Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	divide_v	equal_a	line_n	1,364	5	9.1106	5	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A16236	The theoriques of the seuen planets shewing all their diuerse motions, and all other accidents, called passions, thereunto belonging. Now more plainly set forth in our mother tongue by M. Blundeuile, than euer they haue been heretofore in any other tongue whatsoeuer, and that with such pleasant demonstratiue figures, as euery man that hath any skill in arithmeticke, may easily vnderstand the same. ... VVhereunto is added by the said Master Blundeuile, a breefe extract by him made, of Maginus his Theoriques, for the better vnderstanding of the Prutenicall tables, to calculate thereby the diuerse motions of the seuen planets. There is also hereto added, The making, description, and vse, of two most ingenious and necessarie instruments for sea-men ... First inuented by M. Doctor Gilbert ... and now here plainely set downe in our mother tongue by Master Blundeuile.	Blundeville, Thomas, fl. 1561.; Magini, Giovanni Antonio, 1555-1617. aut; Gilbert, William, 1540-1603. Making, description and use of two most ingenious and necessarie instruments for seamen. aut; Wright, Edward, 1540-1603. aut	1602 (1602)	STC 3160; ESTC S117447	145,552	301

E beginning to account from F to E which is the arch of the said Quadrant which I will call from henceforth the inner Quadrant by helpe whereof you haue to deuide as well the middle Quadrant marked with L N as the outwardmost Quadrant marked with M H as the Figure sheweth And the two last Quadrants doe containe each of them 19 circular lines of diuision making 18 spaces euery space containing fiue degrees and are to be drawn in such order as followeth First you haue to draw a right line paralell to C E beginning at F and so proceeding forward towards your right hand in some sufficient length for the longer the better to serue your purpose Then take with your Compas the distance betwixt C and F and applie that distance to the said right paralell line by putting the one foot of your Compas in F and the other at the end of that distance marking that point with the letter L then by setting the firme foot of your Compas in C and by extending the other foot to L draw a portion of a circle somwhat more than a Quadrant towards your left hand and marke the end of that arch with the letter N which arch is to be deuided into 90 equall parts or degrees by helpe of 19 circular lines of diuision to bee drawne as followeth First set the firme foot of your Compas in F and with the other foot extended to the centre C draw a circle from C to L and that shall be the first circle of diuision shewing that the point L is the first point from whence you haue to account the 90 degrees of the middle Quadrant proceeding vpward by fiue and fiue vntill you come to 90. Then to draw the rest of the circles of diuision belonging to the said middle Quadrant you haue no more to doe but to remoue the firme foot of your Compas to euery fift degree of the first and inner Quadrant and alwayes to extend the other foot to the centre C so shall you justly deuide the arch of the middle Quadrant into 90 degrees Now to draw the arch of the outwardmost Quadrant marked with M H you must doe thus First take with your Compas the distance betwixt the letter L and the centre C and applie that distance to the quarter of the first whole circle on the left hand marked with the letters F K which you shall find to be all one then by setting the one foot of your Compas in F and by extending the other foot to the end of that distance vpon the right paralell line before drawn and marked with the letters F L marke that point or end of distance with the letter M as you see in the foresaid Figure Then set the firme foot of your Compas in the centre C and by extending the other foot to the point M draw a portion of a circle somewhat more than a Quadrant towards your left hand and marke the end thereof with the letter H which shall be the arch of the outwardmost Quadrant and must be deuided into 90 equall parts or degrees by helpe of 19 circles of diuision to be drawne as followeth First by setting the firme foot of your Compas in F and the other in K draw a circle from K to M from which point you must begin to account the 90 degrees of that arch and so to proceed towards your left hand from 5 to 5 vntill you come to 90 which diuision is to be made by remoouing the firme foot of your Compas to euery fift point of diuision contained in the arch of the first inner Quadrant marked with the letters F E extending alwayes the other mouable foot to the letter K and so to draw al the circles of diuision belonging to the outwardmost Quadrant That done you haue to draw the Spirall line which cannot bee rightly done vntill you haue deuided euery one of the circles of diuision belonging to the outwardmost Quadrant each one into 90 parts or degrees beginning your account at euery fift degree of the arch of the same outwardmost Quadrant and so to proceed from 5 to 5 vntill you come to the letter K whereas the 90 degree of euery such circle endeth How to draw the Spirall line You see that in the foresaid Figure the Spirall line beginneth at the point L and endeth at the centre of the first whole circle marked with C as the first circle of diuision belonging to the middle Quadrant drawne from C to L doth plainely shew But because the said Spirall line is to be drawne so as it may containe 18 seuerall portions you haue to draw the first portion thereof thus First deuide the second circular line of diuision belonging to the outwardmost Quadrant into 90 equall parts or degrees proceeding from the fift point of the said second line of diuision vnto K whereas is set downe the 90 degree seruing to all the 19 circles of diuision belonging to the said outwardmost Quadrant which is to be done by deuiding the said second line first into three equall parts and euery one of those parts again into three Then last of all euery one of them into two parts euery part whereof shall containe fiue degrees And after this manner is to bee deuided euery one of the 19 lines of diuision belonging to the said outwardmost Quadrant That done take with your Compas the first fift part of that second circle being so deuided and there make a pricke at which prick lay the one end of your Ruler and lay the other end thereof at the first fift degree of the inner Quadrant and so draw a dead right line which will cut the second line of diuision belonging to the middle Quadrant and there make a pricke from which pricke to the letter L you haue to draw the first portion of the Spirall line Now to draw the second portion of the said Spirall line you must resort to the third circular line of diuision belonging to the outwardmost Quadrant and hauing deuided that line into 90 equall parts or degrees as you did before the second line and taken thereof with your Compas tenne degrees there make a pricke to which pricke lay the one end of your Ruler and the other end to the tenth degree of the inner Quadrant and draw a dead right line which wil cut the third circular line seruing to the middle Quadrant and there make the second pricke from which pricke you haue to draw the second portion of the Spirall line so as it may joine with the first portion Then to draw the third portion of the Spirall line you must proceed to the fourth circular line of diuision belonging to the outwardmost Quadrant and deuide that into 90 degrees as you did before whereof you must take 15 degrees and there make a pricke to which pricke you must lay the one end of your ruler and the other end to the 15 degree of the inner Quadrant and hauing drawne a right dead line

and so passe without any Eclipse 2. The second cause of the change or variable shape of the eclipse of the Moone is the vnequall thickenesse of the shaddow of the earth for the higher that the shadow of the earth ariseth the more narrow it groweth ending with a sharpe point because the bodie of the Sun is greater than the bodie of the earth and therefore the shaddow cannot be of any other shape than Conicall for there be three kinds of shaddowes that is Conicall Cylindricall and Calathoidall The shaddow Conicall is that which endeth with a sharpe point The Cylindricall is of like bignesse euerywhere like a round pillar And the Calathoidall shadow the further it extendeth the greater it is like a cup or bowle that is narrow at the bottome and broad at the brim of which shape that shaddow taketh his name for Calathos in Greeke is as much to say as a cup as these three figures doe plainely shew Conicall Cylindricall Calathoidall ANd it is to be noted that when the Moone is in the lower part of her Epicicle neare vnto the opposite Auge thereof her Eclipse continueth longer than it doth when she is neer vnto the Auge of her said Epicicle 3. The third cause is the variable thickenesse of the shaddow which the earth yeeldeth according as the Sun is either in the Auge or opposit Auge of his Excentrick as you may easily perceiue by this figure following consisting of three circles and certaine right lines 4. The fourth cause of the varietie of her Eclipses is her vnequall mouing in her true motion either swift or slow for when she is in her swift motion the continuance of her Eclipse must needs be shorter than when she is in her slow motion And to know her hourely motion either meane or true is to be found by the Prutenicall tables But now though her Eclipse be thus variable as you see yet such varietie may be brought into two cheefe heads that is when she is said to be totally or partly eclipsed whereof we come now to speake The totall Eclipse of the Moone is twofold that is either without any continuance of time or els with some continuance of time In the former so soone as she hath lost her whole light she presently beginneth to recouer the same again but in the latter she being wholly eclipsed the same continueth some quantitie of time The first way chanceth when the latitude of the Moone and the semidiameter of her bodie being both added together the summe thereof is equall vnto the semidiameter of the earth as this figure plainely sheweth ¶ The first figure belonging to the Eclipse of the Moone IN which figure the great blacke circle signifieth the shaddow of the earth and the three lesser circles being all of like bignesse each of them representeth the body of the Moon and what the right lines doe signifie the letters doe shew for the letters B D doe represent the semidiameter of the shaddow of the earth when the Moone is eclipsed and B K sheweth the latitude of the Moone from the Eclipticke which Eclipticke is marked with the letters A C. Now K D signifieth the semidiameter of the Moons bodie and the letter I sheweth the centre of her bodie in the beginning of her Eclipse and the letter H the centre of her body at the end of her Eclipse And the right line I K H signifieth the way of the Moon during the time of her Eclipse Here for so much as the two semidiameters D K and K B being both added together are equall vnto B D which is the semidiameter of the shaddow you may perceiue that the Moone being in the point I began to loose her light by little and little vntill she came to the point K and there was wholly darkened from whence she presently began again without any stay to recouer her light vntill she came to the point H whereas she is fully restored againe to her light The second kind of totall Eclipses of the Moone is when she is wholly eclipsed and the same continueth some quantitie of time which alwaies happeneth when the semidiameter of the shaddow of the earth in the place of the Eclipse is greater than the latitude of the Moone and of her bodily semidiameter being both added together as this second figure next following plainly sheweth ¶ The second figure belonging to the Eclipse of the Moone IN which figure suppose the semidiameter of the shaddow of the earth in the place of the Eclipse to be the line B K and the line B D to bee the latitude of the Moone at the time of the middle of the Eclipse from the Eclipticke marked with the letters A C and the line R D to bee the semidiameter of the Moon H I to be the way of the Moon in the time of her darkenesse and I to be the place of the beginning of her Eclipse and H the ending of the Eclipse and M her place when she is wholly darkened and L her place when she beginneth to recouer her light againe Now you see that when she commeth to the point M shee is wholly eclipsed like as she is also when she commeth to the point L and because she spendeth some quantitie of time in going from M to L and is wholly darkened therfore is this called a Totall Eclipse with continuance Thus much touching the Totall Ecllipse of the Moone now we will speake of the Partiall Eclipse of the Moone The Partiall Eclipse is when some part of the Moone is darkened and not the whole and of this Partiall Eclipse there are three sorts The first is when halfe of the Moones diameter is darkened and the other halfe keepeth still her light which happeneth when the latitude of the Moone is equall vnto the semidiameter of the shaddow of the earth in the place of the Eclipse as you may perceiue by this third figure next following ¶ The third figure belonging to the Eclipse of the Moone IN which figure B D signifying the latitude of the Moone from the Eclipticke A C is just equall vnto the semidiameter of the shaddow of the earth marked also with B D. The second sort of partiall Eclipse of the Moone is when a lesser part than the semidiameter of the Moone is darkened which happeneth when her latitude is more than the semidiameter of the shaddow of the earth as you may see by this fourth figure ¶ The fourth figure belonging to the Eclipse of the Moone IN which figure B K signifieth the semidiameter of the shaddow and B D signifieth the latitude of the Moon now for that B D is more than B K you see that there is but a little of her light taken away by the shaddow of the earth The third sort of Partiall Eclipses is when more than the semidiameter of the Moone is darkened which happeneth when the latitude of the Moone is lesse than the semidiameter of the shaddow of the earth as you may see by

you shall find that it will cut the fourth circular line belonging to the middle Quadrant and there make a prick from which pricke you haue to draw the third portion of the Spirall line so as it may joine to the end of the second portion thereof Now to find out the rest of the 18 portions of the Spirall line you must obserue the selfe same order of working which you did before in finding out the first three portions Thus hauing plainely described vnto you the making of the immouable part or Mater of the said Instrument I will now shew you how to make the moouable part which as I said before is none other thing but a Quadrant hauing an Index with a Fiduciall line answerable in all respects to the first inner Quadrant differing onely in letters For whereas the inner Quadrant is marked with the letters F C E this for difference sake and for the right placing the same vpon the Mater is marked with the letters A B G. For when you come to vse this Instrument you must place the angle A of the moouable Quadrant vpon the centre C of the inner Quadrant there to be fastened with a pin so as the moouable Quadrant may turne round about vpon the Mater The description of the said Instrument THe outward broad hoope or circle of this Instrument would bee of fine Latton or Brasse containing in breadth about an inch and a halfe and in thicknesse almost a quarter of an inch and the whole diameter thereof would be about fiue inches and in the very middest of the inside of the broad circle is traced a middle circle which is deuided into foure quarters euery quarter containing 90 degrees whereof no more are grauen with numerall figures but the two neather quarters the one on the right hand and the other on the left hand and the 90 degree is placed at the neather end whereas both those quarters doe meet And at the vpper end of the broad circle is to bee placed a ringle to hold the Instrument thereby when you would vse the same Now ouerthwart the said broad circle are fastened in the very middest of the two outsides thereof two thin plates of Latton signifying the Horizon bearing in breadth about a quarter of an inch The one plate on the one side of the broad circle and the other plate on the other side of the said circle standing right and just one against another of which two plates each one is bored in the very middest on the inside with a little hole so as into those two holes may bee put an axletree of yron which axletree must be biggest in the very middest to the intent that the Needle beeing wrought into the axletree may hang just in the middest of the said axletree which Needle would be smaller at the one end than at the other for the smallest and sharpest end thereof being touched with a perfect stone dooth alwaies shew the Magneticall declination of the place whereas you make your triall And the Needle it selfe would be in length almost equall to the whole diameter of the broad circle yet so as it may easily play and turne vp and downe without touching the same These parts being fitly and artificially set together you haue to couer the two outsides of the Instrument each of them with a round and cleare glasse that through them you may alwayes see vpon what degree the sharpe point of the Needle falleth after it remaineth steadie without mouing which glasses seruing to keepe the Needle from wind and dust would be so fastened to the outwardmost edge of the broad circle as they may stand sure and not fall away The vse of the said two Instruments FIrst to find out by this Instrument the declination of the Needle vnder the Horizon vpon the land you must resort into a place void of wind or if you would trie it vpon the Sea I thinke it best to goe to that place or coubbard of the ship wherein the Mariners Compas is wont to stand and there steadily to hold the Instrument hanging vpon your right or left thombe so as it may hang right North and South according as the Mariners Compas dooth direct you or els by helpe of some little Diall whose Needle is touched with a perfect stone and when you see that the Needle standeth still marke well vpon what degree in the middle line of the broad circle it falleth for that shall bee the degree of Declination for that place And hauing found the degree of Declination take into your hand the Instrument of Latitude made of Brasse or Pastbord in such forme as you see set downe on the right hand of the first figure demonstratiue which Instrument of Latitude consisteth as I haue said before of two parts the one vnmoouable called the Mater and the other mouable In the Mater is described a Quadrant deuided into 90 degrees which are the degrees of Latitude and also the Spirall line And the moouable part containeth a just Quadrant deuided also into 90 degrees which are the degrees of Declination together with his Index hauing a Fiduciall line to shew the latitude and this moouable part when you come to vse it must bee placed vpon the Mater so as the angle A of the moouable part must bee fastened with a pin vpon the centre or angle of the Mater marked with the letter C in such sort as the moouable Quadrant may turne round about vpon the Mater That done seeke out in the arch of the mouable Quadrant the degree of Declination before found by the instrument of Declination and lay that degree just vpon the Spirall line described in the Mater and holding it fast there with your thombe looke at that very instant vpon what degree of latitude the Index with his Fiduciall line falleth for that shall be the latitude of that place As for example M. Doctor Gilbert hauing found by the Instrument of Declination as he wrote to me the declination at London to be 72 degrees then by applying the same to the Instrument of Latitude in such order as is before taught he found the latitude of London to be 51 degrees 32 minutes And I prouing the same at mine owne house at Newton Flotman not distant aboue foure miles Southward from Norwich I found the declination of the Needle to bee 73 degrees and a little more and thereby I found our latitude here to be 52 degrees or thereabout Both these Instruments I receiued not long since from my deare friend M. Doctor Gilbert for the which I most heartely thanke him the inuention of which Instruments deserueth more worthie commendation and praise than I am able any way to yeeld hoping that all Sea-men will bee as thankefull to him as I am in heart and good will for whose profit there was neuer inuented from the beginning of the world two such noble and necessarie Instruments as these are and therefore worthie to be esteemed of all men accordingly By

or that part of the Zodiake the eclipse of the Moon continueth longer or shorter time so as she abideth vnder the shaddow of the earth more one time than another All which things are salued by supposing an excentricke Is the deferent of the Sunne and the circle excentrique one selfe thing NO for though they haue both one selfe centre called the centre of the excentrique yet the circle excentricke is the circumference of a circle imagined to be in the middle of the deferent is described by the centre of the Sunnes body deuiding the deferent into two equal parts or hemispheres as you may see in the second figure next following The second Intention sheweth what moouing these orbes and circles before mentioned haue and vpon what poles and axletrees they are turned about BEfore I come to the declaration therof it shall be necessary to set downe one other figure containing the most part of such lines points centres circles semicircles and arches as doe belong to the Theorique of the Sunne and to shew what they signifie I say here fore the most part because both these all the rest shall be more fully declared when wee come to the third Intention whose office is to shew all such things at the full ¶ The second figure belonging to the Theorique of the Sunne IN this figure the outermost white orbe signifieth the Zodiake in which are described the characters of the twelue signes And the next white orbe within that is the deferent of the Sunne in which is a little circle representing the bodie of the Sunne whose centre is marked with the letter H. and the two blacke orbes are the two deferents of the Auges of the Sunne before described and in the middle white rundle are set down the two centres before described that is the centre of the world marked with the letter A. and the centre of the deferent of the Sunne marked with the letter B. Moreouer in this figure are drawne certaine right lines whereof the long perpendiculer line passing through both the foresaid centres marked with the letters C. D. is called the line of the Auges and the ouerthwart line passing through the centre of the world to the Zodiake marked with the letters E. F. signifieth the Axe tree of the Zodiake whose outermost ends are the poles of the eclipticke Then there is another ouerthwart right line paralell to the foresaid line E. F. which passing through the centre excentrique extendeth vnto the deferent of the Sunne from the one side to the other side thereof whose outermost ends are the poles of the said deferent marked with the letters K. L. Besides these three lines there are three other lines whereof that which passeth from the centre of the world to the Zodiake marked with the letters A. G. is called the line of the Sunnes meane mouing Then there is another line paralell to that which passeth from the centre of the deferent to the centre or middest of the Suns bodie marked with the letters B. H. And the third line passing from the centre of the world through the midst of the Sunnes bodie euen to the Zodiake is called the line of the Sunnes true mouing marked with the letters A. H. I. There are also in this figure certaine portions of circles called arches which haue their proper significations as the arch of the Zodiake contained betwixt the first point of Aries and the line of the Auges marked with the letters E. C. is called the Auge of the Sun in his second signification and the arch contayned betwixt E. and G. is called the meane mouing of the Sun and the arch contained betwixt E. and I. is called the true mouing of the Sunne and the arch contained betwixt G. and I. is called the equacion of the Sunne and the arch contained betwixt the line of the meane moouing of the Sunne and the line of the Auges marked with the letters C. G. is called of some Argumentum and of some Anomalia that is the inequalitie of the Sunnes moouing All which arches shall be more fully shewed and declared in the third figure next following There bee also in this figure three little semicircles whereof the two marked with the letters K. P. and L. M. doe signifie those circles which the poles of the excentrique doe describe by the mouing of the two deferents of the Auges and the third semicircle marked with the letters B. N. signifieth that circle which the centre of the excentrique describeth by the mouing of the said deferents of the Auges about the centre of the world the semidiameters of all which circles are equall Doth the Theorique of the Sunne onely consist of the three orbes about mentioned that is of the deferent of the Sunne and of the two deferents of the Auges THough the auncient Astronomers doe appoint no more but those three yet Copernicus hauing found by many obseruations made by himselfe and others since their time that the Auges of the Sunne doe moue vnequally and that the excentricitie doth alter hee therefore to salue that apparence dooth adde another orbe called the excentor of the excentrique which indeed are two shaddowed orbes enclosing one another like as the two blacke orbes doe the shape whereof you may see plainely expressed in the sphere of Mercurie hereafter following Now shew how the foresaid three orbes are mooued and first how the excentrique of the Sunne is moued and in what time he maketh his revolution THe excentrique or deferent of the Sunne is regularly moued vpon his owne centre according to the succession of the signes right vnder the eclipticke and maketh his revolution in the space of one whole yeare that is in 365 dayes and almost sixe houres and by the revolution of this orbe is described or limitted the Suns yeare And you haue to note that the tables of Alphonsus and the Prutenicall tables do in a manner agree touching the daily moouing of this orbe which is i59· ii8· iii19· iiii37· and v. 24· so as his yearely revolution containeth 365 dayes 5. houres i49· ii15· iii46· sauing that the tables of Alphonsus doe faile in the daily mouing v. 5· and thereby in the yearely revolution doe exceed the Prutenicall tables by iii13· and so much is the equall tropicall yeare according to Copernicus counting the same from the very equinoctiall point but the daily moouing of the Sunne beeing counted from the first starre of the Rams horne is i59· ii8· iii11· iiii22· v. 10· so as his yearely revolution containeth 365 dayes 6 houres i9· and ii39· and this is called the syderall yeare The poles of this orbe doe equally obserue the poles of the eclipticke and therfore the centre of the Sunnes bodie doth neuer swarue from the eclipticke line Why doth not this Orbe also cary the Sunne equally about the centre of the world BEcause that euery circuler moouing that is equall maketh in equall time in his circumference both equall arches and also equall

to the second part wherein wee haue to treat of the passions qualities or accidents of the Planets of which though Purbachius maketh fiue kinds counting their motions according to latitude to be one of those fiue yet me thinkes that Mestelyn hath more reason to make but foure generall kinds sith the latitude of euery Planet that hath latitude is rather a principall part of his motion than a passion for all their motions are either according to longitude or to latitude and therefore minding herein to follow Mestelyn I will set downe but foure kinds of passions as he dooth which doe grow of foure seuerall comparisons First by comparing the moouing of the Epicicle of any Planet together with the mouing of his Excentrique Secondly by comparing the moouing of the Planets one to another Thirdly by comparing their moouings to the Sunne And fourthly by comparing their moouings or rather places to the centre of the world and to the globe of the earth euery one whereof containeth certaine speciall kinds of passions or accidents hereafter declared What speciall accidents doe belong to the first generall kind consisting of the comparison of the mouing of the Epicicle to the mouing of his Excentrique BY this passion the Planets are said to be sometime direct sometime retrograde and somtime stationarie which three accidents doe belong onely vnto the fiue Planets the Sunne and Moone not beeing reckoned Moreouer they are said to be sometime swift sometime slow and sometime in a meane Sometime also they are said to be either encreased or deminished in number and sometime to be ascendent and sometime descendent When is any Planet said to be direct retrograde or stationarie IT is said to be direct when the line of the true mouing of the Planet drawne from the centre of the world through the midde bodie of the Planet proceedeth forward according to the succession of the signes following the line of the true mouing of the centre of his Epicicle which goeth alwaies according to the succession of the signes And it is said to be retrograde when the line of the true mouing of the Planet goeth more backward contrarie to the succession of the signes than the line of the true moouing of the centre of the Epicicle proceedeth forward according to the succession of the signes And it is said to be stationarie when both these lines are drawne to the Zodiake with an equall moouing into diuerse parts of heauen so as the line of the Planets true moouing maketh as great an arch of the Zodiake in going backward contrarie to the succession of the signs as the line of the true mouing of the centre of the Epicicle maketh in proceeding forward according to the succession of the signes for then the Planet for a while seemeth to stand still and not to be mooued from his place and thereof is said to be stationarie like to any of the fixed starres And you haue to vnderstand that these diuersities of motions vnder the Zodiake proceedeth of the mouing of the Epicicle which in his vpper part carrieth the Planet according to the succession of the signs and in his nether part carrieth the same contrarie to the succession of the signes called his retrogradation In which inferior or nether part of the Epicicle are the two points of station But for the better vnderstanding of that which hath been said touching the direction retrogradation and station of any Planet it shall be needfull to set downe this figure here following together with the description thereof the signification of whose parts the letters doe shew as you may see in the page next following ¶ The first figure of the second Booke IN this figure the letter A standing at the nether end of the right lines signifieth the centre of the world from whence all the said right lines are drawne to the Zodiake and B signifieth the centre of the Epicicle the middle right line A B passing through the true Auge of the Epicicle marked with C dooth shew the true place of the said Auge vnder the Zodiake marked with the letter D and the letter E sheweth the true opposit Auge of the Epicicle and the highest arch aboue containing certaine degrees of diuision signifieth a portion of the Zodiake and the two outermost lines A F G and A H I be lines of contingence touching the Epicicle in the two points marked with H and F and the two inner right lines marked with the letters A N and A L drawne from the centre A through the two points of station marked with K and M do shew in the Zodiake the retrogradation marked with the letters L N and the two points H F doe deuide the Epicicle into two parts or halfes whereof the one is called the vpper halfe marked with the letters H C F and the other the nether halfe marked with the letters F E H. And as the point F sheweth the Orientall or East part so H sheweth the Occidentall or West part and euery one of the fiue Planets in the vpper halfe of the Epicicle marked with H C F is said to goe from H to F according to the succession of the signes describing the arch of the Zodiake marked with I D G which is called his direction or progression but in the lower halfe marked with F E H the Planet is said to goe contrarie to the succession of the signs called his retrogradation and when he is in any of the two points marked with K M then he is said to be stationarie whereof the point K is the point of the first station whereas the Planet beginneth first to be retrograde and M is the point of the second station whereas the Planet endeth his retrogradation and beginneth his progression which two points are alwaies beneath the two Touch-points F H towards the opposit Auge of the Epicicle marked with E from which the two points of station are alwaies equally distant and also from the true Auge of the Epicicle And the letters C F K doe shew the arch of the first station which arch is otherwise called the first station in the second signification and C F K M doe shew the arch of the second station otherwise called the second station in the second signification and the letters M H C F K doe shew the arch of progression and KM doe shew the arch of retrogradation But you haue to note that though the two points of station are alwaies equally distant as well from the opposit Auge as from the Auge of the Epicicle yet such distance is not alwaies of like qualitie neither is the arch of their progression nor the arch of their retrogradation alwaies of one bignesse but do alter and that for four causes First for that the Epicicle through the moouing of his Excentrique is sometime nigher and sometime further off from the centre of the earth for the nigher that the epicicle is to the earth the more are the stational points distant from the

betwixt the 90 degree and the Sunne setting then the true Conjunction is before the visible Conjunction And generally the further that the true Conjunction is from the 90 degree the greater is the difference betwixt the true Conjunction and the visible Conjunction which things are before fully declared whereas I speake of the Parallax and by help of the celestiall globe are easily perceiued Of the varietie of the Solar Eclipses and why they be not alwaies like but doe differ as well in magnit●de as in time of continuance OF this varietie there be foure causes 1. First the vnequall apparent latitude of the Moone for the greater that the latitude of the Moon is the lesser and shorter is the Eclipse of the Sunne but the lesser that her latitude is the greater and longer is the Eclipse of the Sunne For this is a generall true rule that if the apparent latitude of the Moone at the time of the visible Conjunction be greater than the summe of the two semidiameters of the Sun and of the Moone being both added together then the Sunne shall not be eclipsed at the visible Conjunction but if the apparent latitude of the Moone be lesse than the summe of the two said semidiameters being added together then shal the Sunne be eclipsed at that visible Conjunction and the greater that the difference betwixt the summe of the two semidiameters and the Moones latitude is the greater is the Eclipse of the Sunne 2. The second cause of the varieties of the Eclipse of the Sunne is the vnequall distance as well of the Sunne as of the Moone from the earth for the changing of their distances from the earth maketh the diameters of their bodies to appeare greater or lesser For the neerer that they approch to the earth the greater do their diameters appeare vnto vs for when the Sunne is in the Auge of his Excentrique and therewith in his greatest excentricitie the semidiameter of his shaddow is i15° ii40° But if he be in his greatest excentricitie and in the opposit Auge of his Excentrique then his semidiameter is i17° ii2° which is greater than it was before by i1° ii22· And if the Sunne be in his least excentricitie as it is almost in these our dayes and also in his Auge then his semidiameter is i15° ii49° but being in the opposit Auge of his Excentrique then his semidiameters is ii16· i2° which is greater than it was before by i1° ii3° Likewise when the Moone is in her Auge whether it bee at her Conjunction with the Sunne or at her Opposition to the Sunne her semidiameter is but i15° ii0° but being in her opposit Auge her semidiameter will be i17° ii49° which is greater than it was before by i2° ii49° whereby it happeneth that sometime the whole bodie of the Sunne seemeth to be darkened and at other times but some part of his bodie and that either at some side thereof or els in the very middest of his bodie and then there appeareth round about him a narrow bright circle which we commonly call a borrough all the other part in the midst of his body being darkened 3. The third cause of the varietie of the Solar Eclipses is the twofold inequalitie of the Moones motion whereof the first dependeth vpon the motion of her Epicicle whereby she is sometimes swift and sometimes slow of ga●e And the second inequalitie of her motion happeneth by reason of her Parallax which maketh her motion to appeare variable euery houre and thereby her apparent motion is also sometime swift sometimes slow And it happeneth that not onely the time of the continuance of the Eclipse altereth but also the time of Incidence is made to be vnequall vnto the time of repletion 4. The fourth cause of the inequalitie of the Sunnes Eclipses is the small quantitie of the body of the Moon in respect of the Sunne or of the Earth and the small distance of the Moone from the Earth for by these two meanes neither can the Solar Eclipses appeare of a like bignesse in all places in which they may be seene neither yet can the said Eclipses be seene at one time in all places of the earth as was shewed before Lastly by these two meanes it happeneth that the Eclipse of the Sunne appeareth not at one selfe time in diuers places and it beginneth sooner to them which dwell Westward than to those which dwel Eastward in such sort as the said Eclipse of the Sunne will be ended in one place before it begin in another And thus much touching the causes of the varietie of the Eclipses of the Sunne Of the two speciall kinds of Solar Eclipses that is totall and partiall THe Totall Eclipse is when the Sunne is wholly darkened or seemeth to vs to haue lost his whole light and this Eclipse is alwaies without continuance which happeneth when the Moone hath no apparent latitude at the time of the visible Conjunction as this figure plainly sheweth ¶ The third figure belonging to the Solar Eclipse IN which figure suppose the letter A to be the centre of the Sunnes body and the line A H to bee the semidiameter of his body and D B to be the Eclipticke line and A B to be the semidiameter of the circle in which the Moone is at the beginning and ending of the Eclipse and the line F G to be the way of the Moones motion during the time of the Eclipse crossing the line D B in the point A which point A may also signifie the head or taile of the Dragon and the letter F signifieth the South latitude and G the North latitude and the point F doth also signifie the centre of the Moone at the beginning and G the centre of the Moone at the ending of the Eclipse and the line R F or G S doth signifie the semidiameter of the body of the Moone Now you see that the Moone by her motion commeth by little and little to shaddow the light of the Sunne vntill she haue mooued from the point F where the Eclipse began vnto the point A where his whole light is taken away and then without any stay she moueth on forward from the point A vnto G where the Eclipse endeth And although it falleth out sometimes that the Moone dooth shaddow more than the body of the Sun which is very seldome or neuer although it may so happen yet doth the totall darkenesse continue so little a time as it is insensible and therefore the totall Eclipse of the Sunne is alwaies without continuance Of the Partiall Eclipse of the Sunne THe Partiall Eclipse of the Sunne is when some part of the Sunnes light is taken away and not all his bodie darkened and of this kind there are three sorts 1. The first is when the semidiameter of the Sunne is darkened which happeneth when the apparent latitude of the Moone is equall vnto her apparent semidiameter 2. The second sort is when more than the semidiameter of the Sunne is

darkened which happeneth when the apparent latitude of the Moone is lesse than the apparent semidiameter of her bodie 3. The third is when lesse than the semidiameter of the bodie of the Sunne is darkened which happeneth when the apparent latitude of the Moon is greater than the apparent semidiameter of her bodie Of all which three kinds I haue set an example in these three figures here following ¶ Three figures shewing the three kinds of the Sunnes Partiall Eclipses OF which figures the first sheweth the first kind of Partiall Eclipse the second figure sheweth the second kind and the third figure sheweth the last kind of Partiall Eclipses In euery of which figures the letter A signifieth the centre of the Sunne and the semidiameter of his bodie is the right line A B and vpon the centre A is drawne a great circle marked with the letters C S D L whereof the letter C signifieth the North D the South L the West and S the East vnto which circle when the Moone commeth on the West part the Eclipse of the Sunne beginneth and it endeth when the Moone commeth to the said circle on the East side And the right line S L signifieth the Eclipticke line and the right line H I signifieth the deferent of the Moone and the point marked with the letter E signifieth the place of the Moone at the beginning of the Eclipse and G her place at the ending of the Eclipse and F her place at the middle of the Eclipse or at the time of her greatest darkenesse and the right line F V in the second figure is the semidiameter of the Moone at the time of her greatest darkenesse The caracters of the Nodes on the East or West side of any of the foresaid figures doe shew what way the head or taile of the Dragon doth stand and to which of the Nodes the Eclipse is nearest Of the bounds or limits of the Solar Eclipses ANd now that you know the seuerall kinds of Eclipses it will not be hard to judge which of them will happen at the time of any Eclipse of the Sunne especially if you know the bounds or limits within which the Eclipse of the Sunne must needs be before hee can bee eclipsed which bounds cannot bee better determined than by the apparent latitude of the Moone for if the said latitude be more than the two semidiameters of the Sunne and of the Moone being both added together it is impossible that the Sunne should be eclipsed at that Conjunction but if the apparent latitude be lesse than the said two semidiameters then may the Sun be eclipsed and the least summe of the two semidiameters of the Sunne and Moone that can be which is when both the Sunne and Moone are in the Auges of their orbes and the Sunne in his greatest excentricitie is i30 ii40 and the greatest summe of the said two semidiameters that can be is but i34 ii1 from hence you may gather these three rules here following 1. First if the apparent latitude of the Moone at the time of the visible Conjunction be lesse than i30 ii40 it cannot be but that the Sunne must be eclipsed 2. Secondly if the apparent latitude of the Moone at the time of the visible Conjunction be more than i30 ii40 and lesse than i34 ii31 it may bee that the Sunne shall be eclipsed in some part at the time of the visible Conjunction 3. Thirdly if the apparent latitude of the Moone be more than i34 ii51 the Sun cannot loose any of his light But Ptolomey determineth the said bounds of the Solar Eclipses by the distance of the Moone from either of the two Nodes for if the Moon be distant from either of the Nodes 20 degrees i40 towards the North or 11 degrees i20 towards the South at the time of the meane Conjunction then it may fall out that the Sunne shall be eclipsed but if she be further distant from the said Nodes at the time of the meane Conjunction then cannot the Sunne be eclipsed And note that Ptolomey maketh the North bounds bigger than the Southerne bounds because of the Parallax And this distance from the Nodes may be reckoned either according to the succession or contrarie to the succession of the signes Of the Eclipticall digits belonging to the Solar Eclipses AS the Eclipticall digits of the Moone were 12 so likewise are there 12 Eclipticall digits of the Eclipse of the Sunne but the Eclipse of the Sunne can neuer exceed 12 digits and 15 minutes for the greatest apparent semidiameter of the Moon is but i17 ii49 and the least apparent semidiameter of the Sunne is i15 ii40 which two semidiameters if you adde together the summe will be i33 ii29 Then hauing doubled the least semidiameter of the Sunne which is i15 ii40 the summe will be i31 ii20 which is the least apparent semidiameter of the Sun then say by the rule of proportion if i31 ii20 be equall to 12 digits to what or how much shall i33 ii29 be equall so shal you find the fourth proportionall number to be very neare 12 digits and 50 minutes and this is the greatest number of Eclipticall digits that any Eclipse of the Sunne can haue And this may happen when the Sunne is in the Auge of his Excentrique and in his greatest excentricitie and the Moone in her opposit Auge and therewith insuch places as are situated within the compasse of the Moones shaddow the diameter of which shaddow may at that time be very neare 280 miles in length of our English miles or 70 Germane miles within which compasse whosoeuer dwelleth may loose the whole light of the Sunne at that Eclipse And you shall know the number of the Eclipticall digits by the 62 precept of the Prutenicall tables And many times it may fall out that although the Moone haae no apparent latitude yet the Eclipse of the Sunne will not be so great for if the Moon be in her Auge and the Sunne in the opposit Auge of his Excentrique and therewith in his least excentricitie the number of the Eclipticall digits can be no more but 11 degrees and 15 minutes so as the Sunne will appear to haue lost his light in the very midst and round about that Eclipse will appeare a little circle as it were three quarters of an inch in breadth All which things touching the Eclipticall digits will not be hard to conceiue if you remember what was spoken of this matter in the Eclipses of the Moone What things are to be considered touching the continuance of the Solar Eclipse IN accounting the continuance of the Eclipse of the Sunne the Astronomers doe only obserue two things 1. The first is the scruples of Incidence which are nothing els but the way or arch of the circle of the Moones deferent in which she goeth from the beginning of the Eclipse vnto the middle of the same which in the three last figures is signified by the line E F. 2. The second thing

same is shewed in the 33 Precept 7. The orbe Excentrique is an orbe of one equall thicknesse compassing the centre of the world in which Excentrique the Epicicle is alwaies caried and maketh his reuolution in 29 Aegyptian yeares 183 dayes and almost 5 houres the Diurnall motion thereof is i2· ii0· iii21· iiii16· almost 8. The centre of the Excentrique marked with B is a point in the middle of the Excentrique from which all right lines that are drawn vnto the concauitie of the Excentrique are equall 9. The distance betwixt which centre and the centre of the world is called the excentricitie of the Excentrique and the distance betwixt the two said centres that is of the world and of the Excentrique is 3 degrees i25· 10. The circle Equant is a circle described vpon the point C in the plane of the Excentrique in regard of the centre wherof the motion as well of the Excentrique as of the Epicicle is regular and equall And this circle is sometimes called the circle of equalitie sometimes the Equator and other times the Excentricall Equator the distance of the centre whereof is from the centre of the Excentrique 3 degree i25· and from the centre of the world 6 degrees i50· and this distance from the centre of the world is called the Excentricitie of the circle Equant 11. The Epicicle is a little orbe whose centre is marked with the letter E which the Excentrique carrieth about which Epicicle notwithstanding hath his proper motion for the higher part thereof hath his moouing according to the succession of the signes and the lower part contrarie to the succession of the signes The daily motion of the Epic●cle about his owne centre is i57· ii7· iii44· and maketh one ent●e reuolution in 378 dayes 21 houres i36· 12. But because that the accounting of the motions by the circle Equant is troublesome therefore the Astronomers doe vse to reckon the fame vpon the Eclipticke by imposing a line to be drawne from the centre of the world vnto the Eclipticke in such sort as the same may be paralel vnto the line before drawne as in the foresaid figure the line A G being paralell vnto the line C E is called the line o● the meane moouing of the Epicicle or of the Planet 13. The meane Anomalia of the Excentrique is an arch of the Ecliptick beginning at the line of the Auge and so proceeding according to the succession of the signes vntill at end at the line of the meane moouing as in the foresaid figure the line A F is the line of the Auge and A G is the line of the meane moouing Now the arch of the Eclipticke which is comprehended betwixt the two lines A F and A G that is to say the arch F G is called the meane Anomalia of the Excentrique and of some it is called the meane or equall centre 14. But if the said arch bee reckoned from the first starre of the Rams horne vnto the line of the meane mouing marked with A G then the said arch is called the equ●ll motion of longitude which you may find by the Tables at any time supposed by the 13 and 14 Cannons in the Colume whose title is Longitudinis Saturni in such order as is shewed in the eight Precept The equall or meane moouing of the longitude of Saturne is daily i2· ii0· iii27· iiii18· and the yearely motion thereof is 12 degrees i12· ii46· iii4· and the whole reuolution is in 29 Aegyptian yeares 174 dayes 4 houres i58· ii24· for in that time it returneth to the first starre of the Rams horne 15. The line of the true mouing of the Epicicle is a right line drawne from the centre of the world passing through the centre of the Epicicle vnto the Eclipticke as in the foresaid figure the right line A E L is called the line of the true motion of the Epicicle 16. The true or coequated Anomalia of the Excentrique which is called by the Alphonsines the true centre is an arch of the Eclipticke beginning at the place of the Auge of the Excentrique and endeth at the true place of the centre of the Epicicle as in the foresaid Figure the arch F L is the true Anomalia of the Excentrique 17. The true motion of the longitude of the Epicicle is an arch of the Eclipticke beginning at the first starre of the Rams horne and endeth at the true place of the centre of the Epicicle as in the foresaid figure the arch from the Rams horne marked with a little starre in the Eclipticke of the eight sphere to L is called the true mouing of the longitude of the Epicicle 18. The Prosthapheresis or Equacion of the centre is the difference betwixt the meane Anomalia and the coequated Anomalia of the Excentrique or the difference betwixt the equall mouing and the true moouing of longitude As the arch L G is called the equacion of the centre and this equacion is neuer greater than 6 degrees i30· ii30· and is alwaies greatest when the equall mouing of the centre of the Epicicle from the Auge of the Excentrique is 11 Sex 33 degrees whether the same bee reckoned according to the succession of the signes or contrarie to the succession of the signes and from thence it decreaseth vntill the line of the said mean moouing commeth into the line of the opposite Auge The finding of which Equacion is taught in the 34 Precept by helpe of the 19 Cannon in the Colume whose title is Eccentrici and is to be added or subtracted according as the words Subtrahe and Adde at the head or foot of the said Colume doe shew 19. The two points in which the Prosthapheresis of the Excentrique is greatest are called the meane longitude of the Excentrique and these two points are shewed by a right line perpendicularly drawne vpon the line of Auge and passing through the middle space of the distance betwixt the centre of the world and the centre of the Excentrique as in the former figure in which the point A signifieth the centre of the world and the point B the centre of the Excentrique Now if the space B A be deuided into two equall parts as in the point Q and through the same point Q a right line be drawne crossing the line A F with right angles and is produced as well towards the right hand as towards the left vnto the two points of the circumference of the Excentrique marked with the two letters T and V the said two points T and V are called the meane longitudes of the Excentrique in which meane longitudes the centre of the Epicicle is when the equall motion of Saturnes longitude is 93 degrees or 267 degrees 20. The meane Auge of the Epicicle is a point in the circumference of the Epicicle which is furthest distant from the centre of the circle Equant and this point is found by drawing a

meane Auge of the excentricitie which is iii4· iiii12· as was said in the first definition of this Chapter the summe of that addition will be ii1· iii6· iiii14· and this is the daily distance betwixt the two meane Auges viz. that of the excentricitie and this of the orbes of the Anomalia of the excentricitie 12. The orbe Excentrique is an orbe in the Theorique of the Sunne in which the body of the Sunne is continually caried about This orbe is placed betwixt the two orbes which are the deferents of the Excentrique and mooueth from West to East vpon his owne moouable centre which centre is mouable by reason of the moouing of the two orbes which are the deferents of the Excentrique and the axletree which is also mouable according to the motion of the centre of the Excentrique in the circumference of the said litle circle And the daily motion of this orbe from the meane Auge of the orbes of the Anomalia of the excentricitie is i59· ii9· iii●3· iiii24· and maketh his entire reuolution in 365 dayes 3 houres i36· ii25· which motion is reckoned from the meane Auge of the orbes of the Anomalia of the excentricitie For the Sunne returneth to the said point or meane Auge in 365 dayes 3 houres i36· ii2●° 13. The line of the true place of the Sunne is a right line drawne from the centre of the world through the centre of the Sunne vnto the Eclipticke and the point in the Eclipticke in which the said line endeth is the true place of the Sunne As in the former second figure suppose the centre of the Sunne to be in the point M of the Excentrique and hauing drawne a line from A to M and so forth vnto the Eclipticke in the point R the said line A R is called the line of the true place of the Sunne and the point R is said to be the true place of the Sunne in the Eclipticke 14. The yearely Anomalia of the Sunne which is also called the meane Argument of the Sunne is an arch of the Excentrique which is comprehended betwixt the line of the meane Auge of the Excentrique and the line of the true place of the Sunne As in the foresaid second figure the arch L M is called the yearely Anomalia of the Sunne Or thus The yearely Anomalia of the Sunne is the excesse or difference whereby the daily motion of the Sun from the mean Auge of the orbes of the Anomalia of the excentricitie exceedeth the daily distance betwixt the meane Auge of the Excentrique and the meane Auge of the orbes of the Anomalia and this Anomalia is found by subtracting the daily distance of the said two Auges which is ii1●° iii6· iiii14· as was shewed in the 11 definition of this Chapter out of i59· ii9· iii13· iiii24· which is the daily motion of the Excentrique from the meane Auge of the orbes of the Anomalia of the excentricitie as was shewed before in the 12 definition the remainer of which subtraction will be i59· ii8· iii7· iiii10· And although that this Anomalia doth belong properly vnto the Excentrique yet notwithstanding the said Anomalia is also supposed to be in the Eclipticke by imagining a line to bee drawne from the centre of the world vnto the Eclipticke in such order as that the said line may be paralell vnto another line which is drawne from the centre of the Excentrique vnto the place or centre of the Sun and the line so drawn may be called the line of the Imaginarie motion of the Sun As in the foresaid second figure let a right line be drawn from C to M then vnto the same line draw another paralell right line from the centre A and produce the same vnto the Eclipticke in the point N so shall the arch of the Eclipticke which is comprehended betwixt the points E and N bee the yearely Anomalia or meane Argument of the Sunne in the Zodiake The finding of which Anomalia for any time appointed is taught in the 8 Precept by helpe of the 13 and 14 Cannons in that Collum whose title is Anomalia annua Solis 15. The true Auge of the Excentrique is that point in the Excentrique which is furthest distant from the centre of the world And this true Auge is pointed or shewed by a right line drawne from the centre of the world through the moouable centre of the Excentrique vnto the Eclipticke and the point in the Eclipticke in which the said right line doth end is the place of the true Auge of the Excentrique in the Eclipticke and the said right line is called the line of the true Auge of the Excentrique as in the foresaid second figure the point A signifying the centre of the world and the point C the centre of the Excentrique in the superficies of which Excentrique the point D is furthest distant from the centre A and therefore the point D is the true Auge of the Excentrique and the right line A C D is called the line of the true Auge of the Excentrique and the point K in the Eclipticke in which the said line endeth is the place of the true Auge in the Eclipticke the finding whereof is taught in the 16 Precept 16. The motion of the true Auge of the Excentrique is an arch of the Eclipticke beginning at some principall point in the Eclipticke and ending at the line of the true Auge of the Excentrique which principall point if it be the first starre of the Rams horne then is the said motion called the moouing of the true Auge from the first starre of Aries and if the said motion or arch doth begin at the true Equinox then is the said motion called the moouing of the true Auge from the true Equinox 17. The equacion of the centre is an arch of the Eclipticke which is comprehended betwixt the meane Auge of the outer blacke orbes and the true Auge of the Excentrique as in the foresaid second figure of this Chapter the arch K G in the Eclipticke is called the equacion of the centre and this equacion neuer exceedeth 7 degrees i23· ii36· the manner of the finding of which equacion is shewed in the 15 Precept by helpe of the 17 Cannon in that Colume whose title is Centri 18. The true Argument of the Sunne which is also called the equated yearely Anomalia is an arch of the Ecliptick which is contained betwixt the line of the true Auge of the Excentrique and the line of the Imaginarie motion of the Sunne As in the foresaid second figure the line A K is the line of the true Auge of the Excentrique and the place of the said true Auge in the Eclipticke is the point K. Likewise the line A N is the line of the Imaginarie motion of the Sunne Now the arch of the Eclipticke which is contained betwixt the 2 points K and N is called the true Argument or

right line E G and the caracter of the Moone is called the line of the true Anomalia because it is drawne from the centre of the first Epicicle which is marked with the letter E vnto the body of the Moone marked with the caracter of the Moone 26. The true Anomalia of the Moone which the Alphonsines doe call the true Argument is an arch of the first Epicicle contained betwixt the Auge of the said first Epicicle and the line of the true Anomalia As in the said third figure the arch B G is called the true or equated Anomalia or the true Argument of the Moone 27. The equacion of the centre which in the Prutenicall tables is called the equacion of the second Epicicle is an arch of the first Epicicle whereby the true and meane Anomalias do differ the one from the other As in the said third figure the arch B G is the true Argument of Moone and the arch B F is the mean Anomalia or Argument of the Moone or of the Epicicle defined in the 19 definition of this Chapter the difference betwixt these two arches is the little arch G F and this difference is called the Prosthapheresis of the centre The finding whereof by the Prutenicall tables is taught in the 24 Precept by helpe of the 18 Cannon in that Collum whose title is Secundi Epicycli And this equacion is to be added or subtracted from the mean Anomalia as is shewed in the said 24 Precept to the end that the true Argument or Anomalia may bee had And the greatest equacion that can be is 12 degrees i26· ii57· which then happeneth when the Moone is in either of the Touch-points of the second Epicicle which Touch-points are determined by two right lines drawne from the centre of the first Epicicle and touching the circumference of the second Epicicle on each side thereof 28. The line of the true motion of the Moon is a right line drawn from the centre of the world throgh the body of the Moon vnto the Ecliptick the point in the Eclipticke where that line endeth is the true place of the Moone as in the third figure the line A G T signifieth the line of her true mouing and the point T is the true place of the Moone 29. The true or apparent motion of the Moone is an arch of the Eclipticke beginning at some knowne place of the Eclipticke and ending a● the true place of the Moone which arch dooth begin either at the first starre of the Rams horne or at the Vernall Equinox either meane or true or els at the line of the meane place of the Sunne As in the said third figure the arch * T is the apparent or true moouing of the Moone from the first starre of the Rams horne 30. The equacion of the first Epicicle is an arch of the Eclipticke contained betwixt the line of the meane mouing of the Moone and the line of her true mouing As for example in the third figure of this Chapter the line A V is the line of the meane mouing of the Moon and the line A T is the line of her true mouing and the arch of the Eclipticke contained betwixt these two lines that is to say the arch T V is called the equacion of the first Epicicle or the equacion of the Argument And the finding of this equacion at any time giuen is taught in the 24 Precept by helpe of the 18 Cannon in the Collum whose title is Primi Epicycli But because this equacion doth varie and is sometimes greater and sometimes lesser therefore the absolute and perfect equacion is to be found by the proportionall minutes and the excesse which were defined before in the 29 definition of the fift Chapter and therefore I need not here again to define the same but onely to tell you that the proportionall minutes are to be found in the 18 Cannon in the Collum whose title is Scrupula Proportionalia and the excesse is to be found in the said 18 Cannon in the Colume whose title is Excessus Here endeth my Extract of Maginus his Theoriques And if this my labour shall content you then looke shortly for the vse of the Prutenicall Tables THE MAKING DESCRIPTION AND VSE OF TWO MOST INGENIOVS AND necessarie Instruments for Sea-men to find out thereby the latitude of any place vpon the Sea or Land in the darkest night that is without the helpe of Sunne Moone or Starre First inuented by my good friend Master Doctor Gilbert a most excellent Philosopher and one of the ordinarie Physicians to her Majestie and now here plainly set downe in our mother tongue by Master Blundeuile LONDON Printed by Adam Islip 1602. THE MAKING DEscription and vse of two most Ingenious and necessarie Instruments for Sea-men to find out thereby the latitude of any place vpon the Sea or Land in the darkest night that is without the helpe of Sunne Moone or Starre OF which two Instruments the one serueth to find out the declination of the Needle vnder any Horizon which declination being once had then the other Instrument sheweth the latitude of that place hauing such declination But because the Instrument of Latitude consisteth of two parts that is to say of an immoouable part which I call the Mater hauing therein a Quadrant containing the 90 degrees of Latitude and also a Spirall line and the other part is moouable containing a Quadrant deuided into 90 degrees which are the degrees of declination and also an Index with a Fiduciall line shewing the Latitude I mind first here to set downe the making of the Instrument of Latitude because it requireth a number of circles to find out thereby the Spirall line contained in the Mater of the said instrument of Latitude the order whereof is here plainely set downe as well by this figure demonstratiue hereto annexed as by this my description of the same The Figure FIrst draw a circle vpon a peece of smooth pastbord so great as the whole diameter thereof may containe in length at the least seuen or eight inches and marke the centre of that circle with the letter C and by drawing two crosse diameters marked with the letters I F and K E passing through the said centre and crossing one another in the same with right angles you shall thereby deuide the whole circle into foure Quadrants or quarters And remember that of the two crosse diameters the perpendicular marked with I F must be produced in such sufficient length as may serue to such purpose as is hereafter shewed as from I to H so as this perpendicular line is marked with foure letters that is F C I H and the other crosse or ouerthwart diameter is marked with three letters viz. K C E. That done deuide the nether quarter of the said circle on the right hand marked with the letters F E into 90 degrees proceeding from fiue to fiue till you come to 90 marking the same Quadrant with the letters F C