the Equinoctial under the Meridian of your Place have a continual Sun-Dyal of it and the hour of the Day given on it at once in two places one by the parting the enlightned Hemisphear from the shadowed on the Eastern side the other by the parting the enlightned Hemisphear from the shadowed on the Western side the Globe Much more might be said on this Probleme But the Ingenuous Artist may of himself find out diversities of Speculations therefore I forbear PROB. XLVI To know by the Terrestrial Globe in the Zenith of what Place of the Earth the Sun is THis may be performed by the former Probleme in the Day time if the Sun shines but not else But to find it at all times do thus Bring the Place of your Habitation to the Meridian and the Index of the Hour-Circle to 12 Then turn the Globe Eastwards if Afternoon or Westwards if Before Noon till the Index of the Hour-Circle pass by so many Hours from 12. as your Time given is either before or After-Noon so shall the Sun be in the Zenith of that Place where the Meridian intersects the Parallel of the Suns Declination for that Day Example May 10 at ¾ of an hour past 4. a clock After Noon I would know in what Place of the Earth the Sun is in the Zenith My Habitation is London Therefore I bring London to the Meridian and the Index of the Hour-Circle to 12. and because it is After Noon I turn the Globe Eastwards till the Index passes through 4 hours and 3 quarters or which is all one till 70 degrees 15 minutes of the Equator pass through the Meridian Then I find by Prob. 5. the Suns Declination is 20. degrees 5. minutes which I find upon the Meridian and in that Place just under that degree and minute on the Globe the Sun is in the Zenith which in this Example is in the North East Cape of Hispaniola Having thus found in what Place of the Earth the Sun is in the Zenith Bring that Place to the Meridian and Elevate its respective Pole according to its respective Elevation so shall all Places cut by the Horizon have the Sun in their Horizon Those to the Eastwards shall have the Sun Setting those to the Westward shall have it Rising in their Horizon those at the Intersection of the Meridian and Horizon under the Elevated Pole have the Sun in their Horizon at lowest but Rising those at the Intersection of the Meridian and Horizon under the Depressed Pole have the Sun in their Horizon at highest but Setting Thus in those Countries that are above the Horizon it is Day-light and in those but 18 degrees below the Horizon it is Twilight But in those Countries further below the Horizon it is at that time dark Night And those Countries within the Parallel of the same number of degrees from the Elevated Pole that the Suns Declination is from the Equinoctial have the Sun alwaies above the Horizon till the Sun have less Respective Declination then the Elevated Pole and those within the same Parallel of the Depressed Pole have the Sun alwayes below their Horizon till the Sun inclines more towards the Depressed Pole As you may see by turning about the Globe for in this position that portion of the Globe intercepted between the Elevated Pole and the Parallel Circle of 20. degrees 5. minutes from the Pole doth not descend below the Horizon neither doth that portion of the Globe intercepted between the Depressed Pole and the Parallel Circle within 20. degrees 5. minutes of that Pole ascend above the Horizon PROB. XLVII To find in what different Places of the Earth the Sun hath the same Altitude at the same time FInd by the former Probleme in what Place of the Earth the Sun is in the Zenith and bring that Place on the Globe to the Zenith and on the Meridian there screw the Quadrant of Altitude and turn it about the Horizon describing degrees of Almicantars thereby as by Prob. 23. and all those Countries in any Almicantar on the Globe shall have the Sun Elevated the same number of degrees above their Horizon Thus those Countries in the tenth Almicantar shall have the Sun Elevated 10. degrees above their Horizon those in the 20 th Almicantar shall have the Sun Elevated 20 degrees above their Horizon those in the 30 th 30. degrees c. So that you may see when the Sun is in the Zenith of any Place All the Countries or Cities in any Almicantar have the Sun in one heighth at the same time above their Horizon But to find in what different Places the Sun hath the same heighth at the same time as well Before or After Noon as at Full Noon and that in Countries that have greater Latitude then the Suns greatest Declination and therefore cannot have the Sun in their Zenith requires another Operation Therefore Elevate its respective Pole according to your respective Latitude and let the Degree of the Brazen Meridian which is in the Zenith represent your Habitation and the degree of the Ecliptick the Sun is in represent the Sun Then bring the Sun to the Meridian and the Index of the Hour-Circle to 12 and turn the Globe Eastwards if Before Noon or Westwards if After Noon till the Index point to the Hour of the Day Then place the lower end of the Quadrant of Altitude to the East point of the Horizon and move the upper end by sliding the Nut over the Meridian till the edge of the Quadrant touch the place of the Sun Then see at what degree of the Meridian the upper end of the Quadrant of Altitude touches the Meridian and substract that number of Degrees from the Latitude of your Place and count the number of remaining degrees on the Meridian on the contrary side the degree of the Meridian where the upper end of the Quadrant of Altitude touches the Meridian and where that number of degrees ends on the Meridian in that Latitude and your Habitations Longitude hath the Sun the same heighth at the same time Example May 10. at 53. minutes past 8. a clock in the Morning I would know in what Place the Sun shall have the same Altitude it shall have at London London's Latitude found by Prob. 1. is 51½ degrees Northwards And because the Elevation of the Pole is equal to the Latitude of the Place as was shewed Prob. 15. Therefore I Elevate the North Pole 51½ degrees so shall 51½ degrees on the Meridian be in the Zenith This 51½ degrees on the Meridian represents London The Suns Place found by Prob. 3. is ♉ 29. Therefore I bring ♉ 29 to the Meridian and the Hour Index to 12. on the Hour Circle Then I turn the Globe Eastwards because it is before Noon till the Index point at 8. hours 53 minutes on the Hour-Circle and place the lower end of the Quadrant of Altitude to the East point in the Horizon and slide the upper end either North or Southwards
thereof mark it well first with your Compass observing diligently upon which Point thereof it lieth And secondly you must there take the heigth of the Sun or of the Pole-star as you were taught Prob. 13. of the second Book that you may know in what Point your Ship is and that point you must call the First Point which being so done your Ship may sail on her Course all that day till the day following without losing her Way and the next day mark the Land again and see upon what Point it lieth and then take your heigth and with it cast your Point of Traverse once again and that you may call your second Point Then take a pair of Compasses and placing one foot upon the First Point and the other upon the Rhumb towards which the Land did Bear when you Cast your First Point set also one foot of another pair of Compasses in the second Point and the other foot upon the Rhumb upon which the Land lay when you cast your second Point and these two Compasses thus opened you must move by their Rhumbs till those two feet of both Compasses do meet together which were moved from the foresaid two Points and where they do so meet together there may you say is the Land which you Discovered which Land you may point out with the In lets and Out-lets or Capes and other Signes which you saw thereupon And by the graduation you may see the Latitude thereof that thereby you may find it if a any time after you go to seek for it PROB. XVIII Seeing two known Points or Capes of Land as you sail 〈◊〉 long how to know the distance of your Ship from them PItch one foot of one pair of Compasses upon one of the two foresaid Capes and the other foot upon the Rhumâ— which in this Compass pointeth towards that Cape 〈◊〉 in like manner shall you do with another pair of Compasses placing one foot thereof upon the other known Cape 〈◊〉 the other foot upon the Rhumb which stretcheth towards 〈◊〉 said second Cape and moving the two Compasses so opened by these two Rhumbs off from the Land the very same Point where the two feet which came from the two Capes do meet you may affirm to be the very Point where your Ship is And then measuring by the degrees of the Equinoctial you may see what distance there is from the said Point to either of the foresaid Capes or to any other place which you think good for it is a very easie matter if you know the point where your Ship is PROB. XIX Of Tides and how by help of the Globe you may in general judge of them DIvide the Equinoctial into 30 equal parts as was directed in Prob. 54. of the last Book These 30. equal parts represent the 30. daies of the Moons Age. Then on the North and South point of the Compass in the outmost Verge of the Horizon Write with red Ink 12. From the North Eastward viz. at the Point North and by East Write 11 ¼ At the next point to that the same way viz. North North East Write 10 ½ At the next viz. North East and by North Write 9 ¾ And so forward to every point of the Compass rebating of the last hour ¾ till you come to 12. in the South where you must begin again to mark that Semi-Circle also in the same order you did the last In this Circle is then represented the Points of the Compass the Sun and Moon passeth by every Day and the Figures annexed represent the twice 12. hours of Day and Night Having thus prepared your Globe and Horizon you may by having the Moons Age and the point of the Compass on which the Moon maketh full Sea at any Place given find at what Hour of Day or Night it shall be high Tide in the same Place Thus It is a known Rule that a North and South Moon makes high water at Margarate Therefore Bring the first point of ♈ to the North or South point in the Horizon and Elevate the North Pole into the Zenith Then count in the Equinoctial the Daies of the Moons Age numbred in red figures and the Hour and minutes written in red figures annexed to the names of the Windes that stands against the Moons Age shall be the Hour of High Tide on that Day or Night at Margarate The End of the Third Book The Fourth BOOK Shewing the Practical Use of the GLOBES Applying them to the Solution of Astrological Problemes PRAEFACE THe Practise of Astrology is grounded upon a two-fold Doctrine The first for erecting a Figure of Heaven placing the Planets in it finding what Aspects they bear each other and in what Places they are constituted c. and this we call the Astronomical part of Astrology The second is how to judge of the events of things by the Figure erected and this is indeed the only Astrological part The first of these I shall briefly handle because what therein is proposed may be performed by the Globe both with speed ease delight and demonstration The second I shall not meddle with but refer you to the whole Volumnes already written upon that Subject PROB. I. To Erect a Figure of the 12 Houses of Heaven BEfore you erect a Figure of the 12 Houses of Heaven it will be requisite you place the Planets ☊ and ☋ according to their Longitude and Latitude upon the Globe as was directed in Prob. 55. of the second Book for then as you divide the Houses of your Figure by the Circle of Position you may by inspection behold in what Houses the Planets are scituated and also see what fixed Stars they are applying to or separating from But to the matter There is disagreement between the Ancient and Modern Astrologers about erecting a Figure of Heaven M r Palmer in his Book of Spherical Problemes Chap. 48. mentions four several waies and the Authors that used them whereof one of them is called the Rational way used by Râ—giomontanus and now generally practised by all the Astrologers of this Age. This way the face of Heaven is divided into twelve parts which are called the twelve Houses of Heaven numbered from the Ascendent or angle at East downwards with 1 2 3 c As in the following Figure In a Direct Sphear viz. under the Equator these twelve Houses are twelve equal parts but in an Oblique Sphear they are unequal parts and that more or less according to the quantity of the Sphears obliquity These twelve Houses are divided by 12. Semi-Circles of Position which are Semi-Circles passing from the two intersections of the Horizon and Meridian through any Star degree or point in the Heavens The degrees and minutes of the Ecliptick upon the Cusps of these four Houses that is upon the beginning of these Houses are found all at once only by bringing the Rising degree of the Ecliptick to the Horizon for the Horizon represents the Cusp of the Ascendent and then shall
that shadow shall be a Meridian liâ—e Secondly on the backside the Clinatory discribe a Circle and draw a line through the Center to both sides the Circumference cross this line with an other line at Râ—ght Angles in the Center so shall the Circle be divided into four equal parts These four parts you must maâ—k with East West North South and divide each of them into 90. degrees In the Center of this Plain erect a straight wyer prependicularly when you would find a Meridian line examine by the tenth Prob. of the second Book the Amplitude of the Suns Rising or Setting from the East or West points and waiting the just Rising or Setting that Day turn the Instrument about till the shadow of the wyer falls upon the same degree from the East or West the Amplitude is of for then the North and South line in the Instrument will be the same with the North and South line in Heaven Thirdly by the Suns Azimuth Find the Azimuth of the Sun by Prob. 22. of the second Book and at the same instant turn the Instrument till the shadow of the wyer fall upon the degree on the Instrument opposite to the degree of the Suns Azimuth so shall the Meridional line of the Instrument agree with the Meridional line in Heaven You may the same way work by the Azimuth of any Star Only whereas the shadow of the wyer should fall upon the opposite degree aforesaid Now you must place a Sight or Perpendicular upon that opposite degree and turn the Instrument about till the wyer at the Center the Sight in the opposite degree of the Stars Azimuth and the Star in Heaven come into one straight line so shall the Meridian line of the Instrument agree with the Meridional line in Heaven Fourthly It may be found by any Star observed in the Meridian if two Perpendiculars be erected in the Meridian line of your Instrument for then by turning the Instrument till the two Perpendiculars and the Star come into a straight line the Meridian line of your Instrument will be the same with the Meridian line in Heaven See more waies in Mr. Palmer on the Planisphear Book 4. Chap. 9 If your Plain either Recline or Incline apply one of the sides of your Clinatory Parallel to one of the Semi-diameters of the Quadrant to the Plain in such sort that the Plumb-line hanging at liberty may fall upon the Circumference of the Quadrant for then the number of degrees of the Quadrant comprehended between the side of the Quadrant Parallel to the Plain and the Plumb-line shall be the number of degrees of Reclination if thâ— Center of the Quadrant points upwards or Inclination if thâ— Center points downwards If your Reclining or Inclining Plain Decline draw upon it a line Parallel to the Horizon which you may do by applying the back-side of the Clinatory and raising or depressing the Center of the Quadrant till the Plumb-line hang just upon one of the Semi-diameters for then you may by the upper side of the Clinatory draw an Horizontal line if the Plain Incline or by the under side if it Recline If it neither Incline or Recline you may drawâ— an Horizontal line both by the upper and under sides of the Clinatory Having drawn the Horizontal line apply the North 〈◊〉 â— of the Clinatory to it and if the North end of the Needle 〈◊〉 directly towards the Plain it is then a South Plain If the 〈◊〉 point of the Needle points directly from the Plain it is a Norâ—â— plain but if it points towards the East it is an East Plain if towards the West a West Plain If it do not point directly 〈◊〉 East West North or South then so many degrees as the 〈◊〉 declines from any of these four points to any of the other of 〈◊〉 four points so many degrees is the Declination of the Plain 〈◊〉 respect as aforesaid had to the Variation of the Compass Or if you find the Azimuth of the Sun by its Altitude observed just when its beams are coming on or going off youâ— Plain that Azimuth shall be the Azimuth of your Plain Or you may erect a wyer Perpendicularly on your Plain and wait till the shadow of that wyer comes to be Perpendicular with the Horizon which you may examine by applying a Plumb-line to it for then the shadow of the Plumb-line and the shadow of the Perpendicular will be in one then taking the Altitude of the Sun you may by Prob. 22. of the second Book find its Azimuth and thereby know in what Azimuth the Plain of your Dyal lies for the Azimuth your Plain lies in is distant from the Azimuth of the Sun just 90. degrees PROB. I. How by one position of the Globe to find the distances of the Hour-lines on all manner of Plains YOu may have Meridian lines drawn from Pole to Pole through every 15. degrees of the Equinoctial to represent the Horary motion of the Sun both Day and Night and when the Pole of the Globe is Elevated to the height of the Pole in any Place and one of these Meridian lines be brought to the Brazen Meridian all the rest of the Meridian lines shall cut any Circle which you intend shall represent the Plain of a Dyal in the number of degrees on the same Circle that each respective Hour-line is distant from the Noon-line point in the same Circle Thus if you should enquire the distance of the Hour-lines upon an Horizontal Plain in Londons Latitude The Pole of the Globe as aforesaid must be Elevated 51½ degrees and one of the Meridian lines you may chuse the Vernal Colure be brought to the Brazen Meridian which being done you are only to examine in the Horizon Because it is an Horizontal Plain at what distance from the Meridian which in Horizontals is the Noon-line the several Meridians drawn on the Globe intersect the Horizon for that distance in degrees shall be the distance on a Circle divided into 360. degrees that each respective Hour-line must have from the Meridian or a Noon line chosen in the same Circle and lines drawn from the Center of that Circle through those degrees shall be the Hour lines of an Horizontal Plain If your Plain be not Direct but declines East or West 〈◊〉 must number the Declination Eastwards or Westwards reâ—pectively in the degrees of the Horizon and the Quadrant 〈◊〉 Altitude screwed to the Zenith as aforesaid bring the lower end of the Quadrant of Altitude to the said degrees of Declination and the number of degrees cut by the Meridians in the Quadrant of Altitude numbred downwards is the number of degrees that the Hour-lines are distant from the Noon line in a Circle of 360 degrees And lines drawn from the Center of that Circle through those degrees be the Hour lines of half the Day And if you turn about the Quadrant of Altitude upon the Zenith point till the lower end of it come to the degree of the Horizon
the Moon is alwaies a part of a Circle therefore the Earth and Water which is the Body shadowing must also be a Circular or round Body for if it were three square four square or any other form then would the shadow which it makes in the Moon be of the same fashion Besides Of all figures the Sphear or Globe is most perfect most Capacious and most intire of it self without either joynts or Angles which form we may also perceive the Sun Moon and Stars to have and all other things that are bounded by themselves as Drops of Water and other liquid things But there is another frequent Argument against the Globulus form of the Earth and that is That it seems impossible that the Earth should be round and yet also Inhabible in all Places For though we that inhabite on the top of the Earth go with our heads upwards yet those that inhabite underneath us must needs go with their Heads downwards like Flyes on a Wall or Ceeling and so be in danger of falling into the Air. For Answer hereunto first You must understand that in the Center of the Earth there is an Attractive and drawing power which draws all heavy substances to it by vertue of which Attractive power things though loosed from the Earth will again incline and cling to the Earth and so much the more forcibly by how much the heavier they are as a bullet of Lead let fall out of the Air inclines towards the Earth far more violently and swiftly then a bullet of the same bigness of Wood or Cork Secondly you must understand that in respect of the whole Vniverse there is no part either upper or under but all parts of the Earth are alike incompast with Heaven yet in respect of the Earth it is Heaven which we take for the upper part and therefore we are said to go with our heads upwards because our head of all the parts of our body is nearest to Heaven Now that this Attractive power lies in the Center of the Earth is proved by this Argument If the Attractive power were not in the Center a Plumb-line let fall would not make Right Angles with the Superficies of the Earth but would eb Attracted that way the Attractive vertue lies and so make unequal Angles with the Superficies But by so many Experiments as hath yet been made we find that a Plumb-line continued though never so deep yet it alters no Angles with the Superficies of the Earth and therefore undoubtedly the Attractive power lies in the very Center and no where else CHAP. I. I. What a Globe is A Globe according to the Mathematical Definition is a perfect and exact round Body contained under one surface Of this form as hath been proved consists the Heavens and the Earth and therefore the Ancients with much pains Study and Industry endeavouring to imitate as well the imaginary as the real appearances of them both have Invented two Globes the one to represent the Heavens with all the Constellations fixed Stars Circles and Lines proper thereunto which Globe is called the Celestial Globe and the other with all the Sea Coasts Havens Rivers Lakes Cities Towns Hills Capes Seas Sands c. as also the Rhumbs Meridians Parallels and other Lines that serve to facilitate the Demostration of all manner of Questions to be performed upon the same and this Globe is called the Terrestrial Globe II. Of the two Poles Every Globe hath two Poles the one North the other South The North Pole is in the North point of the Globe The South Pole in the South point III. Of the Axis From the Center of the Globe both waies proceeds a line through both the Poles and continues it self infinitely which is called the Axis of the World and is represented by the two wyers in the Poles of the Globe Upon these two wyers the Globe is turned round even as the Heavens is imagined to move upon the Axis of the World IIII. Of the Brasen Meridian Every Globe is hung by the Axis at both the Poles in a Brasen Meridian which is divided into 360 degrees or which is all one into 4 Nineties the first beginning at the North Pole is continued from the left hand towards the right till the termination of 90 degrees and is marked with 10 20 30 c. to 90. from whence the degrees are numbred with 80 70 60 c. to 0. which is in the South Pole from whence again the degrees are numbred with 80 70 60 c. to 0 and lastly from 0 the degrees are numbred with 10 20 30 to 90. which is again in the North Pole This Brasen Meridian is of great use for by help of it you may find the Latitude of all Places the Declination of all the Stars c and rectifie the Globe to any Latitude V. Of the Horizon The Horizon is a broad wooden Circle encompassing the Globe having two notches in it the one in the North the other in the South point The notches are made just fit to contain the Brasen Meridian that the Globe is hung in In the bottom or under Plane of the Horizon there stands up a rop or as it is called a Bed in which there is also a notch into which notch the Brasen Meridian is also let so lo as that both it and the Globe may be divided into two equal halfs by the upper Plane of the wooden Horizon These Notches are as gages to keep the Globe from inclining more to the one side of the wooden Horizon then the other Upon the upper Plane of the Horizon is several Circles delineated as first the inner Circle which is a Circle divided into twelve equal parts viz. into twelve Signes every Signe having its name prefixed to it as to the Signe of ♈ is the word Aries to ♉ the word Taurus c. every Signe is again divided into 30 equal parts which are called Degrees and every tenth degree is marked with 10 20 30. Next to the Circle of Signes is a Kalender or Almanack according to the Old stile used by us here in England each Moneth being noted with its proper Name as January February March c. and every day distinguished with Arithmetical figures as 1 2 3 4 c. to the end of the Moneth The other Calender is a Calender of the New stile which is in a manner all one with the Old only in this Calender the moneth begins ten daies sooner then they do in the other and to this Calender because it was instituted by the Church of Rome there is annexed the Festival daies Celebrated by the Romish Church The two other Circles are the Circles of the Winds the innermost having their Greek and Latine names which by them were but twelve and the outermost having the English Nanes which for more preciseness are two and thirty The use of the upper Plane of the Horizon is to distinguish the Day from the Night the Rising and Setting of the Sun
respect of warping and shrinking I have had few Globes come to mending that have not had either broken Horizons or some other notorious fault occasioned through the sleightness of the Horizons In the Using the Globes KEep the East side of the Horizon alwaies towards you unless your Proposition requires the turning of it which East side you may know by the Word East placed on the outmost verge thereof For then have you the graduated side of the Meridian alwaies towards you the Quadrant of altitude before you and the Globe divided exactly into two equal parts So oft as I name to at of or under the Meridian or Horizon I mean the East side of the Meridian and Superficies of the Horizon because the East side of the Meridian passes through the North and South points both of the Globe and Horizon and agrees just with the middle of the Axis And the Superficies of the Horizon divideth the Globe exactly into two equal parts It you happen to use the Globes on the South side the Equator you must draw the wyers out of either Pole and change them to the contrary Poles putting the longest wyer into the South Pole And because on the other side the Equator the South Pole is elevated therefore you must elevate the South Pole of the Globe above the Horizon according to the South Latitude of your Place as shall be shewed hereafter In the working some Problems it will be required that you turn the Globe to look on the West side thereof which turning will be apt to jog the Ball so as the degree that was at the Horizon or Meridian will be moved away and thereby the Position of the Globe altered To avoid which inconvenince you may make use of a Quill thrusting the Feather end between the Ball and the Brazen Meridian and so wedge it up without wronging the Globe at all till your Proposition be answered PROBLEME I. To find the Longitude and Latitude of Places on the Terrestrial Globe SEek the Place on the Terrestrial Globe whose Longitude and Latitude you would know and bring that Place to the Brazen Meridian and see how many degrees of the Equator is cut by the Meridian from the first general Meridian which on my Globes pass through Gratiosa one of the Isles of the Azores for that number of degrees is the Longitude of the Place Example I desire to know the Longitude of London and close to the name London I find a smal mark 0 thus which smal mark is in some Globes and Maps adorned with the Picture of a Steeple c. therefore I do not bring the word London to the Meridian but that smal mark for that alwaies represents the the Town or Citty sought for And keeping the Globe steddy in this Position I examine how many degrees of the Equator are contained between the Brazen Meridian and the first general Meridian which I find to be 24. deg 00. min. Therefore I say the Longitude of London is 24. degrees 00. min. For the Latitude See on the Brazen Meridian how many degrees are contained between the Equator and the mark for London which in this Example is 51½ therefore I say London hath 51½ degrees North Latitude PROBLEME II. The Longitude and Latitude being know to Rectifie the Globe fit for use 1. WHen you rectifie the Globe to any particular Latitude you must move the Brazen Meridian through the notches of the Horizon till the same number of degrees accounted on the Meridian from the Pole about which the Hour-Circle is towards the North point in the Horizon if in North Latitude and toward the South if in South Latitude come just to the edge of the Horizon Example By the former Proposition I found the Latitude of London to be 51½ degrees North Latitude therefore I count 51½ degrees from the Pole downwards towards my right hand and turn the Meridian through the notches of the Horizon till those 51½ degrees comes exactly to the uppermost edge of the North point in the Horizon and then is the Meridian rectified to the Latitude of London 2. Next rectifie the Quadrant of altitude after this manner Screw the edge of the Nut that is even with the graduated edge of the thin Plate to 51½ degrees of the Brazen Meridian accounted from the Equinoctial on the Southern side the Horizon which is just the Zenith of London and then is your Quadrant Rectified 3. Bring the degree of the Ecliptick the Sun is in that day to the Meridian which you shall learn to know by the next Probleme and then turn the Index of the Hour Circle to the hour 12. on the South side the Hour Circle and then is your Hour Circle also rectified fit to use for that Day 4. Lastly If you will rectifie the Globe to correspond in all respects with the Position and Scituation of the Sphear you must set the four Quarters of the Horizon viz. East West North and South agreeable with the four quarters of the World which you may do by the Needle in the bottom of the Horizon for you must turn the Globe so long till the Needle point just to the Flower de luce Next you must set the Plain of the wooden Horizon parallel to the Horizon of the World which you may try by setting a common Level on the four Quaters of the Horizon And then positing the degree of the Ecliptick the Sun is in to the Height above or depth below the Horizon the Sun hath in Heaven as by the 11th Probleme your Globe is made Correspondent in all points with the frame of the Sphear for that particular Time and Latitude PROBLEME III. To find the Place of the Sun in the Ecliptick the Day of the Moneth being first known SEek the Day of the Moneth in the Circle of Moneths upon the Horizon and right against it in the Circle of Signes is the degree of the Ecliptick the Sun is in Example Imagine the Day to be given is May 10. therefore I seek on the Horizon in the Circle of Moneths for May and find the Moneths divided into so many parts as there is Daies in the Moneth which parts are marked with Arithmetical figures from the beginning of the Moneth to the end and denote the number of the Day of the Moneth that each Division represents therefore among the Divisions I seek for 10 and directly against it in the Circle of Signes I find ♉ 29. degrees Therefore I say May 10. the Suns Place is in 29. degrees of ♉ But note that if it be Leap Year instead of the 10. of May you must take the 11. of May because February having in a Leap Year 29. Daies the 29. of February must be reckoned for the first of March and the first of March for the second of March the second of March for the third of March and so throughout the year The Leap Year is caused by the six od hours more then 365. daies that are assigned to
what Elevation of the Pole the Daies shall be an Hour shorter By this Probleme may be found the Alteration of Climates for as was said in the Definition of Climates Book 1. fol. 28. Climates alter according to the half-hourly increasing of the Longest Day therefore the Latitude of 56½ degrees having its Daies increased an whole Hour is distant from the Latitude of London by the space of two Climates PROB. L. The Suns Place given to find what alteration of Declination be must have to make the Day an Hour longer or shorter And in what number of Daâ—es it will be REctifie the Globe to the Latitude of the Place and bâ—ing the Suns place to the East side the Horizon and note against what degree of the Horizon it is then bring one of the Colures to intersect the Horizon in that degree of the Horizon and at the point of Intersection make a prick in the Colure and observe what degree of the Equator is then at the Meridian Then turn the Globe Westward if the Daies shorten but Eastwards if they lengthen till 7½ degrees of the Equator pass through the Meridian and where the Horizon intersects the same Colure make another prick in the Colure Afterwards bring the Colure to the Meridian and count the number of degrees between the two pricks for so many degrees must the Suns Declination alter to lengthen or shorten the Day an Hour Example The Suns Place is ♉ 10. I would know how much he must alter his Declination before the Day is an Hour longer here at London Therefore I rectifie the Globe to the Latitude of London and bring ♉ 10. to the East side the Horizon and find it against 24½ degrees from the East point therefore I bring one of the Colures to this 24½ degrees and close by the edge of the Horizon I make a prick with black lead in the Colure then keeping the Globe in this position I look what degree of the Equator is then at the Meridian and find 250¼ and because the Daies lengthen I turn the Globe Eastwards till 7½ degrees from the foresaid 250¼ pass through the Meridian then keeping the Globe in this position I make another prick in the Colure and bringing this Colure to the Meridian I find a little more then 5 degrees of the Meridian contained between the two pricks therefore I say when the Sun is in ♉ 10. degrees he must alter his Declination a little more then 5 degrees to make the Day an Hour longer Now to know in what number of Daies he shall alter this Declination you must find the Declination of the two pricks on the Colure as you found the Suns Declination by Prob. 5. and the Arch of the Ecliptick that passes through the Meridian while the Globe is turned from the first pricks Declination to the second pricks Declination is the number of Ecliptical degrees that the Sun is to pass while he alters this Declination and the degree of the Ecliptick then at the Meridian is with respect had to the Quarter of the Year the place the Sun shall have when its Declination shall be altered so much as to make the Day an Hour longer Thushaving the Suns first place given and its second place found you may by finding those two places on the Plain of the Horizon also find the number of Daies comprehended between them as you are taught by the fourth Probleme This Probleme thus wrought for different Times of the Year will shew the falacy of that Vulgar Rule which makes the Day to be lengthned or shortned an Hour in every Fifteen Daies when as the lengthning or shortning of Daies keeps no such equality of proportion for when the Sun is neer the Equinoctial points the Daies lengthen or shorten very fast but when he is neer the Tropical points very slowly PROB. LI. Of the Difference of Civil and Natural Daies commonly called the Equation of Civil Daies And how it may be found by the Globe THe Civil Day is that space of Time containing just 24. Hours reckoned from 12 a clock on one Day to 12 a clock the next Day in which space of Time the Equinoctial makes upon the Poles of the World a Diurnal Revolution The Natural Day is that space of Time wherein the Sun moveth from the Meridian of any Place to the same Meridian again These Daies are at one time of the Year longer then at another and at all Times longer then the Civil Daies There is but smal discrepancy between them yet some there is made by a two-fold Cause For first The Suns Apparent motion is different from his true motion He being much slower in his Apogeum then he is in his Perigeum For when the Sun is in his Apogeum he scarce moves 58 minutes from West to East in a Civil Day but when he is in his Perigeum he moves above 61 minutes in a Civil Day and therefore increases his Right Ascension more in equal Time The second Cause is the difference of Right Ascensions answerable to equal parts of the Ecliptick for about ♋ and ♑ the differences of Right Ascensions are far greater then about ♈ and ♎ for about ♈ and ♎ the Right Ascension of 10. degrees is but 9. degrees 11. minutes but about ♋ and ♑ the Right Ascension of 10 degrees will be found to be 10. degrees 53. minutes as by the Globe will appear But because of the smalness of the Globes graduation you cannot actually distinguish to parts neer enough for the solution of this Probleme if you should enquire the difference in length of two single Daies it will be requisite to take some number of Daies together Suppose 20. Therefore find by Prob. 3. the Places of the Sun for the beginning and ending of those Daies you would compare and find the Right Ascensions answerable to each place in the Ecliptick and also the differences of Right Ascensions answerable to the Suns motion in each number of Daies Then compare the differences of Right Ascensions together and by substracting the lesser from the greater you will have the number of degrees and minutes of the Equator that have passed through the Meridian more in one number of Daies then in the other number of Daies which degrees of the Equator converted into Time is the number of minutes that the one number of Daies is longer then the other number of Daies Example I would know what difference of Time there is in the length of the first 20. Daies of December and the first 20 Daies of March I find by Prob. 3. the Suns place December 1 is 〈◊〉 19. 45. at the end of 20 Daies viz. on the 21 Day his place is 〈◊〉 10. 11. The Suns place March 1. is ♓ 21. 16. at the 20. Daies end viz. March 21 his place is ♈ 11. 3. I find by Prob. 26. the Right Ascension answerable to â™ 19. 45 is 258. 10. ♑ 10. 11 280. 25. ♓ 21. 16 352. 00. ♈ 11. 3 9. 40. and
off these kind of Planes To these Hour lines I set their numbers as you may see iâ— the Figure Here you may see that in Declining Dyals the Style doth not stand at the same Elevation above the Plane that it doth in Erect Direct Dyals neither doth it stand over the 12 a clock line but swerves from it towards the Quarter of Declination PROB. X. To make a North Erect Dyal declining Eastwards or Westwards AS in Prob. 5. an Erect Direct North Dyal hath the same Delineation that an Erect Direct South Dyal hath and differs only in the placing the Figures of the Hour lines So a North Erect Dyal that declines Eastwards or Westwards differs from a South Erect Dyal that Declines Eastwards or Westwards the same number of degrees only in placing the Hour lines at the same distance on the contrary side of the Plane and by transposing the Figures of 11 for 1 10 for 2 9 for 3. c. Thus if you draw upon Glass Horn or an Oyled Paper the South Dyal Declining Eastwards as in the foregoing Probleme and place it to its due scituation the back side of it shall be a North Dyal declining towards the West so many degrees as the foreside Declines towards the East and the only difference in it will be the Figures of the Hour lines as was said before PROB. XI To make Direct Reclining or Inclining Dyals DIrect Reclining or Inclining Dyals are the same with Erect Direct Dyals that are made for the Latitude of some other Places The Latitude of which Places are either more then the Latitude of your own Place if the Plane Recline or less if the Plane Incline and that in such a proportion as the arch of Reclination or Inclination of your Plane is Thus a Direct South Dyal Reclining 10. degrees in Londons Latitude viz. 51½ degrees is an Erect Direct Dyal made for the Latitude of 61½ degrees And a Direct South Dyal Inclining 10. degrees in the Latitude 51½ degrees is an Erect Direct Dyal in the Latitude of 41½ degrees and is to be made according to the Directions in Prob. 4. PROB. XII To make Declining Reclining or Declining Inclining Dyals THe distances of the Hour lines either for a Declining Reclining Plane or a Declining Inclining Plane may most easily be found upon the Plane of the Horizon That is as some Authors call it by the Horizontal Dyal by changing the Circles of the Globe one into another So as the Plane of the Horizon may serve to represent the Dyal Plane Yet this way not being natural because you must admit one Circle to be another and that in Young Learners might sometimes breed a little difficulty Gemma Frisius Metius and Blaew hath prescribed a thin Brass plate to be made equal to a Semi-Circle of the Equinoctial and divided from the middle point of it either way into 90 degrees which may not unproperly be called a Gnomonical Semi-Circle This Semi-Circle must be bowed close to the Body of the Globe into a Semi-Circular form and so set to any Reclination or Inclination and then it will represent a Reclining or Inclining Plane And by the motion of the Colure through the several degrees of this Semi-Circle the distances of the Hour lines may be found Thus The Globe Quadrant of Altitude Colure and Hour Index Rectified as by Prob. 4. Bring the lower end of the Quadrant of Altitude to the degree in the Horizon of the Planes Declination if your Plane be a South Declining Recliner and count on the Quadrant of Altitude from the Zenith downwards the number of degrees of Reclination or Inclination and to that number of degrees bring the middle of the Gnomonical Semi-Circle and let the ends of â—t cut the Horizon on either side in the degrees of the Planes Azimuth so shall the Gnomonical Semi-Circle represent a Reclining Plane And so oft as 15. degrees of the Equator passes through the Meridian so oft shall you enquire what degrees of the Gnomonical Semi-Circle the Colure cuts for so many degrees asunder must the several respective Hour lines of a Reclining Declining Plane be in a Semi-Circle divided into 180. degrees But if your Plane be a South Declining Recliner or a North Declining Incliner Bring the Quadrant of Altitude to the degree of the Horizon opposite to the degree of the Planes Declination because the upper side of the Plane lies beyond the Zenith counted from the South point in the South Recliners and from the North point in North Incliners Then find the height of the Style and place of the Substyle thus Keep your Gnomonical Semi-Circle in its position But turn the Quadrant of Altitude about on the Zenith point till the lower end of it comes to the degree of the Horizon opposite to the degree it was placed at before and turn about the Globe till the Colure cut the Quadrant of Altitude above the Horizon in the number of degrees the Plane Reclines from the Zenith so shall the Colure cut the Gnomonical Semi-Circle at Right Angles Then count the degrees contained between the middle of the Gnomonical Semi-Circle and the Colure for that number of degrees is the distance of the Substyle from a Perpendicular line in the middle of your Plane and must be placed Westwards of the said Perpendicular if your Plane decline from the South East-wards or Eastwards if your Plane decline from the South Westwards Then observe how many degrees are contained between the Semi-Circle and the Pole for that number of degrees is the number of degrees that the Style is to be Elevated above the Substyle Example Here at London I would make a Dyal upon a Plane Declining from the South Eastwards 30. degrees and Reclining from the Zenith 20. degrees Londons Latitude is 51½ degrees Therefore Having on the Plane discribed a Semi Circle c. as was directed Prob. 4. I Rectifie the Globe Quadrant of Altitude Colure and Hour Index as by the same Probleme and bring the lower end of the Quadrant of Altitude to 30. degrees from the North point of the Horizon towards the West because that is the degree opposite to the degree of the Planes Declination viz to 30 degrees from the South Eastwards And I bring the middle of the Gnomonical Semi Circle to 20. degrees of the Quadrant of Altitude counted from the Zenith downwards towards the Horizon and the ends of the Gnomonical Semi Circle to the degrees of Azimuth the Plane lies in in the Horizon viz. to 30. degrees from the East point Northwards and to 30. degrees from the West point Southwards so shall 11. degrees 10. minutes of the Gnomonical Semi Circle be comprehended between the Quadrant of Altitude and the Brasen Meridian These 11. degrees 10. minutes shews that the 12 a clock line is distant from the Perpendicular A B 11. degrees 10. minutes and because the Plane Declines to the Eastwards therefore the 12 a clock line must stand on the West side the Plane 11. degrees 10
Thus The 1 a clock Hour-line 11.40 whose Complement 90. is 78.20 2 24.15 65.45 3 38.4 51.56 4 53.36 36.24 I measure in a Quadrant of the same Radius with those arches already drawn from the Equinoctial line for the 1 a clock Hour 78.20 2 65.45 3 51.56 4 36.24 and transfer these distances to the Arches drawn on the Ceeling For then straight lines drawn through the mark in the Arch and through the mark in the Equator and prolonged both waies to a convenient length shall be the several Hour-lines a foresaid And when the Sun shines upon the Glass at Nodus its Beams shall reflect upon the Hour of the Day PROB. XVI To make a Dyal upon a solid Ball or Globe that shall shew the Hour of the Day without a Gnomon THe Equinoctial of this Globe or which is all one the middle line must be divided into 24 equal parts and marked with 1 2 3 4 c to 12. and then beginning again with 1 2 3 c. to 12. Then if you Elevate one of the Poles so many degrees above an Horizontal line as the Pole of the World is Elevated above the Horizon in your Habitation and place one of the 12 s directly to behold the North and the other to behold the South when the Sun shines on it the Globe will be divided into two halfs the one enlightened with the Sun-shine and the other shadowed and where the enlightned half is parted from the shadowed half there you shall find in the Equinoctial the Hour of the Day and that on two places on the Ball because the Equinoctial is cut in two opposite points by the light of the Sun A Dyal of this fort was made by M r John Lâ—â—k and set up on a Composite Columne at Leaden Hall Corner in London in the Majoralty of S r John Dethick Knight The Figure whereof I have inserted because it is a pretty peece of Ingenuity and may perhaps stand some Lover of Arâ— in stead either for Imitation or help of Invention PROB. XVII To make a Dyal upon a Glass Globe whose Axis shall cast a shadow upon the Hour of the Day FIrst divide the Equinoctial of your Globe into 24 equal parts and having a Semi-Circle cut out of some Brass plate or thin Wood to the same Diameter your Globe is of or a very little wider Apply this Semi-Circle to the Globe so as the upper edge of each end of the Semi Circle may touch the Poles of the Globe and the middle of the Semi Circle may at the same edge cut through some division made in the Equinoctial for then a line drawn by the edge of the Semi Circle thus posited shall be a Meridian line The same way you must draw Meridian lines through every division of the Equinoctial and set figures to them beginning with 1 2 3 4 c. to 12 and then beginning again with 1 2 3 4 c. to 12 again This Globe being made of Glass and having an Axis of Wyer passing through â—t from Pole to Pole will be an Horizontal Dyal all the World over if its Axis be set Parallel to the Axis of the World in the same Place and one of the Meridians marked 12 be set so as it may directly behold the North point in Heaven and the other the South point in Heaven for then the Axis of the Globe shall cast a shadow upon the Hour of the Day And if you divide the upper half of the Glass Globe from the under half when the Axis stands Parallel to the Axis of the World by a Circle drawn round about the Globe that Circle shall represent the Horizon and the Meridian lines drawn on the Globe shall be the Hour lines and have in the Horizontal Circle the same distance from the 12 a clock line that the same respective Hour line was found to have as by Prob. 3. of this Book But because the shadow of this Axis will not be discerned through the Glass Body therefore you may with Water and white Lead ground together lay a Ground on the Inside of the under half of the Glass to the Horizontal Circle as Looking-glass makers do their Looking Glasses with Tinfoil for then the shadow will appear Such a Glass Globe Dyal hath the Lord Robert Titchborn standing in his Garden supported by Atlas The End of the Fifth Book The Sixth BOOK Shewing the Practical Use of the GLOBES Applying them to the Solution of Spherical Triangles PRAEFACE THe Solution of Spherical Triangles is to know the length of its Sides and the width of its Angles These have already by many learned Men been taught to be performed by a Canon of Sines and Tangents and also by many Instruments some serving as Tables of Sines and Tangents such as are the Sectors Scales the Spiral line c. and others serving to represent the Globe such as be the Mathematical Jewel Astrolabium Catholicum and several other Projections of the Sphear But none hath as yet taught the Solution of Spherical Triangles by the Globe it self though it be the most natural and most demonstrative way of all and indeed ought first to be learnt before the Learner enters upon any other way To this Authors of Trigonometry agree for the most of them in their Books give Caution that the Learner be already sufficiently grounded in the Principles of the Globe For those Lines or Circles which either in Tables or other Instuments your force your Imagination to conceive represents your Line or Circle in question those Lines and Circles I say you have Actually and Naturally discribed on the Globe and therefore may at a single Operation or perhaps only by a sudden inspection have an Answer annexed according as the nature of your Question shall require and that more Copiously then by Tables of Sines and Tangents For therein you find but one Question at once resolved but by the Globe you have alwaies two resolved together Of the Parts and Kindes of Spherical Triangles THEOREMS 1. ALL Spherical Triangles are made of six parts Three Sides and three Angles The Sides are joyned together at the Angles and measured by degrees of a Great Circle from one end to the other The Angles are the distance of the two joyned sides and they are also measured by an Arch of a Circle discribed on the Angular point If any three of these parts be known the rest may be found 2. All Spherical Triangles are either Right Angled or Oblique Angled A Right Angle contains 90. degrees An Oblique Angle either more or less 3. If a Spherical Triangle have one or more Right Angles it is called a Right Angled Spherical Triangle But if it have no Right Angle it is called an Oblique Angled Spherical Triangle 4. If an Oblique Spherical Triangle have one Angle greater then a Right Angle it is called an Obtuse Angled Spherical Triangle But if it have no Angle greater it is called an Accute Angled Spherical Triangle 5. In Right
degrees 30. minutes I screw the Quadrant of Altitude and count in the Horizon from the Intersection of the Meridian with the Horizon on that side the Pole is Elevated the measure of the given Angle B viz. 142. degrees 42. minutes and to this number of degrees and minutes of the Horizon I bring the edge of the Quadrant of Altitude then I turn about the Globe till the first Meridian is distant from the Brasen Meridian 17. degrees 15. minutes of the Equinoctial which is the measure of the other given Angle So shall the Triangle be made on the Globe and the Arch of the Quadrant of Altitude comprehended between the first Meridian and the Zenith shall be the measure of the side B C 25. degrees and the Arch of the first Meridian comprehended between the Pole and its Intersection with the Quadrant of Altitude shall be the measure of the side A C 60. degrees The measure of the Angle C is found by turning the Triangle as in Prob. 7. PROB. XI Two Angles and a Side opposite to one of them given to find the Rest. EXample In the Triangle of Prob. 7. the Angles given are A 17. degrees 15 minutes and B 142. degrees 42. minutes the side given is B C 25. degrees being the side opposite to the Angle A the Angle A is made at the Pole of the Globe and measured in the Equator Therefore I separate the first Meridian from the Brasen Meridian 17. degrees 15. minutes so doth the Pole represent the Angle A the Angle B is made at the Zenith and measured in the Horizon therefore I count in the Horizon 142. degrees 42. minutes and there I make a prick to this prick I bring the edge of the lower end of the Quadrant of Altitude not minding to what degrees of the Meridian the upper end of it is placed Then I count from the upper end of the Quadrant of Altitude 25. degrees downwards the measure of th e side B C and there I make a prick and keeping the lower end of the Quadrant of Altitude to the prick made in the Horizon I slide the upper end of it forwards or backwards till the prick on the Quadrant of Altitude come to the first Meridian so shall the Triangle be made on the Globe Then the Arch of the Brasen Meridian comprehended between the Pole and the upper end of the Quadrant of Altitude shall be the measure of the side A B 38. degrees 30. minutes and the Arch of the first Meridian comprehended between the prick on the Quadrant of Altitude and the Pole shall be the measure of the side A C 60. degrees But the Angle C you must find by turning the Triangle as in Prob. 7. In the working this Probleme I would have placed the given fide B C 25. degrees upon the Brasen Meridian between the Pole and Zenith but then the Angle B being so Obtuse would have had that side which would be intersected by the Quadrant of Altitude viz. the first Meridian under the Horizon which the Quadrant of Altitude cannot reach PROB. XII Three Angles given to find the Sides THis Triangle is taught to be resolved by M r Palmer on the Planisphear Book 3. Chap. 19. It is to be known saith he That if you go to the Poles of the three great Circles whereof your Triangle is made these Poles shall be the Angular points of a second Triangle and the two lesser sides of this second Triangle shall be equal to the two lesser Angles of your first Triangle the greatest side of the second Triangle shall be the supplement of the greatest Angle of the first Triangle that is shall have as many degrees and minutes as the greatest Angle of the first Triangle wanted of 180. degrees see Pitiscus Trigonometry Lib. 1. Prop 61. This second Triangle therefore all whose sides are known from the Angles of the first you shall resolve by Prob. 7. And having by that Probleme found the Angles of this second Triangle know that the two lesser Angles of the second Triangle shall be several and respectively equal to the two lesser sides of the first Triangle and the least Angle to the least side the middle Angle to the middle side and the greatest Angle of this second Triangle being subtracted out of 180. degrees shall leave you the greatest side of your first Triangle Example If the Angles be given 142. degrees 42. minutes 17. degrees 15. minutes and 25. degrees 24. minutes and the sides be enquired Draw by aim a rude Scheam of this first Triangle writing in the Angle A 17 degrees 15. minutes in B 142. degrees 42. minutes in C 25. degrees 24. minutes supposing the sides yet unknown then draw under this by aim also a Scheam of the second Triangle setting his Base Parallel with the Base of the first and making the Base of the second shorter then the Base of the first Set also B at the Vertical Angle and A C at the Base as in the first Triangle Then say Because A in the first Triangle is 17 degrees 15. minutes therefore in the second Triangle B C which subtendeth A shall be 17. degrees 15. minutes and because C in the first Triangle is 25. degrees 24. minutes therefore in the second Triangle the side A B which subtendeth C shall be 25. degrees 24. minutes and because B the greatest Angle in the first Triangle is 142. degrees 42. minutes therefore in the second Triangle the side A C which subtendeth B shall be the complement thereof to 180. degrees viz. 37. degrees 18. minutes Write now upon the sides of this second Triangle the quantities of the sides so is your second Triangle ready to be resolved as by Prob. 7. Whereby you shall find the Angles of the second Triangle as I have expressed them in the Scheam A 25. degrees C 38. degrees 30. minutes B 120. degrees Nâ—w lastly I say these Angles of the second Triangle thus found give me the sides of the first Triangle which I seek in this manner In the second Triangle  In the first Triangle A is 25. degrees Therefore B C is 25. degrees C is 38. 30. A B 38. 30. B is 120. 00. A C 60. 00. Complement of 120. degrees to 180. And thus by all the Angles given we have found out all the sides which was required Having then the Angles of your first Triangle given and his sides now found you shall find his scituation on the Globe thus Place him as in Prob. 7. A B 38. degrees 30. minutes between the Pole and Zenith A C 60. degrees in the first Meridian separated from the Brasen Meridian 17. degrees 15. minutes of the Equinoctial B C 25. degrees on the Quadrant of Altitude counted from the Zenith when it s lower end is applyed to the 142. degrees 42. minutes of the Horizon you shall say Because the East point of the Horizon is the Pole of the Arch A B therefore at the East point of the Horizon shall
Triangle called also Deltâ—ton because it is like the fourth letter of the Greeks Alphabet Δ which they call Delta it consisteth of four stars They say it was placed in Heaven by Mercury that thereby the head of the Ram might be the better known Others say that it was placed there in honour of the Geometricians among whom the Triangle is of no small importance Others affirme that Ceres in times past requested Jupiter that there might be placed in Heaven some Figure representing the form of Sicilie an Island greatly beloved of Ceres for the fruitfulnesse thereof now this Island being triangular at her request was represented in the Heaven under that form Thus much concerning the Constellations of the Northern Hemisphear Now follow the Poeical Stories of the Constellations of the Southern Hemisphear Secondly Of the Southern Constellations 1. CETUS the Whaâ—â— it is also called the Lion or Bear of the Sea This is that monstrous fish that should have devoured Andromeda but being overcome by Perseus was afterwards translated into Heaven by Jupiter as well for a token of Perseus his manhood as for the hugeness of the fish it self This constellation consisteth of 22. Stars 2. ORION this hath 38. Stars The Poetical reason of his translation into the Heaven shall be shewn in the Scorpion amongst the Zodietical Constellations The Ancient Romans called this Constellation Jugala because it is most pestiferous unto Cattel and as it were the very cut-throat of them There are bright Stars in his girdle which we commonly call our Ladies yard or waâ—d Novidius applying this sword of Orion unto Scripture will have it to be the sword of Saul afterwards called Paul wherewith he persecuted the Members of Christ which after his conversion was placed in Heaven In his left shoulder there is a very bright Star which in Latine is called Bellatrix the Warriour in the foeminine gender I cannot find the reason except it be this that Women born under this Constellation shall have mighty tongues The reason of the Ox-hide which he hath in his hand may be gathered out of the next story 3. FLUVIUS the River it comprehendeth 34. Stars It is called by some Eridanus or Padus and they say that it was placed in Heaven in remembrance of Phaeton who having set the whole World on fire by reason of misguiding of his father Phoebus his charriot was slain by Jupiter with a thunder-bolt and tumbling down from Heaven fell into the River Eridanus or Padus which the Italians call Po. Others say that it is Nylus and that that Figure was placed in the Heaven because of the excellency of that River which by the Divines is called Gihon and is one of the Rivers of Paradice Others call it Flumen Orionis the flood of Orion and say that it was placed there to betoken the Off-spring from whence Orion came for the tale is thus reported of him Jupiter Neptune and Mercury travelling upon the earth in the likeness of Men were requested by Hyreus to take a poor lodging at his House for a Night they being overtaken with the evening yeilded unto his request Hyreus made them good cheer killing an Ox for their better entertainment The Gods seeing the good heart of the old man willed him to demand what he would in recompence of his so friendly cheer Hyreus and his Wife being old requested the Gods to gratify them with a Son They to fulfil his desire called for the hide of the Ox that was slain and having received it they put it into the Earth and made water into it all three together and covering it willed Hyreus within ten moneths after to dig it out of the Earth again which he did and found therein a Man-child whom he called Ourion ab Urina of piss although afterwards by leaving out the second letter he was named Orion At such time therefore as he was placed in Heaven this flood was joyned hard to his heels and the Ox hide wherein the Gods did piss was set in his left hand in memorial of his Off-spring 4. LEPUS the Hare which consisteth of 12. stars This Constellation was placed in Heaven between the legs of Orion to signifie the great delight in hunting which he had in his life time But others think it was a frivolous thing to say that so notable a fellow as Orion would trouble himself with so smal and timerous a beast as the Hare and therefore they tell the tale thus In times past there was not a Hare left in the Isle Dâ—râ—s a certain youth therefore of that Island being very desirous of that kind of beast brought with him from another Country thereabout an Hare great with young which when she had brought forth they in time became so acceptable unto the other Countrimen that every one almost desired to have and keep a Hare By reason whereof the number of them grew to be so great within a short space after that the whole Island became full of Hares so that their Masters were not able to find them meat whereupon the Hares breaking forth into the fields devoured their Corn. Wherefore the inhabitants being bitten with hunger joyned together with one consent and though with much ado destroyed the Hares Jupiter therefore placed this Constellation in the Heavens as well to express the exceeding fearfulness of the beast as also to teach men this lesson that there is nothing so much to be desired in this life but that at one time or an other it bringeth with it more grief then pleasure Some say that it was placed in Heaven at the request of Ganimedes who was greatly delighted with hunting the Hare 5. CANIS MAIOR the Great Dog it consisteth of 18. Stars It is called Sirins Canis because he causeth a mighty drought by reason of his heat This is the Constellation that giveth the name unto the Canicular or dog-Dog-days whose beginning and end is not alike in all places but hath a difference according to the Country and Time as in the Time of Hypocrates the Phisitian who lived before the time of Christ 400 years the Canicular days began the 13. or 14. of July In the time of Avicenna the Spaniard who lived in the year of our Lord 1100. the Canicular days began the 15 16 or 17. of July In our Country they begin about S. James-tide but we use to account them from the 6. of July to the 17. of August which is the time when the Sun beginneth to come near unto and to depart from this Costellation Novidius will have it to be referred to Tobias Dog which may very well be because he hath a tail Tobias Dog had one as a certain fellow once concluded because it is written that Tobias his Dog fawned upon his Master therefore it is to be noted said he that he had a tail The Poets say that this is the Dog whom Jupiter set to keep Europa after that he had stolen her away and convâ—ied her into Crete and for his
about the same time and taught at Alexandria as in the Memorials of Pappus were quite of another kind being indeed no other but certain Principles of Astronomy concerning the figure of the World and the Circles of the Sphear and chiefly that of the Zodiack But to return back to the more primitive Greeks I remember I said that Thales Melesius was accounted the First who after old Hesiod and Homers Dayes enquired into the Order of the Stars And certainly He was the Man who among the Grecians may challenge the Palme as to Antiquity for Apuleius calls him ut antiquissimus sic peritissimus Astrorum Contemplator and Eudemus in Laertius attesteth that this was the Opinion of most adding moreover that Xenophanes and Herodotus highly admired him for that he had first predicted the Eclypses and Conversions of the Sun and that Heraclitus and Democritus witnesseth as much And whereas Apuleius further subjoyns that he found out the motions and oblique tracts of the Syderal Lights Pliny ascribes that to Auaximander a Disciple of Thales Milesius whence he was said Rerum fores aperuisse to have opened the Doors of Celestial matters and Diodorus to one Oenopides Chius which Thales could not yet be ignorant of the Obliquity of the Zodiack when he had written of the Solstices and Equinoxes and had conversed a long time with the Egyptians in their own Country as Laertius remembers Further it is delivered to us that among others he predicted that notable Eclipse of the Sun which hapned in the time of the warre betwixt the Meads and Lydians which he could not doe by any other reason but only because coming newly out of Egypt he had learned that Eclipses generally return upon the same Day after the space of nineteen Years and having taken notice of one that fell out 19. Years before he concluded that there would be one at such a time Nor is there reason why any should think that otherwise his whole life might be sufficient to observe all the motions of the Sun and Moon as from thence to be able to invent all things necessary for the calculation of the times of their Several Eclipses Moreover it doth not appear how by any other way but that Helicon Cyzicenus came afterward to fore-tell that Eclipse of the Sun mentioned in Plutarch for which he was so much admired by Dyonisius and rewarded with a Talent of Gold Nor likewise how Sulpitius Gallus could fore-tell that other of the Moon which as most opportunely predicted to the Roman Army then ready to joyne battell with the Persian is so higly celebrated not only by Plutarch and Pliny but also by Valerius Quintilian and other Historians for other Rule for the calculation of future Eclipses there was none before Hipparchus who invented Hypotheses and Tables fit for that purpose Besides what Laertius imputed to Anaximander Plinius as confidently imputes to one Anaximenes an Auditor of his namely that he should be the Inventor of that Gnomon by which the Conversions of the Sun or the Solstices and Equinoxes were indicated and that he set up such a one at Lacedemon Neer upon the same time was it that Pythagoras is said to have first discoursed though Phavorinus in Laertius confers that honour upon Parmenides that Lucifer and Vesper was one and the same Star of Venus Now whether may we conceive that he borrowed this of the Egyptians from whom being taught that not only Venus but Mercury also were carried round about the Sun as their Center so that one and the same might be both Morning and Evening Star possibly from thence he might take the hint of his Conjecture that the Sun was the Center of not only those two but of the other Planets also and consequently of the whole World and moreover that the Earth it self as one of the Planets moved about the Sun For truely this was an eminent and constant Tenent in his School as may be understood not only from Aristotle in the general but also from Laertius in particular of Philolaus and from Archimed of Aristarchus both Pythagorus his Disciples that we may not rehearse all those many passages in Plutarch concerning this memorable particular nor name those who held that the Earth was not so much moved about the Sun as dayly turned rouud upon an Axis of its own as Timaeus a Pythagorian also who is therefore by Synesius esteemed after Plato the most excellent Astronomer Furthermore in the next Age after Thales or neere upon comes Cleostratus the same who was beleeved to have deprehended the Signes of the Zodiack and he seriously remarking that the Intercalation which as we said was wont to be made every fourth Year celebrated with the Olympick Games did indeed restore the motion of the Sun to the same Day again but did not restore the motion of the Moon till the eight Year or two Olympiades in which the intercalatory Dayes amounted to ninety Dayes or three months He we say thereupon interduced instead of the Tetacteris or space of four Years the Octaeteris or space of eight Years which compleatly past the New-Moons and Full-Moons would returne again on the same Dayes But when in short time men had perceived that this Institution failed them in exactness of computation and that sundry wayes had bin attempted to cure this uncertainty at length riseth up Meton somwhat more ancient than Eudoxus and he demonstrateth from the New-Moons and Full-Moons Eclyptical that they did not return upon the same Dayes till after full nineteen Years and thereupon he became the Author of the Enneadecaeteris or Period or Cycle of 19. Years In respect of which discovery together with the Heliotrope or Sun Diall he made at Athens and some other the like Inventions he was in eminent esteem among the Athenians But as concerning that Period Callippos familarly acquainted with Aristotle discovering it to be too long by the fourth part of a Day inferred that from four Periods one whole Day ought to be detracted and so erected a new Period or Cycle of Sixty six Years or four times nine at the end of which one Day was to be cut off and this was called the Callippik Period and remained in use for a long time together After him succeeded Hipparchus who detecting this Period to be yet too long demonstrateth that after four Callippik Periods or three hundred and four Years there would remain one whole Day too much And in truth the experience of many succeding Ages declared that to this detraction of Hipparchus nine or ten Years over and above were to be expected However it is worthy our notice that the Period of Meton together with the Conection of it applied by Callippus was of long use in the Church under the name of the Golden-Number though wanting the Application of Hipparchus his Correction also a mistake of about four Dayes relating to the New and Full Moons crept into the account even from the