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Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
earth_n	body_n	contain_v	diameter_n	5,518	5	15.6944	5	true

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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

which they vsually obserue is the time of Incidence which is nothing els but the quantitie of time which the Moone spendeth whilest she is in going of the said minutes of Incidence both which two things you shall easily find as also the minutes of repletion by the 63 precept of the Prutenicall tables And as the Eclipse of the Moone doth begin on the East side of her bodie and endeth on the West side thereof euen so the Eclipse of the Sunne beginneth on the West side of his bodie and endeth on the East which happeneth by the motion of the Moone which motion is from West to East and if the Eclipse of the Sun be partiall and the apparent latitude of the Moone be North then is the North side of the Sunne eclipsed and the South side retaineth still his light but if her apparent latitude be South then is the South side of the Sunne darkened and the North side keepeth still his light And this is a generall obseruation that no Eclipse of the Sun is vniuersall except that which was against nature at the death of Christ but alwaies perticular that is it may be seene in some few places but not in all places of the world neither doth it begin or end in all places at one selfe instant neither dooth it appeare in all places of one selfe bignesse or of one shape but in one place is totall and in another place at the same time Partiall and in other places againe there appeareth no Eclipse at all The causes of which diuersitie haue been before declared How to find out the quantities encreasing decreasing beginning and ending of the Suns Eclipses without any offence of your eiesight HAuing learned by the Ephemerides or by some other Almanacke at what time the Eclipse shall be resort to some tower or high loft the higher the better and see that the place whereas you would make your obseruation be without light and so darke as you can possibly make it leauing only a litle hole or rift through which the beames of the Sunne may streeke through and vpon the pauement or on the wall that looketh right against that hole or rift behold what light the Sunne yeeldeth for that light will represent the true shape of the Sunne at that present and plainely shew so much portion to be wanting from the lightsome circle as the Moone comming betwixt the Sunne the earth doth take away from our sight Wherefore if you deuide the diameter of the said lightsome circle into 12 parts or points which the Astronomers doe call digits you shall find out all the things aboue mentioned without looking vp to the heauen The Methodicall doctrine of the Eclipses set downe by Reinoldus in his Commentarie vpon Purbachius FIrst Ptolomey found out the true latitude of the Moone and deuided the same from her apparent latitude as he teacheth in the 12 chapter of his fift booke for in the Eclipses of the Moone it is very necessarie to haue knowledge both of her true latitude and also of her apparent latitude for the Eclipse of the Sunne without hauing knowledge of her apparent latitude and of her Parallaxes can neuer be well foreknowne and by this he did not only judge of other things but also by a Geometricall way found that the greatest distance of the Moon from the earth she being either at the change or at the full did contain 64 semidiameters of the earth and one sixt part Moreouer by other obseruations hee did know the proportions of the semidiameters as well of the Moones excentrique and of her Epicicle as also of her excentricitie Then by other obseruations hee sought out the quantities of the apparent diameters of the Sunne of the Moone and of the shaddow as well at the new Moone as at the full in manner and forme following for first by the helpe of an instrument hauing a Diopter he found the Sunne and Moone to be in one selfe angle when shee was most distant from the earth Then he attributed to the Moone two Eclipses in the one whereof when her latitude was i48 ii30 the shaddow darkened one quarter of her diameter and in the other Eclipse the shaddow darkened the one halfe of her diameter when as her latitude was i40 ii40 and in either of the Eclipses the Moone was very nigh to the height of her Epicicle Hereof it manifestly appeared that a quarter of the Moones diameter when she was most distant from the earth contained in heauen according to our aspect i57 ii0 ● which being reckoned foure times doe shew that the diameter of the Moone was at that time i31 ii20 whereunto the obserued diameter of the Sunne was then equall and the semidiameter of the shaddow in the later Eclipse did appeare to be i40 ii40 for the centre of the Moones body did then touch the outermost brim of the shaddow Hereby it likewise appeareth that the diameter of the shaddow hath such proportion to the diameter of the Moones body as 13 hath to 5 and keepeth the selfe-same proportion in all other Eclipses of the Moone and though it most manifestly appeareth by this that the diameter of the shadow doth exceed in greatnesse the diameter of the Moone yet it followeth not by by therof that the Moone is lesser than the earth Now therfore Ptolomey by comparing according to the doctrine of plaine triangles the semidiameters of the Moone and of the shadow together with the distance of the said Moon being measured by the semidiameters of the earth hee found the semidiameter of the Moone only to containe i17 ii●3 and the semidiameter of the shaddow to contain i45 and ii38 such like minutes I say as the semidiameter of the earth hath 60. And therefore it appeareth hereby that either of the semidiameters that is of the Moon or of the shaddow is lesse than the semidiameter of the earth for the semidiameter of the earth is almost in like proportion to the semidiameter of the shaddow as 4 is to 3 and being compared to the semidiameter of the Moone it is almost in such proportion as 17 is to 5 whereof it followeth necessarily that the shaddow of the earth is Conicall that is round growing to a sharpe point and therefore the Sunne must needs be greater than the earth Neither could any right judgement haue been made touching the quantities of the said three bodies that is the Sunne the Moone and the earth vnlesse that the Parallaxes of the Moone had first shewed the distance of the Moone from the earth the said distance being measured by the semidiameters of the earth For if you suppose the distance betwixt the Moone and the earth to be 48 semidiameters of the earth you shall find that the semidiameter of the shaddow will be altogether equall to the semidiameter of the earth and so the shaddow shall be Cylindricall that is to say in all parts round like a pillar And if you suppose the said distance of the Moone from

the earth to be greater as to be 170 semidiameters of the earth then the semidiameter of the shaddow the Moone being in Transit● will contain two semidiameters of the earth and so the shaddow shall be Calathoidall that is to say like a cup or top extending together with his length in breadth and widenesse more and more infinitely All which three shapes of shaddows are before plainely set forth in their figures By this Ptolomey doth proue that the distance of the Sun from the centre of the earth containeth 1270 semidiameters of the earth and that the semidiameter of the Suns bodie containeth fiue such semidiameters and a halfe as the earth hath and that the diameter of the Sun to the diameter of the earth is in such proportion as is 11 to 2. Finally he proueth the axletree of the shaddow to contain 268 such semidiameters as the earth hath Wherefore according to the opinion of Ptol●mey the excentricitie of the Sunne should containe 48 semidiameters of the earth and almost one fourth part Now by knowing the diameters of the three bodies it is easie to find out their proportions for by the last proposition of Euclide his twelfth booke looke what proportion is betwixt the diameters of any two spheres the same proportion beeing tripled is the proportion betwixt the said two spheres And therefore because the diameter of the Sunne is to the diameter of the earth in like proportion as 11 is to 2 the same proportion being tripled shall be 1331 to 8 so as the body of the Sunne doth containe the body of the earth 166 times and almost one halfe In like maner you shall find the bodie of the Moone to be almost the 40 part of the body of the earth for the diameter of the earth to the diameter of the Moon is in such proportion as is 17 to 5 so as the body of the earth containeth the body of the Moone almost 40 times as was said before And the body of the Sunne containeth the bodie of the Moone almost 6600 times The proportions of which three bodies are these numbers here following that is to say for the Sunne 6539203 and for the Earth 39304 and for the Moone 1000. A breefe Extract of Maginus his Theoriques shewing all the definitions of such names and motions as are needfull to be knowne for the calculating of the places of any of the seuen Planets or other motions of any Heauen whatsoeuer that are to be found out by the Prutenicall Tables TO auoid the Paradoxicall supposition of Copernicus supposing the Earth to mooue and the Sunne to stand still in the middest of heauen Maginus is fain to suppose that there be three mouable heauens aboue the eight heauen and so maketh in all eleuen mouable heauens which is one more than all the other Astronomers haue heretofore set downe And he calleth the highest or eleuenth heauen the first mouable describing the same as hereafter followeth next to which is placed in his Theoriques the tenth heauen then the ninth and eight heauen and vnder that the seuen Planets that is first Saturne then Iupiter Mars Sol Venus Mercurie and Luna which is the lowest heauen of all Of which his Theoriques I thought good to make a breefe Extract because that more tearmes belonging to the Prutenicall Tables are therein both defined and demonstrated than are set downe either by Purbachius or by Mes●elyn in their Theoriques And according to the number of this eleuen Heauens I haue deuided this Extract into 11 chapters CHAP. I. The description of the eleuenth Heauen or first mouable together with such definitions as are contained therein THe first mouable is the greatest or highest heauen which carieth all the inferior heauens round about from East to West in 24 houres The concaue superficies whereof is imagined to be traced with certaine circles whereof some be greater and some lesser 2. The greater circles cheefely seruing for our purpose are these the Aequinoctiall the Eclipticke and the two Colures the one called the Colure of the Equinoxes and the other the Colure of the Solstices 3. The Aequinoctiall is a great circle supposed to be in the convex superficies of the first mouable deuiding the same superficies into two equall parts the poles of which circle are the poles of the world vpon which poles the said first mouable continually mooueth making his reuolution in 24 houres 4. The Eclipticke of the first mouable is also a great circle deuiding the superficies thereof into two equall parts cutteth the Aequinoctiall in two opposit points which points are called the Equinoxes one of them being called the Vernall Equinox and the other the Autumnall Equinox and the poles of this Eclipticke are alwaies distant from the poles of the world 23 degrees i40· and doe neuer alter And this Eclipticke is called the meane Eclipticke 5. The Colure of the Equinoxes is a great circle passing through the two Equinoxes and the two poles of the world 6. The Colure of the Solstices is also a great circle deuiding the superficies of the first moouable into two equall parts and is drawne both through the poles of the world and also through the poles of the meane Eclipticke CHAP. II. Of the tenth Heauen THe tenth Heauen is a great Orbe next vnto the first mouable hauing contrarie motion to the first moouable that is from West to East vpon the poles of the Eclipticke of the first moouable or meane Eclipticke and maketh his reuolution in 3434 Aegyptian yeares and 10 daies In which imagine the letter A to be the pole of the meane Eclipticke of the first moouable and also the pole of the tenth heauen about which pole the tenth sphere maketh his reuolution in 3434 Aegyptian yeares and 10 daies And vpon the point A imagine also a lesser circle to be drawne whose semidiameter is A B containing in length i●° and imagine the same lesser circle to be the circle B D F in the circumference whereof suppose the centre of another lesser circle equall to that to be placed in the point D and let the semidiameter of the said second lesser circle be D E containing in length i6· the centre of which second circle viz. D you must suppose neuer to change his place but to mooue about the pole A as the tenth heauen mooueth about the same pole A. And so likewise suppose the second little circle A H E to be fastened to the first so as the said second circle hath no other motion but that which the centre D hath and imagine the right perpendicular line C G to be part of the Solisticiall colure of the first mouable which Colure the circumference of the second little circle A H E will cut in some one point or other as in the point H the place of which intersection wheresoeuer that happeneth vpon the line C G is the pole of the Eclipticke of the tenth heauen whose pole doth continually alter his place and therefore the place of

minutes as the little arch R S signifying the excesse of the longer longitude doth containe 60 minutes Likewise as the line A L is shorter than the line A H by 40 minutes euen so the equacion of the Epicicle marked with Q S his centre beeing in L is greater than the equacion of the said Epicicle marked also with Q S his centre beeing in the point H by 40 of such minutes as the arch S T signifying the nigher longitude dooth containe 60 minutes And remember here that in seeking in this figure to know the length of the line A K by the minutes you must put the firme foot of your Compas in the centre A and the moouable foot in the point L and so to draw the moouable foot from thence to the line A H Q vpon which line the numbers of the 60 proportionall minutes are set downe and to know the length of the line A L you must fit your Compasses to A L and then draw the mouable foot to the line A G Q vpon which line are also set downe the 60 proportionall minutes in like manner as they are vpon the line A H Q sauing that in the line A H Q the said 60 minutes are to be counted from H towards Q and in the line A G Q they proceed vpward from Q to G according as the inferior halfe circles doe shew And after this manner you must deale to know the length of any other line drawne from the centre A to any other point of the Excentrique whereinto the centre of the Epicicle chaunceth to fall considering alwayes whether such line be either longer or shorter than the line A H passing through the point of the meane longitude to the intent you may know thereby how to applie the length of euery line to the right number of the proportionall minutes belonging to the same But you haue to note that neither Copernicus nor the Prutenicall tables doe make any more kinds of excesses or proportionall minutes but that onely which is plainly declared before in the sixt figure of the Moone What is the diameter of the Auges in the Epicicle IT is a right line passing through the centre of the Epicicle and also through the true Auge and the true opposit Auge of the said Epicicle which line deuideth the plane of the Epicicle into two equall hal●es whereof the one is called the Orientall halfe and the other the Occidentall halfe hereafter described in the sixt figure What is the diameter of the mean longitudes in the Epicicle IT is a right line drawne through the centre of the Epicicle erected perpendicularly vpon the diameter of the true Auges of the said Epicicle next before defined and when the Planet falleth into this line it sheweth the meane distance that is betwixt the greatest longitude in the Auge of the Epicicle and the least longitude in the opposit Auge of the said Epicicle and thereof is called the diameter of the meane longitudes And this line deuideth also the plane of the Epicicle into two halfes that is the vpper halfe and the nether halfe The vpper halfe is that which is aboue the diameter of the meane longitudes and is farthest from the earth and the lower or nether halfe is beneath the said diameter and is nigher to the earth What is the Orientall and Occidentall halfe of the Epicicle THe Orientall halfe is that which being contained betwixt the Auge and opposit Auge looketh towards the East and the other halfe looking towards the West is called the Occidentall halfe And you haue to note that as well in these three Planets as in the other two Planets next following that is Venus and Mercurie the first halfe of the Epicicle is Orientall and the later halfe Occidentall but in the Moone the later halfe of her Epicicle is Orientall and the first halfe thereof is Occidentall For the Epicicle of euery one of the foresaid fiue Planets going from the Auge in his vpper part according to the succession of the signes carrieth the Planet first into the Orientall halfe but in the Moon it is cleane contrarie The fourth Intention shewing the twofold latitude of the three vpper Planets and wherein their latitude differeth from the latitude of the Moone THe latitude of the Moone is simple hauing onely respect to the distance of her Excentrique or Deferent from the Eclipticke line whose greatest distance from thence either toward the North or South is but fiue degrees as hath been said before by reason that the poles of her Excentrique are distant from the poles of the Ecliptick no more but fiue degrees But the latitude of the three vpper Planets is to be considered two manner of waies First according to the distance of any of their excentriques from the Eclipticke and secondly according to the distance of any of their Epicicles from the Excentrique thereof which two kinds of latitude Purbachius describeth the first in this manner The first sayth he chaunceth by reason that the plane or superficies of the Excentrique of the Planet declineth from the plane of the Eclipticke in two parts opposit the greatest distance of such declination remaining alwaies invariable like as in the Moone and yet the two Nodes or Intersections that is to say the node ascendent and descendent otherwise called the head and taile of the Dragon are not moued contrary to the succession of the signes as in the Moone but according to the mouing of the eighth sphere so as the Auges of the deferents of those Nodes do describe on the North side paralell circumferences that be equally distant from the Eclipticke and though such Auges be alwaies septentrionall yet notwithstanding those Auges be not in all the three planets the very points or limits of the greatest latitude of their deferents from the Eclipticke yea that falleth out only in Mars the Auge of whose excentrique doth most decline from the Eclipticke to the North but in Saturne the point or limit of his greatest latitude goeth before the Auge of his excentrique contrary to the succession of the signes and is distant from his Auge 50 degrees and in Iupiter such point goeth after the Auge of his excentrique according to the succession of the signs and is distant from his Auge 20 degrees All which things you shall more plainly perceiue by this figure here following set downe by Reinholdus in his Comment vpon Purbacchius ¶ The fifth figure of the three superior Planets IN this figure the letter D signifieth the centre of the world whereupon is drawne a circle signifying the plane of the Eclipticke and the said point D representeth also both the poles of the Eclipticke And vpon the point C is drawn another circle signifying the plane or superficies of the excentrique marked in the vpper part with the letters A B E enclining as you see towards the plane of the Eclipticke And because the two planes that is the plane of the Excentrique the plane of

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

point and a centre for though euery centre is a point yet euery point is not a centre Againe I make a difference betwixt a circle and an orbe for though they bee like in that they both haue round shape yet they differ in that the orbe hath both breadth and thickenesse and the circle hath neither But before I define the tearmes belonging to the Theorique of anie Planet I thinke it best according to the method and order vsed by Michaell Mestlyn to set downe foure principall intentions meet to bee vsed in describing the Theorique of euerie Planet of which foure intentions 1. The first is to shew of how many particular orbes euery Theorique consisteth 2. The second is to shew towards what part such orbes are moued and in what time they make their reuolutions and also vpon what centres or poles they make their regular mouings 3. The third intention is plainely to describe all such points lines arches semicircles and such like things as are needfull to be knowne for the calculating of the mouings of any Planet 4. The fourth intention is to shew how much latitude euery Planet hauing latitude hath for euery Planet hath latitude more or lesse the Sunne onely excepted which hath no latitude because he neuer departeth from the Eclipticke line with whose Theorique I mind here first to deale Why deale you first with the Theorique of the Sun FOr foure causes First because his Theorique is more easie than all the rest Secondly as well for that he excelleth in dignitie all the other Planets as also for that the mouing of all the other Planets dependeth vpon his mouing which vnles it be known none of the others can be throughly known Thirdly for that the mouings reuolutions of all the rest of the Planets are counted by his yearly reuolutions Fourthly by the authoritie of Ptolomey and other auncient writers which in treating of the Theoriques doe first begin with the Theorique of the Sunne NOw here followeth the first Intention shewing by certain figures of how many orbes the Theorique of the Sunne consisteth that is of three orbes hereafter described are contained in this figure next following The first figure belonging to the Theorique of the Sunne shewing his three orbes and their centres and also the two points called Auges hereafter defined THough the Theorique of the Sun consisteth but of three orbes yet you see here that in this figure there be four orbes or circles that is two black and two white whereof the vpper blacke circle marked with the letter D is called the vpper deferent of the Auges and the lower blacke circle marked with the letter E. is called the inferior or lower deferent of the Auges and the largest and greatest white circle marked with the letter C. is called the Excentricke or deferent of the Sunne hauing the bodie of the Sunne fixed therein and in the middle white roundle are set downe two prickes or centres whereof that which is marked with the letter A. is the centre of the world and the other next aboue that marked with the letter B. is the centre of the deferent of the Sun otherwise called the Excentricke and the point which is in the vpper lymbe of the deferent of the Sun marked with the letter F. is called in the Arabike tongue Aux in Greeke Apogaeon in Latine Absis summa that is to say the highest point which I meane to call in our tongue in the singular number Auge and in the plurall number Auges the opposite point whereof marked with the letter G. is called in Greeke Perigaeon and in Latine Absis ima that is to say the lowest Auge It is also called Oppositum Augis that is the point opposite to the Auge so as by this figure you may perceiue that the point Auge is a point in the deferent of the Sunne farthest distant from the centre of the earth and therfore is called of some Longior longitudo that is the farthest longitude marked in the former figure with the letter F and the opposite point to that is called Propior longitud● that is the nigher longitude because it is nigher to the centre of the earth and is marked in the said figure with the letter G. There be also in the said deferent two other points of the meane longitude whereof we shall speake hereafter You see also that the pricke marked with the letter A. is the centre of the world that the other prick marked with the letter B. is the centre of the deferent of the Sunne which because it is out of the centre of the world and distant from the same it is called the centre of the excentricke and the distance betwixt these two centres is called in Latine excentricita● and I likewise from henceforth will call such distance the excentricitie Now describe the three foresaid circles or orbes and shew whereto they serue THe first called the orbe excentricke which in the former figure is made white and marked with the letter C. is that which carieth the body of the Sun and therefore is called in Latine Deferens Solis and I will also call it the deferent of the Sun in the vttermost circumference whereof are set the foresaid two Auges the one right opposite to the other marked with the letters F. G. as before is said The other two blacke orbes marked with the letters D. E. are those which carrie the Auges therfore are called the deferents of the Auges which be two seuerall orbes and yet to auoid Vacuum doe enclose one another in such sort as the slenderest or narrowest part of the vppermost orbe marked with the letter D. doth joine close to the thickest or fullest part of the nether orbe marked with the letter E. and the slenderest or narrowest part of the nether orbe joyneth close to the thickest or fullest part of the vpper orbe and these two orbes do contain within them the orbe excentrique or deferent of the Sunne and also doe make the whole sphere of the Sunne to be concentrique that is to say to haue all one centre with the centre of the world and yet in certaine respects these two orbes are also excentrique that is to say hauing a centre distant from the centre of the world for the concaue superficies of the vppermost blacke orbe and the convexe superficies of the nethermost blacke orbe beeing seuerally taken haue the selfe same centre which the deferent of the Sunne hath which is the centre excentricke marked with the letter B. All which things the former figure doth plainely shew Wherefore was the deferent of the Sunne supposed to be excentrique FOr three principall causes First for that the moouing of the Sunne is vnequall now slower now swifter Secondly for that the bodie of the Sunne by his vnequall distance from the earth seemeth to our sight somtime greater and somtime lesser the grossenesse or thinnesse of the aire being no cause thereof Thirdly for that the Sunne being in this

Collum the dayes of the Moones age after the full during her decrease or wane that is from 15 to 30 ascending vpward The Table followeth in the next Page A TABLE SHEWING THE DIVERS SHAPES OF THE MOONE 1. 2. 3. 4. 5. 6. 7. The daies or age of the Moone The first fiue Aspects of the Moon The places of the Excentrique The diuers shapes and names of the lights of the Moon The places of the Excentrique The second fiue Aspects of the Moone The dates 1. ☌ In the Auge Coniunctio the new Moone In the Auge ☌ 30. 4. ⚹ In the mean longitude of the Excentrique Falcata the horned Moone In the mean longitude of the Excentrique ⚹ 26. 7. □ In the opposit Auge Demidiata the halfe Moon In the opposit Auge □ 22. 11. △ In the mean longitude of the Excentrique Vtrinquegihbosa almost roūd In the mean longitude of the Excentrique △ 19. 15. ☍ In the Auge Pleni luniū the full Moone In the Auge opposition 15. How is this digression or departing of the Moone from the Sunne called IT is commonly called the longitude or mouing of the Moone from the Sunne and the Moone returneth again to the Sunne or rather ouertaketh him in 29 daies and one halfe day in which time she accomplisheth all her diuers illuminations or shapes of light that is to say she sustaineth all her aspects to the Sunne and sheweth to the earth all the diuersities of her lights and apparances And this month is called the month sinodicall for there are two kinds of Lunar months the one periodicall in which she goeth through the whole Zodiake and the other sinodicall in which she ouertaketh the Sunne which Sacrobust● calleth the moneth of Consecution who maketh foure Lunar moneths that is the moneth of Peragration the moneth of Apparition the moneth Medicinall and the moneth of Consecution which are all declared in the sixe and fortieth Chapter of my first booke of the Sphere And you haue to vnderstand that the dayly moouing of the Moone from the Sunne contayneth 12 degrees i11· ii26· iii41· iiii29· v58· and the sinodicall moneth consisteth of 29 dayes 12 houres i44· ii3· iii11· What conclusions doe accompanie this harmonie of the Sun and Moone THese foure here following First in euery meane Conjunction or Opposition of the Sunne and Moone which meane Conjunction or Opposition is said to bee when the centre of the Moones Epicicle is either in Conjuction or in Opposition to the centre of the Sunne the centre of the Epicicle is found to be in the Auge of the Excentrique but in euery Quadrat aspect the centre of the Epicicle is in the opposit Auge of the Excentrique Secondly by this means in euery Conjuction and Opposition as well the Excentrique as the Epicicle are most swift in their motions but in the quarters they are slowest because their Anomalie or Inequalitie is thereby altered as hath been said a little before Thirdly the Moone in one sinodicall month passeth twice through the orbe Excentrique Fourthly the centre of her Epicicle in one ●inodicall moneth describeth about the centre of the world a certain Ovale figure like to this here following ¶ The fourth figure belonging to the Theorique of the Moone IN which Figure the letter A signifieth the centre of the world or of the whole sphere of the Moon and therfore at the new Moon the centre of the excentrique is in B which centre B by turning round about the centre A describeth a little circle in the middest of this figure marked with the letters DFNKMOR and the foure little circles placed vpon the Ovale circle doe signifie the Epicicle of the Moone the foure centres whereof are marked with these foure letters CIPE and the letter C signifieth here also the Auge of the excentrique and so doth the letter P but the letters IE do each of them signifie the opposit point of the Auge Moreouer the line AC signifieth here the line of the mean mouing of the Sun from which line when the centre B departeth towards the right hand and commeth to the point D which is in the little circle then the centre of the Epicicle marked with C descendeth on the left hand to the point E which is in the Ovale circle and then the angles BAD and BAE are equall through the equalitie of their mouings Likewise when the centre of the excentrique commeth to the point in the little circle marked with F the centre of the Epicicle is in the point G. And when the centre of the excentrique falleth into the point H and there hath described a quarter of the little circle then the centre of the Epicicle hath likewise made a quarter of the Zodiake which is 90 degrees counting from the line of the meane mouing of the Sunne wherof such distance of the Moone from the Sunne is called a quarter and is found to be in the point 1 being then in the opposit Auge of the excentrique and so the Moone giueth light with halfe her bodie and is then nighest to the earth Againe when the centre of the excentrique commeth downe into K then the centre of the Epicicle departing from the earth commeth to the point L and when the centre of the excentrique commeth to the point M then the centre of the Epicicle is in the point N. Lastly when the centre of the excentrique falleth into O the centre of the Epicicle shall be in P so as OP shall be both in one right line and thereby the centre of the Epicicle and the centre of the excentrique shall bee distant from the Sunne halfe a circle which is a hundred and eightie degrees and then the Moone shining with her whole bodie is opposite to the Sun And looke what course the Epicicle hath kept in the first half of the Ovale circle during the Moones encrease the like course it obserueth in the other halfe of the said circle whilest the Moone decreaseth How are the Orbes belonging to the sphere of the Moone to be measured AS the line of the Auge marked with the letters AC or AP in the former fourth figure contayneth 60 degrees or parts euen so the opposit Auge marked with the letters AI or AQ contayneth according to Ptolomey of the like degrees or parts 39 degrees and i22· and the semidiameter of the excentrique containeth 49 degrees i41· and the excentricitie AB contayneth 10 degrees i19· and the semidiameter of the Epicicle contayneth 5 degrees i13· But if the degrees be such as the semidiameter of the earth containeth but one degree or one part thereof then he prooueth by demonstration that the line of the Auge contayneth but 59 such degrees and the line of the opposite Auge to contain no more but 38 degrees and i43· and the semidiameter of the excentrique to containe 48 degrees i51· ii30· and the excentricitie to containe 10 degrees i●●° ii30· and the semidiameter of the Epicicle to

more but one cause then she is commonly seene the third day after the change But if she be in the descending halfe of the Zodiake and haue therewith South latitude and is slow of gate there may passe foure daies before she appeareth Here also it is meet to speake of the diuersitie of her shape according as she is distant from the Sunne as well in her increase as decrease for during her increase shee followeth the Sunne and turneth her hornes from the Sunne towards the East and her lightsome part to the Sunne and riseth aboue the Horizon immediatly after the Sunne is set But during her decrease which is from the full vnto the change she goeth before the Sunne and turneth her hornes towards the West and riseth in the morning before the Sunne And as for the diuers names which she hath both in Greeke and Latine according to hir diuers aspects to the Sunne are plainly set down before in a table made by Reinholdus which table immediatly followeth the third figure belonging to the Theorique of the Moone and therefore I would wish you to resort thereunto because I thinke it superfluous to repeat it againe here Notwithstanding loe here the figure which is commonly vsed to shew the diuerse shapes of her light as well in her encrease as decrease The fourth generall kind of passions of the Planets that do● chance by comparing their mouings vnto the globe of the earth BVt you haue to vnderstand that the passions rising of this comparison are not so properly incident to all the Planets as to the Moone because that the greatnesse of the earth is not to be esteemed in respect of the other Planets or at the least not with any great sensibilitie or affection Shew what passions the Moone hath to the earth or the earth to the Moone THese three here following for first the greatnesse of the earth doth not suffer the true place of the Moone to be all one with her visible place Secondly the earth sometime taketh away the light of the Sunne from the Moone and so causeth her to be eclipsed Thirdly the Moone with her apparent magnitude taketh away the light of the Sun causing the same in some parts of the earth to be eclipsed And hereof dependeth the whole doctrine of the Eclipses whereof we shal treat hereafter In the meane time shew what is the true place and also what is the visible place of the Moone or of any other starre THe true place of the Moone or of any other starre is apoint in the outermost heuen determined by a right line beeing drawne from the very centre of the earth through the bodie of the Moone or starre vnto the said outermost heauen And the visible place to our sight is a point in the outermost heauen determined by a right line passing through the body of the Moone or star from our eie vnto the said heauen whilest we stand vpon the vpper face of the earth to behold the starre And the distance or portion of circle contained betwixt those two points is called in Greeke Paralaxis which in English may be called the diuersitie of Aspects All which things you may see plainly expressed in this figure following THis figure as you see is made like a Quadrant the nether right line whereof commonly called the Base signifieth the Horizon and the perpendicular right line falling vpon the same and making therewith a right angle is the axletree of the Horizon and the said right angle marked with the letter A signifieth the centre of the earth whose halfe globe made like a halfe circle is drawne vpon the said centre and the short line marked with the letters A B signifieth the semidiameter of the earth the letter F signifieth the Zenith from which F to G is drawn the arch of the Quadrant signifying here the Verticall circle And you haue to vnderstand that the right line that is drawn from A throgh the bodie of the Moone marked with the letter C vnto the point D set downe in the arch of the Quadrant or Verticall circle sheweth the true place of the Moone and the right line drawne from B through the bodie of the Moone vnto the point of the foresaid arch marked with E sheweth the apparent place of the Moone visible to our sight from the vpper face of the earth and the little arch contained betwixt D and E is the Parallax or diuersitie of Aspects And you haue to note that the apparent or visible place of the Moone is alwayes lower in the heauen than her true place vnlesse the Moone doe chance to be in the right line of the Zenith for then there is no Parallax at all because both the lines and places do concurre and meet in one as the two lines A B and B F doe shew making both one selfe line and the further that the Moone is distant from the earth the lesser is the Parallax and the nigher that shee is to the earth the greater Parallax she hath But the true quantitie of her Parallax in euery place is to be learned by the Prutenicall tables And you haue to vnderstand that the Astronomers doe make the Parallax of the Moone to be threefold that is first simple then according to longitude and thirdly according to latitude For if you haue onely respect to the Verticall circle then it is said to be simple which is before defined but if you haue respect to the Zodiake then it is said to be sometime according to longitude and sometime according to latitude What is the Parallax according to longitude IT is an arch of the Eclipticke intercepted or contained betwixt two great circles drawn through the poles of the said Eclipticke so as the one circle dooth passe through the true place of the Planet and the other great circle passeth through the apparent or visible place of the said Planet What is the Parallax according to latitude IT is an arch of a great circle falling perpendicularly vpon the Eclipticke and is drawne either through the true place or els through the apparent and visible place of the Moone which arch is intercepted betwixt two circles paralels to the Eclipticke whereof the one passeth through the true place and the other through the apparent place of the Moone For the better vnderstanding of all which things it shall be necessarie to set down here once againe the Quadrant before described together with his proper letters of signification and then to adde to the said Quadrant the Eclipticke line and also the two circles which are paralels to the same and thirdly the two circles that are drawne from the pole of the Zodiake so as the one may passe through the true place and the other through the apparent place of the Moon all which things this figure plainely sheweth A figure shewing all the three kinds of Paralaxes The description of the figure FIrst the Quadrant of this figure together with his former letters doe shew the simple Parallax

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

this fift figure ¶ The fift figure belonging to the Eclipse of the Moone IN which figure B D signifying the latitude of the Moone is lesse than B K representing here the semidiameter of the shaddow and therefore more than the semidiameter of the Moone is eclipsed How to know the bounds or limits whereby is easily knowne what kind of Eclipse of the Moone will happen when she is at the full THe limits are most certainely knowne by the latitude of the Moone at the time of her true opposition to the Sunne for if you find the latitude of the Moone by the Prutenicall tables or otherwise to be more than the summe of the semidiameters of the shaddow and of the Moon being added together then there will be no Eclipse at that full but if the latitude of the Moone be lesse than the summe of the two said semidiameters added together you may be sure that the Moon will be eclipsed at her full so that the tearmes or bounds of the Eclipses are knowne by comparing the latitude of the Moone with the summe of the foresaid two semidiameters being added together The least summe of which two semidiameters that is to say of the Moone and of the shaddow of the earth is i53· ii53· which is when the Moone is in the Auge of her Epicicle and the Sun in the opposit Auge of his Excentrique and that in his least excentricitie But the greatest summe of the said apparent diameters that can bee is one degree i7· ii5· which happeneth when the Moone is in the opposite Auge of her Epicicle and the Sunne in the Auge of his Excentrique and that in his greatest excentricitie And hereof you may gather these three rules First if the latitude of the Moone at the time of her true opposition to the Sunne be lesse than i53· ii53· shee must needs be eclipsed Secondly if her latitude be more than i67· ii52· shee cannot be eclipsed at the Full. Thirdly if her latitude be more than i53· ii5●° and lesse than i67· ii52· then she may happen to be eclipsed but not necessarily And these bounds or limits may also be determined by the distance of the Moone from any of the two Nodes that is from the head or taile of the Dragon which distance is neuer lesse than 10 degrees i22· neither at any time greater than 13 degrees i5· which bounds or limits are set downe by Ptolomey thus If the distance of the Moone at the time of her true Opposition from either of the two Nodes be lesse than 12 degrees i12· or if the said distance of the Moone from either of the said Nodes at the time of her meane Opposition bee lesse than 15 degrees and i12· the said distance being reckoned either according to the succession of the signes or contrarie to the succession of the signes vpon the Eclipticke then the Moone may be eclipsed Of the twelue Digits whereinto the bodie of the Moone is wont to be deuided to know thereby how much at any Full she is eclipsed THough that the diameters of the Moone and of the shaddow may bee accounted by degrees and minutes yet notwithstanding the magnitude or greatnesse of her Eclipses is vsually reckoned by digits or ynches by deuiding the diameter of her body into 12 equal parts because her diameter appeareth to our sight as it were a foot in length and therefore as the foot is deuided into 12 ynches so is the diameter of the Moone supposed to be also deuided into 12 parts which parts are called digits or points and by them is the greatnesse of her Eclipse determined and therefore they bee called Eclipticall digits or points And although that the diameter of the Moone is deuided but into 12 digits yet neuerthelesse the Eclipse of the Moone may sometimes happen to be very neer 23 digits by reason of the thicknesse of the shaddow of the earth whose semidiameter sometime exceedeth the diameter of the Moone and such excesse is wont to be deuided also into 12 such parts as is the diameter of the Moone and so the Moon may be eclipsed more than 12 points as you may more plainly perceiue by this sixt figure next following ¶ The sixt figure belonging to the Eclipse of the Moone IN which figure the letters D K representeth the semidiameter of the shaddow and R S the diameter of the Moon at the time of her greatest darkenesse Now supposing the said R S to bee deuided into 12 equall parts the said 12 parts are called the Eclipticall digits for that some part of the semidiameter of the shadow namely S K extendeth further than R S which is the diameter of the Moone the ouerplus S K is supposed also to be deuided in this Eclipse into certaine equal parts namely into three such parts as the diameter of the Moone containeth 12 so as the eclipticall digits in this Eclipse are 15 for you may easily perceiue that if the semidiameter of the Moone were longer by three digits than it is yet it might be wholly eclipsed and as you see the number of eclipticall digits in this Eclipse to be 15 euen so the number of the said digits may amount sometime to be 22 digits and 51 minutes For you may remember that I said before that the summe of the semidiameter of the Moone and of the shaddow being added together may sometimes happen to be i69· ii52· when the Sunne is in his greatest excentricitie and in the Auge of his Excentrique and the Moone in the opposite Auge of her Epicicle at which time the semidiameter of the Moone is i17 ii49· and so consequently her whole diameter is i35· ii38· then say by the rule of proportion if i35· ii38· are equall vnto 12 digits what shall i67· ii52· be equall vnto so shall you find the fourth proportionall number to be 22 digits and 51 minutes and this is the greatest number of Eclipticall digits that any Eclipse of the Moone can haue And the more Eclipticall digits that any Eclipse hath the longer is the time of durance or continuance thereof Of the continance of the Moones Eclipse what it is and how many things are wont by the Astronomers to be considered therein THe continuance of the Eclipse is that space of time which she spendeth in going from the very beginning of the Eclipse to the middest of the same whereas she is most darkened And these fiue things are woont therin to be considered that is the minutes of Incidence the minutes of the halfe continuance the time of Incidence the time of halfe continuance and the halfe continuance it selfe 1. And first you haue to note that the minutes of Incidence are accounted in partiall Eclipses after one way and in totall Eclipses with continuance another way for in partiall Eclipses also in totall Eclipses without continuance the minutes of Incidence are said to be the arch of the Moones way which she maketh in her mouing of longitude from the beginning of her

Eclipse to the midst thereof where she is fully darkened as appeareth by the third fourth and fift figures of partiall Eclipses before set down in all which the point L signifieth the place of the Moone at the beginning of her Eclipse and the point D the place of the Moon at the middle of her Eclipse Now the arch of her way from L to D is called the minutes of Incidence for so long her light decreaseth by little and little vntill so much be taken away as can be in any of those partiall Eclipses But if the Eclipse be totall without any continuance as in the first figure then the way of her motion in going from the point I vnto the point K where she is wholly darkened is called the scruples of Incidence But if the totall Eclipse haue any continuance then the minutes or scruples of Incidence are that portion of the Ecliptick throgh which the Moon goeth from the very beginning of her Eclipse vntill the time that she be wholly eclipsed as in the second last figures the letter I signifieth the point in which the Moon is at the beginning of her Eclipse and M the point in which she is fully darkened and the arch I M is called the minutes or scruples of Incidence and these minutes in the end of the Eclipse are called minutes of repletion as in the third fourth and fift figures the arch of the Moons way namely D M or K H in the first figure or L H in the second and last figures doe shew which minutes of repletion are reckoned from the very time of the beginning of her clearing vnto the time that she hath fully recouered her whole light and the minutes or scruples of repletion are equall to the minutes or scruples of Incidence 2. The second thing which is considered in accounting of the continuance of Eclipses is the scruples of halfe continuance which is nothing els but the arch which the Moone maketh in going from the Sunne from the time of her whole darkenesse vnto the very middle of the Eclipse from which middle Eclipse the Moone going still forward vntill she begin againe to recouer her light the said arch is called the scruples of Emersion as in the second and last figures the arch M D doth shew whereof M representeth the place in which shee looseth her whole light vntill she come to the point D which signifieth her place when she is in the middle of her Eclipse or in her diametrall Opposition to the Sunne And this is called the scruples of halfe continuance but the arch of her motion from D to L where she beginneth again to receiue her light is called the minutes of Emersion and these minutes of Emersion are equall vnto the scruples of halfe continuance as the scruples of Repletion were equall vnto the minutes of Incidence 3. The third thing to be considered in accounting the Eclipse of the Moon is the time of Incidence which is nothing els but the very time which the Moon spendeth in going of the minutes of Incidence or the time of Incidence is that portion of time which the Moon spendeth in mouing from the beginning of the Eclipse vnto the point where she is most darkened if the Eclipse be partiall as in the third fourth and fift figures the time which the Moone spendeth in her mouing from the point L where she beginneth to bee eclipsed vnto the point D where her darkenesse is greatest is called the time of Incidence Likewise if the Eclipse be totall the time which shee spendeth in moouing from the beginning of the Eclipse vnto the point in which she is wholly obscured as in the first figure the time which she spendeth vnto her mouing from the point I vnto the point K so the time which she spendeth in going from I to D in the second and last figures is called the time of Incidence 4. The fourth thing to be considered is the time of halfe continuance which is that quantitie of time which the Moone spendeth in her moouing from the point in which she looseth her whole light vnto the point of the middle Eclipse as in the second and last figures the time which she spendeth in going from the point M to the point D is called the time of halfe continuance And the time which she spendeth in her mouing from D to L in the said second and last figures is called the time of her Emersion which time is equall vnto the time of halfe continuance sauing that the variable motion of the Moone beeing swifter in the one than in the other may make a little difference which in so short a time cannot be sensible And in like manner the time of Repletion is equall vnto the time of Incidence vnlesse the varietie of her motion doe make a little vnsensible difference 5. The last thing that is to be considered in the continuance of the Eclipse is the half time of durance which is nothing els but the time which the Moone spendeth in going from the point in which she began to be eclipsed vnto the point of the middle Eclipse and this time is equall to the time of Incidence in Partiall Eclipses as in the third fourth and fifth figures the time which she spendeth in going from L to D is the time of halfe durance and likewise the time which she spendeth in her mouing from I to K in the first figure is the time of halfe durance but if the Eclipse be totall with continuance then is the time of halfe durance equall vnto the time of Incidence and also to the time of halfe continuance being both added together Furthermore you haue to note that the Eclipse of the Moone dooth alwayes begin on the East side of her bodie I call that the East side which is towards the East for sith that her motion is from West to East and that very swift in respect of the Sunne or of the shaddow of the earth it must needs follow that the East side of her bodie first toucheth the shaddow in the beginning of her Eclipse and so continueth her mouing through the said shaddow leauing the same behind her on the West side of her bodie And although that this be true in all Eclipses of the Moone yet in partiall Eclipses if the latitude 〈◊〉 if the Moone be North then is the South part of her bodie darkened but if her latitude be South then is the North part of her bodie darkened And note that whensoeuer any Eclipse doth happen the said Eclipse may be seene of all them aboue whose Horizon she is in the time of her Eclipse and that at one selfe instant or moment of time be it the beginning middle or ending of any such Eclipse but it is not so in the Eclipse of the Sunne neither can any other of the Planers be eclipsed or darkened by the shaddow of the earth because the same shaddow reacheth not so high as any of the three higher Planets are and as for

Venus and Mercurie their place is alwaies so nigh vnto the place of the Sunne as they cannot be eclipsed at any time Thus much touching the Eclipse of the Moone and now I will speake of the Eclipse of the Sunne Of the Eclipse of the Sunne how and when it chanceth THe Eclipse of the Sunne is nothing but the darkening or depriuing of his light from our sight caused by the interposition of the bodie of the Moon betwixt the bodie of the Sunne and the bodie of the earth and this Eclipse neuer happeneth but when the Moone and the Sunne are in a visible Conjunction For you haue to note that there be three kinds of Conjunctions that is meane true and visible or apparent to our sight What the meane and true Conjunction is hath been before defined and it is called a visible Conjunction when a right line being drawn from our eye or sight passeth through the centre of the Moone vnto the centre of the Sunne whereby the said two Planets appeare to our sight to bee in one selfe degree 〈…〉 that is to say in one selfe point of the Eclipticke For although that the centre of the Moone bee betwixt the centre of the Sunne and the centre of the earth at euery true Conjunction and also neere to any of the Nodes yet perhaps it shall appeare no Eclipse to our sight because the two Planets be not in a visible Conjunction as haue been demonstrated before when we did speake of the Parallax whereupon cheefely dependeth the knowledge of the Eclipses neither can the body of the Moone being farre lesser than the earth possibly shaddow at any time all the earth and the body of the Sun is farre bigger than either of them both by reason whereof the Eclipse of the Sunne may chance to one part of the earth and not to another neither can any Eclipse of the Sunne or Moone chance but when those two Planets are either in the head or taile of the Dragon or els very nigh the same All which things you shal better vnderstand by this figure here following ¶ The first figure belonging to the Eclipse of the Sunne THis figure as you see consisteth of certaine circles both greater and lesser and of certain right lines in which figure the highest circle signifieth the bodie of the Sunne whose centre is marked with the letter P and the middle lesser circle beneath that made most part blacke signifieth the bodie of the Moon eclipsed whose centre is marked with the letter C and the diameter thereof is marked with the letters L K and the lowest lesser circle representeth the bodie of the earth whose centre is marked with the letter A and the two great circles crossing one another in two points opposit that is to say in C where also would be set the caracter of the Dragons head and in the other crosse point opposit is set the caracter of the Dragons taile of which two circles the one is called the deferent of the Moon and the other the Eclipticke Now what the right lines doe signifie the letters doe shew for the two outermost right lines F H and G I doe signifie the outermost beames of the Sunne which doe fall vpon the earth but the two inner lines F L and G K do signifie the beames of the Sunne which do fall vpon the Moone which two lines being drawne out in length do concurre and meet in the point A representing the centre of the earth and thereby doe make the cone to be F A G the axle●●●e of which cone is the right line P A and the little shaddowed cone marked with the letters L K A signifieth the cone of the Moones shaddow at the time of a true Conjunction when the Sunne is eclipsed the axle●ee of which little cone is signified by the line C A and the two lines K E and L D do signifie the outermost sides of the Moones shaddow falling vpon the earth in the two points D and E. Now hereby you may perceiue that those people which haue their dwelling betwixt D and E are wholly depriued of the light of the Sun but those that dwell betwixt E and I or betwixt D and H do still retaine the light of the Sunne Moreouer the Sunne is to some inhabitants of the earth totally eclipsed and to some partly and to some nothing at all as this figure next following doth plainely shew ¶ The sec●nd figure belonging to the Eclipse of the Sunne with the description thereof THis figure as you see consisteth of three circles and certaine right lines of which circles the highest and greatest representeth the body of the Sunne whose centre is marked with P and the middle little circle made almost all blacke signifieth the body of the Moone whose centre is marked with the letter C and her semidiameter with C B and her whole diameter with L K and the small vpper portion of her bodie made white is that which is lightened by the Sunne all the rest of her bodie beeing darkened The third and lowest circle being greater than that of the Moone signifieth the body of the earth whose centre is marked with A and the semidiameter thereof with A E. Now as touching the signification of the right lines the letters thereto belonging doe shew for the outermost lines marked with Q K and O L doe signifie the outermost beames of the Sunne that doe fall vpon the bodie of the Moone concurring or meeting in the point I enclosing the Conicall shaddow of the Moone marked with the letters L K I the axletree of which Conicall shaddow is the middle line C I for to those that dwell vpon the earth vnder the point I the Sunne is totally eclipsed and to those that dwell vnder the point N he is partly eclipsed and partly not and to those that dwell betwixt N and H he is not eclipsed at all Againe the Moone is not alwaies right vnder the Eclipticke line as the Sunne is and therefore her shaddow at the time of the Eclipse cannot point to the centre of the earth as it doth when she is in either of the two Nodes but sometime Northward and sometime Southward from the centre of the earth according as her latitude is either Northerly or Southerly so likewise her said shaddow after euery true Conjunction will point Eastward and before a true Conjunction Westward And further you haue to note that the true and visible Conjunctions doe neuer happen together except the true Conjunction of the Sunne and Moone chance to be in the 90 degree which what it is is before declared for in the 90 degree there is no Parallax at all But in all other places the true and visible places doe differ and the visible Conjunction is before the true Conjunction if the said true Conjunction be in the East part of the Zodiake that is betwixt the Sunne rising and the 90 degree But if the true Conjunction be in the West part of the Zodiake that is