The Horizont what it is.

The Horizonte is a Circle, which goeth a-long by the edge of the ground, and parteth the part of the world which we see, from that part which we see not; and when the [Page 4] Sunne riseth, then he is in our Ho­rizonte, and so is he when he is go­ing downe as lowe as wee can see him.

Also it deuideth the whole Sphere of the world into two equal parts, in such sort, that halfe of the Sphere is euer aboue the ground, and halfe alwayes vnder the earth. This Circle hath great vse in the heauenly motions, that by it wee iudge the rysings & settings of the Sunne and Moone, and all other Starres; And in this Horizonte you shall finde noted, the names of the winds, which the Marriners v­seth, by the 32. poynts of the Com­pas.

[Page 5] The next Circle is noted, the de­grees which euery day in the mo­neth dooth contayn: that is to say, the first day one degree; the se­cond day two degrees; and so forth as they succeed in order, to a point like a little starre, where the last day of euery moneth endeth.

The next Circle sheweth, what day of the moneth the Sunne en­treth into any of the twelue signes, telling euery day one degree, to thirtie degrees, & so they succeed through euer one of the twelue signes, monethlie.

[Page 6] This Horizonte is deuided into foure quarters, East, West, South, and North, euery quarter of the world contayneth 90. degrees: and the whole compasse therof, is 360. degrees.

The next Circle is Motus trepe­dationis, a starry firmament, whose motion is slowe, from the West to the East, that euery hundreth yeere (by the obseruatiō of diuers Astro­nomers) moueth but one degree.

The Zodiacke, is a great broade and slope or shoring Circle, in the which are depictured the twelue signes and fixed starres, in the [Page 7] middest whereof, is the Eclipticke lyne, from which the Sunne neuer swarueth.

Then followeth the two Col­luers, and the Equinoctiall Circle, parting the Sphere in the verye middest, betwixt the two Poles: by reason whereof, there are two La­titudes, the one is North and the o­ther South.

The North Latitude is contay­ned betwixt the Equinoctiall and the North Pole; the South Lati­tude, is betwixt the Equinoctiall and the South Pole: either of these two spaces contayneth in bredth 90. degrees.

[Page 8] A Degree is one part of a Circle beeing deuided into 360. parts, and 360. degrees, is the very Longi­tude of the Earth: and at the fur­thest Meridian in the West, begin­ning with one degree, and so pro­ceede Eastward, vnto 180. degrees of the Equinoctiall, & from thence goe forward to the West, where you come againe to 360. degrees, which is the last degree of Longi­tude.

Next followeth the two tropicall Cyrcles.

That is to say, the North trop [...]ke [Page 9] is Cancer, and is the returne of the the Sunne in Sommer declyning, backe againe towardes the Equi­noctiall, the dayes being then at the longest, and the nights at the short­est with vs, and then beginneth the dayes to shorten againe.

The Winter Tropicke (sayth Proclus) is the most Southerliest Circle of all them that the Sunne dooth describe, by the reuolution of the world, in the which when the Sunne is, he maketh his winter­lie turne, and then is the longest night in all the yeere and shortest day with vs.

Paralels.

The Paralell lynes are described by the wyers in the Globe, and a Paralell of the longest day, is a space of the Earth: by thys is knowne the increase of the day to be a quarter of an hower, going from the Equinoctiall towards any of the Pole starres.

A Clymate contayneth two Pa­ralels, in which spaces the day in­creaseth by halfe an hower: Of these Paralels are made 24. Cli­mates, betweene the Equinoctiall and the tropicke of Cancer.

Then followeth the Artick Circle, and the Antartick Cyrcle.

The Artick Circle is the North Circle: and the contrary Circle in the South, is called the Antartick Circle: by the which Greeke com­position, as you would say, contra­ry or against the Articke Circle, & it well may bee called the South Circle. But now heere how Proclus defineth them.

The Articke Circle is the grea­test of all those Circles which doe alwayes appeare, and toucheth the [Page 12] Horizonte in one only poynt, and is altogether aboue the Earth, and all the starres that be within this Circle neyther rise nor set, but are seene to runne round about the Pole all the night.

The Antarticke Circle is equall & equidistant to the Artick Circle & toucheth the Horizonte in one onely poynt,' and is all vnder the ground, & all the starres that be in it, are euermore out of our sight.

Then is there two other smaller Circles, called Poller Circles, or Pole Circles: in this Circle about the Antartick Pole, is deuided cer­tayne [Page 13] degrees to take the Altitude of the North starre, this starre is in the extremitie, or end of the tayle of the lesse Beare, being a con­stellation, commonly called the Horne: for this North starre (of the most notablest starres aboue the Pole) is neerest vnto it, & shall therefore shewe a lesse Circle than any other, and so shall his Altitude differ little from the Altitude of the Pole.

This starre hath declination 85. degrees, and 51. minutes, and the complement of nintie (which are foure degrees and nine minutes) is his distance frō the Pole. And al­though [Page 14] the Marriners hold opini­on, that it is not distant more than three degrees & a halfe, yet to the iudgmēt of those persons that hath knoweledge in Astronomie, more credite ought to be giuen to the A­stronomer than to the Marriner, for asmuch as the Astronomer doth know the place of the starres, with their Longitudes, Latitudes, declinations, and right ascentions, more perfectly and precisely than dooth the Marriners: for they ac­compt not onely by degrees, but also by minutes and seconds; ther­fore whosoeuer wil precisely know it, let him take the highest Alti­tude of the North starre, which is [Page 15] his beeing ouer the Pole, and the lesse Altitude, which is his beeing vnder the Pole: then take away the lesse from the more, and the halfe of that remayneth, shalbe the distance of that starre, from the Pole of the world. And likewise by thys expe­rience may be known the Altitude of the Pole, and what all the other starres that goe not downe vnder the Horizonte, be distant from it, ioyning the greater Altitude with the lesse: and that shall amount thereof, deuided by the halfe, shall bee the Altitude of the Pole; and taking awaye this Altitude of the Pole, from the greater Alti­tude of the Starre, or the lesse [Page 16] from the Altitude of the Pole, the rest that remayneth, shal be the distance of the starre from the Pole. And as the Pole is inuisible, it can not be seene or known when the North starre is higher & low­er, except it be by the meane of some other marke. And for this is considered, the position of the former Guardes or Watch, beeing one of the two starres called the Guardes, which are in the mouth of the Horne: the Marriners haue noted eyght positions, from the former Guard starre to the North starre, which aunswereth to the eyght principall windes; and as the Guarde is to the North starre, ac­cording [Page 17] to the placing of these po­sitions, so it shall be higher and lower from the Pole.

Let vs heere put the common Rules which the Marriners vse, to compile with those that are of opi­nion of three degrees and a halfe.

And for the opinion of Astro­nomers, (which is the distance of 4. degrees & 9. minutes) I haue in my Sphere or Globe annexed to my Diall in the North end, a Circuler or Figure with a moueable Horne; Vppon the vttermost Margent of the Diall, is noted the eyght winds of the eyght positions, and also the other points belonging to the Ma­riners [Page 18] Compas, and putting the Guardes and the North starre in e­uery of the Windes, it shall be the distance that the North starre is higher and lower than the Pole, as by the thrid appeareth in the cutting of the degrees in the Pole Circle, when the Horne is mooued too and fro.

Commmon Rules after the Marri­ners acompt, but not after the A­stronomers acompt, as may appeare in the Rules next before.

THE former Guarde being in the East, the North starre is [Page 19] one degree and a halfe vnder the Pole.

The Guard being in the North-east, the North starre is three de­grees and a halfe vnder the Pole.

The Guarde being in the North, the starre is three degrees vnder the Pole.

The Guard being in the North-west, the starre is halfe a degree vnder the Pole.

The Guarde in the West, the starre is one degree and a halfe a­boue the Pole.

[Page 20] The Guarde in the South-west, the starre is three degrees and a halfe aboue the Pole.

The Guarde in the South-east, the sayd North starre is halfe a de­gree aboue the Pole.

And thus in the Dyall and the Circle about the same, may you see the North starre, in what part it is of the degrees, high or lowe, from the Pole: not onely by the Marri­ners Rule, but also by the Astrono­mers Rule.

And being thus knowen, howe [Page 21] much the North starre is vnder & aboue the Pole, let vs take the Al­titude thereof.

And that of it that is vnder the Pole, let vs ioyne to his height, and as much of it as is aboue, let vs take away, and that shall rise therof, shall be the Altitude of the Pole aboue the Horizonte.

Thus much for breuitie sake, I haue borrowed and collected out of Martine Cortese, and other good Authors, these fewe notes, for the vse of the Guardes, fixed in the North end of my Sphere or Globe. And nowe I am to intreate of the inwarde part of the Coelestiall [Page 22] Globe, and also of the Terrestiall Globe; and to beginne with the lowest first.

The Terrestiall Globe hath de­pictured vpon it, a Mappe or Cart of the description of all the Earth, and the chiefest Regions, Citties, and Townes vnder Europe, Affrica, Asia, and America: And in thys Globe is contayned two Elements, that is to say, Earth and Water. The Earth is lowest of all Elements, black, ponderous, round, inuironed and inclosed with the other three; she is called the Mother of fruits, the roote of all plantes, the nourse of lyuing Creatures, the foundation [Page 23] of buildings, the Sepulchre of the dead, the Center of the beautifull frame of the world, the matter and substance of mans body, and the Receptackle of heauenly influence: she is also garnished with fragrant flowers, with beautifull collours of Man, Beast, and Foule, inhabited, and comfortably quickned by the nourishing beames of the Sunne, Moone, Plannets, and fixed starres.

The Earth in comparison to the whole world, is but a pricke or mote, the whole compas thereof, is 360. degrees, & euery degree is 60. myles: and yee multiply 360. de­grees by 60. it yeeldeth 21600. [Page 24] myles about the same.

The next Cyrcle aboue the Ter­restiall Globe, is the Element of Ayre: and the next Region aboue the Ayre, is the Element of Fyre: and there are the foure Elements, described in this Sphere or Globe.

Then ensueth the Spheres of the 7. Plannets: that is to say, the first is the Sphere of the Moone: the second is the Sphere of Mercury: the third is the Sphere of Ʋenus: the fourth is the Sphere of Soll: the fift is the Sphere of Mars: the sixt is the Sphere of Jupiter: the sea­uenth is the Sphere of Saturnus: [Page 25] the eyght is the Sphere of the star­rie Firmament; and euery one of these Spheres dooth carrie hys signe and Caracter vpon him.

And according to the common accompt, the Earth is 39. times so much as the Moone. But the Sphere of the Moone is farre big­ger than the Globe of the Moone, & the semidiamiter of her Sphere, is 33. times ½. longer than the Earthes semidiamiter, & the myles of the semidiamiter of her Sphere is 115278. and the myles of her Sphere in compasse, contayneth 724604. 4/7.

The semidiamiter of the Sphere [Page 26] of Mercury, is 64. times so long as the Earthes semidiamiter: the miles of the semidiamiter, containes 220500. 2/33. And the myles of his Sphere in compasse, contayneth 1386000. 4/231.

The semidiamiter of the Sphere of Venus, is 167. tymes so long as the Earthes semidiamiter: the miles of the semidiamiter, contayneth 573872. 3/11. the myles of the Sphere in compas, contayneth 3607200.

The semidiamiter of the Sphere of the Sunne, is 1120. tymes so long as the Earthes semidiamiter: the myles of the semidiamiter, contay­neth [Page 27] 3848367. 3/12 the myles of hys Sphere in compasse, contayneth 34189737. 1/7.

The semidiamiter of the Sphere of Mars, is 1220. times so long as the Earthes semidiamiter: the myles of the semidiamiter, contay­neth 4192363. 7/11. the miles of the Sphere in compasse, contayneth 26352000.

The semidiamiter of the Sphere of Jupiter, is 8876. times as long as the Earths semidiamiter: the myles that the semidiamiter contayneth, is 30501163. 7/11. the myles of the Sphere in compasse, contayneth [Page 28] 191721600.

The semidiamiter of the Sphere of Saturne, is 14405. times so long as the Earthes semidiamiter: the myles that this semidiamiter con­tayneth, is 4950318. 2/11. the myles of this Sphere in compas, contay­neth 311148000.

The semidiamiter of the eyght Sphere, is 20110. times so long as the Earthes semidiamiter: the myles that this semidiamiter con­tayneth, is 69105272. 11/8: the miles of this Sphere in compasse, contai­neth 434376000.

[Page 29] In this Armill or Ring Sphere, are wonderfull conclusions to bee learned, very strange and maruel­lous to the simple & ignorant per­sons, voyd of thys knowledge, no lesse profitable than commendable to them, and to the skilfull & wise; for the vse thereof is very apt and ready in teaching, and is more easie for young learners, than the Sol­lid or Massie Globe. And this is a maruellous excellencie in know­ledge, to bee able so certaynly to iudge of things absent, as if they were present, to be able to tel what hower of the day it is in all parts of the Earth, and when the Sunne ry­seth and setteth in all places vnder [Page 30] heauen: for the howers of the day are dyuers in dyuers Regions; so is the shaddowes that the Sunne causeth in their Dyalls, and all o­ther shaddowes doth disagree ma­ny wayes, not onely from our shad­dowes, but also, one of them from another. Agayne, the tymes of the yeere are not a-lyke through all the world, but when it is Sommer to vs, it is winter to some other, and when it is Spring-tyme with vs, it is Sommer in another Countrey; and when it is Haruest with vs, o­ther people haue Sommer: so whē it is winter with vs, some Nations haue Sommer, yea, when Spring time beginneth with vs, it is Har­uest [Page 31] in some Countryes, and in o­ther Countryes it is Midsommer at the same time: but when it is Midsommer with vs, it is Haruest no where in the world, but middle Winter it is then in two dyuers parts of the world.

And those people whose Zenith is within 23. degrees and a halfe of any of the Poles, haue their shad­dowes running round about them: and the neerer they dwell vnder the Pole, the longer is their day, and therefore dooth their shad­dowes run the oftner about them; for where the day is but 24. howers long, there the shaddowes runneth but once about: and where it is [Page 32] halfe a yeere long, there it runneth about 103. tymes, and in all other meane places accordingly; so that those people that haue these shad­dowes thus running about them, vnder the North Pole. Then they that dwell vnder the South Pole haue no shaddowes at all, for it is continuall darknes with them: and yet doe they not want lyght al­though they lacke the Sunne, but only halfe a moneth together, when the Moone is in that halfe of the Zodiake which is out of their Ho­rizont. And though the Sunne and Moone be out of theyr sight, ye see with vs, that we haue a light before Sunne rysing, and after the Sunne [Page 33] setting: so haue they such a light by the beames of the Sunne, 50. dayes continually, after they haue lost the sight of the Sunne, and so haue they like light 50. dayes toge­ther before the Sunne dooth rise to them. And when the Sunne is at the highest with vs, it is at the lowest with diuers other Nations, namely, to all them that dwell vn­der the Equinoctiall directly, or South from it; And therefore all those Nations haue Mid-winter when we haue Midsommer.

Nowe followeth, how to erect the Sphere.

First, for the vse of the same, you must place and set your Sphere le­uill, that it may stand vpright, and by the needle in the compas in the foote thereof, let it be placed due North and South, then shall the Articke Circle stand North and the Antarticke South.

The next Rule, is to find out the eleuation of the Pole of the heauē, in that place wher you mind to ob­serue the Sphere for, & this being knowne, then turne your Meridi­an [Page 35] Circle, and rectifie the Pole of the Sphere, so many degrees aboue his Horizont, as the Pole of the heauen is eleuated, in the place where you will obserue the same. Then marke the degree of any signe that the Sunne is in that day, whose quantitie you desire to know: set that degree iust in the Horizonte towards the East, and marke what degree of the Equi­noctiall is in the Horizonte at the same time: then turne the Sphere West-ward, till the degree of the Sunne bee iust in the Hori­zonte againe in the West part, and marke then what degree of the E­quinoctiall dooth lyght on the Ho­rizont [Page 36] in the East part, accompting truely howe many degrees bee be­twixt those two degrees, which you haue marked, and that Arke of the Equinoctiall, is called the Arke of that day: which you may easily turne into howers, accomp­ting 15. degrees to an hower, and for euery degree lesse than 15. ac­compting 4. minutes of an hower.

An other way to find the same, more easier. Example.

For London, the Pole of heauen being raysed there, 51. degrees and 34. minutes.

Turne your Meridian Circle 51. degrees & 34. minutes, thē the Pole of your Sphere is eleuated to the Latitude of London, thus being fi­nished.

The next Rule, to knowe the day of the month you will practise on.

That is to be found out in the [Page 39] Horizonte Circle of the Sphere, where you shall find also, what de­gree the Sunne occupieth in the signe that day. Then turne the Circle of the Sunne, that the mid­dle body of the Sunne be brought right against the said degree, in the Zodiake: then turne the whole Globe about West-ward, till the body of the Sunne bee right vnder the Meridian Circle, and there let him stay, till you haue remoued the index of the howerly Circle or Diall, precisely on 12. of the clocke at noone: then turne & bring the Globe backe agayne, to the East part of the Horizonte, where you first found out what degree of the [Page 40] signe the Sunne was in that day; Then looke vpon the Dyall, on the North parte of the Sphere or Globe, & ye shal find what hower the Sunne ryseth: thys being done, bring him back again West-ward, toward the Meridian Circle, & it noteth the place of the eleuation of the Sunne euery hower, till hee be at his full height vnder the Me­ridian Circle, then it is sayd to bee in the very noone steede, for that place where you vse the Sphere for, then turn the Globe or Sphere frō the Meridian Circle, westward, and it sheweth the nūber of howers which he falleth from the Meridi­an height, till the tyme that he set­teth [Page 41] vnder the Horizonte, and the index in the Dyall, will tell you the hower that hee setteth vnder the Horizonte that day.

So thus hauing regard to the for­mer instructions, will tell you the tyme of the length of the dayes & nights, in all places of the world, throughout the whole yeere; Pro­uided alwayes, that ye erect and set the degrees of the Meridian Cir­cle, to the Latitude of the sayde place, where you meane to make your obseruation.

Yet by the way, I will giue you a Rule touching the Sunnes moti­on, in his Excentrick Circle.

[Page 42] The Excentrick Circle in the Sphere or Globe, beeing narrower on the one side than on the other, and hath his Center distant or de­uided frō the Center of the world, and is described in the heauen of the Sunne, imagining a lyne from the Center of the Excentricke to the Center of the Sunne, making a complet reuolution at the proper motion of the Sunne.

In the other heauens, imagining a lyne from the Center of hys Ex­centrick, to the Center of the Epi­cicle.

The Epicicle, is a Circle or little [Page 43] Roundle, fixt in the depth of the Excentrick: in which, the Plannet is fixed, and neere to hys Center is moued Circulerlie.

The Auge, is a poynt in the cir­cumference of the Excentrick, nee­rest vnto the Firmament: or it may bee sayde, that the Auge is a poynt farthest distant from the Earth.

Aux, in the Greeke tongue is as much to say, as the greatest Longi­tude or greatest eleuation from the Earth.

The opposite of the Auge, is an other poynt in the circumference [Page 44] of the Excentrick, neerest vnto the Earth, and farthest distant from the Firmament.

And you must heere note and vnderstand, the Sunne is not moo­ued Regularly in the Zodiake, ma­king so much by his proper moti­on in one day, as in the other, be­cause his Reguler motion is in re­spect of the Center of his own pro­per Sphere, or orbe wherein hee is moued, whose Center is distant without the Center of the world, towards the parts of Cancer: so that the greater part of his orbe Excen­trick, is toward the septentrionall part, where the Sunne passing by the septentrionall signes, is more [Page 45] distant from the Earth, and hath more to goe of hys orbe Excen­tricke, than beeing in the South signes: for, passing by the North signes, he tarryeth 9. dayes more, to describe the halfe of the Zodi­ake, than the other halfe toward the South part.

And for this cause, the Sunne is more swifter in his motion (in the Zodiake) one tyme, than another: for his motion in one day in the South signes, shall bee greater than it is in one day in the North signes.

And further it followeth, that the sayd vnequall moouing of the Sun obliquite of the Zodiake, certayne [Page 46] dayes of winter, with their nights, are longer, than certayne other of Sommer, with their nights: that is to say, that the day naturall in the winter, dooth surmount that in the Sommer, because the right ascenti­on which aunswereth to one dayes motion of the Sunne, beeing in the South, is greater than the ascention for one dayes mouing, being in the North signes.

Next followeth the placing of the o­ther sixe Plannets, in their true order in the Sphere.

These six Plannets, hauing each of them seuerall Spheres, and theyr [Page 47] motions also seuerall, and vnlyke in tyme to any other: and there­fore they are called vvandering starres. These are carryed round about the world, by the vyolence of the first mouer, in 24. howers, that is, euery day once; yet they keepe their places in their Sphere, and haue their proper motions from West towards East.

The Moone, with her heauen or Sphere, by her proper motion, giueth her turne from the West to the East, in 27. dayes and 7. howers, with 45. minutes.

Ʋenus, Mercury, and the Sunne, [Page 48] in a yeere, which is the space of 365. dayes, with 5. howers and 49. minutes.

Mars, in two yeeres. Jupiter, in 12. yeeres. Saturne, in 30. yeeres.

The eyght heauen, which is the Firmament or starry heauen, by his own proper motion is moued by the ninth heauen, vpon the begin­ning of Aries and Libra, and vpon these two poynts, accomplisheth hys Reuolution in seauen thou­sand yeeres.

This motion is called Motus tre­pedationis, (that is to say) the trem­bling motion, of Access or recess.

To rectifie the 6. Plannets, to goe in theyr due courses about the Sphere.

To find out by the Instrument in the Dyall, the age of the Moone, with her chaunge, quarters, and full: her aspects with the Sunne: the ebbes & floods, and other necessary Rules, apper­tayning to the Arte of Na­uigation. &c.

Marke at the Coniunction of the Sunne and Moone, (it is sayde) the chaunge of the Moone, is whē the Sunne and shee meeteth toge­ther, and then the Moone taketh her lyght of the Sunne: and when she is runne in her course, 24. how­ers after the change, it is sayde that she is a day olde; then turne the in­dex [Page 54] of the Moone to the figure of 1. And when she is two dayes old, turne the index of the Moone to the figure of 2. and so proceede, till she come to the figure of 7. and then it is sayd to be in the first quarter of the Moone: then at the figure of 15. shee is in opposition with the Sunne, then it is said to be a full Moone: then shee gathereth euery day in her decrease, towards the Sunne. And when she is 7. dayes past the full, then she hath lost half her roundnes of her light, and is sayd to be last quarter; and so gathereth euery day, neerer and neerer the Sunne, till she be depry­ued quite from her light, and then [Page 55] it is sayd to be at chaunge agayne, and a newe Moone: and after her chaunge, then her lyght begins to increase agayne, euery 24. howers, 48. minutes; which yeeldeth in 15. dayes, 12 howers. And so much she is iust of the Sunne, at the time of the full Moone. And if you will marke the distances, betwixt the index of the Sunne, which poynts the howers in the Dyall, and in the index of the Moone: you shal find alwayes what distance the Sunne and Moone are a sunder; thys is called amongst the Marrines, the shifting of the Sunne and the Moone, & hereby they shall know theyr ebbes and floods, as appea­reth [Page 56] in the vttermost part of the Dyall: and also, the 32. poynts of the Compas sheweth the same.

Another Rule for the hower of the two starres afore-sayde, called the Guardes, and of some, called Charles Wayne, or Charles Carte: likning fower starres to fower wheeles, and the other three starres to three Oxen.

And the first starres I take for my purpose, and declare at euerie monethes end, at what hower they are full West, and the howers that they are West and by North, and North-west, and North-west and by North, and full North; and so [Page 57] round about 24. howers.

A ready note in fewe words, for the difference of howers, according to the distan [...] myles, from East to West vnder the Equinoctiall.

FIRST, you shall vnderstand, that 15. myles difference from East toward West, doth make the Sunne rysing, the noonesteed, and Sunne setting, to be later by one minute of an hower: & so 30. miles, 2. minutes: 120. myles, 8. minutes: 225. myles, 15. minutes: which is a quarter of an hower. And he that is ready in accompt of Arithma­tique, may find it out by the Rule of proportion. As for Example.

London hath Latitude 51, degree [Page 82] and 30. minutes, or there abouts, I trauayle East-wards from London 2000. myles; My desire is, to know the difference of theyr Longi­tudes, and the time of theyr noone steeds, for when it is 12. of the clock with vs at London, 2000. myles East-ward from London, is then but 2. of the clock and 13. minutes at after noone. And 2000. myles West from London, it was then with them, but 10. of the clock and 13. minutes in the fore noone: the difference of these 3. places, one from the other, is to bee founde by the Rules in Arithmatique, as followeth.

If 15. myles in Longitude, East-ward [Page 83] from London giue one mi­nute of time, what gyueth 2000. myles.

I worke it in this manner, deui­ding 2000 miles by 15 myles, and it yeeldeth 133. times 15. myles, and 1. third part of 15. miles, to be deuided into 15 parts. Now, alowe to euery 15. myles, one minute of tyme, (as you haue heard me say before) and reduce them into howers, in thys manner as followeth.

60. minuts maketh a degree of the [Page 84] Equinoctial; so then deuide 133. by 60. minutes of time, & the Cotient will be 2. and 13. will remayne: that is, 2. howers and 13. minutes diffe­rence, betweene that place & Lon­don. And in this wise may you worke by the Rules in Arithma­tique, to find the West Longitude from London.

There bee some persons that make a great obscuritie, in finding out the Longitudes in sayling East and West; a thing once knowne, & of no great importance, as ready to bee found out as the Latitudes. A little Briefe (therfore) I will giue you, to vnderstand the same skill.

Let the Marriner, Sayler, or other [Page 85] persons, prouide him a perfect Watch, or Clock, arteficially made by a Clock-maker. Let him set the same by the hower of the day in that place you are in, and to come by the true place of the Sunne, your Astrolob quadrant crosse staffe, or other Instrument, will serue you to take the heigth of the Sunne, & to find out the true hower in euery seuerall Latitude, with the helpe of the Rules before. And the true hower beeing found of the day in this manner, sette your Clocke or Watch. Then trauell either by Sea or Land, and when you are 40. myles, or 60. more or lesse, distant of the place you went from, then [Page 86] looke to your Clocke or Watch, howe many howers haue passed since you set on your iourney: then take your Quadrant or orther In­strument, & take the heigth of the Sunne in that place you are in; and if the time of the day taken with your Instrument, doe agree with your clock, be you sure your place is North or South, from the place you came from, and therefore haue the same Longitude and Meridian lyne; But if the tyme differ, sub­stract the one out of the other, and the difference turne in degrees and minutes of the Equinoctiall: and 15. minutes of the Equinoctiall, ma­keth one minute of time, according [Page 87] vnto the Rules going before, you may thus knowe the Longitudes, difference of howers, and times, be­twixt any two places East or West ward. The Latitudes are easily found out by the Altitudes of the North or South Poles, and also, by the Meridian heigth of the Sunne at noone.

To know the place of the Sunne, by the Rule of memorie: And to knowe in what degree the Sunne is, without re­spect of minutes.

Beare in memorie these numbers that heere-after followeth. 11. 10. 11. 10. 11. 12. 13. 14. 13. 14. 12. 12.

The first 10. standeth for January, the second for February, with their signes, & so the rest; And to know in what degree the Sun is, you shal take away the dayes that are appli­ed to euery moneth, according to the said numbers of the dayes, for the which you desire to know the place of the Sunne, and in them that remayn, in so many degrees is the Sunne, of the signe into which [Page 105] it entereth that moneth. And if the dayes pass of the moneth, shall bee lesse then the dayes applyed to the same moneth, you shall ioyne 30. with those dayes past of the mo­neth, & of the Sunne that amoun­teth, you shall take away the daies applyed to the sayde moneth, and the rest shall be the degrees, in the which the Sunne shall be, of the signe of the moneth past. As for example.

The 12 day of October, taking a­way 14, that were applyed, remai­neth 28. degrees of Scorpio, where the Sunne is.

A Rule to know when the Sunne en­treth into euery of the 12. Signes.

And that wee may in the yeeres to come, know the day, hower, and minute, in the which the Sun en­treth [Page 108] into euery signe, we will fol­low this order; vpon the day, how­ers, & minutes, that the Sunne en­treth into euery signe, the yeere 1545. we must add for euery yeere 5. howers and 49. minutes, which with the 365. dayes which euery yeere cōtaineth, shalbe the time in the which the Sun accomplisheth his reuolution. And because that in the yeere of the Bebysextile or Leap-yere, is added to February, 1. day more to his 28, which we haue once in 4. yeeres, from 6. to 6. how­ers; if we shal take from the Com­putation, that we haue giuen tur­ning one day backward, as shall be in the yeere 1548. and vppon that [Page 109] remaineth: shall return in the yeere following of 1549 to add 5, howers 49. minutes, and as much more e­uery other yeere following shall be a certaine Rule for euer.

And it is to be noted, that the de­grees and minutes which we haue touched before, are properly for the citty of Cadiz. And if we desire to apply thē for other cities or pla­ces more Eastward, thē for euery 15 degrees that they are distant from Cadiz, in Longitude, we must add one hower, And if for the Cities or places more westward in like man­ner, for euery 15. degrees, we must take away one hower, by reason of the course of the Sun, by his Rapte [Page 110] mouing frō the East to the West. For it is certain, that when with vs in Cadiz it is 12. howers of the clock to them that are 15. degrees East­warde from vs, it is one of the clocke: and to them that are from vs 15. degrees towards the West, it is 11. of the clocke. And thus may you apply it to euery seueral Lon­gitude East or West, gyuing to e­uery 15. miles, one minute of tyme according to the other Rules in A­rithmatique specified.