A BRIEF TREATISE OF THE USE OF THE Globe Celestial and Terrestrial: WHEREIN IS SET DOWN the principles of the Mathematics, fit for all travelers, Navigators, and all others that do love the knowledge of the same Art. By R. T. AT LONDON Imprinted by FELIX KYNGSTON, for Thomas Man. 1616. THE PREFACE TO the Reader. I Do here present thee (gentle Reader) with a brief collection of the use of the Globe, which may serve for an introduction to young Students in the Mathematics, requiring thee to accept thereof: for I doubt not it will be very good for the furtherance of travelers in the Art of Navigation: and to all others that are desirous of the knowledge of the beautiful frame of the celestial Orbs, with their quantities, distances, courses, and marvelous motions of the Globes of the Sun, Moon, Planets and fixed stars. If therefore this my labour shall be gratefully accepted, as I doubt not but it shall, if thou please justly to censure thereof: I shall be encouraged hereafter to set forth a work of more worth: so I refer myself to your favourable judgements and courtesies, committing thee to the sacred tuition of him that ruleth all. Farewell. Thy in all affection, R. T. INTRODUCTION TO Astronomy. Definitions of the Globe. THE Globe is a perfect round body, contained under one plain: in the middle thereof there is a point called the Centre, from whence all lines drawn to the outside are of like length, and called Semidiameters. The axes of the Globe is a diameter, about which it moveth; and the ends thereof are called the poles of the Globe. In this respect the frame of the heavens is called the Globe of the heavens, and the earth his Centre. The axes is a line imagined, passing by the Centre of the earth to the heavens, and the ends thereof is called the poles, which are two points imagined in the heavens, whereof the one is called the North pole, and the other the South pole. Of the Circles of the Globe. Circles of the Globe are certain imaginary lines, and are termed either lesser, or greater Circles. Greater Circles are such as divideth the Globe into two equal parts. Lesser are such as divide the Globe into unequal parts. Greater Circles of the Globe in common account are six in number, viz. The Horizon. Meridian. Equinoctial. Zodiac. Two Collures. Lesser Circles in common account are four in number, viz. The Two Tropics. Two poler Circles. The Horizon divideth that part of the heavens we do see, from that part we see not, and is that Circle, where standing in a plain field, and looking about, you would imagine the earth and heavens do meet together, and cannot be perfectly discerned but at sea. The axes of the Horizon, is an imagined line, passing by the Centre of the earth to the heavens, and the ends thereof, are called the poles Zenith and Nadir. The Zenith is the point direct over our heads, and the Nadir direct under our feet. As a man moveth himself any way, so is altered the Horizon. The Meridian cutteth the Horizon at right spherical angles, and passeth by the poles of heaven, and by the Zenith and Nadir, and is that Circle wherein the ☉ is at noon, and at midnight: it divideth the Globe into two equal parts by East and West, whose axes is a line passing by the Centre of the earth to the heavens, and the ends thereof the poles, which are the two points of the intersection of the East and West. Any many moving directly North and South, keepeth the same Meridian: but going East or West, he altereth the same. The Equinoctial cutteth the Meridian at right spherical angles, and lieth equidistant betwixt each poles, and divideth the Globe into two equal parts, by North and South parts, to which Circle when the ☉ cometh under it, it maketh the day and night of like length to all people in the world, except under the poles, and the ☉ cometh under this Circle two days in the year, viz. the 11. of March, and on the 14. of September. The axes and poles whereof are the axes and poles of heaven. The Zodiac is a great Circle, having in breadth twelve degrees, which breadth is limited for the wandering of planets, upon which Circle are the twelve signs placed, which are twelve Constellations. A Constellation is any certain number of stars, gathered together into one form by the ancient Astronomers, who have given them names, whereby they are known to all Christendom: which signs have certain characters given unto them, and are these following. 1 March. 2 April. 3 May. 4 june. 5 july. 6 August. Northern signs. 1 Aries. ♈ 2 Taurus. ♉ 3 Gemini. ♊ 4 Cancer. ♋ 5 Leo. ♌ 6 Virgo. ♍ 7 Septemb. 8 October. 9 November. 10 Decemb. 11 january. 12 February. Southern signs. 7 Libra. ♎ 8 Scorpio. ♏ 9 Sagittarius. ♐ 10 Capricornus ♑ 11 Aquarius ♒ 12 Pisces. ♓ The first six are called Northern signs, for that they are placed upon the North side of the equinoctial; and the last six are called Southern signs, for that they are placed upon the South side of the equinoctial. In the middle of the Zodiac is a line called the ecliptic, from which line the Centre of the ☉ never swerveth, and this line cutteth the equinoctial at obliqne angles, and swerveth from it 23 degrees 30 minutes: which line when the ☉ and ☽ are in a diameter, that is, opposite, then is the ☽ eclipsed, that is, darkened by the shadow of the earth, the earth being betwixt the ☉ and the ☽. And when the ☉ and ☽ are both under the line in a semidiamiter, then is the ☉ eclipsed, the ☽ being interposed betwixt our sight and the ☉: this line ecliptic is described upon the Globe for the whole Zodiac, whose axe is a line passing by the Centre of the earth to the heavens, and the ends thereof are his poles, which are two points so far distant from the poles of the world, as the ☉ his greatest distance from the equinoctial, viz. 23 degrees 30 min. The two Collures are two meridians cutting the equinoctial, and the ecliptic into four equal parts, the one passing by the first point of ♈ and ♎, and is called the equinoctial Collure. The other passing by the first point of ♋ and ♑, and is called the solstitial Collure: these two Circles do divide the year in four equal parts, viz. Spring-time, Summer, Harvest, and Winter. Spring-time. 1 ♈ 2 ♉ 3 ♊ Summer. 4 ♋ 5 ♌ 6 ♍ Harvest. 7 ♎ 8 ♏ 9 ♐ Winter. 10 ♑ 11 ♒ 12 ♓ The meaning whereof is thus: From that time the ☉ entereth into ♈, till it enter into ♋, is called Spring-time, and so of the rest, so that it is the passage of the ☉ in the signs, that causeth the alteration of season, and the ☉ passeth throughout the whole signs in one year, viz. in 365 days and 6 hours near. Of the lesser Circle. THe Tropic of ♋ is a Circle parallel to the equinoctial 23 degrees 30 min. distant from it, Northward, and is that Circle under which the Centre of the ☉ maketh her diagonal ark, when she is in the first point of ♋, which is to us that have Northern Latitude, the longest day in the year being the 12 or 13 of june. The Tropic of ♑ is a Circle parallel to the equinoctial, so far to the Southward, as the Tropic of ♋ is Northward, viz. 23 degrees 30 min. and is that Circle under which the Centre of the ☉ maketh her diagonal ark, when she is in the first point of ♑, which to us that have Northern Latitude, is the shortest day in winter, viz. the 12. or 13. of December. These two Circles are termed the limit of the ☉ progress: for between these two Circles the ☉ hath his continual course, and never exceedeth beyond any of them. The Circle arctic is a Circle parallel to the equinoctial, so far distant from the North pole, as the tropic of Cancer is from the equinoctial, viz. 23. degr. 30. min. The Circle antarctic is a Circle parallel to the equinoctial so far distant from the South pole, as the tropic of ♑ is from the equinoctial, viz. 23. degr. 30. min. Now you must understand, there is but one Equinoctial, one Zodiac, one Ecliptic, two Collures. But there are divers Meridian's, all which meet in the two poles of the world, and cut the equinoctial at right angles, and are so many in number as there can be points imagined in the equinoctial. There are divers Orisons: for the Horizon altereth to any man, according as he moveth himself from his place of being. There are divers Parallels, so called for that they are parallel to the equinoctial, and are so many in number, as there can be points imagined in the Meridian. Besides these Circles, before mentioned, there are four other kind of Circles of great use, viz. Azimoth and Almicanthars, Circles of Longitude and Latitude. Azimoths are great Circles, and meet all in the Zenith, and Nadir, and cut the Horizon at right angles, and are numbered in the Horizon. Almicanthars are lesser Circles parallel to the Horizon, as the parallels are to the equinoctial, and are numbered from the Horizon towards the Zenith. Circles of Longitude are great Circles, meeting all in the poles of the Ecliptic, and cut the Ecliptic at right angles, and are numbered in the Ecliptic. Circles of Latitude are lesser Circles parallel to the Ecliptic, as the parallels are to the equinoctial, and are numbered from the Ecliptic, to the poles of the Ecliptic. Every Circle of the Globe is imagined to be divided into 360 degrees, and every degree into 60. minutes, every minute into 60 seconds, and so tell the tenth for the preciseness, for that a degree in the heavens is a large space. In every great Circle the degrees are equal one to another. In every lesser Circle they are equal in the same Circle, but unequal to those of another Circle, according as they grow nearer the poles. There belongeth to the furnishing of a Globe two other things, that is, an hour Circle, with Index and a quadrant of Altitude. The hour Circle is of brass, divided into 24. hours by twice 12, and is to be placed upon the Meridian, upon the pole elevated parallel to the equinoctial. The Index is a little ruler to be put upon the pole. The quadrant of Altitude is a bowed ruler of brass, divided into 60. degrees, equal to the degrees of the Globe, and hath a joint to fasten the same upon the Meridian, and is always to be placed upon the Zenith. For the practice of Astronomy & cosmography, there are two Globes made, the one of the Heavens, which is called the Celestial globe, and the other of the Earth, which is called the Terrestrial globe. Upon the Celestial Globe are pictured all the stars upon the Conuexitie thereof, as we behold them in the heavens, in the concavity there of in form and distance. Upon the Globe of the earth is set sea and land, making one perfect body, all the known parts being laid down in form, proportion, and distance by scale, according to the proportion of the earth. Of the superficies of the Celestial Globe. TO the intent that the knowledge of stars might be brought in rule and memory of men, therefore the ancient Astronomers gathered them together into certain constellations, and gave them names, whereby they are known unto all the world, that have the knowledge of letters. A Constellation is a certain number of stars gathered together in one form, and so retain their names, whereby they are particularly known, and are in number, according to the ancient account, 48. and are divided into three parts, viz. Northern Zodiac Southern Constellations 21 12 15 Besides these there are 120. stars that are exempt out of all the Constellations, so that the number of stars set upon the Globe are 1025, and divers of them have proper names, which I here omit. You must understand that all the stars in heaven are not numbered, nor cannot, for that divers of them are so small, but these 2025 are the principallest amongst them, and all that have yet ever been accounted of. You must understand, that of these stars some are greater than other, and 〈◊〉 distinguished in six sorts of b●gnesses, and their measures is the earth, and their proportions are thus delivered, viz. A star of the first bigness is 107. times bigger than the earth. A star of the second bigness is 90. times the globe of the earth. A star of the third bigness is 72 times the globe of the earth. A star of the fourth bigness is 54 times the globe of the earth. A star of the fifth bigness is 36 times the globe of the earth. A star of the sixth bigness is 18 times the globe of the earth. 1 15 2 45 Stars magnitude, 3 and the quantity of each magnitude. 208 4 474 In all 1025 5 427 6 49 Cloudy. 5 Obscure. 9 Parnassus fair. 3 Upon each Globe there is a table set down in what form every star of any bigness is made, whereby you may readily know any star in any Constellation of what bigness it is. And thus much in brief for the superficies of the Globe of the Heavens. have Southern Latitude that devil on the South side of the equinoctial. The earth is divided into four parts, viz. Europa. Asia. Africa. America. Europe is bounded from Asia by the midland sea, and Mary mauritane, by the marches called Palus meotis, and by the river Tanis and Dwiana. The Provinces are these. 1 Germany. 2 Italy. 3 France. 4 Spain. 5 Denmark. 6 Norway. 7 Swedeland. 8 Moscovia. 9 Polonia. 10 Hungaria. 11 Clavonia and 12 Grecia. The principal islands. 1 England. 2 Scotland. 3 Ireland. 4 Sicilia. 5 Candia. 6 Corsica. 7 Sardigna. 8 Negroponte. Asia is bounded from Europe by the river Tanis and Dwiana, from Afrieke by the narrow neck of Land betwixt the read sea, and the midland sea. The Provinces are China. Persia. Part of Moscovia, and Tartary. In this part of the world was Paradise and the Land of promise. Africa is bounded with the midland sea and the read sea. Provinces. 1 Egypt. 2 Barbaria. 3 Aethiopia. 4 Nubia. 5 Abasmies. 6 A●onomotopa. islands. 1 Madagascat, or S. Lorreny● 2 S. Thome. 3 Insule de Capo verde. 4 Insule de Canaria. 5 Insule de Madera. America is wholly bounded by the Sea, and the strait of Magellanus, and consisteth in two parts, viz. Mexicana. Pe●●ana. FIRST PROPOSITION OF the Celestial Globe. The day of the month being given, to find the place of the ☉. Upon the Horizon of the Globe is graduated the theoric of the ☉, that is, there is placed the month, and their days, the signs and their degrees. Therefore find the day of the month, and right against the same you shall find the sign and degree that the ☉ possesseth. Proposition 2. The place of the ☉ being given, to find the day of the month. Find the place of the ☉ in the Horizon, and against the same you shall find the day of the month. Proposition 3. The place of the ☉ being given, to find the Declination. BRing the place of the ☉ to the Meridian of the Globe, and the portion of the Meridian included betwixt the place of the ☉ and the equinoctial, showeth the declination. Proposition 4. The place of the ☉ and the Meridian height of the ☉ being given, to find the height of the Pole. BRing the place of the ☉ to the Meridian of the Globe, and from that point accounted downwards to the Horizon the height of the ☉, and let the ends there of end in the Horizon: then in the opposite part, you shall find cut on the Meridian the height of the Pole, that is, the portion of the Meridian included betwixt the Pole and Horizon, showeth the height of the Pole. Proposition 5. To rectify the Globe fit for use, the elevation of the Pole being known. SEt the poles answerable to the poles of Heaven. Proposition 6. To rectify the quadrant of altitude. SEt the joint thereof upon the Meridian so far distant from the equinoctial, as the poles is elevated above the Horizon, that is, place the joint in the Zenith. Proposition 7. To rectify the Index of the hour Circle, for any day appointed. BRing the place of the ☉ to the Meridian of the Globe, and then put the Index upon 12 of the clock, or upon that 12, which is uppermost from the Horizon. Proposition 8. The elevation of the Pole and place of the ☉ being given, to find the Meridian, height of the ☉. THe Globe rectified, bring the place of the ☉ to the meridian, and the degrees from the place of the ☉ to the Horizon, showeth the demand. Proposition 9 The elevation of the Pole and place of the ☉ being given, to found the hour of the ☉ rising. THe Globe and Index of the hour circle being rectified, bring the place of the ☉ to the East side of the Horizon, and the Index of the hour circle showeth the hour of the ☉ rising. Proposition 10. The elevation of the Pole and place of the ☉ being given, to find the hour of the ☉ setting. THe Globe and Index of the hour circle being rectified, bring the place of the ●●o the West side of the Globe, and the Index of the hour circle showeth the hour of the ☉ setting. Proposition 11. The elevation of the Pole and place of the ☉ being given, to find the length of the day. Find the hour of ☉ setting by the last proposition, and double that time, so have you the length of the day. Proposition 12. The elevation of the Pole and place of the ☉ being given, to find the Amplitude. THe Globe rectified, bring the place of the ☉ to the Horizon, and the portion of the Horizon included betwixt the place of the ☉, and the point of East or West, showeth the amplitude. Proposition 13. The place of the ☉ and Amplitude being given, to find the height of the Pole. Turn the Globe and move the Meridian until you have fitted the place of the ☉ in the point of the Amplitude, and then the pole of the Globe showeth the height of the pole, that is, the place included betwixt the pole of the Globe and the Horizon, showeth in the Meridian the height thereof. Proposition 14. The place of the ☉ being given, to find the right ascension thereof. BRing the place of the ☉ to the Meridian, and the degree cut by the Meridian in the Equinoctial, showeth the right Ascension. Proposition 15. The elevation of the Pole and place of the ☉ being given, to found the crooked Ascension. THe Globe rectified, bring the place of the ☉ to the East side of the Globe, and the degree cut by the Horizon in the equinoctial, showeth the crooked ascension. Proposition 16. To find the difference of ascension. FIrst find the right, and then the crooked Ascension: then take the less from the greater, and that rest showeth the difference of Ascension, except that remainder do exceed 180 degrees, and then that rest taken from 360 degrees, showeth the difference of ascension. Proposition 17. By the difference of Ascension, to find the length of the day. DOuble the difference of Ascension, & reduce that into time, by allowing 15 turn the Globe, until the place of the ☉ touch the edge of the quadrant, than the Index of the hour Circle showeth the hour, and the degree cut on the quadrant of altitude, showeth the height of the ☉ at that time. Proposition 22. The hour of the day being given, to find the Azminth of the ☉. ALL things rectified, turn the Index to the hour: then bring the quadrant of Altitude on the place of the ☉, and the end thereof in the Horizon showeth the Azminth. OF THE STARS. Proposition 1. To find the Declination of any Star. Work by the Star, as you did by the ☉ in the 3. Proposition, viz. An example: Arcturus in Boötes' legs brought to the Meridian of the Globe, the portion of the Meridian betwixt the place and the equinoctial, showeth his declination to be Northern. Proposition 2. The meridian height of any star being given, to find the height of the Pole. Work by the star, as you did by the ☉ in the 4. Proposition, viz. Arcturus meridional height supposed to be given 60 degr. than the height of the Pole opposite is found to be 52 degrees. Proposition 3. To find the hour of rising of any star. ALL things rectified, work by the star, as by the ☉ in the 9 Proposition: for to know at any time the rising of Arcturus, or any other*, you must know in what sign the ☉ is. As for example: The ☉ rising in the 19 degree of ♑, which being brought under the fixed Meridian, and then the Globe and Index rectified, Arcturns is then found to rise at 6 hours, and 30 minutes in the morning, and setteth in the evening at hour 10. 30 minutes. Proposition 4. To find the hour of any star setting. ALL things rectified, work by the star, as by the ☉ in the 10 Proposition, or precedent demonstration. Proposition 5. To find the time of any star above the earth. FIrst find the hour of rising, and then the hour of setting: the difference of which time is the thing required. Example. Arcturus is found by the former Proposition to rise at hour 6. 30, which is 5. 30 before 12, and he setteth at 10. 30: both which times added together, maketh 16 hours, and so is Arcturus found to be 16 hours above the earth. Proposition 6. To find the amplitude of any star. Work as by the ☉ in the 12 Proposition. Example: Arcturus amplitude is found then, when he is brought to the Horizon; in the side is 37 degrees of Amplitude. Proposition 7. The amplitude of any star being given, to find the height of the Pole. Work by the * as by the ☉ in the 13 Proposition. Example: Arcturus amplitude being given, 37 degrees; the Pole of heaven is found to be 52 degr. above the Horizon elevated. Proposition 8. To find the right Ascension of any star. Work by the star, as by the Sun in the 14 Prop. Example: Bring Arcturus to the Meridian, and the point in the equinoctial being then under the Meridian, showeth the right Ascension to be 209 degrees. Proposition 9 To found the crooked Ascension of any star. Work by the star, as you did by the Sun in the 15 Proposition. Example: The place of Arcturus being brought to the Horizon, the degrees of the equinoctial against the Horizon, do prove his crooked Ascension to be 178 degrees. Proposition 10. To find the Latitude of any star. Put the centre of the Quadrant of Altitude, being taken from the Meridian, upon the pole of the ecliptic, viz. Arcturus Latitude is to be measured from the pole ecliptic with the Quadrant of altitude, and is found to be 31 degr. 30 min. and his Longitude is in 19 degrees of ♎, to be reckoned with the quadrant of altitude, being brought from the pole ecliptic, to the ecliptic or zodiac, passing right on the place of Arcturus. Compostella in Galicia is by sundry matters found to be in the 43 parallel, which is in Latitude 43 degrees Northward, and in the 11 meridian 30 minutes, which is in Longitude 11 degr. ½. Circles of Latitude or Altitude, beginneth from the equinoctial by parallels Northward or Southwards, to be reckoned to 90 degrees. Longitude to be reckoned by Meridian's numbered in the equinoctial, which is that meridian passing between the equinoctial and the Isles of the Canaries, & are numbered into the East round about the globe, viz. to 360 degrees. One hour containeth 15 degrees or 60 minutes, and 4 of those minutes contain one degree: therefore dividing still your number of minutes by 4, and the quotient shall be degrees. Example. Twelve minutes of an hour give three degrees of Longitude, which is 12 min. so that every minute of an hours time is ¼ part of one degree in Longitude, as is proved by the work following. Here followeth the 11 Proposition concerning the Stars. Two stars seen in the Horizon to rise or to set at one time, thereby to find the height of the Pole. Example. THe two stars rising together, the one is the first star in Orion's girdle, and the other * is that which is in Pegasus nose: therefore turn the Globe until you fit the said two stars equal with the Horizon in the East: then shall the portion, betwixt the North pole and that Horizon, teach you the poles height to be in 53. degrees. Proposition 12. The place of the ☉ and the length of the day being given, to find the height of the Pole. THe place of the ☉ given is in 17 degr. of ♎, and the length of the day given, is 11 hours. Therefore first find out the right ascension of the ☉, then number from that place so many meridians, as do contain the half length of the day given, and let the end of those degrees rest under the fixed meridian: then move the meridian of the Globe, until you fit the place of the ☉ in the Horizon, and then shall you find upon the meridian the just height of the Pole. For example. The ☉ being in 17. degrees of ♎, her right ascension is found to be 195 degrees, the days length given is 11: therefore take the one half, that is 5 hours ½: which time reduced into degrees, facit 82 degrees 30 min. the which subtracted out of the ☉ ascension 195, there rest 112 degr. 30 min. which number find out upon the equinoctial, and bring it to the fixed meridian, and there keep the same, until by moving the meridian you do bring the 17 degree of ♎ equal with the Horizon: that done, then will the height of the Pole be found elevated just 51 degrees. Proposition 13. The length of the day and amplitude of the ☉ being given, to find the height of the Pole, and the ☉ declination. THe length of the day given, is eleven hours. The amplitude of the ☉ given, is 10 degrees. Therefore number from the first meridian Westward, those degrees that have the length of the given day, reduced in degrees do yield, and let the end of those degrees begin in the equinoctial rest under the fixed meridian: then move the globe until you have fitted the first meridian to cut in the amplitude given, and then shall the meridian of the Globe show the just height of the Pole. Example. The length of the day given, is 11 hours, whose half is 5½, the same reduced into degrees, facit 28 degr. 30 min. the which taken out of 360 degrees, rest 277 degr. 30 min. the latter point whereof fix under the fixed meridian, there holding the same, until by moving of the fixed meridian, you can bring the given amplitude on the East side to fit upon the first point of the meridian: which done, then shall you find the Pole elevated 51 degrees above the Horizon. PROPOSITIONS THAT ARE resolved upon the Terrestrial Globe. That all Propositions concerning the ☉, may as well be resolved upon the Terrestrial as the Celestial Globe. Proposition 1. To find the Latitude of any place. BRing the place, whose Latitude is required, to the meridian of the Globe, and the portion of the meridian included between that place and the equinoctial, showeth the Latitude. And so are the following places in Latitude Northward. London 51. d. 30. m. Hamborough. 54. Amsterdam 52. full. Antwerp. 51. scarce. Bolloigne. 48. 30. Paris. 48. 30. Lions. 46. Bourdeaux. 43. 40. S. Ander. 42. 30. The Groin. 43. Lisbon. 39 30. Seville. 37. 30. Cape-Martin 39 40. Genoa. 45. Roma. 42. Naples. 41 Palermo. 37. 30. Venice. 46. Ragusi. 42. Cyprus. 37. 15. Rhodus, 38. jerusalem. 34. 40. Teneriffe. 28. 30. Capo-blanco. 20. Isla S. Helena. 16. 40. Southward. Nombre de dios. 9 Northward. Panama. 8. Capodevela. 10. Havana. 22. San Domingo. 17. 30. Isle Icaris. 66. Fane Insul●. 64. 30. Islandie. 67. 30. Gibraltare. 35. Proposition 2. To find the Longitude of any place. BRing the place appointed to the meridian of the Globe, and the degrees cut by the meridian in the equinoctial, showeth the Longitude. And so are the places here under found in longitude, viz. London. 20. 30. longitude. Hamborough. 33. 30. Antwerp 26. 30. Paris. 24. Bourdeaux. 22. S. Ander. 18. 30. The Groin. 13. Lisbona. 13. Seville. 17. degrees. Genoa. 35. Roma. 37. Venice. 40. Palermo. 37. 30. jerusalem. 69. San Domingo in the West Indies. 310. Teneriffe. 3. degr. 30. Palona. 1. degr. longitude. Proposition 3. To find the difference between any two places upon the Globe. TAke the distance with a pair of compasses, and apply the same to the equinoctial, accounting for every degree 60 miles, or 20 leagues, or according to that country wherein you are. And so are the distances between London and jerusalem 39 facit 795. leagues. Antwerp 3. 30. facit 70. Paris. 4. 20. facit 86. ⅔. Venice 13. 40. facit 273. ⅓. Bourdeaux 8. 00. facit 170. Lisbona 13. ⅔. facit 273. Seville 14. ¾. facit 295. Roma 16. ½. facit 330 leagues. Teneriffe 27. 00. facit 540. Terra nova 28. 00. facit 560. Proposition 4. The Latitude and Longitude of any place being given, to find the same upon the Globe. BRing the Latitude of that place to the Meridian of the Globe, and under the Meridian in the Latitude, shall the place required be found. By the first and second Proposition is this Proposition resolved. Proposition 5. To find the Antipodes to any place. BRing the place appointed to the Meridian, and note the Latitude: then in the opposite degree of Latitude under the Meridian, you shall find the point of Antipodes. And after this sort are those Antipodes to London, that devil 51 degrees ½ Latitude, and in 198 degrees Longitude in the South-maine. And to Seville, those that devil in 37 degrees, 30 min. Latitude, and 196 degr. Longitude, are Antipodes. And to Lisbon, those that devil in 39 degr. 30 min. Latitude, and 192 deg. ½ Longitude, are Antipodes. And to Antwerp, those that devil in 51 degr. Latitude, and 195 deg. Longitude in the said South-maine. The people dwelling under the North and South pole, and under the Ecliptic poles, are Antipodes the one to the other. Those of Cusco in America, are Antipodes to those of Narsinga in East India. Those of Lyma and Calicut, are Antipodes to each other. The Insulanes of Serrana and jona, are Antipodes to each other. Those of Xalisco, Colinia, Guatatlan, Petratlan, Guaxaca, etc. are Antipodes, to the Insulanes of S. Laurence. Those of Malaca are Antipodes to that people dwelling in the province of Omagua. Proposition 6. To find the difference of time between any two places. BRing the Eastermost place to the Meridian, and rectify the Index: then bring the second place also to the Meridian, and mark where the Index cuts, it showeth the hour at that second place, when it is noon at the first. Or to do this more precisely, find the difference of the Longitude betwixt these two places: which remainder reduce into time, by allowing 15 degr. for an hour, and the difference is found. Proposition 7. To find the difference of the longest day between any two places. Find the length of the day at each place, by the Proposition before taught, and the difference between them is found by their several lengths. First it is to be noted, in Northern Latitude the longest day of the year is, when the ☉ is in the first point of ♋, and therefore according to that place is the longest days of several places here under set down, the which precisely have been calculated, by the difference of Ascension, that the ☉ made at one same time in several places. London lying in the Latitude of 51 deg. 30 m. and the place of the ☉ taken in the first degree of ♋, had right Ascension 90 degrees, and crooked Ascension 58 degr. Lisbona Latitude 39 30, makes 10 degr. difference of ascension: which doubled, facit 40 degr. those reduced into time, facit 2 hours 40 min. those added to 12, facit 14 hours, 40 min. for the longest day. Genoa Latitude 45 degrees, the ☉ right Ascension is 90 degrees, the crooked 68, is always of 12 hours long, but winter or summer the ☉ declineth North or Southward. Capo de vela in the West Indies in 12 degrees of Latitude, at the same time when the ☉ is in the first degree of ♋, hath 90 degrees right Ascension, and crooked 85 diff. is 5, which doubled is 10 min. which reduced make 40 min. of time, which added to 12 hours, showeth their longest day to be 12 hours, 40 min. Havana at the same time differeth the ☉ in Ascension 9 degr. 30 minutes, double makes 19, which is time one hour, 16 min. which added to 12, maketh 13 hours, 16 min. for their longest day. San Domingo Island maketh the ☉ 7 degrees ½ for difference of ascension: which doubled, maketh 15: is one hour time, so is their longest day 13 hours. Fair Island in 64 deg. of Latitude the ☉ hath at the same time 90 deg. right Ascension, crooked 30, rest 60 for difference thereof, which doubled, facit 120 degrees, which maketh time 8 hours, those added to 12 hours, showeth that the longest day there is 20 hours. At Icaria Island in 66 degrees Latitude, the ☉ being in the first degree of ♋, hath 90 degr. right Ascension, crooked 20, which difference is 70: those doubled, maketh 140 degr. which is 9 hours, 20 m. of time, so is their longest day of the year 21h. 20 minutes. Island in 67 degr. Latitude on the same time hath crooked Ascension 8 deg. which taken from 90, differeth 82 degrees, which doubled, are 164 degr. which reduced into time, do give 10 hours, 56 min. and those added to the equinoctial day, facit 22h. 56 min. for the longest day in the year. These differences of ascension is more precisely found by projecting the figures, and then by scale and Compass, and yet more precisely by Arithmetical calculation, by which the said difference and length of days are found. 14h. 20. min. jerusalem. 17. 30. 13. 48d. 56 min. Teneriffe. 13. 37. 13. 12d. 56 min. Capo-blanco. 9 7. 12. 32. Nombre de dios. 4. 12. 28. Panama. 3. 30. 12. — San Thome being under the equinoctial, the ☉ maketh no difference, and therefore always 12 hours. 12. 42. — Capo de vela 5. 15. 13. 20. 48. m. Havana. 10. 6. 13. 3. 4 m. San Domingo. 7. 53. 20. 44. 40 m. Fane Insula. 65. 35. 22. 9 20 m. Icari Insula. 76. 10. Proposition 8. To find the horizontal position and difference betwixt any two places. FIrst rectify the Globe for that place, from the which you would know the horizontal position and distance to the other place: bring also that first place to the Meridian of the Globe, than put the quadrant of Altitude on the Zenith, there let the Globe rest, then bring the quadrant of Altitude over the two places, and the degrees cut by the end of the quadrant in the Horizon, showeth the horizontal position, and the degree cut by the second place in the quadrant, accounted from the Centre downwards, showeth the distance. For example. The bearing of jerusalem to London is 50 degr. accounted from the North point Westward, and the distance is 38 degr. 30 minutes. And from London to jerusalem the bearing is 85 degrees, accounting from the South point Eastward, and the distance is as before. Now to find the rhomb, add the two horizontal positions together, and the one half thereof showeth it. From jerusalem to Aleppo, the bearing is 69 degrees from the North point Westward, the distance is 43 degr. ½: and Aleppo beareth to jerusalem 77 degrees from the North point Eastward. jerusalem to Teneriffe beareth 77 degr. from the North point Westward; and Teneriffe to jerusalem 64 degrees, accounting from the North point Eastwards; and the distance betwixt the two places is 55 degrees ½. jerusalem to Rome beareth 67 degr. from the North point Westward, distance 24. ½: Rome to jerusalem 86 degr. from the South point Westward. jerusalem to Gibraltare beareth 76 degr. from the North point Westward, and the distance is 43 degr. and Gibraltare to jerusalem beareth 73 degrees from the North point Eastward. OF THE WORLD. THe world is divided into two parts, viz. Elemental, and aetherial parts. The first is subject to daily alterations, and containeth four Elements: that is, the Earth, the Water, the Air, and the Fire. An element is that, whereof any thing is compounded, and of itself not compounded; of these four elements, any part of any kind is named for the whole, as any part of the earth is called the earth. The aetherial parts doth compass the elemental parts in the concavity thereof, and containeth 10 Spheres: whereof the first is the sphere of the Moon, and is next unto us. The second is Mercurius: the third Venus: the fourth Sol: the fifth Mars: the sixth, jupiter: the seventh, Saturnus: the eighth sphere is the starry firmament: the ninth is the Crystalline heaven: The tenth, Primum mobile, which doth contain all the rest within it, and whatsoever is beyond or above that, is the habitation of God and his Angels. The reason how these spheres were first found out, were their contrary motions in the heavens, observed by the ancient learned Astronomers, and we find that by our own observations, as thus, viz. First, all things in the heavens turn about the earth, upon the poles of heaven in four and twenty hours, and these motions are from the East into the West, and this we attribute to the motion of the 10 sphere, or Primum mobile, without staying, being so appointed by God from the beginning, and carrieth about with him in violence all the other spheres. All the rest of the spheres have contrary motions, every one in his kind, though far slower than the other, and their motions is contrary from the West to the East, and so are carried about often times by the first mover, before they make one perfect revolution in themselves. The Crystalline or ninth sphere his motion is almost unsensible, and is called the trembling motion, and is performed, according to Ptolemy his opinion, in 36000 years, but by the opinion of others in a far longer time, as in 49000. years. The eighth sphere, being the starry firmament, performeth his motion in 7000 years. The rest of the spheres are the seven Planets, each sphere containeth in it but one star, whereof the uppermost and slowest is Saturn, which performeth his course in 24 years, 162 days, and 12 hours. jupiter performeth in 11. years, 133 days, and 23 hours. Mars performeth in 322 days, and 23 hours. Sol performeth in 365 days & 6 hours, which is one whole year. Venus in 385 days, 9 hours, performeth her course. Mercury performeth as the ☉ in 365 days, and 6 hours. Luna performeth her course once every 27 days, and 12 hours. THE CHARACTERS OF THE Planets are these following. Saturn ♄ Mars ♂ Venus ♀ jupiter ♃ Sol ☉ Mercury ☿ Luna ☽ THere are points movable in the Ecliptic, which are called the Dragon's head, and the Dragon's tail, and their characters are these: Dragons head ☋, Dragons tail ☊. The Dragon's head is the point in the Ecliptic, which the ☽ toucheth, when she crosseth the Ecliptic, and passeth to the Northwards of it. The ☊ is the point in the Ecliptic, where the ☽ passeth by, when she crosseth the Ecliptic, & passeth by it to the South, and these two points are opposite the one to the other. To know how the Planets reign every hour of the day, and night: beginning with Saturday. Hours of the day. 1. 2. 3. 4. 5. 6. 7. 8. 9 10. 11. 12. Sat. ♄. ♃. ♂. ☉. ♀. ☿. ☽. ♄. ♃. ♂. ☉. ♀. ☉. ♀. ☿. ☽. ♄. ♃. ♂. ☉. ♀. ☿. ☽. ♄. ☽. ♄. ♃. ♂. ☉. ♀. ☿. ☽. ♄. ♃. ♂. ☉. ♂. ☉. ♀. ☿. ☽. ♄. ♃. ♂. ☉. ♀. ☿. ☽. ☿. ☽. ♄. ♃. ♂. ☉. ♀. ☿. ☽. ♄. ♃. ♂. ♃. ♂. ☉. ♀. ☿. ☽. ♄. ♃. ♂. ☉. ♀. ☿. ♀. ☿. ☽. ♄. ♃. ♂. ☉. ♀. ☿. ☽. ♄. ♃. Hours of the night. 1. 2. 3. 4. 5. 6. 7. 8. 9 10. 11. 12. Sat. ☿ ☾ ♄ ♃ ♂ ☉ ♀ ☿ ☾ ♄ ♃ ♂ ♃ ♂ ☉ ♀ ☿ ☾ ♄ ♃ ♂ ☉ ♀ ☿ ♀ ☿ ☾ ♄ ♃ ♂ ☉ ♀ ☿ ☾ ♄ ♃ ♄ ♃ ♂ ☉ ♀ ☿ ☾ ♄ ♃ ♂ ☉ ♀ ☉ ♀ ☿ ☾ ♄ ♃ ♂ ☉ ♀ ☿ ☾ ♄ ☾ ♄ ♃ ♂ ☉ ♀ ☿ ☾ ♄ ♃ ♂ ☉ ♂ ☉ ♀ ☿ ☾ ♄ ♃ ♂ ☉ ♀ ☿ ☾ FINIS.