it is also different to wit how much the nearer the place is to the Equator with so much the greater swiftness and space it is moved but the greatest motion is in the places that lie in the Equator For indeed because every place of the Earth in twenty four hours is rouled about by the space of a whole periphery to wit by 360 degrees therefore the space of one hour is found If 360 be divided by 24 the quotient is fifteen which are so many degrees These are the degrees by which the place lying in the Equator or without it is turned about in one hour but they make if the place lye in the Equator two hundred twenty five German miles whence she will be turned in four minutes of an hour through one degree that is fifteen Miles But the places lying without the Equator towards either of the Poles are in the space of the same hour wheeled about by so many degrees but such as are much less forsooth the reason is the same between the swiftness of the motion and the distance of two places as is between the signs of the Arches by which those places are distant from the Pole for example the distance of Amsterdam from the Equator The distance of Amsterdam from the Equator or the Elevation of the Pole or the elevation of the Pole is 52 degrees 23 minutes So the distance from the Pole is 37 degrees 37 minutes whose sign is 61037. Let us take one place to be in the Equator whose distance from the Pole is 90 degrees his sign is 100000. But the place under the Equator in four minutes is carried through 15 miles and in an hour is carried through 225 miles Wherefore by the Rule of Three as 100000 are to 61037 so fifteen to nine miles or as 225 to 135 miles therefore Amsterdam every hour by this motion is carried through 135 miles But the discovery of this is much easier by the Table which we have set in the end of the foregoing Chapter For the division of 360 degrees being made by twenty four hours we find that any place every hour is moved through fifteen degrees of his own Circle and therefore that it is moved through one degree in four minutes If we therefore enter that Table with the Elevation of the Pole or distance from the Equator of that place proposed we shall find the miles set down at the degrees of the given Elevation which are due to the motion of the place proposed in the space of four minutes for example At Stockholme the elevation of the Pole is about 60 degrees The Elevation of the Pole at Stockholme and in the Table at the degree 60 I find seven miles to answer with one degree therefore I say that Stockholme is moved about in four minutes by so many miles The second motion of the whole Earth which is moved with an equal swiftness and by equal peripheries So great is the first motion considered in the places of the Earth but the second motion is of the whole Earth from place to place and all the parts or places thereof are moved with an equal swiftness and by equal peripheries The quantity hereof dependeth of the distance of the Earth from the Sun and is performed in a whole years space and thereby the Earth every day moveth through about one degree Concerning the third motion of the Earth because it hath a more hard consideration I leave it to be treated of by Astronomers because in Astronomy there is a necessity of supposing it Indeed Origanus hath raised a Controversie concerning the second motion also thinking the first motion to be convenient for the Earth but that the second should be left for the Sun and fixed Stars but the Phaenomena's or appearances in the motions of the Planets which we have alledged before do sufficiently enough maintain the Motion of the Earth CHAP. VI. Concerning the situation or place of the Earth in respect of the Planets and Stars THe consideration of the Earths situation in this whole systeme of the World in respect of other Planets hath a contemplation suitable to that which we have alledged concerning the Motion of the Earth in the foregoing Chapter For the common Opinion of Philosophers and Astronomers according to Ptolomy hath decreed The Earth according to the Opinion of the Philosophers and Astronomers of Ptolomy takes up the Center of the Universe The Sun according to the Copernicans the Center of the Universe that the Earth takes up the Center of this whole Universe so that she is conversant in the middle of all the Stars and Planets But they of Copernicus his Sect with the ancient Pythagoreans place the Sun in the Center of all the Stars but they set the Earth as it were a Planet between Mars and Venus and they think that she is carried there about the Sun with a yearly course or space which is understood better by the Diagram or description thereof Yet notwithstanding therein do these two differing Opinions agree that both confess that the Center of that first motion whereby the Stars seem to us in the space of twenty four hours to be carried about is in the Earth For both Astronomy and Geography do want this Supposition insomuch that whether you follow the Ptolomaican or Pythagorean Opinion See Scheme the firmness and certainty of General Astronomy and Geography loseth nothing For the difference of Opinions consisteth in this that the Ptolomaians will have this motion to be in the Stars themselves but the Pythogoreans is to be the Earth the Stars in the mean while resting and never moving neither of which is it necessary either for common Astronomy or Geography to determine The placing the Sun Earth and other Planets according to the Ptolomaians and Copernicans According to the Ptolomaians this is the placing of the Planets to the Earth and fixed Stars The Earth Moon Mercury Venus Sun Jupiter Saturn and the fixed Stars According to the Copernicans such is the situation or placing The Sun is placed in the middle of the consistence or systeme of the World as the heart or fire next to him the Orb of Mercury Venus the Earth Mars Jupiter Saturn and the fixed Stars If you demand how much the Earth and we being on the Earth are distant from the Planets you must know that the distance is not always the same but is changed every day and therefore Astronomers do reckon up three degrees of distances viz. the least the mean and the greatest The mean distance of the Earth from the rest of the Planets is according to many Astronomers this following The mean distance of the Earth from the other Planets The Earth is distant from the Moon with its sixty half Diameters From Mercury 110. From Venus seven hundred From the Sun 1150. From Mars about five thousand From Jupiter about 11000 And from Saturn 18000. But yet indeed the distance
of Mars Jupiter Saturn and the fixed Stars is altogether uncertain by reason of the defect of the parallaxy or mutual changing In the Copernicans Hypothesis the distance is varied not only from the motion of the Planets but also from the motion of the Earth it self The Reasons of either Opinion to wit of the Ptolomean and Copernican concerning the place of the Earth are almost the same with them which in the precedent Chapter we have alledged for this disputation hath great affinity with the same For if you ascribe and allow the second motion to the Sun which is called the proper motion not the Sun but the Earth shall be in the midst but if you allow that second Motion to the Earth not the Earth but the Sun shall be in the middle These Arguments following may be said for the Copernicans Opinion The Sun not only the fountain of Light but also the vital Spirit of the whole Universe 1. The Sun is not only the Fountain of Light which as a most clear shining torch illuminates the Earth Moon Venus and without doubt the rest of the Planets but he is the fire-hearth of heat and vital spirit by which this whole Universe seemeth to be cherished and sustained Therefore it is probable that he holdeth the middle place and that these are moved round about him 2. It is more likely that the Earth should be moved about the Sun that together with the rest of the Planets she may receive light and heat from him The Sun a vast body c. 3. The Sun being placed in the midst some cause is rendred why the rest of the Planets and the Earth may be carried round about him to wit because the Sun is a most vast body and endowed with great vertues and forces therefore he rowleth and stirreth up the rest of the Planets to their motion And this Reason especially taketh place if we admit Keplers Hypothesis concerning the motion of the Planets Spots in the Sun 4. The Observations of Galilaeus and Scheiner concerning the spots in the Sun prove that the Sun is moved about his Axil In the same manner therefore the rest of the Planets have their cause of going about neither seems it consistent with reason that any other should be attributed to him 5. If we allow the Earth a place between Mars and Venus and allow the Center to the Sun the motion of every Planet fittingly answers and agrees to the distance from the Center which in the Ptolomaick Supposition is manifest not to be effected by the consideration of the motions of the Sun Venus and Mercury 6. Those Celestial appearances which we have used in the former Chapter for the proving the second Motion of the Earth are also valid and efficacious for this place which I have said must be assigned to the Earth to wit the Retrograde course and station of the Planets and the admirable apparent motions of Venus and Mercury c. For indeed that second motion of the Earth doth before hand suppose this place and placing of the Earth or hath it joyned to it self very nearly But this Argument in my Opinion is the chiefest Yet for the first motion of the Earth nothing can be fetcht by way of Argument for gathering thence the situation of the Earth For the Earth might be in the Center of the World if she were without or wanted the second motion as Origanus also determines 7. So also the variation of the distance of the Planets from the Earth is well declared The Aristotelians and Platonists Arguments about the Earth Yet notwithstanding the Aristotelians and Platonists oppugn the Pythagoreans Opinion with many Arguments and endeavour to challenge the Center of the Earth for a place by these Arguments First heavy things are carried to the Center of the World but the Earth is the heaviest body therefore it takes up that Center Secondly heavy things would go from the Earth towards the Center of the Universe unless this Center were in the Earth Thirdly the Center is the ignoblest place and the Earth also is the vilest part of this Universe therefore it shall have the Center thereof Fourthly if the Earth were without the Center of the World and motion of the Stars then the Stars and Constellations would be seen in some seasons of the year and some days bigger than in others Fifthly neither would the middle part of Heaven always be conspicuous as Taurus rising the Scorpion should set c. Sixthly neither would there be Equinoxes Seventhly neither the Moon rising eclipsed would the Sun set c. Eightly neither would the number of Miles in the Earth equally answer every degree in Heaven The aforesaid Reasons of the Aristotelians refuted by the Copernicans The Copernicans do easily weaken these Reasons of the Aristotelians For the first and second is refell'd because the motion of heavy things is not to the Center of the Vniverse but to the homogeneal body as is proved by the parts of the Moon the Sun and Loadstone The third Reason taketh a false major and minor proposition For the Center is also a noble place and the Earth is not ignoble or base The other Reasons are easily disproved by Diagrams or Descriptions this at least being fore-supposed that the distance of the Earth from the Sun or Center how great soever it be yet if it be compared with the distance of the fixed Stars from the Sun it would be so little as that it would have no proportion to it The distance of the Moon Venus and Mercury from the Earth not so great as of Mars Jupiter and Saturn Moreover the Explication of the Theorem belongeth to this place that the distance of the fixed Stars and superiour Planets Mars Jupiter and Saturn is so great from the Earth that the half Diameter of the Earth hath no proportion to it but the distance of the Moon Venus and Mercury is not so great touching the Sun there is as yet a doubt surely if there be any proportion of the half Diameter of the Earth to the distance of the Earth from the Sun that will be very small But the Theorem is proved thus First the fixed Stars and higher Planets appear to us to rise at the same moment at which they would appear to rise by a right contrived supputation and calculation if we were set in the Center of the Earth Therefore the distance of our place from the Center of the Earth that is the half Diameter bears no proportion to the distance of the fixed Stars Secondly if we take the Meridian or Altitude of a fixed Star or one of the superiour Planets with an Astronomical Instrument we find the same as if we had observed it in the Center of the Earth Therefore the semidiameter of the Earth vanisheth away in respect of that distance Thirdly if there were any proportion then the distance of two Stars would be found to be lesser about the Horizon than
Authors for the confirmation thereof do use they propose so obscurely and confusedly that they cannot compel or convince an obstinate and pertinacious Defender of the contrary Opinion We therefore as much as may be will most clearly set forth those very Opinions and examine them that the Readers may have a distinct knowledge thereof Reasons to prove the Earth round First I reject the slighter Reasons or Arguments which are probable or rather Sophistical First the Spherick figure is most capacious therefore the Earth ought to have such a kind of figure Secondly all the parts of the Earth tend to the same Center therefore all those parts make a round figure Thirdly when as in the Creation the Water as yet was confusedly mixed with the Earth without doubt the Earth was moist and soft but the figure or shape of Liquid things is round or spherical therefore such also the figure of the Earth remained after the separation of the moist from the dry These and the like Arguments being slighted let us view and consider the stronger and most solid There is but one Argument of one and the first kind which is taken à priori but the other two kinds are taken à posteriori to wit some Arguments are taken from the Celestial appearances some again from them which we either observe in the Earth or in Heaven As for the first Argument concluding à priori it is taken from the nature of Water and this demonstration is wont to be taken either from Aristotle or Archimedes Aristotle in his second Book de Coelo chap. 5. hath proposed his Demonstration in these very words The superficies of the Water round It shall manifestly appear that the superficies or surface of the Water is round if we shall take the Supposition That Water of its own nature makes its confluence always to a hollow place and that that place is more concavous which is nearer the Center Therefore from the Center A let the strait lines A B and A G be drawn and from B unto G let the line B G be drawn See Scheme unto which from A let a perpendicular line A D be drawn into E. It is manifest therefore that the line A D is less than the lines A B and A G by the 18th of the first Book of Euclid's Elements Geometrical therefore this place D is more concavous wherefore the Water shall flow from B and G until the lines A B A D A G may be equal But A E is equal to A B A G therefore it must needs be that the very water should be in these lines which are drawn in the Center this part of the Demonstration is clearly known but A E c. makes nothing for the Demonstration But that line which toucheth them which are drawn from the Center is the circumference therefere the superficies of the Water which truly is B E G is round Things to be noted This is Aristotles Demonstration in which besides the confused and evil composure thereof these things I observe First that it supposeth some Center of the whole Vniverse Secondly that it taketh the place more or less bending down in regard of that Center For he which shall deny the shape or figure of the Earth to be spherical would call these things into question Yet the first may be sufficiently concerning the Center of the Universe proved or corrected For we must say that either the Stars are wheeled round about by a Diurnal motion or that the Earth is turned round about its own Center for this the apparent motion of the Stars forceth and causeth If the Stars then that point about which they are turned shall be the Center of the Vniverse if the Earth then the middle point of the Earth or that about which it is turned shall be taken in the Demonstration for the Central point of Aristotle But the chiefest difficulty lies in the second Supposition to wit that the lesser or greater declivity or bending downward ought to be considered in respect of that Center For he which would defend the superficies of the Water to be plain and of another figure he would deny this Supposition and would say that the declivity must be considered according to our senses to wit in respect of our Horizontal plain according to which the Earth with infinite spaces is extended into profundity or else he would define the declivity in another manner And thus this demonstration concludeth nothing at all unless it be granted that the declivity of the places of the Earth must be taken in respect of that Center about which the daily apparent motion of the Celestial Bodies is performed which thing although it may be true and all other definitions of declivity according to which the Water may be moved may also be confuted yet notwithstanding it can scarce be admitted for a principle seeing that it in a manner supposes the figure of the Earth to be Spherical Archimedes his demonstrations by some preferred before those of Aristotles Others therefore prefer Archimedes his Demonstration before this of Aristotle which is found in his first Book concerning those things that are carried in the Water This indeed is more Artificial than that of Aristotle yet it is opprest with the same difficulties forasmuch as it supposeth the Spherical figure of the Earth and its Center in respect of which it taketh the depression of the Water We will bring hither some Arguments framed from those that are taken from Celestial appearances First let us conceive the Meridian line of our place or of any point of B in the Earth See Scheme or a Section of the Earth made in plane which through the Poles of the World M N passeth through A B C D this line is usually called the Latitude of the Earth and the line which is drawn perpendicular to this is named the Longitude of the Earth or another plain Parallel to the Celestial Equator making in the Earth the line E B F C. I say as well the line A B C D as the line E B F C in the Earth to be circular But it is a Geometrical Thorem If any Superficies according to one dimension be cut through any point and the section be made in the periphery or circumference of the Circle then according to the other dimension through the same point the section be made in plain which is perpendicular to the former plain and the section again be made in the periphery of the Circle that superficies is spherical Therefore because we have taken the point B in the superficies of the Earth according to our own pleasure and have shewed the Section A B C D and E B F C to be the peripheries of the Circles The Earth a Spherical body therefore by the aforesaid Theorem we conclude that the superficies of the Earth is spherical and that the Earth is a spherical Body The Section of the Earth according to the dimension
Moon from the Earth It is worthy observation that the half Diameter of the Earth is the measure of all Celestial dimensions as well in assigning the distances of the Planets from the Earth and from themselves as in numbring and computing their magnitude So we say that the Sun is distant from the Earth ubout 1200 half Diameters the Moon 40 c. But seeing in Geography we do not only consider the great Circles of the Earth as the Equator c. but also the Parallels of the Equator Therefore we must likewise determine how many miles or perches answer one degree in every Parallel We have taken the accounting of the Perches out of Snellius but I my self have reckoned up the miles to wit 1900 Perches for a German mile 1500 for a Belgick or Holland mile 475 for an Italian mile A TABLE of the Quantity of one Degree in every Parallel The Degrees in which the Parallels are distant from the Equator or the Elevation of the Poles of the Parallels Equator of the Perch of one degree Holland miles German Italian The Latitude Of a Perch of one degree Holland miles German Italian   mil. per. miles min. miles min.   mil. per. miles min. miles min.  28500 19 0 15. 0 60. 0         1 28496 18. 1496 14. 59 59. 56 46 19798 13. 298 10. 25 41. 40 2 28483 18. 1483 14. 59 59. 55 47 19437 13. 0 â—0 14 41. 0 3 â—8461 18. 1461 14. 58 59. 52 48 19070 12. 1070 10. 2 40. 8 4 28431 18. 1431 14. 57 59. 50 49 18698 12. 698 9. 50 39. 20 5 28392 18. 1392 14. 56 59. 46 50 18319 12. 319 9. 38 38. 32 6 28344 18. 1344 14. 55 59. 40 51 17936 11. 1436 9. 26 37. 44 7 28288 18. 1288 14. 53 59. 37 52 17546 11. 1046 9. 14 37. 0 8 28223 18. 1223 14. 51 59. 24 53 17152 11. 652 9. 2 36. 8 9 28149 18. 1149 14. 48 59. 12 54 16752 11. 252 8. 49 35. 26 10 28067 18. 1067 14. 46 59. 4 55 16347 10. 1347 8. 36 34. 24 11 27976 18. 976 14. 43 58. 52 56 15932 10. 937 8. 23 33. 32 12 27877 18. 877 14. 40 58. 40 57 15522 10. 522 8. 10 32. 40 13 27769 18. 769 14. 37 58. 28 58 15103 10. 103 7. 57 31. 40 14 27653 18. 653 14. 33 58. 12 59 14671 9. 1179 7. 44 31. 0 15 27529 18. 529 14. 29 50.  60 14250 9. 750 7. 30 30. 0 16 27653 18. 453 14. 25 57. 40 61 13817 9. 317 7. 16 29. 4 17 27255 18. 255 14. 21 57. 20 62 13380 8. 1380 7. 2 28. 8 18 27105 18. 105 14. 16 57. 4 63 12939 8. 939 6. 48 27. 12 19 26947 18. 0 14. 11 56. 44 64 12494 8. 994 6. 34 26. 16 20 26781 18. 0 14. 6 56. 24 65 12045 8. 45 6. 20 25. 20 21 26607 17. 1107 14. 0 56. 0 66 11592 7. 1092 6. 6 24. 24. 22 26423 17. 925 13. 54 55. 36 67 11136 7. 636 5. 52 23. 28 23 26234 17. 734 â—3 48 55. 12 68 10676 7. 176 5. 38 22. 32 24 26036 17. 536 â—3 42 54. 48 69 10213 6. 1213 5. 23 21. 32 25 25830 17. 330 â—3 36 54. 24 70 9748 6. 748 5. 8 20 32 26 25616 17. 116 13. 29 54. 0 71 9279 6. 279 4. 53 19. 32 27 25394 16. 1394 13. 22 53. 28 72 8807 5. 1307 4. 38 18. 32 28 25164 16. 1164 13. 15 53. 0 73 8333 5. 933 4. 23 17. 32 29 24927 16. 927 13. 7 52. 28 74 7846 5. 346 4. 8 16. 32 30 â—4681 16. 681 13. 59 51. 56 75 7376 4. 1376 3. 53 15. 32 31 24429 10. 429 12. 51 51. 24 76 6895 4. 895 3. 38 14 32 32 24169 16. 169 12. 43 50. 52 77 6411 4. 411 3. 23 13. 32 33 23902 15. 1402 12. 35 50. 20 78 5925 3. 1425 3. 8 12. 32 34 23628 15. 1128 12. 26 49. 44 79 5438 3. 938 2. 52 11. 28 35 23346 15. 846 12. 17 49. 8 80 4949 3. 449 2. 36 10. 24 36 23057 15. 557 12. 8 48. 32 81 4458 2. 1458 2. 20 9. 20 37 22761 15. 261 11. 59 47. 56 82 3966 2. 966 2. 5 8. 20 38 22458 15. 0 11. 49 47. 16 83 3473 2. 473 1. 50 7. 20 39 22149 14. 1149 11. 39 46. 36 84 2979 1. 1479 1. 34 6. 12 40 21832 14. 832 11. 29 46. 0 85 2484 1. 984 1. 18 5. 12 41 21509 14. 509 11. 19 45. 16 86 1988 1. 488 1. 3 4. 12 42 21180 14. 180 11. 9 44. 36 82 1492 0. 1492 0. 47 3. 12 43 20843 13. 1343 10. 58 43. 52 88 995 0. 995 0. 31 2. 4 44 20501 13. 1001 10. 47 43. 8 89 497 0. 497 0. 16 1. 4 45 20152 13. 652 10. 36 42. 24 90 0 0. 0 0. 0 0. 0 CHAP. V. The Pythagorical motion of the Earth is the cause of many Celestial appearances THE Pythagorical motion or turning the Earth about as with a wheel not that quaking and shaking is the cause of very many Celestial appearances according to the Copernicans opinion seeing that without it every place would have a perpetual constancie of these But indeed there is no property or quality of the Earth concerning which there can be greater disputations fith that not very long ago it hath suffered the Censure of the Church of Rome Yet because to many men it seemeth likely to be true that such a motion of the Earth may be given therefore I will endeavour briefly to unfold the same The Motion of the Sun Moon and Stars and their appearances It is not unknown to any of the very Vulgar sort that the Sun Moon and all the Stars of Heaven appear every day that is in the space of 24 hours to be moved from East to West and commonly to return to the same places of Heaven It must therefore needs be that either they are really moved or that we are moved and that our motion or moving be imputed to the Stars For if two things change their dâ—stance one of them at least was moved which principle is most manifest The opinion of the Ptolomaians and Pythagoreans concerning the motion of the Stars c. That the Earth standeth still and that the Stars with the Heavens are moved was and is yet the common opinion of Astronomers which are called Ptolomaians or of such as follow the Doctrine of Ptolomy yet the Pythagoreans long ago maintained that the Stars held their place constantly without budging from thence and that the Earth was rouled and wheeled about its Center one of whom was the famous Aristarchus of Samos who for his defending this Opinion was by his Adversary accused of prophaning and violating Religion before the most famous and severe Bench of the Areopagites but he was nevertheless quitted by the sentence of those
Del Majo with the Southern-motion in the end of August in 35 degrees of the Meridian of Tristian de Cunha in May in the New Moon the West-wind rageth and Shipwracks but in 33 degrees of the same Meridian the North and North-east Winds predominate 8. In June and July in the Sea of China at Pulon Timor the West-winds are violent and dangerous 9. Between China and Japan many Storms are from the New Moon of July to the twelfth day of the Moon 10. There if in June other winds blow besides the motion sometimes from this sometimes from that quarter until that they are setled in the North-east quarter of a certain a Storm followeth THE SECOND BOOK OF General Geography CONCERNING The Affections of the places of the Earth depending on the apparent motion of the Stars CHAP. XXII Of things requisite to be foreknown in the knowledge of Geography Itherto we have been employed in an absolute contemplation of the Earth we now draw near the Second Part of this Doctrine in which we shall consider those Properties or Affections which happen to the Earth from the apparent motion of the Sun and Stars Neither would they be except this Motion were evident The Explication of which Affections will with greater right appertain unto Geography if so be that same Motion be attributed unto the Earth it self of which we have treated in the Sixth Chapter Now for the right knowledge of these Affections these following Hypotheses and Definitions are necessary to be understood Definitions An Artificial Terrestrial Globe termed a factitious Glâ—be First the Artificial Terrestrial Globe is termed a factitious Globe from whose Superficies the parts of the Earth and their scituation a◠〈◊〉 presented as they have an existence in the Earth it self according â—o the proportion of this Superficies to the Superficies of the Earth A Map a plain Figure and of what Lines it consists A Map or Geographical Card is a plain figure in which the scituations of the Terrestrial Superficies are represented And this again is either Universal or Particular The first exhibiteth the whole Superficies of the Earth the other some one or other Region Some Maps consist of strait Lines and others of crooked These of strait are such in which the Peripheries or Circumferences of the Terrestrial Circles are represented by right Lines the other in which the same Peripheries are exhibited by crooked Lines But as for the composure of a Terrestrial Globe and Geographical Maps we shall take an occasion to treat of in the end of our Book by reason the same cannot be understood before the Doctrine which we now handle be well apprehended Of the Poles and Axis of the Earth Secondly The Poles of the Earth are two points diametrically opposite in the Superficies of the same which remain immoveable in the Diurnal circumrotation of the Earth or which are subjected unto the Poles of the apparent Quotidian motion of the Stars But the Axis of the Earth is said to be the Diameter conjoyning the Poles Or thus The Axis of the Earth is that Diameter of the Earth about which the Diurnal motion of the Stars or Earth it self is perfected Now the Poles are said to be the Extream points of the Axis in the Superficies of the Terrestrial Globe and that Pole which is subjected to the Constellation termed the Bear is called the Artick Septentrional or Northern Pole the other is called the Antartick or Southern Pole These are by more facility explained by an Artificial Terrestrial Globe than by words If the former be wheeled round those two immoveable points will appear which are the Poles and the Diameter imaginarily drawn from one Pole to the other through the Center of the Earth shall be the Axis The Aequator or Aequinoctial Line Thirdly The Aequator is said to be the Periphery or Circumference of the greatest Circle in the Globe of the Earth equally distant from both the Poles or placed in the middle between the Poles or whose Poles are the same with the Poles of the Earth It is also termed the Aequinoctial Line and that by Mariners All the Stars in their Diurnal motion make Peripheries equidistant or parallel to the Aequator wherefore the Aequator is the Rule of Diurnal motion Parallels Fourthly The Parallels of the Aequator are said to be lesser Peripheries which are parallel to the Aequator In an Artificial Globe the Aequator by reason of its Magnitude is more conspicuous than the others and its name is ascribed and it is divided into 360 degrees The Parallels are also conspicuous which are likewise termed the Circles of the Latitude of Places as we shall shew in the following Chapter Of Maps These may also be shewed in Geographical Maps that are Universal Indeed in Maps of Right Lines the Poles are not represented but the Extremities of every Meridian are the Poles but in Maps consisting of Crooked Lines the Poles are those points in which the Crooked Lines do meet the Aequator being transverse in both kind of Maps passeth through the middle of them and hath a greater Latitude than the other Lines and withal it is a strait Line although in the particular Maps of Asia and Europe it be made crooked The Parallels of the Aequator in strait-lined Maps are strait-lâ—â—â—s and in crooked-lined Maps they are crooked The Ecliptick Fifthly The Ecliptick is the greatest Circle of the Heavens which the Sun describeth in his Annual motion In truth it existeth not in the Earth but by reason of its notable use it is marked in the Artificial Globe as also in Geographical Maps The Tropicks Sixthly The Tropicks are two Parallels of the Aequator which are distant from the Aequator by so great an interval as the greatest recess of the Sun is from the Aequator towards the Poles or as the greatest declination of the Sun or obliquity of the Ecliptick The Tropick of Cancer is that which is interposed between the Aequator and Pole Artick The Tropick of Capricorn is that which is between the Aequator and the Southern Pole The Polary Circles In the Globe and in Maps they are wont to be noted by a double Periphery and the same appellation is ascribed The Polary Circles are two Parallels so called whereof one is distant from the Pole Artick the other from the Antartick so many degrees as the Sun is from the Aequator in his greatest recess and the first is termed the Artick Circle and the other the Antartick The Circles hitherto explained do not depend on certain Places such as the following do which in divers places are various and different The Meridian Seventhly The Meridian of any place in the Superficies of the Earth is a Line so termed which passeth through that place in which when the Sun cometh the Meridies is in that place Now the Meridies is that moment of the day which is equally distant from the rising and setting of the
Sun Theorem The Meridian of every place passeth through both the Poles of the Earth The Meridians are drawn through every ten degrees of the Aequator which are the Meridians of all those places through which they pass But instead of the Meridians of all other places that doth supply the place which is made of Brass and in which the Globe doth hang. For Instance If that any place in the Superficies of the Globe be brought unto the Brazen Meridian that shall be the Meridian of the place In Maps of Strait lines the Meridians are Strait lines drawn from the top or uppermost part unto the bottom In Maps of Crooked lines they are those Crooked lines which joyn in the Pole The Norizou Fightly The Horizon of any place in the Superficies of the Earth is the greatest imaginary Circle in the Heavens which terminateth the visible part of the Heaven in that place It is also termed the Rational Horizon that it may be distinguished from the Visible Horizon which is improperly so called It hath no place in the Artificial Globe but a Wooden Circle in which the Globe is sustained with its Brazen Meridian and serveth instead of the Horizon of any place as shall be shewed in the next Chapter and therefore it is termed the Wooden Horizon and simply the Horizon These are the Definitions whose knowledge is necessary for the attaining the following Doctrine besides which it behoveth us to borrow from Astronomy the mode of the Motion of the Sun and Stars The Motion of the Sun Moon and Stars The first and common Motion is that by which the Sun Moon and all the Stars seem to be carried round about the Earth to arise to us to make the Meridian and to set and that in the space of twenty four hours Every one of the Stars and the Sun every day by this their common Motion seem to deseribe Parallel Circles unto the Aequator because that this motion is performed upon the Axis of the Earth and the Poles of the same and therefore the Aequator is the greatest Circle of this Motion and the Rule and Square by which we measure the Motion of the other Parallels In every hour they pass fifteen degrees through the Meridian both of the Aequator and every other Parallel for 360 degrees divided by 24 the hours gives unto every hour fifteen and therefore one hour and fifteen degrees of the Aequator make an equal proportion The Horary Circle sheweth the hours which Circle being affixed unto the Artificial Globe is seen in the Brazen Meridian where the Pin or Hand adhereth to the extremity of the Axis of the Earth and it is turned about in the Horary Circle to shew the hours The second motion of the Sun Secondly The proper and second Motion of the Sun which is also Annual is that in which the Sun or rather the Earth is moved from West to East or contrary to its first motion The time or number of the days in which the Sun returneth unto the same point from whence it departed or in which it performeth its whole Period or Circle is termed a Year Now such a Year is 361 days and one fourth part of a day or thereabouts The Way of this second Solary motion is termed the Ecliptick as we have said before which is divided into twelve parts which are called Signs For Astronomers have observed these Constellations of the Heaven through which this Way of the Sun doth lye and from these Constellations denominated the twelve parts of the Ecliptick And because that all Constellations represent the forms of Animals therefore the Ancients termed that Way or Ecliptick The Zodiack Zone or Girdle in the Weaven the Zodiack Yet those which spake more distinctly call the Zodiack a Zone or Girdle in the Heaven whose middle is the very Ecliptick it self or Path of the Sun but the extream parts from both sides of the Ecliptick are distant from it eight degrees by reason that the rest of the Planets have a certain peculiar motion from East to West In which motion they do not describe the Ecliptick it self but paths declining somewhat from the Ecliptick which declination by reason that it exceedeth not 8 degrees therefore they do attribute 16 degrees of Latitude unto the Zodiack viz. Eight from both parts of the Ecliptick so that the Zodiack is that space of the Heaven in which the Planets are always moving neither do they ever move out of it and the Ecliptick is the middle Line of the Zodiack which the Sun passeth through by an Annual motion in which it always keeps its fixed course Moreover the Signs or Constellations of the Heaven through which the Ecliptick and the Zodiack passeth are these March 21.   The Signs of the Zodiack ♈ ♉ ♊ Aries Taurus Gemini June 21.   ♋ ♌ ♠Cancer Leo Virgo September 21.   ♎ ♠♠Libra Scorpius Sagitarius December 21.   ♑ ♒ ♓ Capricorn Aquarius Pisces Moreover the Ecliptick obliquely cutteth the Aequator Ecliptick so that its greatest distance is twenty three degrees and about thirty minutes Where therefore the Ecliptick cutteth the Aequator which he doth in two points in one of these is placed the beginning of the Ecliptick and also the beginning of the accounting of the Sigus In those points the Sun then being in causeth the equality of the days and nights in all places as also the beginning of the Vernal and Autumnal quarters We begin to number from that point in which the Sun makes the beginning of the Spring to us that is we being scituate from the Aequator towards the Pole Artick the first Sign or first twelfth part of the Ecliptick is termed Aries the second Taurus the third Gemini and so forth as aforesaid because about twenty Ages past those Signs of the Heaven were in these very parts of the Ecliptick Every one of these twelve Signs are divided into thirty Degrees for the whole Ecliptick hath three hundred and sixty Degrees which being divided by 12 makes 30. Moreover seeing that the Sun passeth over the whole Ecliptick that is 360 Degrees in 365 days and one fourth part of a day hence we collect that in every day he passeth 59 Minutes and 8 Seconds which is something less than a Degree The Motion of the Sun Now as the Sun in a years time or 12 Months runneth over the whole Ecliptick or 12 Signs of the Zodiack so also in every Month he passeth about one Sign but his entrance into the Sign is not at the beginning of the Months but on the 21th day of every Month and this is according to the Gregorian Kalender and on the 11th day of every Month according to the old Julian Account viz. on the 21th of March he entreth the Sign of Aries or the very Section of the Ecliptick with the Aequator then on the 21th of April he entreth Taurus and so on Now
collect the increase or decrease of the Declination of the Sun from the Aequator or of the Points of the Ecliptick to be the Cause of this unequal increase of the days but in the places of the Aequator it self all days are equal and therefore here is no increase or decrease although the Sun seem to stand about the days of the Solstice that is a little changing the Meridian Altitude Now it is manifest that the greater inequality of this encrease and decrease of the days is to be found where the places are more remote from the Aequator if that the Pole be Elevated for the distance of the divers places from the Aequator and the Arches of the Parallels Elevated above the Horizon be considered in both scituations Proposition XXV In the places of the Torrid Zone or those scituated in the Aequator or in the midst of the Torrid Zone the Sun much sooner departeth from the Vertex than in places near the Tropick of Cancer or Capricorn Of the departure of the Sun in places of the Torrid zone Let any Degree in the Brazen Meridian of the Globe be noted for Example the Fifth Degree from the Aequator and another place in the Torrid Zone being taken for Example one whose Latitude is 18 Degrees Let this be brought to the Meridian make a sign with a Chalk in this and let 5 Degrees from this towards the Tropick be reckoned on the Brazen Meridian and here again make a sign with a Chalk We must shew that the Sun in fewer days is removed from the Vertex of the places of the Aequator 5 Degrees in the Meridies than from the Vertex of another place so many Degrees Let the Globe be turned until some Point of the Ecliptick come under some noted Point of the Meridian near to the Aequator And let the Degrees of the Ecliptick between the first of Aries and Libra and between that Point and the Arches here to be noted Then let the Globe be turned again until some Point of the Ecliptick pass through the Note made in the Meridian for the place and let this Point of the Ecliptick be noted then let the Globe be turned again until another Point of the Ecliptick pass through by that Point removed five Degrees which is noted which must again be noted and let the Arch between the two last Points of the Ecliptick be reckoned which will be found to be much bigger than that which was first noted and thence the Sun shall stay in this Arch more days than in the former and therefore he more slowly recedeth from the Vertex of the second place than from the Vertex of the place taken in the Aequator THE THIRD BOOK OF General Geography TO WIT THE COMPARATIVE PART Of the Affections from Comparing of Places CHAP. XXXI Of the Longitude of a place Definitions 1. _â—HE Circle of the Longitude of any place in the Earth Definition is a Circle passing through that place and both the Poles of the Earth It is also termed the Meridian Circle because the Meridian of a place and the Circle of the Longitude of a place are one and the same Circle But they are only rationally distinguished because the Meridian hath respect to the Motion of the Stars the Circle of the Longitude to the extension of the Earth having no respect to the Celestial Motions But the use of the term Meridian is more frequent and convenient and therefore we shall also use the word They are conspicuous in Globes and Maps passing through every Ten Degrees of the Aequator 2. The distance of a place from a certain Meridian is termed the Longitude of a place or else it is the Arch of the Aequator or Parallel intercepted between the Meridian of that place and a certain other Meridian This Meridian from which the Meridians of other places are reckoned from West towards the East is called the first Meridian The Longitude of the Earth it self is termed its extension from West to East conceived according to the Line of the Aequator The first Meridian in the Maps and Globes is notable above the rest for Magnitude and Colour and it is apparent to the eyes 3. The distance of one place from another is a very short Line intercepted between those two places in the Superficies of the Earth 4. Any Point in the Globe and Maps is truly said to represent and exhibit any place of the Earth if that it hath that Scituation and distance to the other points of the Maps such as the place of the Earth which it ought to represent hath to the other places of the Earth which are represented by the other Points of the Earth Proposition I. Nature hath put no beginning or end to the dimension of the Earth or of the extension from the West to the East or according to the Aequator but all and every one of the places may be taken for a beginning and the first Meridian may be placed in them For the better understanding of this the matter must be more fully searched into No beginning or end of the Dimension of the Earth c. because that some I know not upon what account suppose great mysterias to lâ—e herein that every Superficies as well plane as crooked as a Line â—y one and a Body by three is measured and terminated by two Dimensions or extensions as is evident from Principles of Geometry and common use of which extension one is termed the Longitude of the extension or figure and the other the Latitude and the one is conceived perpendicular to the other Neither do these extensions differ in their nature but that which we take for Longitude may also be taken for Latitude and so on the contrary but yet for the most part if these two extensions be unequal we take the longest for Longitude and the shortest for Latitude But in Ordinate Figures as in the Aequilateral Triangle a Quadrate and the like the two extensions are equal neither is there any difference between Longitude and Latitude For the Figure of the Superficies of the Earth is Spherical and Latitude doth not truly differ from Longitude which we so conceive in it for the more distinct cognition Now those two extensions in the Spherical Superficies are commodiously so conceived as in other crooked Superficies if that first the Periphery of the Semicricle be taken in it drawn from one point to the opposite point and this Line be made one extension of the Superficies then for the other extension you shall take another Periphery cutting the former Periphery in the middle at Right Angles for so Longitude and Latitude are taken in all Figures and this must be conceived to extend about the whole Superficies until it return to it self that so a crooked Superficies may be supposed to be extended into a plane Because therefore the first assumed Periphery or extension is only the Semicircle that shall be the Latitude of the Globe the
of the latitude from one Pole to another is circular Furthermore that the Section of the Earth according to the dimension of the Latitude from one Pole to another A B C D is circular is proved by many Celestial appearances First if this line A B C D any place whatsoever being taken in B some man go forward towards either Pole M or towards the Star near it he observeth by his progresses made equally that he approacheth equally to the Pole But this could not be done unless the line of his Journey B A C D were circular and it is commodiously shewed by the Artificial Terrestrial Globe Secondly because A B C D is the Meridian line into which when the Sun cometh it is midday to us and to all People dwelling in this line A B C experience witnesseth that the Sun in the line A B C doth perpendicularly hang over any place to wit in the Torrid zone for example P and if we take equal spaces equal to B Q Q P we shall perceive that the distance of the Sun from the vertex or top of Q is equal to the excess of the distance of the Sun from the vertex of B above the distance from the vertical point of Q which could by no means be accomplished unless the line B P Q were circular Thirdly the same is the reason of all the Stars which when they come into the Meridian A B C their distances from the vertexes P Q B have the same reason as the distances PQ P B Q P. So when our Mariners sail towards the South the Stars which before were not conspicuous become higher and more manifest to the eye according to the proportion of their sayling Fourthly so if many Stars be taken and the places of the Earth through whose Zenith they pass in one Meridian you shall perceive that the distances of these places have the same proportion among themselves as the distances of the points of the Meridian in which those Stars keep their Noon or full Soâ—th point Now forasmuch as belongeth to the Longitude of the Earth for example E B F C that is also circular and that the Earth hath a spherical tumor or swelling according to this dimension Of the rising and setting of the Stars is proved by that because the Sun and Stars do sooner by a great deal rise to those People which live from us towards the East than to us and do also sooner set to them than to us But to them that dwell from us Westwards contrariwise they rise and set later than to us and indeed according to that proportion of time which the distances of the Meridians of those places have from our Meridian So if two places be taken from ours to wit the distance of one Meridian towards the East 225 miles the distance of the other 450 then we shall find that in this place the Sun riseth two hours sooner than with us but in the other place it riseth but one hour sooner than in ours The Argument becomes more clear if this Theorem be proposed of the Suns coming to the Meridians of divers places Of the rising of the Sun For indeed look what is the account of the distance of places from ours and the same will be observed the account of times which come in between the arrivings to those Meridians and ours or between the Arches of the Equator intercepted between their Meridians and ours which is made evident by the Eclipses for these things are shewed by the Artificial Globe if we ascribe a Spherick form to the Earth but other shapes thereto applied are very absurd So now the Spherical form hath as well been demonstrated as touching the latitude as the longitude of the Earth Other Reasons to prove the Earth Spherical Yea but the Spherical form thereof may also be proved by the only Latitude of the Earth for indeed all divisions of the Earth which are made according to the latitude thereof in divers places are the Peripheries of the places but they pass through the same point of Heaven to wit the Pole of Conversion near adjacent to the Polar Star From these two Reasons we may solidly infer and prove that the figure of the Earth is spherical For it is a Geometrical Theorem which therefore ought to be demonstrated by Geometricians thus if any solid body be cut in many planes it matters not how passing through some one point and all the sections or divisions be performed in the superficies of the periphery of the Circle that body is spherical Other reasons Here cometh another Reason taken from the shadow which the Earth on her averse part to the Sun disperseth to the Moon whereby she suffereth an Eclipse forasmuch as this shadow is conical or like a spire of a Steeple as is declared by the obscuration of the Moon But if we deal rigidly the Arguments taken from the spherical roundness of the Earth from the viewing and consideration of the Earth are these following First Again from the sayling round the Earth because our men of Europe hoisting Sail eight times from Europe with a direct Journey to the West and South even unto the streights of Magellan afterwards to the West and North they returned again from the East into Europe and all those appearances hapned to them which arise from the property of the Globe which surely had not been done if the Earth had not been round And certainly upon the supposition of that figure of the Earth all those Circumnavigations were grounded which therefore had not taken such happy success if the form had been otherwise Secondly Furthermore when either by Sea or Land we take our departure from high Towers and Mountains then the lower parts thereof are absconded from us and by degrees more and more till at last the very tops thereof are quite taken from our sight In the same manner when as for a long distance we come to a Tower or Mountain first the top presenteth it self to our view then the inferiour parts till at last through our nearer distance the foot thereof is seen And this increase of Apparition and Occultation is altogether made according to such a proportion as the spherical tumor or swelling of the Earth is able to make neither can it be explicated by any other figure The Diagram will make the Proposition more clear Thirdly because that the measuring the height of Mountains or great Hills which is grounded upon the hypothesis of the globous form of the Earth is found by experience to agree with a real truth of the thing it self Further Reasons to prove the rotundity of the Earth Furthermore that we may draw together the whole number of these Arguments taken à posteriori into one sum although they might be handled Geometrically but that business would be of great labour and difficulty for it must be demonstrated that this or that different property being put that the line is circular
therefore a round spherical figure is to be assigned to the Earth Because all the appearances as well Celestial as the divers elevation of the Pole the divers altitude of the Sun of that day in divers Countries the reason of the Shadows the difference and increase of the Longest days towards the Pole times of the rising and setting of the Stars c. as Terrestrial as the direction of Navigations the appearing and hiding of Towers and Mountains the distances of Places the Ports Coasts Winds c. are most commodiously declared by that round or spherical form or figure neither can another figure be devised which can perform that as it is manifest by the consideration of divers figures and forms of Bodies And our artificial Terrestrial Globe so justly represents all these things as they are really found to be in the Earth which certainly could not be done if the Earth had any form or figure than that of our artificial Globe And what other form soever you shall chuse there will follow innumerable absurdities For it is manifest that it is not plain by the appearances hither alledged and that it neither can be hollow is clear from this that the Sun and Stars ought first then to appear to the western People than to the Eastern if it were of such a figure as we see the Sun rising first to illuminate the Valleys before it can give light to the averse parts of Mountains CHAP. IV. Concerning the Dimension and Magnitude of the Earth The Opinions of divers Writers concerning the Dimension and Magnitude of the Earth THe Dimension or measuring of the Earth comprehends three principal Heads First the Longitude or length of the Diameter or half Diameter that is of a line from the Superficies to the Center as also of a periphery of the Earth or the Circumference Secondly the magnitude of the Superficies of the whole Earth Thirdly the solidness or corporeal Dimension of the Earth But these things are so contrived together that one of them being known the other two come to our knowledge by Geometrical Instruments because the Earth is a certain Sphere as it is shewed in the second Chapter This property is the most noble and hard to know and hath exercised the most excellent Wits for many Ages insomuch that some Men have written whole Books concerning this matter And therefore I have thought that it would not prove ungrateful to the Students of Geometry if I should fully relate here the History of this Dimension Diogenes Laertius praiseth Anaximander the Milesian the Scholar of Thales Anaximander the Milesian the Scholar of Thales that besides other Astronomical Inventions he first of all others described the circuit or perimeter of both Land and Sea But Anaximander lived about the year 550 before the Birth of Christ The Mathematicians of succeeding Ages seem to have followed his Dimension even until Eratosthenes Aristotle because Authors make mention of none other and therefore I judge that to be the Magnitude assigned by Anaximander which Aristotle hath noted in the end of his second Book de Coelo saying The Mathematicians also which endeavour to measure out the Magnitude of the World report that the Earth is bounded in and girt with four hundred Stadiums By this perimeter it is no difficult matter to assign the half diameter of the Earth according to Anaximander But because we can find nothing noted concerning Anaximanders Invention besides that one place of Diogenes Laertius Eratosthenes his and Eratosthenes his diligence is obscured who next after Anaximander undertook this business with great applause of all men he lived about two hundred years before Christ and as he was most conversant in the rest of the Mathematicks and Dimensions so he is esteemed most accurately to have perfected Gâ—eodaesia or Surveying and this glory is principally ascribed to him But he discovered and delivered The circuit of the Earth that the perimeter or circuit of the Earth is two hundred fifty thousand Stadiums or Furlongs but others two hundred fifty two thousand which Pliny reports to make up three hundred fifteen thousand Roman miles every one of which are thought to be a thousand Paces Eratosthenes had written three Books of Geography Eratosthenes which by reason of the injury of time are now not to be found Strabo Strabo the famous Geographer relateth the Contents and Arguments of each Book Cleomedes and Cleomedes hath noted up his manner which Eratosthenes used for the discovery of the Circuit of the Earth in which what can be wanted we will hereafter declare For indeed Eratosthenes his measuring forth the Earth was by many Mathematicians especially Hipparchus a hundred years after Eratosthenes judged to swerve from the truth although there is nothing written touching Eratosthenes his Dimension or measuring forth the Earth but that he added twenty five thousand stadiums to the perimeter Possidonius But Posidonius being not only a most knowing Astronomer and Practioner but also in every part of Philosophy most expert did next after Eratosthenes enter upon this Doctrine a little before the birth of Christ to wit in the time of Cicero and Pompey This man by his Dimensions found the circumference of the Earth to be two hundred forty thousand stadiums Cleomedes as Cleomedes hath noted but 180000 stadiums Strabo as Strabo hath delivered whereby ariseth a great doubt concerning the cause of this difference between Cleomedes and Strabo his allowance seeing this of Strabo is the truer although uttered in a few words But Cleomedes his assignation of the same is far from truth although he read and expounded Posidonius his Geodesie to many Concerning his size or manner we will speak hereafter But the Dimension of Eratosthenes was used as yet of many even to Ptolomy's time the year 144 after Christ who used a Perimeter of 180000 stadiums and affirmed it to be more agreeable to truth insomuch that this very Invention was by Theon ascribed to him Theon It is gathered that Marinus a famous Geographer Marinus and by whose Writings Ptolomy was much aided did attempt something in this business as appeared by his Geographical Writings of the same Ptolomy After these times when as the study and prosecution of the Sciences by little and little vanished away in Greece nothing was done in this business neither did the Romans undertake any thing herein But the Arabians and Sarazons having obtained the Empire or glory of other Arts from the Grecians to themselves so likewise they left not this part of the Mathematicks untouched Forasmuch as Snellius relates out of Abelfedea an Arabian Geographer who flourished about the year of Christ 1300 and whose Writings were printed at Rome about the 800 year of the Christian Account Maimon Ring of Arabia studious in Geography in whose days it flourished Maimon King of the Arabians or the Calife of Babylon being studious in the Mathematicks forasmuch as he
commanded the great construction of Ptolomy to be turned out of Greek into the Arabian Language which is called by the Arabians the Almagest of Ptolomy This Maimon I say having assembled together certain skilful Mathematicians commanded them that they should search after the Perimeter of the Earth To perform which task they chose the Fields of Mesopotamia and they under the same Meridian proceeding from the North to South until the Elevation of the Pole had decreased one degree found after an even level that the space or Journey was fifty six or fifty six and a half from whence it is found that the Perimeter according to them â—is twenty thousand and sixty or twenty thousand three hundred and forty Miles From that time even to our Age no man hath assayed this but many Arabians have used this dimension of their own Mathematicians The dimension of the Earth by the Latins But the Latines when they began to handle Astronomy used that of 18000 Stadiums which Ptolomy had used which makes 324000 Italian miles or 5400 German miles for 15 German or 60 Italian miles are allotted to one degree when as there ought to have been assigned thereto 15 and â— 8 because about 38 Stadiums are given to one German mile and so the Perimeter should be 5625 German miles But about thirty years ago Snellius a famous Mathematician It s dimension according to Snellius Professor of Leyden observed that usual Perimeter of the Earth or the magnitude of one degree defined in 15 miles to depend on no ceâ—tain demonstration but to be uncertain therefore with very great industry he set upon this dimension and happily finished it demonstrating the magnitude of one degree in the Earth to be 28500 Perches or Poles every one of which contain 12 Rhindlandish feet or 19 Dutch miles and the whole Perimeter to be 8640 miles But he defines a mile with 1500 Poles or 18000 Rhindlandish feet We will now speak concerning the manner of measuring the Earth But indeed this Invention depends on the Figure of the Earth which in the foregoing Chapter we have proved to be Spherical For indeed we conceive the Earth to be cut by a Plain passing through the Center This Section or Division maketh the greatest Circle of the Earth For a Sphere being cut in any manner the Section is made a Circle but if it be cut through the Center it shall be the greatest Circle and therefore the Periphery of this Circle in the Superficies of the Earth shall be the Circumference Circuit and Perimeter of the Earth And this work of measuring beginneth from the magnitude of this Periphery The Circumference of the Sphere divided into 360 degrees because therefore this Periphery or Circumference as others are is divided in the mind into three hundred and sixty degrees as hath been said in the second Chap. but indeed we cannot perform the magnitude of the whole Periphery and therefore the Problem is thither reduced that we may find out the magnitude of one degree or other part in the known measure For example the magnitude of half a degree the necessity of which also meets in other Problems And we take the Periphery of the Earth for the most part to be that of the Meridian Circle because this is more easily and with less occasion of errour determined by our own place and by the North or Polar Star or other means which we will declare in the Three and twentieth Chapter The first mean or way which the Arabians and other Mathematicians have used Let the Horizon therefore of our Terrestrial Meridian which lieth just under the Celestial a bed and is concentrical thereto be H h R ss let the Periphery A B C D R the Center of the Earth our place B the Vertex See Scheme or supreamest point over our heads the Pole of the Earth A lying under the Celestial the Elevation of the Pole above the Horizon shall be A H a h Let us now take another place in the same Meridian A B C D or G lying under the same a b c d the Vertex g the Horizon f F R t T. Let here now the Elevation of the Pole be exactly observed in the place B viz. a h or a H also of the place G to wit f a or F A and let F A be taken away from H A and the remainder is H F to which the Arch B G intercepted between the places is equal After that the interval or space between B G must be measured accurately in a certain measure For example how many Perches or Poles it may contain or how many miles For these shall be correspondent to the Arch B G. And by the Golden Rule as B G is to A B G c d the 360 degrees so the space or interval found out or the Perches or Miles are to the Perches or Miles of the whole Perimeter A B G C D or as the Arch B G is to one degree so the Perches or Miles found are to the Perches or Miles which are due to one degree Note if your pleasure be not to measure the interval B G thus but to follow the vulgar determination then according to that way the quantity must be determined As for example that to 1 degree 15 such miles answer as between B G may be 10 c. Elevation of the Pole at London Example B London where the Elevation of the Pole A H a h is 51 degrees 32 minutes Let G be Hartford lying under the same Meridian with London the Elevation of whose Pole a f a f is 51 degrees 54 minutes therefore f h or B G is 29 minutes But the distance between London and Hartford is 20 English miles or 13875 Rhinlandish Perches of 12 foot therefore as 29 minutes are to 60 minutes so 9 ¼ to 19 Holland miles therefore 19 Holland miles make one degree in the circumference of the Earth Or the interval B G is accounted to be 7 ¼ German miles a German mile being reckoned to be 1900 Rhinlandish Perches therefore let it be wrought thus as 29 parts are to 60 The Elevation of the Pole at Prague so is 7 ¼ to 15 such German miles So at Prague the Elevation of the Pole is 50 degrees and 6 minutes at Lincium it is 48 degrees and 16 minutes the difference of B G shall be one degree and 50 minutes and it is thought to be distant 26 German miles therefore the Perimeter was 5105 miles and the whole Circuit of the Earth is 5400 miles The second manner of Eratosthenes Eratosthenes's manner used about the dimension and magnitude of the Earth See Scheme Let there again be two places of the Earth in the same Meridian let B be the City Alexandria in Egypt let G be Syene another City of Egypt under the Tropick of Cancer let now the same places in one and the same day in the full southing of the Sun when he comes into the Meridian line
a b c d the distance from the Verticles b g be observed by a Quadrant Let at Alexandria in the day of the Solstice 21 of June g f or G F be observed 1 50 of the Periphery or 7 degrees 12 minutes but in Syene let there be no distance the Sun hangeth perpendicularly over their heads therefore B G shall be the Arch intercepted between those two places And because the distance put is 5000 Stadiums therefore according to the Golden Rule it shall be as 7 degrees 12 parts to one degree or as 1 50 to 1 360 or as 5 to 36 so 5000 to 694 4 9 Stadiums which are requisite for one degree or as 1 50 is to 50 or as 1 to 50 so 5000 to 250000 Stadiums of the whole Periphery A B C D according to this measure Yet seeing there are divers ways to take the Meridian Altitude of the Sun and the distance from the Vertical point g b Eratosthenes wrought it by a hollow Spherical Scioterick or Sundial which they called Scaphe where the Style B x sheweth the Vertex o x z but the Radius or beam of the Sun terminaitng the shadow of the Style or Pin marks out B z how much the distance of the Sun o b from the Vertex 7 degrees 12 firsts at Alexandria But in the City Syene the Style G x makes no shadow that day because o the Sun hangeth perpendicularly over it and therefore there is no distance of the Sun then because therefore the Angle B x z is equal to the Angle b x o whose measure is B o or B z there B o is equal to B z 7 degrees 12 first minutes or 1 50 of the Periphery The other things are performed as it hath been said The third manner of Posidonius Posidonius's manner used about the magnitude c. of the Earth Let two places B G be under the same Meridian Posidonius took B Rhodes and G the City Alexandria in Egypt let the Altitude of some Star in these two places when it cometh into the Meridian above the Horizon and that in the same day or in divers days which matters not at all Posidonius took the shining Star Canobus which is of the first magnitude in Argonavi See Scheme but this Star did not rise above the Horizon of Rhodes h H S but did only touch the Horizon in S yet it was elevated above the Horizon of Alexandria F R t in the Arch t S 1 48 part of the whole Periphery or 7 degrees 30 minutes Therefore the distance of the Arch T s that is B G shall be 7 degrees 30 minutes unto 1 degree or as 1 48 part unto 1 360 that is as 1 to 48 so 5000 to 240000 Stadiums of the whole Perimeter of the Earth according to these Hypotheses of Posidonius The fourth manner or way of Snellius Snellius's way about the dimension and magnitude of the Earth Because in the former ways we have taken two places B G lying under the same Meridian and yet the places fit for this business may lye under divers Meridians therefore we thought it requisite that an example and that of Snellius should be also concerning this case here proposed Let therefore A B C D be the Meridian of Alcmaria B Alcmaria it self the Elevation of the Pole h a 52 degrees 40 ½ minutes the distance from the Pole B A 37 degrees 19 minutes 30 seconds See Scheme Let the other place be P Bergenapsome the Meridian A P V V the distance from the Pole that is the Complement of the Elevation 51 degrees 29 minutes A P is 38 degrees 31 minutes therefore P G a Perpendicular Line being drawn to A B G the difference of the distances from the Pole is B G 71 minutes 30 seconds or 1 degree 11 minutes 30 seconds Moreover Snellius by a laborious Geodesie or Earth-meeting found the distance of Alcmaria from Bergen B P to be 34710 Rhindlandish Perches and the Angle of Position P B G to be 11 degrees 26 minutes 2 seconds Therefore in the Triangle strait angled P B G the Hypotenuse B P and the Angle B P G is given therefore by the Problem of the second Chapter B G is found 34018 for which Snellius takes 33930 for he detracts 88 Perches from the Stations of the Elevations of the Pole But the Arch B G 71 ½ scruples is the difference of the Elevation of the Pole therefore as 71 ½ minutes is to 1 degree or 60 minutes so is 33930 or 34018 to 28473 Perches for one degree or according to the round number 28500 or 19 Holland miles They which understand Spherical Trigonometry from the given A B A P the Angle A B P may find the Arch B P to be 1 degree 14 minutes which when they are equal with 34710 Perches 1 degree shall be equal to the Perches or of 18 miles and ⅘ But the cause that this number differeth from that of Snellius is first that Snellius did not take the very points of the Towers B P by which he obtained the Angle G B P for the knowing the Elevations of the Pole but he took the places a little distant from them See Snellius in page 197. Notwithstanding no man can doubt but the same may be found to be the Altitude of the Pole The other cause is that he taketh the Lines B G B P P G as strait which nevertheless are not strait although this discord may seem to make little or no difference of any moment But let Snellius his quantity of a degree of 28500 Perches be taken mine of 28300 Perches his makes 19 147 150 miles mine 18 ⅘ miles the Perimeter or Circuit according to Snellius shall be 10260000 Perches 123120000 feet or 8640 Holland miles The fifth manner being the first Terrestrial way of measuring the Earth The first Terrestrial way for the finding out the magnitude c. of the Earth The three following manners or ways are Terrestrial performing the work without the Heaven or Meridian Line Let B P be the Altitude of the Tower this is to be sought out in a Land-measuring way then let P s be the distance of the most remote term from whence the Tower may be seen And although P s be not a strait Line yet because it is the least part of the Periphery of the whole Earth therefore it is taken for a strait line and the Triangle strait angled B P s in which by the given B P P s the Angle B s P is found to whom B R s is equal whose measure is the Arch S P. Therefore as this Arch is to one degree so P s the found distance See Scheme is to the quantity of one degree As for Example let B P the Altitude be 480 Paces and let the distance P s of the point s which endeth the Sight be 40000 Paces or 10 German miles therefore let it be wrought according to the Problem of the second Chapter As
of the same day after the Sun and in the morning before the Sun may be seen I forbear to bring hither any more appearances but they are the principal from which I think an Argument of greatest moment may be fetcht for this Motion of the Earth when as by this Motion of the Earth they may be so commodiously declared that it should rather be admired if the Earth could not be moved by such evident appearances These are the easier Arguments by which the Copernicans would evince the motion of the Earth which although they be not demonstrative yet they make this hypothesis more probable than that which determines the Heaven to be moved for one of them must needs be admitted The Reasons of â—ome against the moving of the Earth as the Ptolomaians But these Reasons which some men to wit the Ptolomaians alledge to the contrary are easily dissolved which are these First that the Earth is unfitting for motions by reason of its ponderosity Secondly that the parts of the Earth are naturally moved with a strait motion to the Center therefore a circular motion is contrary to the nature thereof Thirdly if the Earth should be moved a stone cast down from a Tower could not fall to the foot thereof Fourthly a bullet shot out of a piece of Ordnance towards the East at some mark it could not come home to it or hit it if the mark with the whole Earth were moved towards the East or at least the hitting the mark should be more swift than if the bullet were shot towards the East Fifthly neither the Towers nor buildings could stand stedfast but would fall by reason of that motion of the Earth neither could men be without giidiness by reason of the whirling about of the Earth Sixthly because we see that the Stars change their place but not the Earth Seventhly because the Earth is in the Center of the World but the Center is not moved Eightly because the holy Scriptures do confirm the stability or stedfastness of the Earth The aforesaid Reasons of the Ptolomaians answered by the Copernicans Yet indeed the Copernicans to these Arguments use to answer after this manner To the first they Answer denying the whole Earth to be heavy for ponderosity is a tendency of the parts to their whole homogeneous of the same kind and such a heaviness is also discovered in the parts of the Sun and Moon and yet notwithstanding neither the Sun nor Moon is said to be heavy To the second they Answer That that right motion of the parts of the Earth not of the whole Earth and the circular motion thereof doth not hinder the strait carrying of those parts which is evidenced by the parts of the Sun and Moon To the third Argument they reply in a threefold manner First that such heavy things are not primarily carried to the Center of the Earth and therefore are born by a very short line to the superficies thereof as Iron tendeth not to the Center of the Loadstone but to the Loadstone Secondly the whole Air cleaveth to the Earth and is moved together with her therefore all such heavy things being thrown together downwards get this circular motion and are moved as it were in a Vessel And Thirdly The Opinion of Gassendus therein Gassendus by frequent experience hath demonstrated that if any thing be cast from a moved body that which is so cast is also moved with that motion of the moved body as for example a stone thrown down from the top of the Mast of a Ship moved most swiftly is nevertheless not left by the Ship but falls down to the foot of the Mast and from the foot of the Mast a bullet being shot perpendicularly out of a hand-Gun falleth again perpendicularly therefore the alledged Objection is nothing worth To the fourth Reason they answer in the same manner as unto the third To the fifth they say That some such thing hath no place because the motion is equal neither doth it dash against another body and the buildings as it were heavy bodies and homogeneous or of like to the Earth are moved as in a Ship for we find in a Ship moved very swiftly or slowly the bodies set upright therein are not overthrown yea Cups and pots full of Wine or other liquor shed nothing thereof at all To the sixth we say That the change of the Stars place is not perceived but we find the change of their situation in respect of our selves but this mutation of position may be observed and be whether we be moved with the Earth or the Stars be moved we being stedfast or also both we and the Stars In the seventh Objection both the major and minor proposition is false or at least doubtful To the eighth they reply First that the holy Scripiure in physical or natural things doth speak according to appearances and the capacity of the Vulgar for example when the Moon with the Sun is called a great light because it was created to give light to the Night Of the Moon whenas indeed the Moon is not great in respect of the Stars and Earth neither hath she any light of her own proper nature nor doth she give light in all Nights to the Earth So the Scripture saith Of the Sun that the Sun goeth to the extreamest part of the Earth and that he returneth to that end again when as notwithstanding there is no such end or furthermost part So in the book of Job a plane and square figure is attributed to the Earth under whom Pillars are set upon which it leaneth which indeed must not at all be so understood as the very Vulgar well know There might more places be alledged hither but these are sufficient For the holy Scriptures were not given to us thereby to play the Philosophers but to practice Piety Secondly certain places of Scripture are wont to be alledged which speak not concerning the immobility thereof but concerning its constancy and durance as that place which we have brought hither out of Job Thus have we briefly declared of what sort the motion may be which the Copernicans ascribe to the Earth of which a more exquisite explication is usually given in Astronomy But that being supposed all those things are to be applied to the Earth which are wont to be considered in a Globe turned round about Of the Axil Poles Periphery Parallels c. of the Globe to wit the Axil about which it is turned is one of the Diameters the Poles are the extremities or two points which are not moved the greater circle or periphery according to which the circumrotation or wheeling about is made and its parallels Now let us see concerning the swiftness of that motion The first motion by which the Earth is turned round about his Axil cannot be seen and considered in the whole Earth at once Of the motion of the Earth its difference swiftness c. but in divers
not a long distance from the shoars which subsidency or sinking continued for many Ages at length caused Isles therefore in the middle of the Ocean are few Islands 1. Because that place is more remote from the shoar than that any of the eaten off parts should be carried thither 2. Because that the commotion and force of the water is greater there which moveth the earth of the Channel or rather promoteth the depth than suffereth Islands to be generated there 3. Because there are no Continents there therefore neither can troops or heaps of Islands be according to the first mode by which we have shewed such heaps of Isles to be produced yet in times past when that the middle of the Ocean was not where 't is now it is not unlikely that such Isles were here and by degrees were swallowed by the Ocean OF Absolute Geography SECT V. Containing an explication of the Atmosphere and the Winds In three Chapters CHAP. XIX Of the Atmosphere and Air. Proposition I. From the parts of the Earth as well dry as moist or from the Earth and Water vapours and fumes do continually exhale into that space which is about the Earth THE Cause is twofold first the Celestial heat of the Stars especially the Sun and Moon Of vapours and fumes The other is a Terrestrial heat or subterranean or rather terrestrial fire or which is admixed with the parts of the earth For we see that almost all bodies the least fire being moved towards them send forth a fume Seeing therefore that both the Celestial and Terrestrial heat is naught else but a certain fire therefore it is also necessary that vapours and fumes should be advanced by it from the parts of the earth So the truth of the Proposition is evidenced à priori Experience also confirmeth the same For those that travel in the night time especially when the Moon shineth and that towards the water discover many vapours to wander and be advanced about the Superficies of the earth Also it is vulgarly known that in the day the Sun doth raise many vapours also when that a mist ariseth upwards which is a certain token of rain to follow Proposition II. The Atmosphere is a space about the whole earth in which the exhalations raised from the earth are always present And it is uncertain whether that anything or body else be contained in it besides these exhalations It is also taken for the exhalations themselves about the whole earth There is no small controversie amongst modern Philosophers Of the Atmosphere concerning the body which consisteth about the earth For many Mathematicians of sound knowledge determine that there is nothing besides exhalations elevated from the earth and therefore they take the Atmosphere and Air for one and the same and immediately after the Atmosphere place the Aetherial substance But other Philosophers suppose that besides these exhalations in the space about the earth that there is a certain peculiar and simple body which they call Air although that they freely grant that exhalations may be changed into Air and contrariwise into clouds and thick vapours The same Persons after this Air even to the Lunary Orb place another subtile thin body different from the Aether which indeed they tearm Fire but they confess that it is less properly done and that it doth not agree with our fire for it is a calid substance not burning dry and very subtile not to cause the refractions of the rayes of the Sun and Stars which yet they will have to be done in this Air. Those being well considered these two opinions of the Philosophers seem rather to differ in words than in matter it self For as for the Air because that they grant it so gross that a refraction of rayes may be made in it and that it may be generated from exhalations by a light mutation the Air seemeth nothing else but a subtile exhalation although it was not exhaled from the earth As for the Sublunary Fire when that they confess that it is so improperly tearmed but they affirm that it is so tenuous that it causeth no refraction of rayes this seemeth little to differ from the Aether We affirm therefore that the Atmostphere and Air are a body about the earth on which the rayes falling are refracted laying aside the controversie whence this body hath its original which definition agreeth with the former For neither is it likely that any exhalations can be elevated from the earth so subtile that they should cause no refraction or impediment to the luminous rayes proceeding from the Aether yet if that such be granted we cannot know their Altitude and whether that they be excluded from the Atmosphere which yet if that any one will sharply urge supposing that the little fires or rayes cast from the Sun on the earth again recoil to the Sun he will not deny but that the latter definition is commodious Therefore the Atmosphere and Air are naught else but a contexture of many small bodies which adhere to the earth as a down or wool circumvesteth a Peach Proposition III. Sometimes more sometimes lesser exhalations are drawn from the earth especially in divers places Of exhalations The cause is 1. The various elevation of the Sun above the Horizon or depression beneath it 2. The diversity of the age of the Moon and its elevation above the Horizon 3. The rising and setting of the other Stars and their constitution above the Horizon 4. The diversity in the parts of the earth them selves for watery and humid places do more easily send forth vapours than earthy and dry Proposition IV. The exhalations which constitute the Atmosphere are of a divers kind especially in sundry Regions viz. watery saltish earthy sulphureous spirituous The sensible compounded exhalations or parts of the Atmosphere are divers viz. mixed of simple particles Of the exhalations which constitute the Atmosphere The cause is because that in the parts of the earth such bodies are of a divers sort and are advanced by heat some more easily and other some with greater difficulty Concerning the earthy particles some one may doubt because that those are scarcely apt to be elevated 1. By reason of the smalness of their dusts which are light seeing that gravity is an affection of compacted bodies 2. By admixture of sulphureous particles which violently carry those earthy ones with them Moreover that there are sulphureous particles in the Air is proved from the fiery Meteors Lightnings Thunder and the like yea a sulphureous odor or scent after Thunder and Lightning manifestly asserteth the same As for the watery parts we ought not to question for saline and spirituous exhalations by reason of their tenuousness are easily exhaled from the earth Little Animals generated in great number and abundance in the Air confirm the same The Aristotelians divide exhalations into two kinds to wit vapours and fumes Vapours are generated of water and easily return into the same again Fumes
Air F H being rarified now requireth more space Now you will find the degrees of accretion and diminution of the heat and cold if that you divide the Line F A on the Table into certain parts of numbers Or without putting a Vessel under set the Glass L H even at the extremity L have a Globe with a little hole from the side and let this Globular Vessel be filled with Air for so also the degrees of heat will be shewed by the ascent and descent of the water Proposition X. The serene Air may be carried so by a most vehement fire that it may occupy a space 70 times greater than it did before On the contrary it may be so condensed in a Wind-gun that it may only possess a 60 part of the former space but the heat of the Sun bringeth not so great a rarification or the cold so great a condensation to the Air The same is proved from that that if you take an Aeolopile and heat it with fire so that it may then contain 13 ounces but the same being cold and returning to its former natural estate it will contain 13 ounces a dram and a half Therefore the space that the Air occupied whilst that it was hot is greater than the space that the Air possessed when refrigerated that the difference of the space is that part of the Aeolopile that receiveth half a dram of water if that the whole receiveth 13 ounces with half a dram and the part of this Aeolopile is almost the 70 part of the whole space in the Aeolopile therefore the Air being hot hath possessed a space 70 times greater than it doth when it returneth to its natural estate Proposition XI Why in the places in the Frigid Zone at the time in which the Sun ariseth not altogether unto them on some days the Air is clear and serene and for the most part cloudy and foggy Of the Air in places of the Frigid Zone I answer the cause of this gross and almost perpetual Mist or Fogg is the small heat of the subterraneous Earth it self or else it is derived from the Sun and likewise the Moon which in the time of the obscurity of the Sun remaineth many days and nights continually above the Horizon the other Stars which heat because it is weak cannot dissipate this Mist Now that some days or nights afford a serenity of the Air this happeneth not because the thick vapours are attenuated but because that they either sink down into the earth or else are forced into other places by the winds Proposition XII Why oftentimes in the greatest cold of the Winter the Air is yet subtile and serene when that yet the cold condensateth and contracteth the Air The Air subtile and serene in the greatest cold of the Winter Cold is twofold Moderate or Extream Moderate cold rendereth not the Air serene but cloudy by reason that vapours are elevated but not discussed by that little heat which is mixed or adjoyned to that cold But an extream cold maketh the Air serene for a twofold reason 1. Because it rendereth the grosser vapours of the Air more gross and so causeth them to fall and make the Air more subtile 2. Because that the pores of the earth are shut and bound up and the vapours themselves cannot exhale and render the Air turbid The Sea it self indeed is not bound up with Ice yet the particles are so condensated with Ice that it is not so apt for exhalations although it sendeth forth many for the condition of it and the earth are different Proposition XIII Why the Air being beheld at the Horizontal Line appeareth more thick and cloudy than that in which we are The cause is twofold 1. Because that the Air about the Horizon is indeed more cloudy The other is a fallacy or deception of the sight or judgment from our sight for the eye apprehendeth the distances of columns placed in a long order and series and therefore as the judgment supposeth the remote columns to be conjoyned so also it apprehendeth not the distances of the particles of the Horizontal Air but imagineth them conjoyned but the eye beholdeth the distances of the elevated Air under greater Angles and therefore better apprehendeth it The same is the reason why the Air which appeareth cloudy to us removed from it when we come to it or are in it seemeth less misty or cloudy Proposition XIV Whether that the Altitude of the Atmosphere or Air above the Earth be the same in all places at one and the same time and whether its figure be spherical Of the Altitude of the Atmosphere That the Altitude is not the same but divers in sundry places seemeth to follow from thence that the Sun is only Vertical to one place at one time and it sendeth forth oblique rayes and therefore more weak unto other places by how much the place is more remote from the Sun and nearer to the Poles therefore the pores of the rayes of the Sun are very different to the elevating of the vapours and therefore they are raised to different Altitudes to wit in a place unto which the Sun is vertical his Altitude is the greatest in the opposite place the lesser in the places about the Pole moderate so that the Air receiveth an oval figure But the contrary is more probable viz. that the Altitude of the Atmosphere is the same in all places for although that the Vapours and Air be more elevated in some places than in others yet because that the Air is fluid and tendeth by its gravity to the Center of the earth therefore the more elevated part of the Air presseth down the Air placed under it and this thrusteth down another more depressed until all the parts acquire the same Altitude And after the same mode the Spherical Figure of the Air shall be demonstrated as in the thirteenth Chapter we have proved with Archimedes concerning the water by reason that the same Hypotheses are prevalent here which we there assumed to wit that the part of the Air less pressed is expelled by that which is more pressed for every part is pressed by the Air that is above it wherefore the Figure of the Air is spherical not oval as some will have it but if the forementioned Hypotheses be not granted the demonstration falleth Des Cartes also maketh the Air oval in figure for a peculiar reason see Chapter fourteen Proposition XV. Condensation or Rarefaction of Air changeth not its Altitude Condensation of Air changeth not its Altitude Because that the whole Atmosphere is not condensed but only some parts and at all times some parts are condensed sometimes these sometimes those wherefore the condensation or rarefaction of one time doth no more alterare the Air than the condensation or rarefaction of the first time There only seemeth to be a difference that at one time there may be a greater condensation or rarefaction than at another but this
either more thick or subtle than the former they are refracted where they have entered at this other Medium or deflect from a strait direct course to the sides The Explication is easie from a Vulgar Experiment Let any Vessel be taken and let a ball of Gold or Copper or Gold money be affixed to the bottom then depart back from the Vessel by reason of the obstacle of the sides of the Vessel you can no longer see the Money at the bottom Then pour water into the Vessel which being done you shall see again in the former distance the Money at the bottom From hence it followeth that seeing no Ray could directly come from the Money to the eye by reason of the interposition of the sides of the Vessel and yet afterwards the water being infused the Rays arrived at the eye It followeth I say from hence that the Rays proceeding from the Money where they enter into the Air from the water do deflect or are refracted from the direct way and being so refracted they arrive at the eye It is called refraction by reason that for this cause an Oar being partly in the water doth appear refracted or broken See Scheme So let the Center of the Earth be T L the eye in the superficies let d r f p be the superficies of the Atmosphere or Air. Therefore no ray can directly arrive at the eye L because it is beneath L f g for other inferiour rays would fall in on the tumor of the Earth L o. Wherefore no Star can appear in a direct ray until it come to the Horizontal line L f g And the Stars appear before viz. whilst that they are yet beneath L g for Example in S and yet from S to the eye L no ray can directly come because that it should first fall on L o. Therefore of necessity the ray which cometh from the Star S to the eye L is not a direct but a refracted ray viz. L f which refracted ray is propogated from the incident ray S f to wit S f falling from the Aether on the more thick Medium viz. the Atmosphere in f is refracted and becometh f L when that it was direct in n And so the Star appeareth before that it could truly appear by a direct ray that is before that it arriveth at the Horizontal line L f g. So a Star being in S is not seen by the direct ray S L but by the refract r L whose incident ray is s r and direct r m and therefore the Star S appeareth higher by reason of refraction than it is and in another place it appeareth high in the Arch x g or in the Angle r l g as if it were in x when indeed it is in s For this is the nature of refractions that the rays falling from a more rarified medium on a more thick as from the Aether upon the Air they become refracted or decline towards the perpendicular drawn through the point of incidency or falling into the superficies of the incidency or medium For Example the ray S f falleth in from the Aether on the Air f is the point of the incidency T f the perpendicular drawn through f to the superficies d r f p therefore the ray S f n shall be refracted f T that of f n may be made f L. So of r m is made r L but the contrary is when that the rays proceed from the water to the Air for then they more recede from the perpendicular line drawn Lastly this also is the nature of refractions that the rays falling in perpendicularly on the superficies of another medium are not refracted but only those that fall obliquely and not perpendicularly and by so much they are the more refracted by how much they fall in the less perpendicularly or by how much the more they depart from the perpendicular So the rays S T f T H d T are not refracted because that they are perpendicular on the superficies d r f p but the rays S f S r are refracted because that they fall obliquely and indeed S f more than S r. From whence it followeth which Experience also testifieth that by how much the Stars are more near the Horizon by so much the more they refract their rays by how much the higher by so much the less And Astronomers have observed that the refraction is insensible where the Star hath attained the altitude of 20 degrees not that there is no refraction but that it is very small And for many Examples the skilful in the Opticks and later Mathematicians have derived the Rule of refraction of all Rays falling in obliquely viz. that in every medium there is one constant account between the sign of the Angle falling in and the sign of the Angle refracted to wit the Angle n f T is termed the Angle of incidency L f T the Angle refracted n f L the Angle of refraction and so in the refraction of the ray s r m. Therefore as the sign of the Angle T f n is to the sign of the Angle T f L the same is the reason of the sign of the Angle T r m to the sign of the Angle T r L. Thence it followeth that if from observation we have the quantity of refraction to the elevation of one Ray we may thence know the quantity of the refraction of all others howsoever elevated Proposition XXII The Atmosphere or Air causeth the Sun or the rest of the Stars to be seen before that they arise in the Horizon also to appear for some small space of time after that they have set also that they appear higher than they are and in another place of the Heavens as long as that they are no higher than 20 degrees The Air causeth the Sun and Stars to be seen before they arise in the Horizon We have sufficiently explained the Cause in the precedent Proposition only we shall add some Experiences or Natural Phaenomenons When that the Dutch wintered in Nova Zembla the Sun appeared to them sooner by sixteen days than it was in the Horizon that is when that it was as yet depressed beneath the Horizon about four degrees and that in a serene Air. And famous Astronomers have found it out with Tycho Brahe that in our places the Morning-sky or Air being serene we may behold the Sun elevated above the Horizon 34 minutes when that as yet he is wholy under the Horizon yet so that his limbus or skirt doth enlighten the Horizon And the Sun seemeth to arise when that as yet he is depressed about 34 minutes beneath the Horizon to wit the Air of the place where we are being serene So the Spica Virginis a bright Star seemeth to rise to us when that yet he is depressed 32 minutes beneath the Horizon which is thence collected because is seemeth to arise when the Cauda Leonis is 34 degrees 30 minutes high and in the same quarter in which this Star of the
the other places for when that he is more depressed beneath the Horizon and therefore ascendeth more obliquely and in a longer time to the Horizon of those places thence it followeth that he is seen far sooner before his rising in the Frigid Zone than in the Torrid But it is a question whether that the Air be lower in the Frigid Zone and though the Sun appeareth sooner before his rising whether that only a thickness of Air is sufficient of which more afterwards Proposition XXVIII Of the thickness of the Air. If that the Air of one place be of a more thickness and than the other it may be an excess of thickness so that they may not see the Stars before the rising in so great a depression beneath the Horizon than in the other Air also the excess of thickness may be such that the Stars may begin to be beheld in the same depression Lastly the excess of thickness may be such that the Stars may be beheld in aâ—ar distanter or longer depression beneath the Horizon than in the other Air. Yea this thickness may bring with it a far greater depression than the lowness of the Air and instead of refractions in Nova Zembla a notable altitude of the Air with thickness is required Proposition XXIX It cannot be that the refractions of any one Star in two Altitudes in one Air should be equal to the refractions of the same Star in the same Altitudes in another Air that is higher or lower or thicker or more subtile In the former Proposition we have demonstrated that if in the altitude of the Air T f See Scheme the incident ray S f n maketh the refraction n f L viz. T 4 the ray S 4 in another altitude which is parallel with S f by reason of its great distance and the rays are from one point make the same refraction 34 L which is equal to the refraction n c L viz. if that the Air 40 L W be less thick than f o L d. Now therefore it is demanded whether that this may be done in the two altitudes of the Star For Example It being supposed that in the scituation of the Star S the Air f o L d and the Air f o L W are so that they cause an equal refraction whether that in the altitude of another Star for Example in S in the same Atmospheres f r d L o 4 W L o can again be an equal refraction or the same m c L. And I say that it cannot be for let the Periphery of this Air T 4 be described in the Center T the interval of another Altitude cutting L r in 3. Therefore 3 L shall be the ray refracted in this other Air through which the Star S is seen for the ray 3 L is the same with r L by reason that the same apparent altitude x g or Angle r L f of the Star S is laid down Moreover for this refracted Angle let the incident ray be drawn through 3 73 W which shall be parallel with S r m if that the refraction L 3 W were equal to the refraction L r m for let T 3 be also drawn the Angle T 3 W shall be the Angle of incidency T r L the Angle refracted W 3 L the refraction Therefore as the sign 34 T is to the sign L 4 T so is the sign W 3 T to the sign L 3 T. And as the sign n f T is to the sign L f Y so is the sign m r T to the sign L r T. And now 34 L is equal to n f L wherefore W 3 L is not equal to m r L or W 3 is not parallel with m r. Now this consequence requireth a more difficult and operose Demonstration than can be propounded in this place seeing that it rather belongeth to Geometry yet it shall be made manifest from the Analysis of the following Proposition Proposition XXX The two refractions of any Star being observed in two Altitudes to find thence both the altitude of the Air and the thickness of the Air in respect of the Aether or the rule of Refraction in this Air. Of refractions of Stars The refraction of a Star is of an equal difference between his observed Altitude and the true one which is known by calculation and therefore it is easie to know the refractions of the Stars Now to come to the purpose let the refraction n f L of a Star in S and ejaculating his ray S f be given then again in the altitude of the same S g the same refraction m r L. Then in the Circle d r f p d whose Center is T. T L is given the Semidiameter of the Earth and T r T f L f L r being drawn let the Angles T L f T L r be given compounded of the Altitude of the Star and 90 minutes and the Angles n f L m r L are given and we know besides that the same is the account of the sign of the Angle n f T to the sign L f T which is the account of the sign m r T to the sign L r T. From these we must find the Semidiameter of the Circle T f or T r and moreover the account or equality of the sign n f T to the sign L f T or we must find out the Angle T f L. Indeed the Analysis doth teach that it may be found out but by a most difficult Solution so that the Synthesis or collection cannot be found out without many Propositions premised like so many Indexes which are altogether improper to this place Yet we will produce the Analysis both that we may shew this Problem to be determinated and also that the truth of the preceding Proposition may also be confirmed Let T L be f The sign of the right Angle T L f S. b The sign T L r S. c The sign n f L S. d The sign of the Complement S. g. The sign m r L S. h The sign of the Complement K. The sign L f T S. a Let us seek the Angle L f T because that after we have gained this also T f and the rest will be known Therefore it is in the Triangle f L T. As the sign L f T is to the sign T L f so T L is to T f. As a to b so is f to And because that the sign of both the Angles T f L L f n is given the sign also of the whole Angle n f T shall be given viz. if that the signs of both Angles be multiplied alternately unto the sign of the Complement of the other and the aggregate of the produced be divided by the ray b therefore the sign of the Angle n f T is Then in the Triangle T L r are now known T r T L the sign T L r. Therefore as T r is to T L so is the sign T L r to the sign Y r L. As is to f so is c to for the sign T
Sea and the like is in Guzurat but for very many Months when it beginneth to blow in Congo and Guzurat in September it continueth even to March The Anniversary wind of the Grecians which they call Ornithia or the Bridges wind this they say bloweth after the Vernal Aequinox the Sun ascending to the Vertex of the Europeans Proposition V. Why the Etesian winds blow not in Italy France Germany Persia and other Regions especially seeing that they are more near the Northern Mountains from whence we assert the Etesian winds of the Grecians Congo and Guzurat do arise and blow The Etesian winds blow not in all Regions though near the Northren Mountains The Question is of no small moment and I wish that we had more accurate Observations concerning this matter viz. the notations of the winds which at that time are observed in each Region whether in every Year the same never return Yet if that any thing must be said to the Question these seem convenient 1. We cannot deny but that the North wind often bloweth in our Canicular or Dog daies 2. That it is discovered less continual and in each year peradventure the Cause is the often blowing of other winds which hinder the discovery of the same 3. We may say that the Mountain from which this first resolution of the Snow begineth is scituated directly from Greece and therefore the first Canicular wind is carried hither but the Vapours are carried hither from the Snow of the other Mountains because that here they find a free passage made but I shall reject these my extemporay thoughts when that I shall see a better reason and more accurate Observations Proposition VI. Some winds are proper and almost perpetual to some place or tract of Land others are ceasing Places which have a certain wind at a fixed time Those places of the Earth are very few which have a certain wind at a fixed time viz. these 1. The places of the Torrid Zone especially of parts of the Pacifick and Aethiopick Sea scituate in the Zone enjoy a perpetual wind viz. an Oriental wind or its Collateral which they call a General wind as we have shewed in the second Proposition where we have treated largely of it Yea this wind is not so much to be reckoned amongst the proper winds but rather to be determined to be common to all places for although by accident it happeneth that it be not discerned in all places viz. because other winds blow more strong yet it is proper to some the Cause is alledged in the place cited 2. On the Coasts of Peru and part of Chili and to the adjacent Sea the South wind is almost perpetual and his Collateral wind at the West It beginneth at the 46 deg of Latitude and bloweth to Panama the American Isthmus and causeth that in few daies Ships arrive from Lima at Panama laden with Gold Silver c. But it requireth many daies sail from Panama to Lima. But this wind bloweth not in the Sea remote from the Coasts of Peru It is difficult to render the cause of this wind by reason that the South Land from whence it seemeth to blow is not yet known unto us Yet I think it probable that because that Mountains are found in it covered with perpetual Snow therefore the winds are generated from a continual resolution of them But I will not infect the mind of the Reader with these my suspicions or conjectures For peradventure the Snows which are found all the year long in the high Mountains at the Streights of Magellan are the cause of these winds but yet it may be Objected that those Mountains lie from the South towards the West declining from the South wherefore we shall leave this to a more diligent inquisition or a more full knowledge of the South Continent 3. At the Coasts of the Land of Magellan or Del Fugo about the Streight Le Mair continual or at least very frequent Westernly winds do blow and that with that force that they make the Trees to bend towards the East from their perpendicular rectitude neither is there any part of the Earth in which those Occidental winds so often blow but on the other part of the Streights Le Mair at the Coast of the South Land the South wind bloweth I can render no other cause of those Occidental winds but that I suppose them to be raised from Snow and Clouds in the South Continent which extendeth it self from the side of that Occidental Streight from the South towards the North. But these are doubtful and more diligently to be inquired after 4. On the Malabarian Coasts of India for almost the whole year the North and North-East winds blow the cause proceedeth from the resolution of the Snows of the Mountains of the Asiatick Sarmatia viz. Imaus or Caucasus from the Clouds on the other Mountains of Asia which are collected and press the subject Air. 5. In the Sea near to Guinea the North West wind is frequent and in the remote Sea the North East 6. In the middle passage between Japan and Liampo a Maritimate City of China even unto these are found Occidental winds which blow in Japan in November and December 7. At the Isle Guotou not far from the Isle Dos Cavallos in the Sea of China is a frequent South wind when that yet in the neighbouring Ocean a North wind is predominate Proposition VII Vnto these Periodical or state Winds appertain those also that are tearmed day Winds which in some Regions and at a certain time of the year blow for some hours every day Of Day Winds so called Now they are found to be twofold and that only in some Maritimate places for some blow from Mediterranean places to the Shore towards the Sea and others on the contrary from the Sea to the Shoars 1. On the Malabarian Coasts in the Summer season viz. from September to April the Terrestial winds or Terrinhos do blow from the twelfth hour of the night to the twelfth hour of the day now these winds are Eastern winds But from the twelfth hour of the day to the twelfth hour of the night the Sea wind or Viraconus to wit the West wind bloweth but this is very weak so that by its assistance the Ships can hardly arrive at the Shoar I suppose the cause of those Oriental winds from twelve at night to twelve in the day partly to be a general wind and partly Clouds on the Mountain Gatis But the cause of the Occidental Winds that blow from twelve in the day to twelve at night is the resolution of thick Clouds caused by the setting of the Sun which Clouds before by the Oriental wind were forced towards the West Out of those named Months the North wind predominateth also the East and North-East neither by reason of the often Tempests are these Terrestrial and Marine winds discerned 2. In Musulipatan a City on the Coasts of Charomandel these Terrinhos begin to blow
shall be placed on the Meridian line of the plain and so the Map shall have its required scituation Proposition IX To find the Latitude of the place from the Heaven or the Elevation of the Pole above the Horizon of any place by the benefit of the Stars To find the Latitude of a place above the Horizon by the Stars Although the Latitude of a place exist in the Superficies of the Earth viz. its distance from the Aequator yet it cannot be found without the Stars The modes of finding the same are various First Let the Altitude of the Sun above the Horizon be observed when he cometh to the Meridian line and let its complement or distance from the Vertex of the Sun be taken For this take away the declination of the Sun to the day of the Observation that is if that the Sun be fixed in the Southern part of the Zodiack but let it be added if that it be in the Southern the residue shall be the Latitude of the place But the declination of the Sun that is his distance from the Aequator in the day of the Observation is found from the place of the Sun and that from a Table of the declination of the parts of the Ecliptick or from the Globe for let the place of the Sun be noted in the Globe at the day of the Observation and brought to the Meridian the degrees of the Meridian being intercepted between the Aequator and the place of the Sun exhibit the declination of the Sun at the day given Secondly The Sun rising or setting by the benefit of the Globe the Latitude shall thus be found Let the Plaga or part in which the Sun riseth or setteth be observed which Mariners are accustomed to do by their Compass but the true Meridian line is required to this Let the same Plaga or degree be marked in the Wooden Horizon of the Globe Let the place also of the Sun in the Ecliptick for the day of the Observation be noted then let the Brazen Meridian in the Crena of the Horizon be turned thereunto the Pole being more or less elevated until the noted place of the Sun meet with the noted place of the Horizon so the elevation of the Pole in the Globe shall be the same which the place hath where the Observation was made The Solution will be more easie by Calculation but by reason very few Students of Geography understand the solution of Spherical Triangles therefore I omit the same which shall also be observed in the following Problem Note That in the time of the Aequinoxes when the Sun is in the begining of Aries or Libra then this method hath no use because that then the Sun in one and the same Plaga or part riseth and setteth to all places viz. in the part of the true East or West or in the Plaga of the Aequinoctial rising or setting Thirdly When the Sun shineth at Noon let the style or pin A B be perpendicularly erected on an Horizontal plain See Scheme and let the Longitude of the shadow A C and the style A B be taken in some divided line Therefore in the right Angled Triangle A B C shall be both the noted sides A B A C whence the Angle A B C shall be found to be the distance of the Sun from the Vertex viz. if that it may be that as A B hath its self to A C so the whole sign hath it self to the Tangent of the Angle A B C from thence the Latitude of the place shall be found as we have shewed in the first Mode But if the Observation be made on the day of the Aequinox then the distance of the Sun from the Vertex being found the same is the Latitude of the place The elevation of the Pole at Rome and Carthage So Pliny writeth in the 72 Chap. of his Second Book that in the City of Rome the ninth part of the Gnomon or pin is wanting unto the shadow whence the elevation of the Pole is collected to be 41 degrees 25 minutes At Carthage the Gnomon hath the same proportion to the shadow as 11 hath to 7 whence the elevation of the Pole is collected to be 32 degrees 13 minutes Fourthly In the Night time when the Stars can be seen if we take the Altitude of any Star in the Meridian with an Instrument or from a Table know the declination of the Stars thence with little trouble we shall find the Latitude of the place For if that Star be scituate between our Vertex and the Semicircle of the Aequator elevated to us we must then add But if the declination of the Star be Northernly and the Star seated between our Vertex and the Polary Star we must then subtract from that declination the distance of the Star from our Vertex the remaining number shall be the Latitude of the place If that the Declination be Northern and the Star be seated between the Pole Star and the proximate part of the Horizon the complement of the declination shall be added to the found out Latitude of the Star The aggregate number shall give the Latitude of the place or the elevation of the Pole If the Declination shall be Northern and the Star is placed between our Vertex and that part of the Horizon remote from the Polary Star that declination shall be added to the distance of the Star from the Vertex or to the Complement of the Altitude The aggregated number shall be the Latitude of the place Finally if that the Declination of the Star be Southern this must be deducted from the Complement of the Altitude observed and the remaining number will shew the Latitude of the place Neither in this casualty doth any variety occur as in the Star of the Northern declination which is to be understood of the places scituated between the Aequator and the North Pole for it is otherwise with the places which lye between the Aequator and the South Pole Fifthly If the Plaga or part be observed in which any Star riseth or setteth the Latitude of that place may be found by the benefit of the Celestial Globe according to what we have said in the third Mode Sixthly If that you have not a Table of the Declination of the Stars at hand you may obtain the thing required if that you observe some Stars not setting viz. such a one which in its whole circumrotation is remaining above the Horizon for those Stars come twice to the Meridian and therefore their Meridian altitude is twofold one greater and the other less Both these must be observed and the half difference must be added to the lesser Altitude or taken from the greater so we shall obtain the Latitude of the place Seventhly If we enquire not after an accurate Latitude of a place but would be contented with one not much receding from the true we must take the Altitude of the Polary Star when that it hath far
of both the Planispheres are those demanded The places of the second demand shall be found in the same degrees in the Parallel distant from the other Pole In the Tables of the Declination let the Latitude be found for the place demanded Proposition XI To compute the Latitude and Magnitude of all the Zones in Miles or some other famous Measures The computation of the Latitude and Magnitude of the Zones in Miles c. The Latitude of the Torrid Zone is 47 degrees viz. 23 ½ from both parts of the Aequator the Latitude of both the Temperate is 43 degrees The Latitude of both the Temperate is 43 degrees The Latitude of both the Frigid 47 degrees These Degrees if changed into Miles one degree being estimated at 15 German miles the Latitude of the Torrid Zone will be 705 miles one of the Temperate 645 and one of the Frigid 705. The place requireth that we should now treat of the Seasons in the divers Zones and places but because some of them do appertain unto the following Chapter I have omitted them here CHAP. XXV Of the Longitude of the Days in divers Places of the Earth And of the division of the Earth into Climates which proceed from them Proposition I. In two Days of the year are the Aequinoxes or the Night equal to the Day in all places of the Earth The Days and Nights in all places are equal in two days of the year THe Days are those in which the Sun entreth the Aequator whether he describes the same by Motion or Diurnal circumvolution which is when that he entreth the first degree of Aries and the first degree of Libra viz. on the 21th of March and the 21th of September according to the Gregorian Kalendar Now we shall shew that on these days the Night is equal to the Day consisting of twelve hours in all places of the Earth Now this Day noteth the stay of the Sun above the Horizon and the Night the stay beneath the Horizon Take any place in the Globe and let the Pole be elevated for the Latitude of that place so that the Wooden Horizon may become the Horizon of that place Then let the first degree of Aries or Libra be placed in the Oriental Horizon the Index at the twelfth hour of the Horary Circle then turn the Globe until the first degree of Aries come to the Occidental Horizon you shall see that the Index in the Horary Circle hath passed twelve hours The same method may be used to manifest the Night consisting of twelve hours In Places scituated in the Poles of the Earth which are only two the Sun neither riseth nor setteth in these two days of the year but his Center shall be wheeled round in the Horizon which is the same with the Aequator so that they shall have at one time both Day and Night Seeing therefore that in other places the term of the Days and Nights is a moment there on the contrary the intire revolution or Natural day is the term or medium of the perpetual appearancy or disappearancy of the Sun And in these two days of the Aequinoctials the 21th of March and 21th of September the half Sun shall be above the Horizon in those two places and half beneath it And on the 21th of March in the Pole Artick it shall make the beginning of a long day of six Months and on the 21th of September shall be the beginning of a long night of six Months as we shall shew anon therefore it is no absurdity that some places for twenty four hours should neither have night or day Here I shall mention many things peculiar to the Poles above other places of the Earth viz. Several things here noted peculiar to the Poles above other places of the Earth 1. The Sun in a whole year only once riseth and once setteth that is to say it riseth in one Aequinox and setteth in the other 2. They have no Meridies or Midnight at a certain time but at all hours they have a perpetual Meridies for six Months or perpetual Night for six Months 3. No Fixed Stars arise nor set but some remain perpetually above the Horizon and some always beneath it 4. The Stars keep the same Altitude above the Horizon and distance from the Vertex as the Sun also doth in his whole Diurnal circumvolution 5. No Winds there can be called Northern for they are all Southern in the Artick Polé and contrariwise in the Antartick Pole all Northern and none Southern Western or Eastern 6. If the Stars and Sun do not move but the Earth according to Copernicus his Hypothesis then if the Eye were a point that it could be seated in the Pole all the Stars Sun and Moon would appear immovable in the same Plaga All these are easily shewed by the Globe Proposition II. In places scituated in the Aequator the days and nights are always equal In the places of the Poles there is only one day and one night in the whole year Now the day is longer than the night in the North Pole but in the South the day is shorter than the night The days and nights alwaies equal in places seated in the Aequator Take any place you please in the Globe you must shew that in every day in the year the night is equal to the day that is that the Sun for so long time remaineth beneath the Horizon as he doth above it Take the day of the year as you please and let the place of the Sun be enquired after to it which is noted in the Ecliptick then let the place taken be placed in the Vertex that the Poles may hang over the Horizon for so the Wooden Horizon shall be the Horizon of the places of the Aequator Let the place of the Sun be brought to the Meridian and the Parallel described which the Sun perfecteth that day Then let the two Points of this Parallel in the Horizon be noted and it will be manifest that the Arch of this Parallel above the Horizon will be equal to the Arch which is beneath the Horizon And because the Motion of the Sun Diurnal is equal as that of all the Stars therefore in an equal time it will pass through the equal Arches of the Parallels So that the first part of the Proposition concerning every day is shewed Now for the shewing of the other part of the places of the Poles either of the Poles must be placed in the Vertex of the Wooden Horizon so shall this be the Horizon of the Pole And the Globe being turned round we shall see that one half of the Ecliptick remaineth above the Horizon and the other beneath it Therefore whilst the Sun is in this he setteth not whilst in that he riseth not And he is more daies in the Northern Semicircle of the Ecliptick than in the Southern by nine daies Therefore his perpetual stay above the Horizon shall be longer than beneath it
according to this Complement but this is better learned by Instruction than long Precepts Proposition XXIV To make a Scioterick in our Horizontal or other Plain which shall shew the hours of other places although remote from ours This may be done on our Scioterick which was made to shew the hours of our place First consider whether the place given lie East or West from ours if Eastwards the 12th hour must be reckoned there before in our place if Westwards mare later Then let our place be brought to the Meridian the Index to the hour 12 and let the Globe be turned until the other place come to the Meridian the Index will shew what hour is in this place when it is 12 in ours From hence it is easie to collect the hours of that place which may agree with the 1 2 3 4 also 11 10 9 8 c. of ours which then must be ascribed to them But this may be done more elegantly without the Globe according to the Mode that the Horizontals are composed Proposition XXV To elevate a Plain above the Horizon of our place and in that Plain to make a Scioterick in which the shadows of the Hours may seem to go backwards as in the places of the Torrid Zone Because the Elevation of the Plain is left to our choice therefore we shall chuse such an one as is commodious to our purpose For Example we shall so place the Plain above our Horizon or above the Aequinoctial line East and West that the Axis of the World or Pole may be elevated ten degrees above it So the shadow shall begin to be retrograde the Sun being entred into the 26th degree of Aries and it shall so do until the Sun comes to the 4th degree of Virgo Therefore let the Plain be so constituted and the Horologue so made that it may be in the place of the Latitude of 52 the Plain shall be elevated 42 degrees so the Pole shall be elevated above that 10 degrees See Proposit 22. In this Plain an Horizontal Scioterick may be made for the Elevation of the Pole 10 degrees Where when the lines of the shadows are brought from the Center of the Horologue and extended far enough let their parts about the Center be blotted out and the Center also and let a perpendicular Style be erected in any point of the Altitude of the Meridian line such as shall exhibit a Gnomonical Triangle and the extremity of this Style by its shadow falling on the lines of the shadows shall shew the hours and also the shadow shall seem to be retrograde on those days Also by the assistance of the Terrestrial Globe Meridional Polary and Inclining Sciotericks of all sorts may be described But because this matter appertaineth to another Discipline viz. to Dialling therefore I think it unnecessary to treat of all these here CHAP XXVIII Of the Comparison of the Celestial Affections in divers places of the Earth See Scheme FRom the consideration of the agreement and difference of the Celestial Appearances in the divers places of the Earth proceedeth the denomination of the Inhabitants which some have mistaken for the division by which some are said to be Antoeci others Perioeci and others Antipodes Of the denomination of the Inhabitants of the Earth Those are said to be Antoeci or the Inhabitants of two places which lye in the same Semicircle of the same Meridian but from a divers quarter of the Aequator to wit one towards the North and another towards the South but yet so that they are equally distant from the Aequator Perioeci are the Inhabitants of two places which lye in the same Parallel and in divers Semicircles of the same Meridian Sometimes the word is taken for all the Inhabitants of any one Climate but to avoid confusion we shall abstain from that use of it Antipodes are the Inhabitants of two places which diametrically are opposed one to the other Note That these three words are so taken for the most part that they denote the Inhabitants of both places which are compared as we defined them but yet sometimes when any certain place is adjoyned to them they only denote the other place as when we say the Perioeci or Antipodes of this or that place Proposition I. Those who live in the same Semicircle of the same Meridian they have also the same Meridies or 12 hours and also reckon together all the other hours For the Meridies is defined by the existency or appulse of the Sun to the Meridian because therefore those places of the Earth which inhabit in the same Meridian of the Earth have also the same Meridian of the Heaven thence it is manifest that the Sun in the same Meridian to those that inhabit it maketh the Meridies and the 12th hour to them all at one time Moreover an hour is defined to be that 24th part of that time which intercedeth between two vicine Noons or appulses of the Sun to the same Semicircle of the Meridian Because therefore that it is the same time which intercedeth between the two Meridies of the places of the same Meridian therefore also the 24th part of the same shall be equal and the same in all and on that account they shall together number all their hours from the Meridies Proposition II. They which dwell in the divers Hemispheres of the Earth which the Aequator maketh or distinguisheth or those who live in the divers parts or quarters of the Aequator they I say have contrary Seasons of the year at the same time and the same Seasons in a different time of the year so that in one Hemisphere it is Winter when as in the other it is Summer and when the Spring is in that Autumn is in this Of the different Seasons which the Aequator maketh For the Summer beginneth in every place according to the Celestial course viz. the motion of the Sun when he obtaineth a small distance from the Vertex of the place the Winter when a great distance Now because the Sun moveth from one Hemisphere to the other thence it cometh to pass that when it draweth near the places of one Hemisphere it more and more departeth from the places of the other and so the Summer of one Hemisphere agreeth in time with the Winter of another and the Spring of one with the Autumn of another In the places of the Torrid Zone the vicissitude of the Seasons hath something peculiar See Chap. 26. of which we have treated at large in the 26th Chapter Proposition III. Those who live in the Northern Hemisphere of the Earth to them when they turn their faces towards the Aequator the East is on the left hand and the West on the right the South before them and the North behind them Those who inhabit the Southern Hemisphere of the Earth they turning their faces to the Aequator the Stars rise on their right hand and set on their left Of those
who live under the Aequator Those who live under the very Aequator if they turn their faces towards the Northern Pole they then have the East on their right hand and the West on their left but if they turn their faces towards the Southern Pole it is contrariwise Those who live in the Northern Hemisphere to them their faces being turned to the Aequator the Sun going in the Northern Semicircle of the Zodiack will seem to rise and set behind them but perambulating the other Semicircle he will seem before them The contrary hapneth in the Northern Hemisphere and the contrary will also be observed if you turn your faces towards the Poles These are manifest from the consideration of his circumvolution and may be illustrated on the Globe but Mariners and others unskilful of the Celestial motions are wont to wonder at it when they sayl from our Hemisphere into the Southern Hemisphere Proposition IV. The Celestial Affections of the Antoeci compared amongst themselves are thus 1. They have the same Meridies See Propos 1. the same Midnight and reckon all their hours together as is manifest from the first Proposition of this Chapter 2. They have contrary Seasons of the year at the same time for when it is Spring in one place it is Autumn in another when that hath Summer this hath Winter Proposition 2. as is manifest from the second Proposition of this Chapter 3. The days of one place are equal to the nights of the other and the days of this to the nights of the former 4. When the days of one place increase to the longest day in the mean while the days of the other decrease even to the shortest for they have opposite equal days in their Kalendar For Example the day of one place at the twentieth of April is equal to the twentieth of October in the other place 5. On the days of the Aequinoctial the Sun riseth and setteth together to them but on other days sooner to the one than the other also in those two days the Sun hath the same altitude above the Horizon of the Antoeci at every moment of time but on other days a different Altitude 6. To those that turn their faces one towards another or those who regard the Aequator to one the Sun shall seem to rise on the right hand and set on the left and to the other to rise and set contrary After the same Mode all the Stars shall rise to one on the right hand and to the other on the left 7. When the Sun riseth and setteth behind to the one he riseth and setteth before to the other contrariwise to this on the left hand when to that on the right 8. They have the divers Poles elevated by an equal Elevation 9. The Stars appearing perpetually to one place or not setting never arise to the other place but always remain depressed beneath the Horizon contrariwise those which never set to this place never rise to that These are all manifest from the Globe Proposition V. Those which inhabit in the Aequator have no Antoeci but the Perioeci of those are the same with the Antipodes of these The Poles of the Earth have no Perioeci for they are mutually one to the other Antoeci and Antipodes The truth of this Proposition is evident from the Definitions of the Antoeci Perioeci and Antipodes and therefore needs no probation Proposition VI. A place being given in the Globe to exhibit the place of the Antoeci Perioeci and Antipodes of the same Let the place be brought to the Brazen Meridian and as many degrees as are intercepted between this and the Aequator let so many be numbred from one part of the Aequator the term of the Numeration shall be the place of the Antoeci Then let the Index be applied to the 12th hour of the Cycle and let the point of the Meridian be noted which hangeth over the place given also that which hangeth over the place of the Antoeci this being done let the Globe be turned round until the Index shall shew the other 12 hours so the point of the Globe which is subjected to the noted point of the Meridian of the place given shall be the place of the Perioeci and the point of the Globe subjected to the other noted point of the Meridian shall be the place of the Antipodes Proposition VII Those who live in the same Parallel of the Earth have every day and every night equal every one of the Stars also remaineth an equal time above their Horizons the same Stars never set the same Stars never rise the Sun every day and all the Stars also rise and set to them in the same quarter and in the same hour also the Stars are equally elevavated above the Horizon or depressed beneath it They have the same Pole equally elevated their faces being turned to the Aequator or the same Pole the Stars rise to them from the same side and set on the same side they have the same seasons of the year Spring Summer Autumn Winter together and at the same time excepting the singular properties of some places These are manifest from the very consideration of the motions of the Stars and scituation of the Places of the Earth In the Globe if that one certain Parallel be taken and the Pole be elevated near its Latitude or distance from the Aequator the Wooden Horizon of all places shall be the Horizon of that Parallel viz. if that every place be brought to the Meridian and then will be manifest what this Proposition containeth Proposition VIII The Celestial Affections of the Perioeci compared one with another are thus The Celestial Affections of the Perioeci compared together 1. They have all those things common which we have related in the preceding Proposition concerning the Inhabitants of one and the same Parallel 2. They reckon contrary hours of the day in reality but yet the same in name viz. when in one place it is Noon and the 12th Meridian hour then in the other it is Midnight and the 12th hour of Midnight and the Inhabitants of this number 1 2 3 from Midnight whilst they number 1 2 3 from Midnoon 3. On the days of the Aequinoxes the Sun setteth to one place whilst it riseth to another and therefore the time of the day of one place is the night of another but on other days of the year viz. on the half year in which the Sun runneth through the vicine Semicircle of those places of the Zodiack that is in the Spring and Summer it first riseth to one place before he setteth to another and therefore in some hours or some parts of an hour they have both the day and the night conspicuous together viz. whilst the Sun tendeth towards the setting to one place he beginneth to ascend towards the Meridian to the other having now emerged above the Horizon But in the other half of the year Autumn and Winter in which the Sun runneth the
hath observed the beginning also in his Maps But seeing that there are other places in the Earth where the Magnetick Needle doth the same neither doth it do it in all the Meridian of this place therefore other Geographers have not thought that Cause sufficient and some have placed the first Meridian in the Brazilian Shore the more Modern especially the Hollanders having gone back to the Fortunate or Canary Isles have chose in one of them called Teneriffe The Longitude by the Hollanders begun at Teneriffe a Mountain which is thought to be the highest in the whole World called El pico de Teneriffe and from the Meridian of this Mountain they judge the Numeration of the Longitude of places ought to be begun because they think fit that a Famous and durable place for all Ages may be best chosen for this purpose concerning which in Ages to come Posterity should not easily doubt and moreover that that assignation of Ptolomy which hath been observed for so many Ages should not be deserted on a trivial account The Longitude by the French begun at the Isle of Fer in the Canaries The French at this day from the Year 1634 observe that for the first Meridian which passeth through the Occidental part of the Isle of Fer one of the Canary Isles Which beginning Lewis the XIII King of France commanded his Mariners and Geographers to observe Astronomers also take divers places for the first Meridian For those who follow Tycho are wont to place it at Vranoburge scituate in an Island in the Danish Sea and at this place to compute their Celestial motions and thence to other places Others make other beginnings as they follow this or that Author of the Ephemerides The Longitude likewise begun in sundry places by Astronomers For the Writers of Ephemerides as also the computers of the Planetary Tables are wont to calculate the motions and appearances of the Planets to the Meridians of their own Country as Origanus to Frankford Maginus to Venice because that Padua is an Academy of the Venetians Ecstadius to Stetin Lansbergius to Goesa in Zeland Reinholdus to Regium a Mountain of Borusia But to speak freely what I think all this dissent of Authours proceedeth from no sufficient Cause so that those who first removed the Ptolomaick-beginning out of its place are blame worthy But it is all one whatsoever beginning of this account is taken in the Earth whether the place be noted or the ultimate to the Occident or Orient so that the scituation and distance of the other places be accurately known at it Yet this variety of the beginning of the Meridians expresseth the reading of Geographical Writers with many confusions and difficulties Yet because the knowledge of the Declination of the Loadstone is of great utility and that that Declination encreaseth even to a certain Meridian and then again decreaseth I think it not altogether inconvenient for the observation of the Declination of the Load stone and the more easy comparison of the increase or decrease of it if that that be taken for the first Meridian in which the Magnetick Needle maketh little or no Declination so that such a Meridian might be given viz. in all the places of which or the most at least the Magnetick Needle would do it But seeing that the Hollanders at this time take the Mountain of Teneriffe for the beginning of their Longitude and that they Sail at this day into all parts of the World therefore it is convenient to acknowledge the same beginning with them for the better understanding of the Diaries that they are wont to publish Now you must know that the Reading of Authours where mention is made of the Longitude of a Place or of a certain numbred Meridian that then you ought to consider what beginning of Longitude that Author determineth or through what place he bringeth his first Meridian as you are to observe that the Maps which are used in the Second Part of this Book being the Geographical Description of the parts and places of the Four Parts of the World the Longitude I say of those places are taken according to the French Account beginning at the Isle of of Fer being one of the Canary Isles they being Composed by Monsieur Sanson Geographer to the King of France and whose Method is not convenient to be allow'd for to that the Longitude of other places must be brought and inquired of Proposition III. The Latitude and Longitude of any place or the distance of any place from the Aequator or a certain Meridian being given which is found in the Maps or Globes to exhibit the scituation and Point of that place on the Maps or Globes Or thus If that we be in any place of the World either at Land or Sea which is unknown unto us or whose scituation we are ignorant of to the other parts of the Earth so that if we can find the Latitude and Longitude of this place thence to find out the scituation of this place in the Earth and its distance from other places This is that Problem for which a Method is sought so anxiously and with so great industry by which the Longitude of a place at any time in which we are in it may be found and therefore although we should first treat of the invention of this Longitude yet I thought it fitter to premise the Problem it self for which that Longitude is sought for and that for this reason seeing that we must treat largely of this Longitude least you should be cloyed not knowing to what end so great a labour is undertaken and so many various ways tryed The Longitude and Latitude of places of great importance to Mariners to know For Mariners having Sailed far from the Shoar and being in the Ocean because they cannot accurately know the way of their Voyage made by reason of the divers hindrances and note it in their Maps are often ignorant in what place of the Earth they are what scituation this place hath to those places whither they go or what places are to be gone to if that they will avoid danger and therefore also they are ignorant unto what quarter they must direct their course Unto the knowledge of which there is no more ready a Method than for to certainly find the Longitude and Latitude of the place that is its distance from the Aequator and some certain Meridian of the Earth And Mathematicians have taught them with no great difficulty by divers ways to find out the Latitude of a place in the day by the Sun and in the night by the Stars Such Modes we have shewed before for those who think to know it only by the help of the Compass sufficiently discovered their ignorance from which Latitude being found they know in what Parallel of the Earth they are which indeed is no small part of the demand But seeing that the Points of the Parallel are infinite they do not yet know from the