De Theorica Astrolabij But though it be an Ingenious device yet I have found by experience that it is a ticklish Instrument and hardly managed for which reason I have hanged it by 2 The Bow now commonly used is an Instrument not so artificial but more tractable and steddy then the former It is made of too steel rulers the shorter of them must be of good substance as three quarters of an inch in heighth and as much in breadth that it may be stiff and lie flat the length must be somewhat more then the Diameter of your Instrument The other may be an inch longer of the same heighth but much narrower that it may be bent out with screws into an arch of any Circle required which ruler so bent being laid to the three points given you may by it draw the arch required as easily as you draw a straight line by a straight ruler The stiff ruler carries the screws and it must have rivets by which the bending ruler may be staied at both ends while it is bent by the screws See the figure CHAP. VI. How to draw the Tropiques and Polar Circles and to finish the Mater BEsides the 180 Parallels aboy ementioned you have four more to draw before the Mater is finished viz. the two Tropiques and the two Polar Circles of which the Northern is called the Arctique and the other the Antarctique Circle How to draw these you are sufficiently instructed Chap. 4. if you know but their Declination for they be Parallels The Tropique of Cancer declineth from the Equator toward the North Pole 23 degr 30 min. and the Tropique of Capricorn declines as much toward the South Pole The Arctique Circle declines Northward 66 degr 30 min. and the Antarctique as much Southward And these being drawn after the manner of the other Parallels you have drawn all the lineaments of the Mater And the better to adorn and distinguish them you shall with your Graver hatch every fifteenth Meridian for they are hour lines The South arch of the great Meridian A C B is the hour of Noon and his North arch A D B the hour of Midnight These need not be hatched being the Semicircles of the great Meridian or fundamental Circle which contains all but the Axtree line A E B which is the hour line of the sixes and the rest of the hour lines counted from him both waies would be hatched on both fides to shew like a ragged staff for distinction sake Also every fifth Meridian not being a fifteenth you shall make a pricked line not punching it with a round point lest you make your plate warp but making many short strokes cross the line with your Graver which will be more conspicuous Every tenth Parallel also would be a ragged line and the intermediate fifths pricked lines likewise the Tropiques and Polar Circles would be pricked lines Also if your plate be large you may set figures to the hour lines and to every tenth Meridian at the Equator but if your plate be smal the divisions of the Label applied upon the Equator may supply the lack of them CHAP. VII Of the Reet or Nets HAving shewed you what belongs to the Fabrique of the first part of this Instrument called the Mater A few words more will instruct you how to make the Reet whose lineaments are for the most part the same The Reet is a round plate of metal or pastboard like unto the Mater but of less Diameter it must be well planished and polished and the thinner the better if it hold working it would not be thicker then a shilling being of a foot Diameter It is called the Reet or Rete that is the Net because it must be pierced through and made like unto a Net or Lettess that the lincaments of the Mater may be perceived through it If we had a transparent metall much labour might here be saved A clear Lanthorn horn may serve for a smal Instrument but for large Instruments it is best to have it either of fine pastboard or if you will go to the cost of metal cancelled as shall be taught 1 For the delineation of the Reet first draw your fundamenttall Circle equal to the fundamental Circle of the Mater leaving a border or Limb without of such breadth as may receive the graduations of the Circle and figures set to them which breadth may be three tenths of an inch where the Reet is a foot in Diameter draw likewise two Diameters A B and C D crossing one another in the Center E at right Angles and dividing the Circle into his four Quadrants which you shall subdivide again into 90 degr apeece as you did in the Mater 2 You shall inscribe two arches which shall represent the Semicircles of the Ecliptique which shall meet at the points C and D of the Equator and the middle points of these arches shall be found in the Diameter A B thus The Diameter A B being divided as before you were taught to divide the Diameters of the Mater number from A toward the center E 23 degr 30 min. and there make the point F for ♑ and likewise number from B toward E 23 degr 30 min. and there set the point K. for ♋ then join the points C F D in one arch and the points C K D in another arch as is taught Chap. 3 and your Ecliptique is drawn But now you must make him a narrow Limb inward toward the Center to receive the scale of his degr and the characters of the Signes And to divide him you shall do thus Number in the Axtree line A B from F inwards 90 degr there is the Pole of the arch C F D to this Pole fasten one end of your ruler having an ey-lid-hole in the edge for that purpose and carrying about the other end over the several degr of the Semicircle C A D you shall cut the arch C F D into his correspondent degrees As if you lay the ruler from C to 10 degr in the Limb toward A it shall cut the Ecliptique in ♎ 10 and so of the rest Likewise for the other Semicircle C K D find his Pole 90 degr from K toward F and A and from that Pole by like reason you shall divide the Semicircle C K D by the divisions of the Semicircle C B D. This is the best way Or you way divide the Ecliptique by a Table of Right Ascensions thus Lay your ruler from the Center E to 27 deg 54 min. in the Limb which is the Right Ascension of ♉ 0. to be counted from D towards B and the ruler shall at the same time cut the Ecliptique in ♉ 0 to which that Right Ascension belongs and so for any other deg or you may defer the dividing of the Ecliptique till you have finished and cut out the Reet and then if you set the line C D of the Reet in A B the Axtree line of the Mater the Ecliptique will lie among the
010352 16 02867 010402 17 03057 010456 18 03249 010514 19 03443 010576 20 03639 010641 21 03838 010711 22 04040 010785 23 04244 010863 23.30 04348 010904 24 04452 010946 25 04663 011033 26 04877 011126 27 05095 011223 28 05317 011325 29 05543 011433 30 05773 011547 31 06008 011666 32 06248 011791 33 06494 011923 34 06745 012062 35 07002 012207 36 07265 012360 37 07535 012521 38 07812 012690 39 08097 012867 40 08390 013054 41 08692 013250 42 09004 013456 43 09325 013673 44 09656 013901 45 10000 014142 46 10355 014395 47 10723 014662 48 11106 014944 49 11503 015242 50 11917 015557 51 12348 015890 52 12799 016242 53 13270 016616 54 13763 017013 55 14281 017434 56 14825 017882 57 15398 018360 58 16003 018870 59 16642 019416 60 17320 02000 61 18040 020626 62 18807 021300 63 19626 022026 64 20503 022811 65 21445 023662 66 22460 024585 66.30 22998 025078 67 23558 025693 68 24750 026694 69 26050 027904 70 27474 029238 71 29042 030715 72 30776 032360 73 32708 034203 74 34874 036279 75 37320 038637 76 40107 041335 77 43314 044454 78 47046 048097 79 51445 052408 80 56712 057587 81 63137 063924 82 71153 071852 83 8144â— 082055 84 9514â— 095667 85 11430 114737 86 14300 143355 87 19081 191073 88 28636 286537 89 57289 572986 90 Â Â CHAP. IIII. To find the Centers of the Parallels six several wayes THe first way but the worst for our purpose as was said before for the Meridians is by the fifth Proposition of the fourth book of Euclid to find the Center of the Circle circumscribing the Triangle made by the three points given 2 A better way is by profers Take this upon trust that as you found the Centers of all the Meridians in the Equator so shall you find the Centers of all the Parallels in the Axtree line prolonged and by making like profers as you were taught for the Centers of the Meridians Chap. 3. you may quickly find the Centers of the Parallels 3 A third way You must consider that the Axtree line represents the East Meridian as well as the Axis of the world which is a common Diameter to all the Meridians Also that every Parallel cuts the East Meridian as it doth the rest in two points Equidistant from the Equinoctial and two Equidistant also from the Poles Therefore having one point already given in the Axtree line within the fundamental Circle where the Parallel shall cut number the distance from this point to the next Pole and number also the same distance again beyond the Pole in the axtree-Axtree-line prolonged being divided also as you were taught to divide the Equator line Chap. 3. and at the end of this number shall the Parallel out the Axtree line again And the middle between these two sections is the Center For example the 50th Parallel is 40 degr distant from the Pole Count therefore in the Axtree line prolonged 40 degr beyond the Pole and there is the utter end of this Parallels Diameter which if you part in two the middle at G is the Center 4 If from the point given where the Parallel cuts the great Meridian you raise a Tangent line this Tangent shall cut the Axtree line in the Center of the Parallel Example The said 50th Parallel cuts the great Meridian at H there I raise the Targent H G perpendicular to the Radius E H. And this Tangent as you see cuts the Axtree line in G the Center of the Parallel 5 Hence ariseth a fifth way For it appears by this figure that the Tangent of the Parallels distance from the Pole is equal to his Semidiameter and that the Secant of his distance from the Pole is equal to the distance of his Center from the Center of the great Meridian For here E H is Radius H B an arch of 40 degr H G the Tangent thereof and Semidiameter of the Parallel E G the Secant thereof and the distance of the Center of the Parallel from the Center of the Meridian And all this is evident by the structure in the Scheam Wherefore making E H Radius take from your Scale or Sector with your Compasses the Secant of the Parallels distance from the Pole and set it from E in the Axtree line and it shall end in the Center of the Parallel Or take the Tangent of the Parallels distance from the Pole and set it from the point of his Section with the Meridian toward the extension of the Axtree line and where the end of it just toucheth the Axtree line there is the Center 6 For want of a Sector or other fit Scales of Tangents and Secants you may do thus Set one foot of your Compass in the Center E and extend the other upon the Diameter of the Equator or Axtree line to twice so many degr as your Parallel is distant from the Pole That distance is the very Tangent you seek For example for the 40th Parallel from the Pole I number from E toward D 80 degr to 8. now E 8 is the Tangent of 40 degr though it contain just twice so many degr of the Circle foreshortned in this projection as hath been shewed Chap. 3. Sect. 3. and so if you will have the Secant of 40 degr take with your Compasses the length from 8 where the Tangent ends to A. and that is the Secant to be used as was taught in the last Section Thus have you wayes enough for finding the Centers of the Meridians and Parallels And you may have occasion in the making of the Instrument to use most of them one time or other However the knowledge of them is both pleasant and usefull for the right understanding of this and other Projections of the Sphear as also for the examination of your work when you shall chance to doubt of it CHAP. V How to draw the straighter Meridians and Parallels whose Semidiameters are very long IT may trouble you very much to draw those Meridians and Parallels which lie near to the Diameters because they be arches of great Circles and require Compasses larger then you can well get or manage when you have gotten them Till you come to the 80th Meridian from the Limb a Beam-compass of a yard long will reach if your Mater be not above a foot Diameter and a longer Beam you cannot well manage for it will be apt to tremble with it's own weight and draw double lines though it be made very thick and massie But the 89th Meridian will require a Beam-compass of almost ten yards long For his Semidiameter will contain the Semidiameter of the great Meridian 57 times Therfore to draw the 10 last Meridians and the 10 last Parallels you may help your self one of these wayes 1. Guido Vbaldus hath devised an Instrument for this purpose consisting of three rulers in form of an obtuse Triangle The description and use thereof you may see in Blagr l. 4. c 2 3. and in Vbaldus his book
PROBLEMES And to make all sorts of SVN DYALS very easily by the PLANISPHEAR CHAP. I. The Preface Of the kinds of Dyals ALthough Gnomoniques pertain to Astronomy yet I think it not amiss for the ease of the Reader in finding them to place the Gnomonical Problemes in a distinct Book by themselves Suns Dyals may be reduced to two sorts Some shew the hour by the Altitude of the Sun as Quadrants Rings Cylinders c. for the making whereof you must know the Suns Altitudes for every day or at least every 10th day of the year and for every hour of those dayes which Altitudes you may find immediately upon this Planisphear as in a Table made to your hand for any Latitude by Book 3.25 and so make them of any shape according to your mind The other sort shew the hour by the shadow of a Gnomon or Style Parallel to the Axis of the World and of those I treat cheifly in this Book Those be all Projections of the Sphear upon a plain which lies Parallel to some Horizon or other in the World And if upon such a plain the Meridians onely be projected they shall suffice to shew the hour without projecting the other Circles as the Ecliptique the Equator with his Parallels of Declination the Horizon with his Almicantars and Azimuths which are sometimes drawn upon Dyals more for ornament then for-necessity CHAP. II. Theorems premised FOr the better understanding of the reason of Dyals these Theorems would be known 1. That every plain whereupon any Dyal is drawn is part of the plain of great Circle of the Heaven which Circle is an Horizon to some Country or other that the Center of the Dyal represents the Center of the Earth and World and the Gnomon which casteth the shade representeth the Axis and ought to point directly to the two Poles And if upon the Center of the Dyal you fasten a Label with Sights of equal Altitude and keeping your eye in the line of the Sights turn this Label round you shall thereby describe in the Heavens that great Circle wherein your Dyal-plain lies and see where it cuts our Horizon and how much it is Elevated above it on one side and depressed on the other 2. That those Dyal-plains Geometrically are not in the very plains of great Circles for then they should have their Centers in the Center of the Earth from which they are removed almost 4000. Miles and in truth they lie in the plains of Circles Parallel to the said Horizons but so near them that Optically they seem to be the plains of those Horizons because the Semidiameter of the Earth beareth so smal proportion to the Suns distance that the whole Earth may be taken for one point or Center without any perceivable error 3. That as all great Circles of the Sphear so every Dyal-plain hath his Axis which is a straight line passing through the Center of the plain and making right angles with it and at the ends of the Axis be the two Poles of the plain whereof that above our Horizon is called the Pole Zenith and the other the Pole Nadir of the Dyal 4. That every Dyal-plain hath two faces or sides and look what respect or situation the North Pole of the World hath to the one side the same hath the South Pole to the other and these two sides will alwayes receive 24 hours so that what one side wanteth the other side shall have and the one is described in all things as the other 5. That as Horizons so Dyal-plains are with respect to the Equator divided into 1. Parallel or Equinoctial 2. Right 3. Oblique 6. A Parallel or Polar Dyal-plain maketh no angles with the Equator but lies in the plain of it or Parallel to it Such Dials are Scioterica Orthognomonica that is have the Gnomon erected on the plain at Right angles as the Axis of the World is upon the plain of the Equator because the Axis and Poles of the Dyal be here all one with the Axis and Poles of the World and the hour lines here meet all at the Center making equal angles and dividing the Dyal Circle into 24. equal parts as the Meridians do the Equator in whose plain the Dyal lies 7. A right Horizon or Dyal-plain cutteth the Equator at right angles and so cutteth through both the Poles of the World Therefore such Dyals are Paralielognomonical that is have the Gnomon Parallel to the plain and so the hour lines and the hour lines all Parallel one to another because their plains though infinitely extended will never cut the Axis of the World Yet have those Dyals a Center though not for the meeting of the hour lines viz. through which the Axis of the Dyal Circle passeth cutting the plain at right angles and cutting also near enough for the projecting of a Dyal the Center of the World 8. An Oblique Horizon or Dyal-plain cutteth the Equator at Oblique angles such Dyals are Scalenognomonical that is have for their Gnomon the side of a Triangle whose angles vary according to the more or less Obliquity of the said Horizon and the Gnomon shall alwayes make an angle with the plain of so many degrees as the Axis of the World maketh with the plain or as either of the Poles of the World is Elevated above the plain 9. Every Oblique Horizon is divided by the Meridians or Hour Circles of the Sphear into 24. unequal parts which parts are alwayes lesser as they are scarer to the Meridian of that Horizon or plain and greater as they are further off and on both sides the Meridian of the plain the hour Circles which are equally distant in Time are also equally distant in Space whence it is that the divisions of one Quadrant of your Dyal plain being known the division of the whole Circle is likewise known 10. The Hour-lines in an Oblique Dyal are the Sections of the plains of the Hour-circles of the Sphear with the Dial plain And because the plains of great Circles do alwayes cut one another in halfs by Diameters which are straight lines passing through the common Center therefore lines drawn from the Center of the Dyal to the Intersections of the Hour-circles with the great Circle of the plain shall be those very Sections and the very Hour-lines of the Dyal 11. Every Dyal-plain being an Horizon to some place in the Earth as was said Theorem 1. hath his proper Meridian which is the Meridian cutting through the â—oles of the plain and making Right angles with the plain If the Poles of the Dyal-plain lie in the Meridian of our place then is the Meridian of the plain all one with the Meridian of the place and the Gnomon or Style shall stand erected upon the Noon-line or line of 12 a clock as in all direct Dyals but if the plain decline then shall the substylar or line wherein the Gnomon standeth which is the Meridian of the plain vary from the Noon-line which is the
being placed upon the sole of the Window shall supply the use of the Nodus in the Gnomon and the beams of the Sun being Reflected by this Glass or Water shall shew the Hours upon the Ceeling The Planisphear shall help you to make this Dyal two wayes If the Window Decline not much from the South you may make it most easily the First way But if it Decline much and so the lines fall much upon the partition Walls or if you would adorn this Dyal with the Parallels or other Circles you shall use the Second way The First way is this Draw a Meridian line upon the Floor by Book 4.3 so that it may point upon the Perpendicular which you shall imagine to fall from the Nodus upon the plain of the Floor prolonged And this may be most easily done if you hang a Plumb-line in the Window dnecuy over the Nodus of place of the Glais for the shadow which that Plumb-line gives upon the Floor at Noon is the Meridian line sought and by a Ruler or a line stretched upon it you may prolong it as far as you shall need Then let a Plumb line fall from the Ceeling upon this Meridian line of the Floor and behind it Northward or Southward place your Ey so that the Plumb-line may hide the Meridian line of the Floor from your Ey then keeping your head steddy cast you Ey up to the Ceeling and direct One to make two points at a good distance in the line upon the Ceeling which the plumb-Plumb-line now covereth from your Ey and by these points you shall draw a straight Meridian on the Ceeling Then having fastned one end of a Line at Nodus let Another stretch this line up to the Meridian on the Ceeling and let him move his hand nearer or further in the Meridian till you find by a Quadrant that this line pointeth up Northward as many degrees as the Elevation of the Equator is in your Country and then you shall cause him to make a point where the line toucheth the Meridian of the Cieling and through that point you shall draw the Equinoctial line of your Dyal cutting the said Meridian at Right angles The length of the thred from the Nodus to the point in the Meridian where the Equinoctial cuts him is Radius of the Equinoctial to that Radius you shall find the Tangents of 15 30 45 60 75. as you found the Co-tangents Chapter 27. knowing that the Co-tangents of 80 and 70. be the Tangents of 10 and 20 and so of the rest and beginning in the Meridian make pricks in the Equinoctial line at the end of the Tangent of 15. Eastward for 1. and Westward for 11. and at the end of the Tangent of 30. prick Eastward 2. and Westward 10. c. Then by Chapter 9. seek what angles the Hour lines of a Vertical Dyal make at the Center which in our Latitude are 1.11.58 minutes 2.24.32 minutes 3.38.20 minutes 4.53.52 minutes 5.71.17 minutes and with the Complements of these angles shall these Hour lines cross the Equinoctial so the Hour line of 1. shall Incline to the Meridian on the South side the Equinoctial line and shall make his lesser angle with the Equinoctial 78.02 minutes and the rest as in the Figure The Second way is this Fit a plain smooth Board about a foot Square to lie level from the fole of the Window inwards and near the outer edge thereof make a Center in the board in the very place of Nodus or a little under it remembring that the Nodus or Center of the Glass must be set so much higher then this board as the Center of your Quadrant is placed higher in the Projecting of the Dyal Upon that Center taken in the board describe as much of a Circle as you may with the Semidiameter of your Quadrant which Circle shall be Horizon Draw here from the Center to the Horizon inwards a Meridian line by Book 4.3 and where it cuts the Horizon begin to graduate the Horizon into degrees of Azimuths both wayes which you may speedily do by transferring the graduations of your Quadrant or so much as you shall need to this Horizon Next you must devise to make your Quadrant stand firm and upright upon one of his straight sides which I will call his foot for this time and that you may thus do Take a short peece of a Ruler or sinal Transom and saw in one side of it a notch Perperdicularly in which notch you may stick fast or wedge the heel or the toe of your Quadrant in such sort that his foot may come close to the board and the other straight side or leg may stand Perpendicular upon it Those things prepared put your Planisphear in the Meridional Projection with the Finitor at your Latitude and first observe there the Altitudes of the Sun in the Meridian which in Latitude 52.15 minutes you shall find in the Tropique of ♋ 61.15 minutes in the Equator 37.45 minutes and in the Tropique of ♑ 14.15 minutes Now having stuck a short needle in the Center of the Horizon close to which you must alwayes keep the Center of your Quadrant set the foot of your Quadrant in the Meridian line of the Board and from the Center of your Quadrant extend a thred by 14.15 minutes of Altitude straight on to the Cieling the thred only touching the plain of the Quadrant and making no angle with it but held Parallel and where the thred thus extended touches the Cieling make a point then the Quadrant unmoved extend the thred by 61.15 minutes of Altitude and make another point as before and between these two points draw a straight line and that shall be your Meridian and shall be long enough for your use then extend the thred by 37.45 minutes of Altitude and where it touches this Meridian cross the Meridian at Right angles with an infinite line which shall be the Equator Then seek upon your Planisphear for one a clock and you shall find in the Tropique of ♑ the Suns Azimuth 14. and his Altitude 13.06 In the Tropique of ♋ his Azimuth 27½ and his Altitude 59.04 minutes therefore setting the foot of the Quadrant in the Azimuth 14. from the Meridian Eastward I extend the thred by 13.06 of Altitude and make a prick in the Cieling and again setting the foot of the Quadrant in Azimuth 27 ½ and extending the thred by 59.04 minutes of Altitude I make another prick in the Cieling and the straight line which I shall draw between these two pricks shall be all the Hourlines of One and so of the rest And if you be minded to have the other Parallels drawn you may find points for them as you have done for the Tropiques and by those points draw them And note that two points made in the Cieling for the same Hour line in any two Parailels or in the Equator and any Parallel shall suffice to direct the line though it is best
follow this Azimuth to the Finitor there is Nonagesimus gradus and the Altitude thereof 42 degrees counted from the Limb here Horizon the Azimuth thereof lies in the Limb between the Finitor and the Meridian 36 ⅓ as before equal to the Amplitude of the Ascendent I number also from ♓ 25 ½ in the Meridian 23. 41 minutes to the left hand still and there I have ♈ 19. 11 minutes the Suns place which cuts on the Label 41 ⅔ for the Altitude of the Sun there and the Label at the same time cutteth in the Limb about 29. from South East-ward for the Azimuth of the Sun and after the same manner you have before you the Altitude and Azimuth of every other degree of the Ecliptique for the time proposed CHAP. LVIII To do the same by the Nonagesimal Projection if the Altitude of Nonagesimus gradus be first given instead of the Altitude of Culmen Caeli SEt your Planisphear in the Nonagesimal Projection by Book 2.3 that is make the Limb now to represent the Circle of Longitude or Azimuth for it is both which cutteth the Nonagesimus gradus and make the Equinoctial line here to be Horizon and from the Equinectial line number in the Limb the Altitude of Nonagesimus gradus and thereto set the Finitor so shall the Finitor be Ecliptique the Nonagesimus gradus at the Limb the Ascendent and Descendent at the Center and because the Equinoctial line is Horizon in this Projection therefore the Meridians become Azimuths and the Parallels Almicantars shewing the Altitude and Azimuth of every degree of the Ecliptique if you reckon as you ought in this manner Reckon in the Equinoctial line here Horizon from the Center the Amplitude of the Ascendent to the right Hand if it be a North Signe and contrarily if it be a South Signe Where this Amplitude ends is the East point from whence you shall reckon all your Azimuths Count thence to the Limb and back again if need be in the said Equinoctial line till you have made 90 degrees there is your Meridian as far distant from the Limb as the East point was from the Ascendent Follow this Meridian to the Finitor and there he shewes you Culmen Caeli and the Parallel there cutting shewes the Altitude thereof Now may you find every degree of the Ecliptique above the Horizon if you know but what Ascends or Descends or Culminates and of every such degree the Parallels shew you the Altitude and the Meridians shew his Azimuth if you begin your numbring from the East or South Azimuth Example When ♋ 24 degrees was Ascending as in the Example before used as by consequence ♈ 24. in Nonagisimo gradu ♂ was in ♉ 4. 45 minutes and had but 3. or 4. minutes South Latitude I would know ♂ his Altitude and Azimuth setting go the Finitor above the Equinoctial line 42 degrees which is the Altitude of Nonagesimus gradus I say because the Nonagesimus gradus at the end of the Finitor in the Limb is ♈ 24. therefore I must count back 10. 45 minutes toward the Ascendent for Mars and there the Parallel 41 degrees with 10 minutes cutteth the Finitor for the Altitude of ♂ and the 14th Meridian East-ward from the Limb gives me his Azimuth which if I begin to reckon from the East point falleth out to be almost the 40th Azimuth from the East Mars his Latitude here is not regarded CHAP. LIX The Nonagesimus gradus and his Altitude and Azimuth given as in the former Chapter How in the same Projection to get the Altitude and Azimuth of any Planet or Star by his Longitude and Latitude YOur Palnisphear set as in the former Chapter you shall number the Longitude of the Star upon the Finitor here Ecliptique beginning at the Descendent or Nonagesimus gardus and in the Azimuth serving his Longitude count his Latitude by the Almicantars at the end of which account is the Stars place for this time The Parallel cutting there shewes his Altitude and the Meridian cutting there shewes his Azimuth if you count from the East point as you were taught in the former Chapter Example Lucida Pleiadum was in Longitude ♉ 25. 10 minutes Latitude 4 degrees 00 minutes North. Therefore from the Nonagesimus gradus ♈ 24. I number in the Finitor toward the Ascendent 31. 10 minutes and there is the Longitude of Lucida Pleiaedum in the Azimuth that cuts here I go up Northward 4 degrees and there I make a prick for Lucida Pleiadum Now the Parallel 38 ½ shewes me his Altitude and the 48th ½ Meridian from the Center shewes me that Lucida Pleiadum is gone 48 ½ in Azimuth from the Ascendent but from the East point onely 12 degrees 10 minutes CHAP. LX. The Altitude and Azimuth of any Star taken and either the Ascendent Nonagesimus gradus or Culmen Caeli known How by the same Nonagesimal Projection to find the Stars Longitude and Latitude IF you know either the Ascendent Nonagesimus gradus or Culmen Caeli you have enough to put your Planisphear in the Nonagesimal Projection by the former Chapters And your Planisphear so set you shall seek out the Meridian which standeth for the Azimuth in which you observe the Star and therein number from the Equinoctial line the Altitude observed the Azimuth and Almicantar cutting there shew the Longitude and Latitude of the Star inquired If the Azimuths reach not the place of the Star turn the Reet half round and let the Zenith and Nadir points change places and your turn is served Example Febr. 13 1657 8. I observed somewhat near that ♃ was gone West-ward from the Meridian in Azimuth 14 degrees and that his Altitude was 61 degrees Sirius was then in the Meridian by which I have the Ascendent Culmen and Nonagesimus gradus any or all of them given For when in the Equinoctial Projection I bring Sirius to the Meridian line it is all one as if I had set the Suns place to the hour of the Night by Chapter 46. and I see there Culminates with Sirius ♋ 7. 10 minutes whose Meridian Altitude by the 46. is 61. 5 minutes and I see ♎ 5 ½ ascending in my Horizon and ♈ 5 ½ descending therefore ♋ 5 ½ is Nonagesimus gradus which is 90 degrees distant both from the Ascendent and Descendent his Altitude by Chapter 55. 61. 10 minutes almost Therefore I set the Finitor 61. 10 minutes above Meridies as Chapter 58. and in the Finitor at the Limb I count ♋ 5 ½ Nonagesimus gradus thence I go inwards in the Finitor 1. 40 minutes where I come to ♋ 7. 10. the degree of Culmination this degree is cut by the 4th Meridian from the Limb whereby I learn that this 4th Meridian will be the Meridian of my place and that the Amplitude of the Nonagesimus gradus and likewise of the Ascendent is 4 degrees Now to place ♃ in the Mater I count his Azimuth first beginning from the Meridian of my
of the Place East or West The Reclination is the distance of his Poles from the Zenith and Nadir of your Place Inclination is the nearest distance of the Poles of the plain from your Horizon And whatsoever the Reclination of the upper face of a plain is the Inclination of the lower face is the Complement thereof CHAP. IX How to make the Vertical Dyal IN the Meridional Projection the Finitor being set to the Latitude of your Place you shall see the Limb which is your Meridian and the Axtree-line which is the sixt hour-circle dividing the Finitor into 4 Quadrants and the rest of the Meridians dividing every Quadrant alike Mark now at what degree numbred from the Limb every hour-circle that is every 15th Meridian being a ragged or blacker line cutteth the Finitor at the same distance shall the same hour-circle cut the Limb of your Dyal in the plain Lastly for the Gnomon set your Compasses to the Chord of the arch of the Poles Elevation in the Limb that is measure in the Limb from the Pole to the Finitor and setting that distance in the Circle of your Dyal from 12. either way make a point through which if you draw a deleble line from the Center you have between this line and the line of 12. the angle of your Gnomon by which when you have shaped him you must set him upright over the 12 a clock line with the point of the said angle at the Center and all is done CHAP. X. How to make the South and North Horizontal Dyal THis is usually called the Erect Direct Dyal and belongs to an upright Wall looking full North or South and the plain of it lies in the East Azimuth which on the Planisphear in the Meridional Projection is represented by the Axis of the Reet The Finitor set to the Latitude as in the former Chapter mark where the hour Circles cut the Axis of the Reet which is the proper Horizon of this Dyal you shall find the first cutteth 9. 20 minutes from the Meridian the second 19. 30 minutes the third 31. 30 minutes the fourth 46. 45 minutes the fifth 66. 24 minutes the sixt 90. And you shall see the North Pole depressed under this plain as much as is the Complement of our Latitude and the South Pole as much Elevated above it 1. Wherefore for the South Dyal draw an Horizontal line about the top of your Dyal plain which shall be the hour of Sixes from the midst whereof let fall a Perpendicular which shall be both the Vertical and the Meridian both of the Place and of the Plain wherein the Gnomon must stand Elevated 37. 45. minutes or the Complement of your Latitude toward the South Pole Another way Because the Almicantars may oft obscure the Intersections of the Hour Circles with the Axis you may avoid that inconvemence if you reduce this Dyal to a Vertical Dyal For the South Horizontal Dyal being the very Vertical Dyal of those People that live 90 degrees Southward from us that is in South Latitude 37. 45 minutes if you set the Finitor to the Latitude 37. 45 minutes you shall see the sections of the Hour Circles with the Finitor more â—pparently and thereby make your Dyal 2. For the North face Imagine you had for you Gnomon a wyre thrust aslope through the Center of the plain from the South side Northward and you will presently conceive that in the North Dyal the Horizontal or 6 a clock line will be lowest and that the Gnomon will turn upwards toward the North Pole as much as he turned downwards on the other side and that all the hours save 4 5 and 6. in the Morning and 6 7 and 8. at Night may be left out in our Latitude because the Sun shineth no longer upon it and those hour-distances you may find and set off from the 12 a clock line or from the 6 a clock line as you did the hours of like distance in the South face Another general and pleasant way to delineate the opposite face of any Dyal see hereafter in the end of the 12th Chapter CHAP. XI How to Observe the Declination of any Declining Plain A B is a Wall or plain declining East by the arch S p to which E B or W A are equal for so much as the Wall bendeth from the East Azimuth so much doth his Pole at p decline or bend from the Meridian 1. Now to find how much any plain declineth and so in what Azimuth he lies one good way is this when the Sun begins to inlighten the Wall or when he leaves it then is the Sun in the same Azimuth with the Wall take at that instant his Altitude and thereby get his Azimuth according to Book 4.27 and that is the Azimuth of the Wall 2. Another way First draw upon the Wall an Horizontal line by Chapter 3. then your Planisphear being fastned to a Square board as in Chapter 4. set one side of the board to that Horizontal line or Parallel to it and fix there your board and Planisphear level by the help of a Square set under him like a bracket the place your Label and Sights in one of the Diameters of your Planisphear and mark when the Sun comes into the line of the Label casting the shadow of one Sight upon the other if the Label be then in the Diameter which is Parallel to the Wall then is the Sun at that time in the Azimuth of the Wall if the Label be in the other Diameter which is Perpendicular to the Wall then the Sun coming to it is in the Azimuth of the Pole of the plain Now having the hour or the Altitude of the Sun get his Azimuth by 4.27 the same is the Azimuth of the Wall or plain if the Label were Parallel to the Wall or the same is the Azimuth of the Pole of the plain that is the very Declination if the Label stood Perpendicular to the Wall 3. Another way If you have not time to watch till the Sun come into the Azimuth of the Wall or the Vertical of it which cutteth the Pole thereof then get the Suns Azimuth by the said Book 4.27 when you can and at the same time Observe by your Label the Suns Horizontal distance from the Pole of the plain and by comparing these together you may easily gather the Declination of the Wall as in Example I observed the Sun to be gone West from the Pole of the plain 70 degrees and by the Altitude of the Sun then taken I found his Azimuth 60 degrees here I reason thus The Sun is gone from the Pole and Vertical of the Wall 70 degrees and from the Meridian but 60 degrees therefore the Meridian lies between the Pole of the plain and the Sun and because ☉ p is 70. and ☉ S 60. therefore S p the Declination of the plain is 10 degrees the difference of 70. and 60 and the Declination is East for the Sun is neerer to the
the Noon line of my plain cut by the Almicantar 61 ¼ I make a prick and in the Hour lines of 11 and of 1. where the Azimuth 27 and the Almicantar 59 meet I make pricks and where the Azimuth 49 ½ and the Almicantar 53 ⅓ do meet upon the Hour lines of 10.2 I make pricks and so for the rest Lastly I draw with an even hand a crooked line without angles through those pricks and that shall be the Parallel or Tropique of Cancer and in like manner I put in all the other Parallels and the Equator in the midst of them though for the Equator you may draw him more speedily by striking a line through the Center of the Almicantars making Right angles with the Substyle And that may be a general Rule for the Equator in all Dyals which have a Substyle and in the Polar Dyal where there is no Substyle the Equator shall be a Circle as before is shewn Note here that if your Dyal be great and you have not points enough to govern you in the draught of the Conical sections you may draw half-hour-lines and find points in them also after the same manner CHAP. XXXI To do the same by the Hour-lines of the Place although the Plain Decline or Recline IF you like not to draw the proper Dyal of the plain where it Declines or Reclines because being useless in your Country it must be wiped out again it shall suffice you to find the Hour lines of your Country upon the plain by Chapter 21 and 22 and in the posture your Planisphear hath in those Chapters to observe what Almicantars or Azimuths do cross those Hour lines at the several Hours in any Parallel and thereby make pricks upon the Hour lines of your Place as in the former Chapter you did upon the Hour lines of your plain and by these pricks you may draw your Parallels as before Note that if you work this way you shall find the Suns greatest Altitude to be in the Meridian of the plain or Substyle and not in the Noon-line of your Place whereat you must not wonder so if the Substyle be about 9 in the Morning there you shall find the Sun at highest and that his Altitude decreaseth from thence till he leaves the plain CHAP. XXXII How to inscribe the Horizon of the Place with his Azimuths and Almicantars in the Horizontal Dyal THe Nodus may be chosen in any part of the Gnomon but with the eaution given Chapter 27. and a Perpendicular falling from the Nodus on the Sub-style shall touch the Center of the Azimuths and Almicantars of the plain as hath been shewed Chapter 27. Here you have no use of those Azimuths and Almicantars but through the Center of them you shall draw an Horizontal line by Chapter 3. and that shall be Horizon Now if your plain Decline not from the Meridian and so this Center fall upon the Noon line you shall divide your Horizon both wayes from the Center as you were taught to divide the Azimuthal lines by Tangents Chapter 27. and shall number those divisions from the Center on both sides 5 10 15 20. c. and from the several points so made for 5 10 15 c. In the Horizontal line let fall Perpendiculars or Vertical lines on the plain and they shall be Azimuths of your Place But if your plain Decline you shall divide the Horizontal line thus Draw a short Vertical line through the said Center downwards by Chapter 3. which shall be the Verticle of your plain For the Almicantars they will not be so handsome lines but if you will have them do thus If the plain Decline not set the Finitor to the Latitude of your Place as Chapter 10. and if it Decline set the Finitor to the Latitude of your plain as Chapter 21. Then keeping your ey above the Horizon and within the Tropiques mark what Hour lines the 10th Almicantar for Example cutteth and what Azimuth there with him cutteth the same Hour lines also and in the interfections of the same Azimuths and Hour lines upon your plain you shall make marks through which the tenth Almicantar shall be drawn and so of the rest Note here That your Azimuths and Almicantars must not be drawn beyond the Tropiques nor beyond the Horizon neither must the Hour lines if the Nodus be the end of the Gnomon The Scheam shews you how the Azimuths may be drawn on the Dyal of Chapter 12. and 21. Declining East 30 degrees CHAP. XXXIII How by the help of this Furniture to place any moveable Dyal-Plain in his true Situation and consequently to find the Meridian-line of the Place without any other Instrument then the Dyal it self SEt the Dyal upon a level Table or Board and turn it till the shadow of the Nodus touch the Suns Parallel Azimuth or Almicantar any or all of them but the Parallel shall best guide you because that is most easily known by memory without Observation And when the shadow of the Nodus toucheth the Suns Parallel it shews there the Hour also and moreover it shews the Suns Altitude and Azimuth for the same Time if the Azimuths and Almicantars also be drawn upon your Dyal But you shall note here that the shadow of the Nodus may touch the Parallel at like distance from the Sub-style on both sides Therefore if you be in doubt which is the true place of touching as you may well doubt when the shadow cuts the Parallel near the Sub-style you shall Observe a while whether the sh dow of the Radius be lengthning or shortning If it shorten the Sun is not come to the Sub-style and so the earlyer Hour shewed is the true Hour If it lengthen the Sun is past the Sub-style and the later Hour is the true Hour And when the Dyal shews the true Hour the Gnomon and the plains Parallel thereto do point North and South And here you may see that the further the Sun is from the Sub-style the more easily is the Dyal placed Thus may you make a very commodious Polar Dyal to stand in a chamber Window and to remove from Window to Window as the Sun goes which shall find the Meridian line it self any where in the 4. Summer and 4. Winter Moneths and if you will make him a Limb like the Limb of a Box-lid of a Cheese-fat to receive the Parallels near the Equinoctial which else fall beyond the plain he shall serve for all the Year CHAP. XXXIV How to make a Vertical Dyal upon the Ceeling of a Floor within Dores where the Direct Beams of the Sun never come THe greatest part and as much as you shall use of the Vertical Dyal described Chapter 9. may by Reflection be turned upside down and placed upon a Ceeling but the Center will be in the Air without Dores A peece of a Looking-glass as broad as a Groat or Six-pence set level or a Gally-pot of fair Water which will set it self level
to take your points in the Tropiques at the largest distance as I have here done if there be room enough on the Cieling But because it often happens that part of your Dyal falls beside the Cieling and the plain of the Cieling and of the Walls is often interrupted and made Irregular by Beams Wal-plates Corrishes Wainscot Chimney-peeces and such like bodyes I will â—hew you one absolute device to carry on your Hour lines over all Extend the thred for any Hour line to the Tropique of Cancer â—n the Cieling as you where taught before and fix it there and extend another thred in like manner to the Tropique of Copricorn where ever it shall happen as perhaps beyond the middle beam or quite beyond the Cieling upon the Wall and fix that thred also Then place your Ey so behind these threds that one of them may cover the other and at the same instant where the upper line to your Sight or Imagination cuts the Cieling Beams Wall or any Regular or Irregular body above the end of the lower line there shall the Hour line pass from Tropique to Tropique direct any By-stander to make marks as many as you shall need and by these marks draw the Hour line according to your desire If the arch of the Horizon between the Tropiques be within view of your Window you shall draw the same on the Wall to bound the Parallels the Horizons Altitude you know is nothing and therefore he will be a level line and the Suns Azimuth when he riseth commonly called Amplitude and Ortive Latitude is in Cancer 40.40 minutes East Northward and in Capricorn as much Southward and these will be reflected to the contrary coasts on the Dyal The end of the Fifth Book A breif Description Of a CROSS-STAFF THe Cross-staff consisteth of two Rules joyned by a socket or else pinned in the form of a Romane T and three Sights or more The longer Ruler is called Radius Index and the Yard as A B of which I call A the neer end B the further end The breadth would be ¾ of an inch the depth an inch and half the length 70 or 80. inches and every of those inches would be divided by Parallels and Diagonal lines into 100. equal parts The shorter Ruler E F is called the Transom it would be half an inch or three quarters both in breadth and depth and in length about 2. foot for the Sights there if I may advise you would never be set above 20 inches asunder This Transom would be divided into whole inches onely beginning in the midst at B in the visual line ☉ B. and numbred to 10 both wayes The Sights C and D must have sockets at the bottom through which the Transom must pass so that the Sights may be set to any division of the Transom The Vanes or tops of those Sights must have onely two edges on their sides visible to your ey namely those edges which touch the Transom and the two other edges must be pared away The middle Sight at B would have half his head cut away and a shoulder left as in the Figure and a tenon at the bottom fitted to a mortess made in the middle of the Transom that you may stick him in and take him out when you please for to this mortess you shall do well to fit two other moveable Sights very narrow for observing the Diameter of the Moon or the distance of Stars which are very neer one may be about half an inch broad and the other about a quarter This Cross-staff is exactly made by Mr. Anthony Thomson in Hosier lane London When you would use this Staff you shall first set the Sights of the Transom to like inches as at 10 and 10. if the angle be great or at 5 and 5. as in the Figure they are placed alwayes set them at whole inches and at like numbers on both sides from the middle of the Transom and choose to place those Sights so that your Ey-sight may be far distant from them in observing for so you may the more distinctly observe the minutes and seconds of the angle inquired Then resting the further end of the Index upon a Wall or some device fitted for that purpose put the neer end over your right shoulder and setting your Ey to the Ey-hole slip the Index backward or forward till you see the objects by the sides of the Sights of the Transom and mark what number the backside of the Ey-sight cutteth upon the Index for that shall give you the angle sought in this manner Example The Sights of the Transom being set at 5 and 5 that is 10. inches asunder I observed two Steeples by their edges and the Ey-sight then cut upon the Index 6625. that is inches 66 ¼ from the Transom I say therefore As C B 500. to B G 6625. so C B Radius or 100000. to B G the Co-tangent of half the angle Here I have no more to do then to divide 662500000. by 500. or 6625000. by 5. which is an easy work and the Quotient 1325000. is the Co-tangent of 4. degrees 18. minutes 57. seconds 43. thirds for half the angle Note here that if the Sights had stood at 10 and 10. then had the number 6625. been the very Co-tangent of half the angle and remembring that your Radius on the Transom hath but 1000 actual parts go to the Canon and cutting off so many places as may leave the Radius there but 1000. you shall find your number 6625 to be the Co-tangent of 8. 35 minutes Note also that you may observe the angle between the middle Sight and one of the other and then you find the Co-tangent of the whole angle to that Radius to which your Sight is set on the Transom as to the Radius 200. 300. or any other even hundred to 1000. Note further that you must evermore observe neer the tops of your Sights that the visual lines may run above the Transom as much as the Ey is placed above the plain of it He that will may have room to set several Scales of degrees and minutes to several Radiusses as one to the Radius 300. another to 500. another to 700. by which the very degrees and minutes may be presently had without recourse to the Tables To me the Scale of equal parts is in stead of all The Commodities of this disposition of the Staff are these 1. It is better managed when it rests upon the shoulder and the Ey-sight being made to move while the Transom and his Sights stand Fixed shall save you much labour of coursing up and down from one end of the Staff to the â—â—â—er in observing 2. The Ey-sight being made to shew the angle by the length of the Co-tangents shall alwayes give you large differences insomuch that if your Staff be but 6. foot long you may observe to Seconds and Thirds in lesser angles and till you come beyond 20. degrees your Sight shall seldom move
and Mars in twain Sets forward and comes round again Then in one Year the Sun displaies Three hundred sixty and five dayes And near a quarter which in four Encompassings makes one day more Between the Sun and us there fly Fair Venus and swift Mercury These alwayes near the Sun we find Not far before nor far behind The Moon 's the lowest who in seven And twenty dayes goes round the Heaven And above two dayes more do run Before she overtakes the Sun So twenty nine and an half in all Do make a Moneth Synodical These Planets make their course to th' East Though they be faster hurled West And six degrees the rest may stray Beside the Suns Ecliptique way The Circles of the Sphear SIx greater Circles mark you shall Which equally divide this Ball. Just in the midst between the Poles From East to West th' Equator rolles Th' Ecliptique cuts him and doth slide Scarce twenty four degrees aside Horizon even with the ground From Stars below our sight doth bound Meridian upright doth rise Parting the East and Western Skies Two Colures through the Poles do run Quarrring the Circle of the Sun One where the Spring and Fall begin Th' other where longest dayes come in Four lesser Circles mark them well Are to th' Equator Parallel Two Tropiques bound the Suns high way Shewing the Long'st and Shortest day The Arctique Circle curs the Beares Th' Antarctique opposite appeares Meridians half twenty four For Hours and for Degrees ninescore Through both the Poles o th World do pass And th' Equinoctial down right cross And ninescore Parallels hath that line By which Stars North and South decline Th' Ecliptique hath his Longitudes And Parallels of Latitudes For Stars but in Geography The Towns beside th' Equator lie Over our Head and under Feet The ninescore Azimuths do meet And here as many Parallels Of Altitude Horizon tells Longitudes and Meridians all And Azimuths great Circles call But all their Parallels in Heaven Being lesser cut the Globe uneven Degrees three hundred and threescore Hath every Circle and no more When I consider thy Heavens the work of thy Fingers the Moon and the Stars which thou hast ordained What is Man that thou art mindfull of him Or the Son of Man that thou visitest him Ps 8. Errata Some Faults have been committed between the Writer and the Printer the cheif whereof the Reader is desired to amend as followeth pag. and line Faults Amendments 2 3 4. c. to pag. 30. in the Title The first Book of the Fabrique of the Planisphere The first Book Of the Fabrique of the Planisphear 31 and 32. in the Title The second Book of the Projections of the Sphear The second Book Of the Projections of the Sphere 1. 13. mossie massie 2. 7. Declination Delineation 3. ant Declination Delineation 4. 16. look up look upon 4. 36. eye beam eye-beame 5. 13. Euclid 4 5. Euclid 4.5 22. required of your Compass over reach required If your Compass reach short 5. 23. if it reach short if it over-reach 6. 39. structures structure 8. secant 67. 25693. 25593.  The 5. last Tangents want a place You must add a Cypher to each of them 9. 16. two so 12. 18. all but all But 13. 07. working it working It 16. 19. foure fewer 17. 18. Alamath Alamach 21. Henerichus Heniochus 17. antop little rain little Waine 18. 8. brow Crowne 18. 30. Praecepe Praesepe 19. 16. Bedalgieure Bedalgieuze 23. Alhaber Alhabor 20. 6. round the inner circle or edge of this Ring it must round The inner circle or edge of this Ring must 20. 14. naile screwes male screwes 17. small screwes female screwes 19. bare beare 22. 30. is made and gon for that year your scale is made And so for that year your scale 24. 9. but one degree but for one degree 25. 7.  put out the marks of Parenthesis 26. 8 year Henr. 3. year of Henr 3. 23. Periodus Periodus 28. alwayes upon alwayes upon 35. thus set thus set 28. 1. and 5. Grostons Grastons 30. 3 second Meridional second or the Meridional 33 6. set for London namely for London 33. â—1 on Elevation no Elevation 34. â—◠〈◊〉 the which the 9. Azimuth Azimuthes 37. 6. the eyes place the eye is placed 41. 3. Center B A Center B A 48. 4. either way either way 22. A C C A 50. 16. Zenith of Zenith of 32. Zenith and B Zenith A and B 53. 12. 12 and 13 number 12th and 13th numbred 56. 8. these sides the sides 20. subâ—endeth A which subâ—endeth A 62. 17. fall falls 63. 7 9. wayes rayes ult of deleatur 64. 10. min. at 70 min. and at 70 11. between 8 degr 34. min. between 18 and 24 min. 12. Here Refraction is as the Sun Her Refraction is as the Sun 's 65 1. your Meridians your Meridian 66. 30. require enquire 67. 3. Michals Michaels 68. 39. Long long 73. 6 CHAP. II CHAP XI 74. 20. Alrucabe Alrucaba 75. 8. Alrucabe Alrucaba 75. 12. first made first mode 76. 29. prick here prick here 8â— 16 17. by Declin by their Declin 82. 12. her Declin his Declin antep sta Star 86. 16 17 18 19. Pleiades Riseth setteth Pleiades Rise set 86. 30. to be least to be lost 87. 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 88. 4. could happen could not happen â— 14. note know 17. Asera Asera 91. â—1 Duet Deut. 99. 21. 23 degrees 23d degree 102. 6 and 30. Eniph Alph. Eniph Alph. 23. 35 â…“ 56 â…“ 105. 8. Stars I Stars I â— Caeti Ceti 19. 120 deg 125 degr 110. pen. by Oblique Problemes by Probl 2 Obliqu 111. 25. in 39 ½ in all 39 ½ 114. 17. grees setting grees Setting 11. Houses also Houses also 31. 49 30 50 51. 118. 6 7. 49 50 50 51. 24. and so and to 119. 1 Astrologers Astrologie 17. futurus futurus 122. 29. no man no men 123. 3. princeps Nero princeps Nero 4. citherae citharae 10. dereliquit Nero dereliquit Nero 12. persuesum persuasum 27. se nore temerè 128. 26. as by and by 29. setting go setting therefore 130. 34. Jupiter in that Meridian Iupiter In that Meridian 139. 6. Christ time Christs time 17. Ticius Tacitus 141. 6. 4 5. 11. 4. 5 11. 145. 13. Suns Dyals Sun Dials 147. 5. or Equinoctial deleatur 19. so the hour lines to the hour-hour-lines 154. in the scheam the letter I is wanting at the lower end of the hour-line of 11.  157. 17. with an extension with any extension 174. 32. precrucem per crucem 176. 11. by the arch by R T the arch 180. 9. Declination plain declining plain 181. 20. pre per 184. 27. the Vertical of my Dial and also deleatur 185. 28. and so and to 188. 9. Tumiture furniture 190. 7. you use you may use 192. in the scheme the prickt line last save one should be put out  193. an t a Vertical plain a Vertical or a South Horizontal