A BRIEF TREATISE OF THE VSE OF THE Globe Celestiall and Terrestriall:
WHEREIN IS SET DOWNE the principles of the Mathematicks, fit for all trauellers, Nauigators, and all others that doe loue 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 Doe here present thee (gentle Reader) with a briefe collection of the vse of the Globe, which may serue for an introduction to young Students in the Mathematikes, requiring thee to accept thereof: for I doubt not it will be very good for the furtherance of trauellers in the Art of Nauigation: and to all others that are desirous of the knowledge of the beautifull frame of the celestiall Orbs, with their quantities, distances, courses, and marueilous motions of the Globes of the Sunne, Moone, Planets and fixed starres. If therefore this my labour shall be gratefully accepted, as I doubt not but it shall, if thou please iustly to censure thereof: I shall be incouraged hereafter to set foorth a worke [Page] of more worth: so I referre my selfe to your fauourable iudgements and curtesies, committing thee to the sacred tuition of him that ruleth all. Farewell.
INTRODVCTION TO Astronomy.
Definitions of the Globe.
THE Globe is a perfect round bodie, contained vnder one plaine: in the middle thereof there is a poynt called the Cē ter, from whence all lines drawne to the outside are of like length, and called Semidiameters.
The axes of the Globe is a diameter, about which it moueth; and the ends thereof are called the poles of the Globe.
In this respect the frame of the heauens is called the Globe of the heauens, and the earth his Center.
The axes is a line imagined, passing by [Page 2] the Center of the earth to the heauens, and the ends thereof is called the poles, which are two points imagined in the heauens, 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 certaine imaginarie lines, and are termed either lesser, or greater Circles.
Greater Circles are such as diuideth the Globe into two equall parts.
Lesser are such as diuide the Globe into vnequall parts.
Greater Circles of the Globe in common account are sixe in number, viz.
- Horizon.
- Meridian.
- Equinoctiall.
- Zodiake.
- Two Collures.
Lesser Circles in common account are foure in number, viz.
- Two Tropicks.
- Two poler Circles.
The Horizon diuideth that part of the [Page 3] heauens we doe see, from that part wee see not, and is that Circle, where standing in a plaine field, and looking about, you would imagine the earth and heauens doe meete together, and cannot be perfectly discerned but at sea.
The axes of the Horizon, is an imagined line, passing by the Center of the earth to the heauens, and the ends thereof, are called the poles Zenith and Nadir.
The Zenith is the point direct ouer our heads, and the Nadir direct vnder our feet.
As a man moueth himselfe any way, so is altered the Horizon.
The Meridian cutteth the Horizon at right sphericall angles, and passeth by the poles of heauen, and by the Zenith and Nadir, and is that Circle wherein the ☉ is at noone, and at midnight: it diuideth the Globe into two equall parts by East and West, whose axes is a line passing by the Center of the earth to the heauens, and the ends thereof the poles, which are the two points of the intersection of the East and West.
Any many mouing directly North and South, keepeth the same Meridian: but going East or West, he altereth the same.
[Page 4] The Equinoctiall cutteth the Meridian at right sphericall angles, and lieth equidistant betwixt each poles, and diuideth the Globe into two equall parts, by North and South parts, to which Circle when the ☉ commeth vnder it, it maketh the day and night of like length to all people in the world, except vnder the poles, and the ☉ commeth vnder this Circle two daies in the yeere, viz. the 11. of March, and on the 14. of September.
The axes and poles whereof are the axes and poles of heauen.
The Zodiack is a great Circle, hauing in breadth twelue degrees, which breadth is limited for the wandring of planets, vpon which Circle are the twelue signes placed, which are twelue Constellations.
A Constellation is any certaine number of stars, gathered together into one forme by the ancient Astronomers, who haue giuen them names, whereby they are knowne to all Christendome: which signes haue certaine characters giuen vnto them, and are these following.
- [Page 5]1 March.
- 2 Aprill.
- 3 May.
- 4 Iune.
- 5 Iuly.
- 6 August.
- 1 Aries. ♈
- 2 Taurus. ♉
- 3 Gemini. ♊
- 4 Cancer. ♋
- 5 Leo. ♌
- 6 Virgo. ♍
- 7 Septemb.
- 8 October.
- 9 Nouember.
- 10 Decemb.
- 11 Ianuary.
- 12 February.
- 7 Libra. ♎
- 8 Scorpio. ♏
- 9 Sagittarius. ♐
- 10 Capricornus ♑
- 11 Aquarius ♒
- 12 Pisces. ♓
The first sixe are called Northen signes, for that they are placed vpon the North side of the equinoctiall; and the last sixe are called Southerne signes, for that they are placed vpon the South side of the equinoctiall.
In the middle of the Zodiacke is a line called the ecliptick, from which line the Center of the ☉ neuer swarueth, and this line cutteth the equinoctiall at oblique angles, and swarueth from it 23 degrees 30 minutes: which line when the ☉ and ☽ are in a diameter, that is, opposite, then is the ☽ eclipsed, that is, darkned by the shadow [Page 6] of the earth, the earth being betwixt the ☉ and the ☽.
And when the ☉ and ☽ are both vnder the line in a semidiamiter, then is the ☉ eclipsed, the ☽ being interposed betwixt our sight and the ☉: this line eclipticke is described vpon the Globe for the whole Zodiack, whose axe is a line passing by the Center of the earth to the heauens, and the ends thereof are his poles, which are two points so farre distant from the poles of the world, as the ☉ his greatest distance from the equinoctiall, viz. 23 degrees 30 min.
The two Collures are two meridians cutting the equinoctiall, and the eclipticke into foure equall parts, the one passing by the first point of ♈ and ♎, and is called the equinoctiall Collure. The other passing by the first point of ♋ and ♑, and is called the solstitiall Collure: these two Circles do diuide the yeere in foure equall parts, viz. Spring-time, Sommer, Haruest, and Winter.
- 1 ♈
- 2 ♉
- 3 ♊
- 4 ♋
- 5 ♌
- 6 ♍
- [Page 7]7 ♎
- 8 ♏
- 9 ♐
- 10 ♑
- 11 ♒
- 12 ♓
The meaning wherof is thus: From that time the ☉ entreth into ♈, till it enter into ♋, is called Spring-time, and so of the rest, so that it is the passage of the ☉ in the signes, that causeth the alteration of season, and the ☉ passeth thoroughout the whole signes in one yeere, viz. in 365 daies and 6 houres neere.
Of the lesser Circle.
THe Tropick of ♋ is a Circle parallel to the equinoctiall 23 degrees 30 min. distant frō it, Northward, and is that Circle vnder which the Center of the ☉ maketh her diagonall arke, when she is in the first point of ♋, which is to vs that haue Northen Latitude, the longest day in the yeere being the 12 or 13 of Iune.
The Tropick of ♑ is a Circle parallel to the equinoctiall, so farre to the Southward, as the Tropick of ♋ is Northward, viz. 23 degrees 30 min. and is that Circle vnder which the Center of the ☉ maketh [Page 8] her diagonall arke, when she is in the first point of ♑, which to vs that haue Northen Latitude, is the shortest day in winter, viz. the 12. or 13. of December. These two Circles are termed the limit of the ☉ progresse: for betweene these two Circles the ☉ hath his continuall course, and neuer exceedeth beyond any of them.
The Circle articke is a Circle parallel to the equinoctiall, so farre distant from the North pole, as the tropicke of Cancer is from the equinoctial, viz. 23. degr. 30. min.
The Circle antarticke is a Circle parallel to the equinoctiall so farre distant from the South pole, as the tropick of ♑ is from the equinoctiall, viz. 23. degr. 30. min.
Now you must vnderstand, there is but one Equinoctiall, one Zodiacke, one Ecliptick, two Collures.
But there are diuers Meridians, al which meete in the two poles of the world, and cut the equinoctiall at right angles, and are so many in number as there can be points imagined in the equinoctiall.
There are diuers Horizons: for the Horizon altereth to any man, according as he moueth himselfe from his place of being.
There are diuers Parallels, so called for [Page 9] that they are parallel to the equinoctiall, and are so many in number, as there can be points imagined in the Meridian.
Besides these Circles, before mentioned, there are foure other kinde of Circles of great vse, viz. Azimoth and Almicanthars, Circles of Longitude and Latitude.
Azimoths are great Circles, and meete all in the Zenith, and Nadir, and cut the Horizon at right angles, and are numbred in the Horizon.
Almicanthars are lesser Circles parallel to the Horizon, as the parallels are to the equinoctiall, and are numbred from the Horizon towards the Zenith.
Circles of Longitude are great Circles, meeting all in the poles of the Eclipticke, and cut the Eclipticke at right angles, and are numbred in the Ecliptick.
Circles of Latitude are lesser Circles parallel to the Ecliptick, as the parallels are to the equinoctiall, and are numbred from the Eclipticke, to the poles of the Eclipticke.
Euery Circle of the Globe is imagined to be diuided into 360 degrees, and euery degree into 60. minutes, euery minute into 60 seconds, and so tell the tenth for the precisenes, [Page 10] for that a degree in the heauens is a large space.
In euery great Circle the degrees are equall one to another.
In euery lesser Circle they are equall in the same Circle, but vnequall to those of another Circle, according as they grow neerer the poles.
There belongeth to the furnishing of a Globe two other things, that is, an houre Circle, with Index and a quadrant of Altitude.
The houre Circle is of brasse, diuided into 24. houres by twice 12, and is to be placed vpon the Meridian, vpon the pole eleuated parallel to the equinoctiall.
The Index is a little ruler to be put vpon the pole.
The quadrant of Altitude is a bowed ruler of brasse, diuided into 60. degrees, equal to the degrees of the Globe, and hath a ioint to fasten the same vpon the Meridian, and is alwaies to be placed vpō the Zenith.
For the practise of Astronomie & Cosmographie, there are two Globes made, the one of the Heauens, which is called the Celestiall globe, and the other of the Earth, which is called the Terrestriall globe.
[Page 11] Vpon the Celestiall Globe are pictured al the starres vpon the Conuexitie thereof, as wee behold them in the heauens, in the Concauitie there of in forme and distance.
Vpon the Globe of the earth is set sea and land, making one perfect body, all the knowne parts being laid downe in forme, proportion, and distance by scale, according to the proportion of the earth.
Of the superficies of the Celestiall Globe.
TO the intent that the knowledge of starres might bee brought in rule and memorie of men, therefore the ancient Astronomers gathered them together into certaine constellations, and gaue them names, whereby they are knowne vnto all the world, y t haue the knowledge of letters.
A Constellation is a certaine number of starres gathered together in one forme, and so retaine their names, whereby they are particularly knowne, and are in number, according to the ancient account, 48. and are diuided into three parts, viz.
- Northen
- Zodiake
- Southerne
- 21
- 12
- 15
[Page 14] Besides these there are 120. starres that are exempt out of all the Constellations, so that the number of stars set vpon the Globe are 1025, and diuers of them haue proper names, which I here omit.
You must vnderstand that all the starres in heauen are not numbred, nor cannot, for that diuers of them are so small, but these 2025 are the principallest amongst them, and all that haue yet euer been accounted of.
You must vnderstand, that of these stars some are greater then other, and [...] distinguished in sixe sorts of b [...]gnesses, and their measures is the earth, and their proportions are thus deliuered, viz.
A starre of the first bignes is 107. times bigger then the earth.
A starre of the second bignes is 90. times the globe of the earth.
A starre of the third bignes is 72 times the globe of the earth.
A starre of the fourth bignes is 54 times the globe of the earth.
A starre of the fifth bignes is 36 times the globe of the earth.
A starre of the sixth bignes is 18 times the globe of the earth.
| 1 | 15 | |||
| 2 | 45 | |||
| Stars magnitude, | 3 | and the quantitie of each magnitude. | 208 | |
| 4 | 474 | In all 1025 | ||
| 5 | 427 | |||
| 6 | 49 | |||
| Cloudie. | 5 | |||
| Obscure. | 9 | |||
| Parnassus fayre. | 3 |
Vpon each Globe there is a table set downe in what forme euery starre of any bignes is made, whereby you may readily know any starre in any Constellation of what bignes it is.
And thus much in briefe for the superficies of the Globe of the Heauens.
[Page 18] haue Sotherne Latitude that dwell on the South side of the equinoctiall.
- 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 riuer Tanis and Dwiana.
- 1 Germanie.
- 2 Italy.
- 3 France.
- 4 Spayne.
- 5 Denmarke.
- 6 Norway.
- 7 Swedeland.
- 8 Moscouia.
- 9 Polonia.
- 10 Hungaria.
- 11 Clauonia and
- 12 Grecia.
- 1 England.
- 2 Scotland.
- 3 Ireland.
- 4 Sicilia.
- 5 Candia.
- 6 Corsica.
- 7 Sardigna.
- 8 Negroponte.
Asia is bounded from Europe by the riuer Tanis and Dwiana, from Afrieke by the narrow necke of Land betwixt the red sea, and the mid-land sea.
- [Page 19]China.
- Persia.
- Part of Moscouia, and
- Tartaria.
In this part of the world was Paradise and the Land of promise.
Africa is bounded with the mid-land sea and the red sea.
- 1 Egypt.
- 2 Barbaria.
- 3 Aethiopia.
- 4 Nubia.
- 5 Abasmies.
- 6 A [...]onomotopa.
- 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 straight of Magellanus, and consisteth in two parts, viz.
- Mexicana.
- Pe [...]ana.
FIRST PROPOSITION OF the Celestiall Globe. The day of the moneth being giuen, to finde the place of the ☉.
VPon the Horizon of the Globe is graduated the theoricke of the ☉, that is, there is placed the moneth, and their daies, the signes and their degrees. Therefore finde the day of the moneth, and right against the same you shall finde the signe and degree that the ☉ possesseth.
Proposition 2. The place of the ☉ being giuen, to finde the day of the moneth.
FInde the place of the ☉ in the Horizon, and against the same you shall finde the day of the moneth.
Proposition 3. The place of the ☉ being giuen, to finde the Declination.
BRing the place of the ☉ to the Meridian of the Globe, and the portion of [Page 23] the Meridian included betwixt the place of the ☉ and the equinoctiall, sheweth the declination.
Proposition 4. The place of the ☉ and the Meridian height of the ☉ being giuen, to finde the height of the Pole.
BRing the place of the ☉ to the Meridian of the Globe, and from that point account 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 finde cut on the Meridian the height of the Pole, that is, the portion of the Meridian included betwixt the Pole and Horizon, sheweth the height of the Pole.
Proposition 5. To rectifie the Globe fit for vse, the eleuation of the Pole being knowne.
SEt the poles answerable to the poles of Heauen.
Proposition 6. To rectifie the quadrant of altitude.
SEt the ioynt thereof vpon the Meridian so farre distant from the equinoctiall, as the poles is eliuated aboue the Horizon, that is, place the ioynt in the Zenith.
Proposition 7. To rectifie the Index of the houre Circle, for any day appointed.
BRing the place of the ☉ to the Meridian of the Globe, and then put the Index vpon 12 of the clocke, or vpon that 12, which is vppermost from the Horizon.
Proposition 8. The eleuation of the Pole and place of the ☉ being giuen, to finde 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, sheweth the demaund.
Proposition 9. The eleuation of the Pole and place of the ☉ being giuē, to find the houre of the ☉ rising.
THe Globe and Index of the houre circle being rectified, bring the place of the ☉ to the East side of the Horizon, and the Index of the houre circle sheweth the houre of the ☉ rising.
Proposition 10. The eleuation of the Pole and place of the ☉ being giuen, to finde the houre of the ☉ setting.
THe Globe and Index of the houre circle being rectified, bring the place of the [...] [...]o the West side of the Globe, and the Index of the houre circle sheweth the houre of the ☉ setting.
Proposition 11. The eleuation of the Pole and place of the ☉ being giuen, to finde the length of the day.
FInde the houre of ☉ setting by the last proposition, and double that time, so haue you the length of the day.
Proposition 12. The eleuation of the Pole and place of the ☉ being giuen, to finde 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, sheweth the amplitude.
Proposition 13. The place of the ☉ and Amplitude being giuen, to finde the height of the Pole.
TVrne the Globe and moue the Meridian vntill you haue fitted the place of the ☉ in the point of the Amplitude, and then the pole of the Globe sheweth the height of the pole, that is, the place included betwixt the pole of the Globe and the Horizon, sheweth in the Meridian the height thereof.
Proposition 14. The place of the ☉ being giuen, to finde the right ascention thereof.
BRing the place of the ☉ to the Meridian, and the degree cut by the Meridian [Page 27] in the Equinoctiall, sheweth the right Ascention.
Proposition 15. The eleuation of the Pole and place of the ☉ being giuen, to find the crooked Ascention.
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, sheweth y e crooked Ascention.
Proposition 16. To finde the difference of Ascention.
FIrst finde the right, and then the crooked Ascention: then take the lesse from the greater, and that rest sheweth the differēce of Ascention, except that remainer do exceed 180 degrees, and then that rest taken from 360 degrees, sheweth the difference of Ascention.
Proposition 17. By the difference of Ascention, to finde the length of the day.
DOuble the difference of Ascention, & reduce that into time, by allowing 15 [...] [Page 30] turne the Globe, vntill the place of the ☉ touch the edge of the quadrant, then the Index of the houre Circle sheweth the houre, and the degree cut on the quadrant of altitude, sheweth the height of the ☉ at that time.
Proposition 22. The houre of the day being giuen, to finde the Azminth of the ☉.
ALL things rectified, turne the Index to the houre: then bring the quadrant of Altitude on the place of the ☉, and the end thereof in the Horizon sheweth the Azminth.
OF THE STARS.
Proposition 1. To finde the Declination of any Starre.
VVOrke by the Starre, as you did by the ☉ in the 3. Proposition, viz. An example: Arcturus in Bootes leggs brought to the Meridian of the Globe, the portion of the Meridian betwixt the place and the equinoctiall, sheweth his declination to be Northerne.
Proposition 2. The meridian height of any starre being giuen, to finde the height of the Pole.
VVOrke by the starre, as you did by the ☉ in the 4. Proposition, viz. Arcturus meridional height supposed to be giuen 60 degr. then the height of the Pole opposite is found to be 52 degrees.
Proposition 3. To finde the houre of rising of any starre.
AL things rectified, work by the starre, 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 signe the ☉ is. As for example: The ☉ rising in the 19 degree of ♑, which being brought vnder the fixed Meridian, and then the Globe and Index rectified, Arcturns is then found to rise at 6 houres, and 30 minutes in the morning, and setteth in the euening at houre 10. 30 minutes.
Proposition 4. To finde the houre of any starre setting.
AL things rectified, work by the starre, as by the ☉ in the 10 Proposition, or precedent demonstration.
Proposition 5. To finde the time of any starre aboue the earth.
FIrst finde the houre of rising, and then the houre of setting: the difference of [Page 33] which time is the thing required.
Example.
Arcturus is found by the former Propositiō to rise at houre 6. 30, which is 5. 30 before 12, and hee setteth at 10. 30: both which times added together, maketh 16 houres, and so is Arcturus found to be 16 houres aboue the earth.
Proposition 6. To finde the amplitude of any starre.
VVOrke 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 starre being giuen, to finde the height of the Pole.
VVOrke by the * as by the ☉ in the 13 Proposition. Example: Arcturus amplitude being giuen, 37 degrees; the Pole of heauen is found to be 52 degr. aboue the Horizon eleuated.
Proposition 8. To finde the right Ascention of any starre.
VVOrke by the starre, as by the Sun in the 14 Prop. Example: Bring Arcturus to the Meridian, and the point in the equinoctiall being then vnder the Meridian, sheweth the right Ascention to be 209 degrees.
Proposition 9. To find the crooked Ascention of any starre.
VVOrke by the starre, as you did by the Sunne in the 15 Proposition. Example: The place of Arcturus being brought to the Horizon, the degrees of the equinoctiall against the Horizon, doe proue his crooked Ascention to be 178 degrees.
Proposition 10. To finde the Latitude of any starre.
PVt the center of the Quadrant of Altitude, being taken from the Meridian, [Page 35] vpon the pole of the eclipticke, viz. Arcturus Latitude is to be measured from the pole eclipticke 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 eclipticke, to the eclipticke or zodiack, passing right on the place of Arcturus.
Compostella in Galicia is by sundrie matters found to bee 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.
- Latitude or Altitude, beginneth from the equinoctiall by parallels Northward or Southwards, to bee reckoned to 90 degrees.
- Longitude to bee reckoned by Meridians numbred in the equinoctiall, which is that meridian passing betweene the equinoctial and the Iles of the Canaries, & are numbred into the East round about y e globe, viz. to 360 degrees.
[Page 36] One houre containeth 15 degrees or 60 minutes, and 4 of those minutes containe one degree: therefore diuiding still your number of minutes by 4, and the quotient shall be degrees.
Example.
Twelue minutes of an houre giue three degrees of Longitude, which is 12 min. so that euery minute of an houres time is ¼ part of one degree in Longitude, as is proued by the worke following.
Here followeth the 11 Proposition concerning the Starres.
Two starres seene in the Horizon to rise or to set at one time, thereby to finde the height of the Pole. Example.
THe two starres rising together, the one is the first starre in Orions girdle, and the other * is that which is in Pegasus nose: therefore turne the Globe vntill you fit the said two starres equall 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 giuen, to finde the height of the Pole.
THe place of the ☉ giuen is in 17 degr. of ♎, and the length of the day giuen, is 11 houres. Therefore first finde out the right ascention of the ☉, then number frō that place so many meridians, as doe containe the halfe length of the day giuen, and let the end of those degrees rest vnder the fixed meridian: then moue the meridian of the Globe, vntill you fit the place of the ☉ in the Horizon, and then shall you finde vpon the meridian the iust height of the Pole. For example.
The ☉ being in 17. degrees of ♎, her right ascention is found to be 195 degrees, the daies length giuen is 11: therfore take the one halfe, that is 5 houres ½: which time reduced into degrees, facit 82 degrees 30 min. the which subtracted out of the ☉ ascention 195, there rest 112 degr. 30 min. which number finde out vpon the equinoctial, and bring it to the fixed meridian, and there keepe the same, vntill by mouing the meridian you do bring the 17 degree of ♎ equall with the Horizon: that done, then [Page 38] will the height of the Pole be found eleuated iust 51 degrees.
Proposition 13. The length of the day and amplitude of the ☉ being giuen, to finde the height of the Pole, and the ☉ declination.
THe length of the day giuen, is eleuen houres. The amplitude of the ☉ giuen, is 10 degrees. Therfore number from the first meridian Westward, those degrees that haue the length of the giuen day, reduced in degrees doe yeeld, and let the end of those degrees begin in the equinoctiall rest vnder the fixed meridian: then moue the globe vntill you haue fitted y e first meridian to cut in the amplitude giuen, and then shal the meridian of the Globe shew the iust height of the Pole. Example.
The length of y e day giuen, is 11 houres, whose halfe 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 fixe vnder the fixed meridian, there holding the same, vntill by mouing of the fixed meridian, you can bring the giuen amplitude on the East [Page 39] side to fit vpon the first point of the meridian: which done, then shall you finde the Pole eleuated 51 degrees aboue the Horizon.
PROPOSITIONS THAT ARE resolued vpon the Terrestriall Globe. That all Propositions concerning the ☉, may as well be resolued vpon the Terrestriall as the Celestiall Globe.
Proposition 1. To finde 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 betweene that place and the equinoctiall, sheweth the Latitude.
- London 51. d. 30. m.
- Hamborough. 54.
- Amsterdam 52. full.
- Antwerpe. 51. scarce.
- Bolloigne. 48. 30.
- Paris. 48. 30.
- [Page 40] Lyons. 46.
- Bordeaux. 43. 40.
- S. Ander. 42. 30.
- The Groyne. 43.
- Lisborne. 39. 30.
- Seuill. 37. 30.
- Cape-Martin 39. 40.
- Genoa. 45.
- Roma. 42.
- Naples. 41
- Palermo. 37. 30.
- Venice. 46.
- Ragusi. 42.
- Ciprus. 37. 15.
- Rhodus, 38.
- Ierusalem. 34. 40.
- Teneriffe. 28. 30.
- Capo-blanco. 20.
- Isla S. Helena. 16. 40. Southward.
- Nombre de dios. 9. Northward.
- Panama. 8.
- Capodeuela. 10.
- Hauana. 22.
- San Domingo. 17. 30.
- Isle Icaris. 66.
- Fane Insul [...]. 64. 30.
- Islandie. 67. 30.
- Gibraltare. 35.
Proposition 2. To finde the Longitude of any place.
BRing the place appointed to the meridian of the Globe, and the degrees cut by the meridian in the equinoctiall, sheweth the Longitude.
And so are the places here vnder found in longitude, viz.
- London. 20. 30. longitude.
- Hamborough. 33. 30.
- Antwerpe 26. 30.
- Paris. 24.
- Bordeaux. 22.
- S. Ander. 18. 30.
- The Groyne. 13.
- Lisbona. 13.
- Seuill. 17. degrees.
- Genoa. 35.
- Roma. 37.
- Venice. 40.
- Palermo. 37. 30.
- Ierusalem. 69.
- San Domingo in the West Indies. 310.
- Teneriffe. 3. degr. 30.
- Palona. 1. degr. longitude.
Proposition 3. To finde the difference betweene any two places vpon the Globe.
TAke the distance with a paire of compasses, and apply the same to the equinoctiall, accounting for euery degree 60 miles, or 20 leagues, or according to that countrey wherein you are.
And so are the distances betweene
- Ierusalem 39. facit 795. leagues.
- Antwerpe 3. 30. facit 70.
- Paris. 4. 20. facit 86. ⅔.
- Venice 13. 40. facit 273. ⅓.
- Bordeaux 8. 00. facit 170.
- Lisbona 13. ⅔. facit 273.
- Seuill 14. ¾. facit 295.
- Roma 16. ½. facit 330 leagues.
- Teneriffe 27. 00. facit 540.
- Terra noua 28. 00. facit 560.
Proposition 4. The Latitude and Longitude of any place being giuen, to finde the same vpon the Globe.
BRing the Latitude of that place to the Meridian of the Globe, and vnder [Page 43] the Meridian in the Latitude, shall the place required be found.
By the first and second Proposition is this Proposition resolued.
Proposition 5. To finde the Antipodes to any place.
BRing the place appointed to the Meridian, and note the Latitude: then in the opposite degree of Latitude vnder the Meridian, you shall finde the point of Antipodes.
And after this sort are those Antipodes to London, that dwell 51 degrees ½ Latitude, and in 198 degrees Longitude in the South-maine.
And to Seuill, those that dwell in 37 degrees, 30 min. Latitude, and 196 degr. Longitude, are Antipodes.
And to Lisbone, those that dwell in 39 degr. 30 min. Latitude, and 192 deg. ½ Longitude, are Antipodes.
And to Antwerpe, those that dwell in 51 degr. Latitude, and 195 deg. Longitude in the said South-maine.
The people dwelling vnder the North and South pole, and vnder the Eclipticke [Page 44] 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 Iona, are Antipodes to each other.
Those of Xalisco, Colinia, Guatatlan, Petratlan, Guaxaca, &c. are Antipodes, to the Insulanes of S. Laurence.
Those of Malaca are Antipodes to that people dwelling in the prouince of Omagua.
Proposition 6. To finde the difference of time betweene any two places.
BRing the Eastermost place to the Meridian, and rectifie the Index: then bring the second place also to the Meridian, and marke where the Index cuts, it sheweth the houre at that second place, whē it is noone at the first. Or to doe this more precisely, finde the difference of the Longitude betwixt these two places: which remainder reduce into time, by allowing 15 degr. for an houre, and the difference is found.
Proposition 7. To finde the difference of the longest day betweene any two places.
FInde the length of the day at each place, by the Proposition before taught, and the difference betweene them is found by their seuerall lengths.
First it is to be noted, in Northen Latitude the longest day of the yeare is, when the ☉ is in the first point of ♋, and therefore according to that place is the longest daies of seueral places here vnder set down, the which precisely haue been calculated, by the difference of Ascention, that the ☉ made at one same time in seuerall places.
London lying in the Latitude of 51 deg. 30 m. and the place of the ☉ taken in the first degree of ♋, had right Ascention 90 degrees, and crooked Ascention 58 degr.
Lisbona Latitude 39. 30, makes 10 degr. difference of Ascention: which doubled, facit 40 degr. those reduced into time, facit 2 houres 40 min. those added to 12, facit 14 houres, 40 min. for the longest day.
Genoa Latitude 45 degrees, the ☉ right Ascention is 90 degrees, the crooked 68, [...] [Page 48] is alwaies of 12 houres long, but winter or sommer 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 Ascention, and crooked 85 diff. is 5, which doubled is 10 min. which reduced make 40 min. of time, which added to 12 houres, sheweth their longest day to be 12 houres, 40 min.
Hauana at the same time differeth the ☉ in Ascention 9 degr. 30 minutes, double makes 19, which is time one houre, 16 min. which added to 12, maketh 13 houres, 16 min. for their longest day.
San Domingo Iland maketh the ☉ 7 degrees ½ for difference of Ascention: which doubled, maketh 15: is one houre time, so is their longest day 13 houres.
Faire Iland in 64 deg. of Latitude the ☉ hath at the same time 90 deg. right Ascention, crooked 30, rest 60 for difference thereof, which doubled, facit 120 degrees, which maketh time 8 houres, those added to 12 houres, sheweth that the longest day there is 20 houres.
At Icaria Iland in 66 degrees Latitude, [Page 49] the ☉ being in the first degree of ♋, hath 90 degr. right Ascentiō, crooked 20, which difference is 70: those doubled, maketh 140 degr. which is 9 houres, 20 m. of time, so is their longest day of the yeere 21 h. 20 minutes.
Island in 67 degr. Latitude on the same time hath crooked Ascention 8 deg. which taken from 90, differeth 82 degrees, which doubled, are 164 degr. which reduced into time, doe giue 10 houres, 56 min. and those added to the equinoctiall day, facit 22 h. 56 min. for the longest day in the yeere.
These differences of Ascention is more precisely found by proiecting the figures, and then by scale and Compasse, and yet more precisely by Arithmeticall calculation, by which the said difference and length of daies are found.
14 h. 20. min. Ierusalem. 17. 30.
13. 48 d. 56 min. Teneriffe. 13. 37.
13. 12 d. 56 min. Capo-blanco. 9. 7.
12. 32. Nombre de dios. 4.
12. 28. Panama. 3. 30.
12. —San Thome being vnder the equinoctial, the ☉ maketh no difference, and therefore alwaies 12 houres.
[Page 50] 12. 42. —Capo de vela 5. 15.
13. 20. 48. m. Hauana. 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 finde the Horizontall position and difference betwixt any two places.
FIrst rectifie the Globe for that place, from the which you would know the Horizontall position and distance to the other place: bring also that first place to the Meridian of the Globe, then put the quadrant of Altitude on the Zenith, there let the Globe rest, then bring the quadrant of Altitude ouer the two places, and the degrees cut by the end of the quadrant in the Horizon, sheweth the Horizontall position, and the degree cut by the second place in the quadrant, account from the Center downwards, sheweth the distance.
For example.
The bearing of Ierusalem to London is 50 degr. accounted from the North point Westward, and the distance is 38 degr. 30 [Page 51] minutes. And from London to Ierusalem the bearing is 85 degrees, accounting from the South point Eastward, and the distance is as before.
Now to finde the Rhombe, adde the two Horizontall positions together, and the one halfe thereof sheweth it.
From Ierusalem to Aleppo, the bearing is 69 degrees from the North point Westward, the distance is 43 degr. ½: and Aleppo beareth to Ierusalem 77 degrees from the North point Eastward.
Ierusalem to Teneriffe beareth 77 degr. from the North point Westward; and Teneriffe to Ierusalem 64 degrees, accounting from the North point Eastwards; and the distance betwixt the two places is 55 degrees ½.
Ierusalem to Rome beareth 67 degr. from the North point Westward, distance 24. ½: Rome to Ierusalem 86 degr. from the South point Westward.
Ierusalem to Gibraltare beareth 76 degr. from the North point Westward, and the distance is 43 degr. and Gibraltare to Ierusalem beareth 73 degrees from the North point Eastward.
OF THE WORLD.
THe world is diuided into two parts, viz. Elementall, and Etheriall parts.
The first is subiect to daily alterations, and containeth foure Elements: that is, the Earth, the Water, the Aire, and the Fire.
An element is that, whereof any thing is compounded, and of it selfe not compounded; of these foure elemēts, any part of any kinde is named for the whole, as any part of the earth is called the earth.
The Etheriall parts doth compasse the elementall parts in the concauitie thereof, and containeth 10 Spheres: whereof the first is the sphere of the Moone, and is next vnto vs. The second is Mercurius: the third Venus: the fourth Sol: the fifth Mars: the sixth, Iupiter: the seuenth, Saturnus: the eighth sphere is the starrie firmament: the ninth is the Christaline heauen: The tenth, Primum mobile, which doth containe all the rest within it, and whatsoeuer is beyond [Page 53] or aboue that, is the habitation of God and his Angels.
The reason how these spheres were first found out, were their contrarie motions in the heauens, obserued by the ancient learned Astronomers, and we finde that by our owne obseruations, as thus, viz.
First, all things in the heauens turne about the earth, vpon the poles of heauen in foure and twentie houres, and these motions are from the East into the West, and this wee attribute to the motion of the 10 sphere, or Primum mobile, without staying, being so appointed by God frō the beginning, and carrieth about with him in violence all the other spheres.
All the rest of the spheres haue contrarie motions, euery one in his kinde, though farre slower then the other, and their motions is contrary from the West to the East, and so are carried about often times by the first mouer, before they make one perfect reuolution in themselues.
The Christaline or ninth sphere his motion is almost vnsensible, and is called the trembling motion, and is performed, according to Ptolomie his opinion, in 36000 yeeres, but by the opinion of others in a [Page 54] farre longer time, as in 49000. yeeres.
The eighth sphere, being the starrie firmament, performeth his motion in 7000 yeeres.
The rest of the spheres are the seuen Planets, each sphere containeth in it but one starre, whereof the vppermost and slowest is Saturne, which performeth his course in 24 yeeres, 162 daies, and 12 houres.
Iupiter performeth in 11. yeeres, 133 daies, and 23 houres.
Mars performeth in 322 daies, and 23 houres.
Sol performeth in 365 daies & 6 houres, which is one whole yeere.
Venus in 385 daies, 9 houres, performeth her course.
Mercurie performeth as the ☉ in 365 daies, and 6 houres.
Luna performeth her course once euerie 27 daies, and 12 houres.
THE CHARACTERS OF THE Planets are these following.
Saturne ♄ Mars ♂ Venus ♀ Iupiter ♃ Sol ☉ Mercurie ☿ Luna ☽
THere are points mouable in the Eclipticke, which are called the Dragons head, and the Dragons taile, and their caracters are these: Dragons head ☋, Dragons taile ☊.
The Dragons head is the point in the Eclipticke, which the ☽ toucheth, when she crosseth the Eclipticke, and passeth to the Northwards of it.
The ☊ is the point in the Eclipticke, where the ☽ passeth by, when she crosseth the Ecliptick, & passeth by it to the South, and these two points are opposite the one to the other.
To know how the Planets reigne euery houre of the day, and night: beginning with Saturday.
| 1. | 2. | 3. | 4. | 5. | 6. | 7. | 8. | 9. | 10. | 11. | 12. | |
| Sat. | ♄. | ♃. | ♂. | ☉. | ♀. | ☿. | ☽. | ♄. | ♃. | ♂. | ☉. | ♀. |
| ☉. | ♀. | ☿. | ☽. | ♄. | ♃. | ♂. | ☉. | ♀. | ☿. | ☽. | ♄. | |
| ☽. | ♄. | ♃. | ♂. | ☉. | ♀. | ☿. | ☽. | ♄. | ♃. | ♂. | ☉. | |
| ♂. | ☉. | ♀. | ☿. | ☽. | ♄. | ♃. | ♂. | ☉. | ♀. | ☿. | ☽. | |
| ☿. | ☽. | ♄. | ♃. | ♂. | ☉. | ♀. | ☿. | ☽. | ♄. | ♃. | ♂. | |
| ♃. | ♂. | ☉. | ♀. | ☿. | ☽. | ♄. | ♃. | ♂. | ☉. | ♀. | ☿. | |
| ♀. | ☿. | ☽. | ♄. | ♃. | ♂. | ☉. | ♀. | ☿. | ☽. | ♄. | ♃. |
| 1. | 2. | 3. | 4. | 5. | 6. | 7. | 8. | 9. | 10. | 11. | 12. | |
| Sat. | ☿ | ☾ | ♄ | ♃ | ♂ | ☉ | ♀ | ☿ | ☾ | ♄ | ♃ | ♂ |
| ♃ | ♂ | ☉ | ♀ | ☿ | ☾ | ♄ | ♃ | ♂ | ☉ | ♀ | ☿ | |
| ♀ | ☿ | ☾ | ♄ | ♃ | ♂ | ☉ | ♀ | ☿ | ☾ | ♄ | ♃ | |
| ♄ | ♃ | ♂ | ☉ | ♀ | ☿ | ☾ | ♄ | ♃ | ♂ | ☉ | ♀ | |
| ☉ | ♀ | ☿ | ☾ | ♄ | ♃ | ♂ | ☉ | ♀ | ☿ | ☾ | ♄ | |
| ☾ | ♄ | ♃ | ♂ | ☉ | ♀ | ☿ | ☾ | ♄ | ♃ | ♂ | ☉ | |
| ♂ | ☉ | ♀ | ☿ | ☾ | ♄ | ♃ | ♂ | ☉ | ♀ | ☿ | ☾ |