far as that which is lengthened POB one straight line DB even with the straight line DB of the II figure for it must reach unto it viz. In the Equinoctial at the point O and in an other place at an other time lengthen sufficiently III figure this straight line BD. Make in it the segments or cuttings even with the beams of the Sun of the I figure BD BF BC. Take in the III figure in the straight line POB conveniently a point I other than B. Make in the IIII figure three rods or sticks CI DI FI each of them sharp at both ends and equal with the three spaces CI DI FI of the third figure Draw a straight line along the Axeltree rod mark in this line of the Axeltree conveniently figure IIII one Cut BI equal with the space BI of the III figure Set figure IIII one of the ends of the stick CI to the point of shadow C one of the ends of the stick DI to the point of shadow D and one endâ— of the stick FI to the point of shadow F. Let the ends of those sticks or rods be so well fastened to the points of shadow CDF that they cannot stir Bring together the other ends I of those sticks in one point I. Put one of the point B of the Axeltree rod to the point of the pin B and the other point I with the three ends of the sticks CI DI FI set or joyned together And if you have been very exact in the work the point I of the pin will go and place it self with the three ends of the sticks set together in the point I if not you have not wrought exactly 6 To the Theoriciens It is no matter whether the Figures come right to the Compasses you are only to take notice what this insuing Discours ordains you to do MAke figure I with three straight lines CQRD DIPE and CF a Triangle even and like unto the Triangle figure III of the three points of shadow CDF upon the straight line CQRD figure I. make a Triangle CBD both like and equal with the Triangle figure III. of the Sun-beams CBD and upon the straight line FPID figure I. make a Triangle FDB like to the Triangle figure III. of the Sun-beams FDB make longer if need be figure I. on the side of D the straight lines CQRD and FPID By the points B and B draw a straight line BRAYH perpendicular to CQRD and a straight line BIAKL perpendicular to the straight line FPID find out the end or point A common to these two straight lines BRAYH BIAKL and by this end A draw a straight line AE perpendicular to the straight line BRAYH and a straight line AG perpendicular to the straight line BIAKL from the point R draw as far as the straight line AE a straight line RE even with RB from the point I draw as far as the straight line AG a straight line IG even with IB. From the point E carry to the straight line BRAIH a straight line EH perpendicular to the straight line RE from the point G carrry to the straight line BIAKL a straight line GL perpendicular to the straight line IG from the points B and B carry a straight line BQ that may divide in half the Angle CBD and a straight line BP that may divide in half the Angle DBF By the points Q and H draw a straight line QOH and by the points P and L draw a straight line POL find the end or the point O common to the two straight lines QOH and POL and from the point A for center and space AO draw an half circle that may meet with the straight lines AL in K and AH in Y. Now make in some other place even or flat as in the second figure in one and the same line BDFC three cuts BC BD BF even with the Sun beams figure III. BC BD BF each of them to his own from the point B of this second figure for center and from the interval or space EY or GK of the first figure draw an half Circle O from the point C figure II for center and from the space CO of the first figure draw an other half Circle O from the point D of the II figure for center and space DO of the first figure draw an other half Circle O and from the point F also of the II figure for center and space FO of the I figure draw an other half Circle O and if you have done right all these half Circles will meet in the same point O if not you have not been exact in working By the points B and O draw a straight line BO take in this line a point at discretion first make three rods even with the spaces CI DI FI of the second figure and every one sharp at both ends make in the length of the axeltree rod figure III the space BI even with the space BI of the II figure Lastly set these rods to the axeltree figure III as I have said at the end of the fifth table and the axeltree of the Dyal is placed There are some situations of superficies of Dyals where practising this manner of drawing one or the other of the points LH or O comes so far from the straight line CF that you should have need of too great a space to come to it But in what manner soever the superficies of the Dyal may be situated and at all times or seasons of the year I mean in any strange or odd kind of example that may be found you may work or practise these kinds of draughts with as much ease as in the most easy pattern 5 And by means of these three angles even with those in the air between the beams of the Sun you may chuse at pleasure within the lines that represent those beams other points CDF and otherwise disposed between them then those which the shadow of the point of the pin hath given upon the superficies of the Dyal and upon those three points chosen out at pleasure you may make an other triangle CDF and practise afterwards this manner of drawing as far as the triangle CBO figure II than in this triangle and in the straight line BC make BC BD BF even with the beams in the air BC BD BF of the third figure contained from the point of the pin B to the points of shadow CDF in the superficies of the Dyal each of them to his own and after you have taken as it is said the point I in the straight line BO you must make use of the points CDF last made in the triangle OCB for to set the rods CI DI FI to the axeltree BI then to work on as before To make other points instead of those of the superficies of the Dyal you need only to make some at the two extremities or furthest ends CF and make BC and BC equal one to the other and unequal with the middlemost BD but a little bigger
more or lesse according as the angles DBC DBF are more or lesse unequal among themselves and instead of making figure I the triangle CDF of the spaces between the points of shadow CDF of the superficies of the Dyal you shall make it of the spaces between the points that are set in the place of these points of shadow 6 To the Theoriciens MAke in one and the same plain as in the first figure vith three right lines CgkD CrtF DieF a triangle CDF equal and like to the triangle of the three points of shadow fig. IV. CDF make upon the said three straight lines CgkD CrtF DieF three other triangles CBD CbF DBF equal and like to the triangles in the air of the beams of the Sun III. fig. CBD CBF DBF every one to his own By the points B and b I. fig. draw a straight line Bqg that may part in two the Angle DbF. Draw out of the point C at your discretion a straight line aqkty perpendicular to the straight line CgkD and out of the point F draw a straight line hPirx perpendicular to the straight line FeiD make in the triangle Fcb the section or cutting Cl equal with Ca of the triangle CBD and the section Fs with Fh of the triangle FbD from the point t center and space tl draw a bow lm from the point k center and space ka draw a bow am that may meet with the bow lm in m and draw along the straight line km from the point r center and space rs draw a bow sn from the point i center and space i h draw a bow in hn that may meet with the bow sn in n draw along the straight line in Make in the straight line km the section or cutting ku equal with kq. By the point u bring to the straight line aqkty a straight line uy perpendicular to the straight line km make in the straight line in a section iz equal with iP by the point zx carry to the straight line hPirx a straight line zx perpendicular to the straight line in finde out the butt end y common to the two straight lines aqkty and uy And also the butt end x common to the straight lines hPirx and zx draw the straight lines goy and eox find the butt end o common to these straight lines gov eox Make in an other place figure II. a Triangle gqy of the three straight lines as gq gy and yu of the first 7 figure make in the II. fig and in the straight lines gy and gq the section go equal to go of the I. fig. And the section gb also equal to go of the I. figure draw if you will the straight line bo of the second figure Make again in another place fig 3. a Triangle cbo of the three straight lines bo of the Triangle gbo of the second figure And of CB and CO of the first figure and upon bc fig. 3. make the cuts bc bd bf equal to the lines BC BD bF of the first figure every one to his own respectively And if you have done rightly the spaces fo do co of the Triangle cbo fig. 3. are equal with the spaces FO DO CO of the first figure every one to his own respectively Take fig. 3. in the straight line bo according to your discretion the point i other then b make three sticks sharp at both ends and equal to the three spaces ci di si of the third figure mark along upon`the rod or Axeltree the space BI equal to the space bi of the third figure work as I have said and as the fourth figure doth shew you and you shall find the Axeltree of the Dial placed in his right place You may after this manner as in others substitute or bring in other points CDF in stead of those of shadow of the superficies or face of the Dyal and work by this mean every where with the like ease Figure 8 For those that have skill in Geometry THe higher figure is the place of the Dyal with the face unequal to the pin AB and to the three points of shadow CDF all markt as it is said Get a flat and solid thing as a slate a board paceboard or the like Draw upon it in the lower figure a straight line BDFC make in that line three cuts BC BF BD equal with the three spaces BC BF BD of the place of the Dyal each of them to his own respectively then from the point B of the lower figure for the center and from the spaces BC BF BD draw some circles DH FE CG By this means you see whether the spaces BC BD BF of the higher figure or Dyal are equal or unequal one unto another and when these spaces are unequal among themselves as it happens in this example you see which is the least and which is the biggest as in this example the space BD comes to be the shortest of the three Now from the point C of the lower figure for the center and from the space between the two points of shadow C and F of the higher figure draw a circle E that may meet in one point E the circle of the space BF viz. the circle FE for it must meet with it then draw the straight line FB that may go and meet in one point H the circle of the shortest space BD viz. the circle DH Again from the point C of the lower figure for center and space between the two points of shadow C and D of the higher figure draw a circle N that may go and meet in the point N the circle of the shortest space BD viz. the circle DH for it must meet with it From the point F in the lower figure for center and from the space between the two points of shadow FD of the higher figure draw a circle that may meet in the point R the circle of the shortest space BD viz. the circle DH for it must meet with it By this means the three spaces or straight lines DH DR and DN of the circle DH which is that of the shoreâ—t space BD have the conditions that are requisite for the making of a triangle Figure 9 For those that are skilled in Geometry MAke in another place as in the lower figure a triangle DGV of three straight lines equal with the three spaces DH DR DN of the higher figure every one to its own Find in the lower figure the center O of a circle the edge whereof may reach to the points VDG according as the lower figure doth declare Draw a straight line DOE through the Diameter or midd'st of this circle By the point O in the lower figure draw a straight line POQ perpendicular to this Diameter DOE From the point D in the lower figure for the center and space BD of the higher figure draw a circle that may meet as in B the straight line QOP for it must meet with it in one or two points viz. In the times of the
Mr. DESARGVES vniversall way of makeing all manner of Sun dialls Published by Daniell king Sold by Isaake Pridmore at y golden falcon in y strand Aâ— 1659 Mr. De SAKGVES UNIVERSAL WAY OF DYALING OR Plain and easie directions for placing the Axeltree and marking the hours in Sun-dyals after the French Italian Babylonian and Jewish manner Together with the manner of drawing the lines of the signs of finding out the heighr of the Sun above the Horizon and the East rising of the same the Elevation of the Pole and the position of the Meridian All which may be done in any superficies whatsoever and in what situation soever it be without any skill at all in Astronomy By DANIEL KING Gent. LONDON Printed by Tho. Leach and are to be sold by Isaac Pridmore at the Golden Faulcon in the Strand near the New Exchange 1659. TO THE ILLVSTRIOVS GEORGE VILLIERS Duke and Marquess of Buckingham Earl of Coventry Viscount Villiers Baron Whaddon and Ros Knight of the most noble Order of the Garter c. Sir HAving had the honour to observe your Graces great affection and love to Sciences and Arts and your own excellency being most eminent therein together with your unparallel'd love and inclination to the splendour of your Native Country in promoting Learning and Ingenuity These high merits with my own particular obligations and attendance encourage my endeavours of the patronage to a new birth never presented to the English Nation presuming by Gods assistance to bring forth something of worth that hathnot yet seen light and if your Grace shall please to pardon my observant presumption you will hereby more strictly engage him ever to honour your Heroick worth who is The very humblest of Your Servants Daniel King The Preface Concerning the particulars of this TREATISE WHereas the Superficies or outsides whereon Dyals may be made may be either flat bowed or crooked plain or rugged situated diversly the most part of the books treating of this matter contain severally the manner of making flat Dyals in all kinds of positions Horizontal Vertical Meridional Septentrional Oriental Occidental Declining Inclining Inclining and Declining and accordingly in all other kinds of superficies They may also shew for those that are ignorant of it the way to find the elevation of the Pole the Meridian line the Declinings Inclinings and other particularities But Monsieur de Sargues intention being to publish nothing if it be possible that is to be found in another Book and to give you only the general Rule to make and not to copy out a number of examples all differing one from another I will give you but one example only in this volume by this universal manner the discourse whereof may be applyed generally to all kinds of superficies and in what situation soever they be without having any knowledge of the Pole nor of the height of the Sun nor of the declining or inclining nor of the Meridian line nor of any other thing in Astronomy and without a needle touch'd nor of any kind of thing that may give a beginning to that as you shall see yet better when we shall treat of the practice And in practising this general Rule you shall find at one and the same time the elevation of the Pole and the position of the Meridian you shall know how to place the needle of your Dyal and so you shall come to find the equal hours which are called hours after the French way alias Astronomical The rest being more curious than necessary I thought to set down nothing else but those two things But I have been perswaded for the satisfaction os some to add also the manner of drawing upon the same superficies the lines of the signs the hours after the Italian and Babylonian way and of the Antients the height of the Sun and the situation thereof in respect of the Horizon Of the Practice of Sun-Dyals MAny diverse things are represented in Sun-Dyals by the shadow of the Sun to divers ends the hour is shewn by them and serves only for that purpose every day Other things are represented also by it as the signs and other particularities whereby it may serve sometime for the divertisement of a few In antient time the hours were not counted as they are now a dayes and in Italy at this day they are counted otherwise than in France The manner that they count their hours in France is according to Astronomy and here is at length a generall way of framing and making Dyals with houres equal to the Sun according as the hours are now counted in France after which way one may come to shew if need be by the shadow of the Sun and also of the Moon whatsoever can be shewn concerning other circumstances to satisfie curiosity There are two things which together do compose those kinds of Dyals of equal hours after the French way the one is as piece that shoots out or sallies out of the superficies of the Dyal the shadow whereof falling upon this superficies shews what a clock it is the other are the lines drawn upon the superficies of the Dyal each of them representing one of the hours after the French way They make Dyals after the French way wherein there is only the shadow of one portion alone as might be a button of the piece that shoots out that shews what a Clock it is But in this general way there is still the whole shadow of all the length in a direct line of this piece that shoots out shewing continually what a Clock it is of which piece or length you may take if you will a button and mark the hours with that button only together with all the other particularities that may be added to such Dyals Some call by one and the same name these two kinds of pieces the shadow whereof shews the hour as well that same whose shadow shews continually the hour at length as that which hath but the shadow of a button to shew it But to the end we may distinguish both kinds of pieces one from the other that same whose shadow shews the hour at length and is the original spring of all the others I call it the axeltree of the Dyal This axeltree may be made as well with a straight round and smooth rod of yron or brasse as with a flat piece and cut of one side in a straight line There are often other rods in the Dyals which serve to bear up the axeltree that shoots out and those kind of rods I call the supporters of the axeltree The lines that are drawn upon the superficies of the Dyal and that shew each of them one of the hours after the French way I call them lines of the hours after the French way In the innumerable number of such kinds of Dyals as may be made after the French way it happens that the superficies of the Dyal is either all flat or is not so altogether When the superficies
B that next the Sun termed Conus luminosus or the light Cone the other whereof our Author makes use termed Conus umbrosus the dark Cone now in this dark Cone if by any three points equally distant from the Apex B the Cone be cut the Section will be a Circle parallel to the Equinoctial And thereby as the Author shews many wayes the position of the Axis or Gnomon may be found out and the Dyal easily made Now it rests courteous Countryman that we be very gratefull and every way forward to encourage Mr. D. King one very industrious in the studies of Antiquities and Heraldry who out of his desire to serve his Country hath caused this piece speak English hath been very carefull to see the Cutts well done and will no doubt proceed to cause some of those rare pieces of perspective in French to be translated Then prosper King untill thy worthy hand The Gallick learning make us understand JONAS MOORE Mathesios Professor Books Printed for Isaac Pridmore and are to be sold at the Golden Faulcon near the New-Exchange THE Rogue or the life of Gusman de Alpherache the witty Spaniard written in Spanish by Matthew Aleman Servant to his Catholick Majesty the fifth and last Edition Corrected A Physical discourse exhibiting the cure of Diseases by signatures whereunto is annexed a Philosophical discourse vindicating the Souls prerogative in discerning the truths of Christian Religion with the eye of reason by R. Bunworth Seif-Examination or Self-Preparation for the worthy receiving of the Lord Supper delivered in a Sermon concerning the Sacrament by Daniel Cawdrey sometimes Preacher there with a short Chatechism the third Edition The Obstinate Lady a Comedy written by Sir Aston Cockaine Sportive Elegies written by Samuel Holland Gent. A New discovery of the French Disease and running of the Reins with plain and easie directions for the perfect curing the same by R. Runworths The Vnspotted high Court of Iustice erected and discovered in three Sermons Preached in London and other places by Thomas Baker Rector of St. Mary the More in Oxon. A Chain of Golden poens imbellished with wit Mirth and Eloquence together with two most exelent Comedies viz. the Obstinate Lady and Trapolin suppos'd a Prince by Sir Aston Cockaine The Ascent to blisse by three steps viz. Philosophy History and Theology in a brief discourse of Mans felicity with many remâ—â—keable examples of divers Kings and Princes The Heroical Loves or Anthcon Fidelta a poem by Thomas Bancroft Advice to Balams Asse or Momus Catechised in Answer to a certain scurrulous and abusive scribler by Iohn Heydon Aâ—â—hor of advice to a daughter by T. P. Genâ— The Analysis of all the Epistles of the new Testament wherein the chief things of every particular chapter are reduced to heads for the help of the Memory and many hard places explained for the help of the understanding by Iohn Dale Master of Arts and fellow of Magdal 〈…〉 in Oxford 1 I Figure To all sorts of People I come now to the first of those two things that you are to doe for to make one of those Dyals which is the manner how to find the position or the placing of the Axeltree WHen you have a mind to find out the right placing of the Axeltree of one of those Dyals by this general way mark first which way the light of the Sun comes to the place where you will make your Dyal and which way it goes out again Then make fast upon the place as the figure above doth shew with cement plaister mastick or the like a peg or pin AB by the great end A putting the other small or sharp end B as far out of the superficies of that place as you can In such sort that while the Sun doth shine upon that place the shadow of the end of the pin B may fall always upon this superficies and for the rest it is no matter how this pin or peg be framed or placed or turned you are only to look to the small end thereof that must be in such a manner that you may set or apply upon it one of the feet of the Compass Then in a fair Sunshiny day when the light is very clear and the shadow very clean whilst it falls upon this superficies in the figure below mark in it as the figure shews in one and the same day at three several times as far asunder as you can three several points CDF each of them at the end of the shadow of this pin AB that answers to the small end of it B. You must nore that there is a certain time and place in which you cannot mark the points of the shadow That is when this superficies is flat and situated after such a manner that the ground plot thereof being stretch'd at length answereth and reacheth into the center of the Sun For in that case how short soever the peg or pin B may be the shadow hereof cannot goe and fall in this superficies but at the end of an extreme length Therefore when the days are equal with the nights or very near you cannot mark in this manner three points of shadow in a flat superficies which is situated in that manner called parallel to the Equator When you have thus mark'd three points of shadow you have no more need of the light of the Sun and you may make an end of the rest in any other time and season as well by night as by day as I shall say three times together for one and the same manner in three several ways to be expressed after I have briefly satisfied the Theoriciens that take pleasure to see the reasons of the precepts or rules of the practice of the Arts before they see the precepts themselves 1 To the Theoriciens This Resolution will serve you AFter you have conceived that the Sun in his full revolution of a natural day makes a Circle parallel to the Equator and the rest of this Hypothesis for Dyals The three beams of the Sun or straight lines BC BD BF make in their point or common end B. some angles or corners equal one to another with an other straight one that makes the fourth which is the Axeltree of the Dyall Now the position or placing of these three straight lines BC BD BF is given out Therefore the placing of this fourth which is the Axeltree of the Dyal is given also You shall have hereafter in the fourth figure an other resolution of this kind before you have the way to compose some problemes or propositions about it I said to the Theoriciens because if you were not at all versed in any kind of practice either of Geometry or Art you might hardly understand me at first concerning the 2d third figures following because of the short compendious way whereby I expresse my self unto those that are skilled in Geometry but I can assure you that when you have understood what is written in order for
all sorts of people if you come again to these second and third figures you shall know at the very first sight what they mean For the Theoriciens And for those that are skilled in Geometry THe I figure is a plate of some thin flat smooth and solid stuff as Iron tinned or the like being round and having a hole just in the Center greater or lesser according to the occasion The II figure is a straight rod round smooth and solid as of Iron or the like of the bigness of the hole in the plate The III figure is as it were a whirl made of the plate and of the rod put thorow the plate in such sort that it is perpendicular to the said plate as the squire that turns round about doth represent unto you and is so fast that it cannot stir or move In the V figure AB is the peg or pin that hath mark'd unto you the points of the shadow CDF the rods or sticks BC BD BF are solid and strong as of wood or the like having each of them a slope edge in a direct line all along going from the point of the peg B to each point of the shadow CDF and are so turned or ordered that in applying the whirl unto them the edge of the plate may goe andtouch the three slope edges of the rods all at once and the rods or sticks are made fast in this situation in such sort that they cannot move nor stir The rule that crosseth over the three slope edges BC BD BF toucheth them all three or else two at the time only whereby it shews whether those slope edges are all three in one and the same situation or upon one and the same ground or no and on which side is their hollowness when there is any The hand applies the whirl unto it and keeps it there till the Axeltree BOâ— come to touch the end of the peg or pin B and that at the same time the edge of the plate EDH touch the three slope edges of the rods And when the whirl is placed or setled after this manner the rod is the Axeltree of the Dyal and placed as it ought to be and there remains nothing else but to make it fast in this situation or position The IV figure doth shew that if you goe to make use of thin and supple strings in this practice or working in pulling those two mark'd with Ie and Ih to make them fast in direct lines they would make the two strings mark'd with bc bf to bend so that you can doe nothing exactly with them which is the reason that Monsieur Desargues hath not thought fit to make use of them for the Beams of the Sun but rather of the slope edges of the rods that are both stiff and strong 2 3 To the Theoriciens And others that are skill'd in Geometry THis foregoing figure shews to the eye that all the pieces of the Instrument are made so strong and firm that they cannot bend AB is the pin by whose point B you have had the points of shadow C D F. The three sticks or rods BC BD BF have each of them a slope edge in a direct line at length going from the point of the pin B to the three points of shadow C D F. The slope edges of the two longest sticks or rods BC BF have some portions made in them equal every one to the third and shortest stick BD. The three sticks IH ID IE are every one longer than BD and all three made even then they are joyned all by the end to one of the points EDH of the slope edges of the other sticks BC BD BF and their other ends I are brought together in one and the same point I. The rod BI is straight round smooth and strong as of yron or the like it hath a straight line BI drawn from one end to an other and one of the points B of this line of the said rod toucheth the point of the pin And with an other point I of the same it toucheth the point I of the three rods or sticks This being so the rod BI comes to be the Axeltree of the Dyal rightly placed there remains nothing else but to make it fast in this position or situation The figure shews in the rods that goe from the point of the pin B to the points of shadow CDE how one may make fast those rods at one end to the pin and also all together to one point by binding them to it And how they may be made fâ—â—t at the otherend to one point of the superficies of the Dyal by fastning them to it with mastick plaster cement or thelike This way is more sure than that with the strings But yet it is not the easiest nor the least troublesome in my judgement To the Theoriciens Another resolution of the same kind with the former THe position or placing is given of the four points BC DF and the placing of the two straight lines BE BH that divide in two the angles CBD and DBF and of the two ground plots that passe unto those two straight lines BE and BF and that are perpendicular to the ground plots of those Angles CBD and DBF are given out Therefore the intersection or intercutting of these two ground plots so perpendicular is given But this intercutting is the axeltree of the Dyal therefore the position of the axeltree of the Dyal is given Any one may frame at his pleasure upon that which is granted concerning this composition many other resolutions and divers compositions of problemes and divers general ways of practice In the mean time you shall have here three several ways one after another to see which is the most advantagious for the actual practizing of the Art and to induce you to seek or try if there is any other shorter 4 For the Theoriciens The Composition of the Probleme or Proposition in Consequence of the Resolution made upon the lowermost figure of the first draught THe first figure is the place of the Dyal with the pin and the points of shadow CDF Make a ground plot of it II upon one straight line BD and with one point B three Angles DBN DBR DBH equal to the three Angles of the first figure that are between the beams of the Sun DBC DBF CBF every one to his own respectively From the Center B II figure and from any space BD draw a half circle that may meet in the points DNRH the straight lines BD BN BR BH Make in the third figure a triangle DGV with three spaces equal to the three spaces DH DR DN every one to his respectively as having the condition necessary for that purpose Find the Center O of the circle EVGD drawn about this triangle VGD Draw two Diametters DOE POB of this circle perpendicular one unto another Lengthen one POB sufficiently of one side and on the other From one of the ends D from the other EOD draw as
all sorts of People that have neither skill in Geometry nor in Arts but are apt and sit to learn them both BEfore you undertook to make this Dyal you had nothing about you nor knew nothing wherewith to further you in it and going about it you have made use of the pin AB as it were at a venture Now you must consider that having placed the pin AB in this manner you have given out of your self in the end thereof a point alone unmovable and fixed in the air Then by means of this fixed point in the air B and of the Sun-beams you have found out three other unmovable and fixed points of shadow CDF on the outward face of the place where you have a mind to make your Dyal So you see that by means of this end of pin B and of the Sun-beams you have established upon the place where you intend to make your Dyal four points fixed and divided one from another viz one in the Air which is the point or the end B of the pin AB and three in the superficies of the Dyal which are the three points of shadow CDF Whereby you have found also six spaces that is to say the lengths of six straight lines unmoveable fixed distinct and divided one from the other For if you consider well you shall see that you have found out by this means the spaces or lengths or distances that are from the point B of the pin AB to every one of the three points of shadow CDF viz. the space from the point of the pin B to the point of shadow C the space from the same point of the pin B to the point of shadow D and the space again from the same point of the pin B to the point of shadow F. And for your better instruction if you will make these three lines visible to the eye set unto every one of them either a ruler or a string stretch'd out in a direct line from the point of the pin B to every one of the points of shadow CDF as the points do shew it unto you And so you may see the three lines BC BD BF which otherwise are invisible in the Air And besides these three spaces or lengths you have also found out the three spaces or lengths that are from every one of the three points of shadow CDF unto the other viz. the space from the point of shadow C to the point of shadow F the space from the point of shadow C to the point of shadow D and the spaces from the point of shadow F to the point of shadow D as you may see by the points that are there So you have six spaces or lengths BC BD BF CF CD DF which you have already found unmovable and fixed to the place wherein you intend to make your Dyal which are so great a furtherance unto your work that there remains nothing else to do but by the help and means of the said six spaces or lengths to find also three or four more that you may have all that is requisite for the placing of the Axeltree rod of your Dyal as it ought to be You must know that there are several wayes whereby these six spaces which you have found already viz BC BD BF CF CD DF are made use of to find out those three or four more which you must have to inable you to place the Axeltree rod of your Dyal as it must be And that of all those several wayes a man may have a liking to one for one reason and another man to an other for some other reason and of those several wayes Monsieur de Sargues hath shewed me three or four at the most viz. that which he hath set down in the figure of his model or project page and of the others for which you must know how to make sometimes somekind of alteration and which I have set down in short there is one in the sixth figure and another in the seventh As for this it is such that there is no occasion but you may practise it in effectually and with the like ease every where without you need either to add or alter any thing as you shall see presently Draw with the rule as you see in the figure below in some flat or even place a straight line BD FC then go to the figure above and open your Compasse and set one of the feet to the point B of the pin AB and the other foot to the point of shadow C and by that means you shall take with your Compasse the space or the lengths that are from the point of the pin B to the point of shadow C whereof you will be pleased to remember to the end that when I shall bid you for brevity sake take after the same manner with your Compasse such a space you may be able to do with your Compasse even as I told you just now of the space BC in the figure above Now with this space BC of the figure above come back to the figure below and set at your discretion one of the feet of the Compasse upon the straight line that you have drawn there as for example set it to the point B then turning the Compasse about upon this point B draw with the other foot a circular line CG which circle by this means shall have a space BC equal with the space BC of the higher figure and will meet the line BD for example in the point C. Go back again to the figure above take there after the same manner the space from the end or point of the pin B to the point of shadow D and with this space come back to the figure below and set again one of the feet of your Compasse to the point B and holding it still upon this point B draw with the other foot a second circular line DH that will be equal with the space above BD and that may meet the line BC for example in the point D. Go back again to the figure above and take with your Compasse the space betwixt the point of the pin B and the point of shadow F and with this space come back to the figure below set one of the feet of the Compasse to the point B and draw with the other foot a third circular line FE with the space BF of the figure above and that may meet the line BD for example in the point F. By this means you have set away and transported the three spaces BC BD BF from the rise or place which they had in the place of the Dyal above in a flat and even place below and all of them united together in one single line BDFC in which you may see whether those spaces be equal amongst themselves as they may be in some occasions which is indifferent or whether they be unequal by seeing whether the points CDF are united together two or three in one single point or whether they are disunited or
from the center of the half circle Q go razing or laying even the string 24. VI by making it longer or shorter as need requires as you see in O g mark many several points in the superficies of the Dyall one after an other as for example 24 g VI more or lesse according as the superficies of the Dyall is more or lesse uneven Draw an obscure line by the points 24 g VI and it will be a line of houres after the Italian or Babylonian way and so of all the rest The string h OH shews that you may if need be do the like both of one and of the other side of the center O to go and place of one part or other according to the occasion the line as 2 3 4 5. And if you have a straight line as might be O q which may turn about the center O and be perpendicular to the Axeltree BI and you hold the half circle with this straight line set one at a convenient or reasonable distance from the other And let it be alwayes exactly of the distance of six hours after the French way First of all this string describes the Equinoctial line in the superficies of the Dyall Secondly when one of the two either the half circle or the straight line O q is found in one of the points of the hours of the Equator th' other is likewise found in it in an other point of hour then drawing with a string coming from the center O a straight line that may go from the point as t to the end of the straight line O q which you shall go drawing with this string made shorter or longer as need requires and mark some points of line of hour after the Italian or Babylonian way in the superficies of the Dyall And for this purpose there is nothing so easie as to have a circle of Equator that may be fitted to the half circle and where you may have alwayes a space ready made for it's hour 25 To mark the houres after the Manner of the Iewes 24 for the houres after the Italian way Figure 25 To mark the hours after the manner of the Ancients or the Jewes YOu must know first that it would be very troublesome to draw in the superficies of the Dyall the lines of this kind of hours in such a manner as that they might be alwayes just and right in theory all the year long And therefore it is sufficient to draw them just by demonstration in three points onely viz in their points of both ends and of the middle which are the points of those circles that appear the greatest above the Horizon being parallel to the Equator and of the Equator it self The rest goes as it may and therefore it may be said that the lines of such hours traced in this manner are false in the rest of their length yet Curiositie makes them passe for current Wherefore to mark this kind of lines of hours The higher figure 4 shewes which way you must make this half Circle to turn about viz. about a straight axeltree line placed levell in the center of the Axel-tree of the Dyall And to be short set up and make very fast a rod in a straight line passing to the center O and let it be first within the joynt of the axeltree rod secondly let it be level as the figures do shew of a plummet P. and of a level A this being done tye some strings with a loose knot to this rod so levelled NL as you see NR and LT. Take the string from about the center O stretch it out in a direct or straight line from the center O to one of the points of hour after the French way of the Equinoctial line of the Dyall for example to the point of 1 hour as you see the string OI This string being thus strecht out take the other strings of one or th' other end NL and Crosse over this string OI with them and so go and mark many points in the superficies of the Dyall as TIR Draw an obscure line by those points as TIR it is a line of hours after the manner of the Ancients or the Jews do the like with the other hours and half hours of the Equinoctial line If you leave a rod in the Dyall as NOL the shadow thereof will go and shew these hours continually at length if you will not leave it in the button or center O of the axeltree of the Dyall will shew them 26 for the hight of the sun Figure 26. How to mark the Elevation of the Sun above the Horizon THE higher fig. 3. shews which way you must turn the half circle viz. about a straight axel-line hanging down right Set up your half circle so that it may turn like a weather-cock about a rod hanging down right or plum above or below the axeltree of the Dyal it matters not which VVhilest you turn it thus as it is above said cause in the mean time the string comming from the center O to passe by one of the degrees of the edge of the circle and make the string shorter or longer as need shall require mark with it many several points in the superficies of the Dyal according as you see them rankt one by an other in four places Draw a small or obscure line through all these points and this will be one of the lines of the Elevation of the Sun Count the Degrees in the edge of the circle beginning at the first of the beam which is level and ending at the 90. Beam which is down right or plum Mark in the line of the Dyal the number of the Degrees of the border of the circle where the string passes that hath mark't the points of that line and so of all the others and the shadow of the button of the axeltree which is in the center of the circle will shew the Elevation of the Sum above the Horizon Figure 27 How to mark the Sun rising or East rising of the Sun THE figure 2 above shews how you must place the half circle viz. parallel unto the Horizon I would not put a levell to it to avoid confusion It shews also that one of the Diameters of the circle must be set within the center of the Dyal that is to say thar it must go directly from the south to the North and accordingly the Diameter which is perpendicular to it will go from East to West When your circle is set fast in this position let a plummet op in the lower figure hang from the center O. This being done from each point of Degree of the edge of the circle as from x and from z. mark with a string XT or ZR many points in the superficies of the Dyal Draw a small or obscure line through these points as TY or SR. it is a line of the Suns Eastrising Mark in it the number of Degrees of the point of the circle from whence the string comes according as you will count them to begin either from the East or from the South And so of all the other Degrees accordingly And the shadow of the button O will shew which way the sight of the Sun comes upon the Dyal I will take here occasion to tell you that if for some reason or other you could observe in one and the same day but two shadows of the Sun in stead of three as we have said in the placing of the axeltree in the Dyal the declining of the Sun in that day will serve you for a third shadow or else two other shadows observed in an other day I mean you may find equally the placing of the axeltree by one or other of those ways above mentioned and with 3 shadows and with 2 shadows and the declining of the Sun in that day and with 4 shadows two of one day and two of an other which are three wayes that come all to one 27 for the Eastrising of the sun 28 Figure 28. I do not specifie in this volum these kinds of flat Dyals wherein you may work without knobs or middle rule And where you may draw the Equinoctial line trace out and divide the circle Equator in a word where you may do all yea and in the very superficies of the Dyal you may easily come to know them you self by putting this universall way into practice Here is onely a way how to trace out all the twelue lines of the hours equal after the French way in the flat Dyals where the axeltree meets the superficies athwart in the space that you work in so that you shall have no need of a greater place And what I have already said and what I am now going to say again will serve to find out the way to do the like in all kinds of Dyals universally When you have drawn upon your Dyal the Equinoctial line M 12 M drawn conveniently and divided the circle Equator Q 12 Q bring to the Equinoctial line the beam of the 12 hours Q 12. Draw of both sides of the Equator and from the Equinoctial line a straight line MQ parallel to the beam of 12. hours O 12. bring the beams of the other hours to the first which they shall find of the Equinoctial in rt and of MQ in c dâ—g Q Bring in the Dyal the line of the twelve hours B. 12. draw by the point M of the Equinoctial line and from the center of the Dyal B a straight line ML parallel to the line of twelve hours B 12 make upon this line ML and upon the point M a triangle LMN like to the triangle in the aire OB 12. and let the angles of these triangles in the points L and B be equal one unto an other Carry the spaces Mq Mg Md Mc from the straight line MQ into the straight line MN viz. from M into N into u into i into o bring by the points N u i o some straight lines NL ub if oh parallel to the side NL of the triangle LMN Carry from the center of the Dyal B by the points r t h f o L Some straight lines BL Bh Bf Bh Bt Br These are such lines of hours as you may continue beyond the center B and mark them according to their orders THE END i.e. That are made without any aim or heed
of the Dyal is all flat every line of the hours is a straight line And when the superficies of the Dyal is not altogether flat it may be that every line of hours is not all straight also To make one of those Dyals of equal hours after the French way by this universal way there are two things to be done one after another The first is to place the axeltree as it ought to be that is shooting out of the superficies of the Dyal The second is to draw the lines of the hours as they must be upon the same superficies And by means of this general way you shall do those two things without knowing in what day nor in what time of the year nor in what Country you are without knowing what the superficies of the Dyal is whether it is plain or rough nor which way it looks without knowing any thing concerning the making and the placing of the parts of the world or without any skill in Astronomy without any needle touch'd with the loadstone or any instrument or figure that may serve for a beginning towards the making of a Dyal But by the means only of the Beams of the Sun by one general rule you shall place the axeltree and draw the lines of those hours upon one of those Dyals whatsoever the superficies may be and which way soever it looks with all the celerity and exactnesse that is possible in art and if you are equally exact in every operation you shall make by this means many Dyals upon different superficies and turned towards several parts of the world which shall agree plainly among themselves and if you do not do it you may be sure that the fault is on your part and not in the rules since that others do succeed well in it There are some pieces that are requisite for the framing of a Dyal and whereof it is composed such are the axel-tree rod with its supporters There are other pieces that must be used in the making of a Dyal as Rules Compasses a Squirt a lead with his two frames one to mark with and the other to level There are some other things that you shall use also as pegs and rods either of yron or of brasse or of wood some sharp at both ends the others sharp at one end only a table either of wood or of slate or of any other stuff flat and solid to draw upon if need be some straight lines with the rule and in case the superficies of the Dyal were plain and even you must use some fine strings supple and strong some mastick cement or plaster or such like stuff fit to seal with c. all which things you must have in readinesse whensoever you will go about the making of a Dyal And though you would learn to make but one of these Dyals well it is fit you should have some models of all those pieces and when you are upon those chapters that concern them as you shall understand an Article it will be requisite that with the models of those pieces you work at the same time an actual model of the thing which that article shall teach you to do and so you must work from one end to another till you have at last every way compleated an actual model of this kind of Dyals and you shall need to make but few of such models of Dyals upon any superficies turned towards several parts of the world to bring you acquainted with the practice of making Dyals to the life or after the natural in what kind or odd situation of superficies soever they may be Lastly you shall find the precepts and the descriptions to be more troublesome than the actual making or working study only to be as exact in every one of these operations of making of these Dyals as in the practice of other Arts The Epistle to the READER Courteous Reader THis Treatise being originally written in French and generally approved of all those that have any skill in the Art of Dyalling I have thought it my duty to lay hold upon this occasion to shew how desirous I have ever been to procure any good unto my Country Therefore I have caused it to be carefully translated into English and have set it forth for the good and utility of all such as are curious and true lovers of that Art Reputing my self most happy to meet with any occasion whereby I may contribute any thing towards the advancement of learning and of the publick good Non enim nobis solum nati sumus We are not meant to be wholely and soly for our selves As for the work it self I am so confident it will so gain the attentive Readers approbation as that I shall forbear to say any more in commendation of it than that it is an expedite and sure way of obtaining the site of the Axis and of other requisites in the framing of all sorts of Dyals of no lesse curiosity than use performed without the ordinary rules and presupposals of the spiritual calculations and practice I need premise no more but advise to follow the directions that are set down through all the book for effecting that which is promised and thou shalt see the same plainly and readily performed Accept then Courteous Reader this small labour the undoubted Testimony of my Love as kindly as I offer it cordially unto thee hoping that God will enable me to give thee hereafter some thing of more consequence So Farewell Vtere fruere Thine D. K. To all Lovers of Ingenious Practices THe French have excelled all other Nations in the Art of Perspective for this last Age their many Books and curious Writings so excellently composed do witnesse for them Dyalling I accompt one kind of Perspective for that glorious Body the Sun the Eye of the world traceth out the lines and hour-points by his Diurnal Course and upon the resubjected Plane by the laws of Picture Scenographically delineates the Dyal Many have writ upon this subject of several Countryes in several Ages many are the Rules and Practices set down But among all those of forein Parts none hath performed the same with more ease and lesse trouble than Monsieur du Sargues the Author as wholy laying aside those tedious observations of Azimuth's Declination Reclination Inclination Meridian Substile c. and performing the operation only by three observations of the Suns shadow from a Point It will not be amisse to give the Reader a small consideration hereof the point B of the pin AB in all the figures is alwayes one part of the Axis or Gnomon of the Dyal and may be used to shew the hour this point B you must imagine to be the Center of the Earth for the vast distance to the Sun maketh the space betwixt the Center and superficies of the Earth to be insensible and from it at all times of the year excepting the Aequinoctial day the Sun in its course forms two Cones whose Apex is the point
have opened your Compasse and set one foot upon one of the stroaks and the other upon the other stroak And moreover that the points NR may well come out from betwixt the points D and H and that I have caused them to come in so betwixt them by reason of the smallnesse of the place and what way soever they come to be disposed it is but one and the same thing still Fig. 9 To the workmen of many sorts of Arts SEt your Compasse upon the points D and H of the higher figure and with that space go to some flat or even place in the lower figure and make two points D and V so that the space DV below may be even with the space DH above Then go to the figure above and set your Compass upon the points D and R and with this space come back to the figure below and set one foot of the Compasse to the point V and with the other foot draw a line from the point D to the point G so that the space VG below may be even with the space DR above Go back again to the figure above and set your Compass to the points D N and with this space come back to the lower figure set one foot of the Compass to the point D and with the other foot draw a line from the point V to the point G so that the space DG below may be even with the space DN above and may meet in G the other circular line that you have drawn about the point V for it must meet with it And so you have made in the lower figure three points VGD that will be perdus or lost Now find a center O upon which having set one of the feet of the Compass and the other upon D let this foot in turning the Compass about go and passe by those three points perdus VGD then draw with the rule by the points as it were O and D a line DOE and setting again one foot of the Compass to the point O and turning the other foot to E make in the line DOE the side OE even with OD. Then by the point O draw a line QOP that may cut the line DOE in two equal parts again set your compass to the points B and D of the figure above and with this space go to the figure below set one foot of the compass to the point D with the other foot draw from the point E a line B that may meet as it were in the point B the line QOP and make with this other foot of the compass a point B in the line QOP for it must meet with it if you have done exactly 9 9 When the dayes and the nights are equal it meets with it in one point alone viz. O and at some other times it meets in two points one of one side of the O and the other on the other side as in the point E. Then remove your Compass out of his place and with the same space of the points B and D of the figure above set one foot of the Compass to the point E and with the other foot draw from the point D with your Compass another line B that may go and meet the line QOP with the line that you have traced with the Compass about the point D and both of them in one and the same point B for it must do it if you have been exact And that serves to mark more exactly this point B in the line QOP how neer soever it is to the Point O. After that Whether the Point B of the lower figure meets with the Point O or not draw with the rule by the points B and D the line BD and draw this line BD as you see beyond the point D. That being done open your Compass upon the points B and C of the higher figure and carry this space to the line BD of the lower figure and from B into C. Set your Compass again upon the points B and F of the higher figure and bring this space to the line BD of the lower figure and from B into F. And finally make in the line QOP a point I at your discretion of one side or other of the point B and let it be as far distant from the point B as occasion will give you leave And so you have in this lower figure from the point I to every one of the points BDFC all the measures that are necessary for the placing of the axeltree or needle in your Dyal in the manner hereafter following Figure 10 To the workmen of many sorts of Arts CUt three rods or sticks sharp at both ends as you see below one CI of the length that is betwixt the point C and the point I of the figureâ— above the other FI of the length that is betwixt the point F and the same point I of the higher figure the other DI of the length that is betwixt the point D to the same point I of the higher figure then open your compasse upon the points B and I of the higher figure and bring down this space upon the Axeltree rod and make in the same as you see two points B and I with this same space BI of the figure above 10 11 Figure 11 To the workmen of many sorts of Arts GOe to the place of the Dyal below which I have expressed again a purpose to avoid the confusion of lines and put the end of the rod CI to the point of shadow C the end F of the rod FI to the point of shadow F and the end D of the rod DI to the point of shadow D and set the point B of the Axeltree rod to the point B of the pin AB Then bring together into one point in the Air I the three other ends of the three rods CI DI FI for they must come in there together and bring the point I of the Axeltree rod to the same point I in the Air together with the three other ends of the rods I for these four things must come alltogether into one and the same point in the Air I if so be you have been exact in working And when these three ends of the rods and the point I of the Axeltree rod are all four gathered together into one and the same point in the Air I the Axeltree rod will come to be placed directly as it must be in the Dyal and so you need no more but to make it fast in that place or to fasten an other either near it or farr from it that may be even with it or parallel to or equally distant from it If the four points I should go and meet in the body of the Dyal you must but take in it's figure the point I nearer or in the other side of the point B and make an end of the rest as I have said 8 Figure 8 I will say the same thing over again but more at large To
from the point O two other circles that may meet in two points with the two circles that you have drawn about the point D and as for example in the two points Q and P and draw with the rule by these two points as Q and P a long straight line QP that must reach to the point O if you have been very exact in the working if it doth not reach to it you have not been very exact and I advise you to begin it again If it reaches to it go back to the figure below and take with the compass the distance between B and D then with this space go to the figure below set one foot of the compass upon the point D and turning it about draw with the other foot from the point O a circle that may meet the line QOP as for example in the point B for this other foot of the compass must go and meet that straight line POQ either in one or in two points because the space from B to D of the higher figure ought never to be smaller or lesser than the space DO of the figure above It is true that twice in the year viz. in Autumne and in the Spring when the dayes and nights are equal that space BD of the figure above comes to be equal with the space DO of the figure below and in those times that other foot of the Compasse that tutns about the point D of the figure below meets the line QOP just in the point O. But at all other times the space BD of the figure above is somewhat bigger than the space DO of the lower figure And then the other foot of the Compasse that turns about the point D meets the line QOP in two points one of each side of the point O as for example in B for one And that you may be the more exact remove the Compasse from one part of the straight line BO unto the other and with the same opening of the space BD of the higher figure set one of the feet upon the point E of the figure below and turning this foot upon this point E draw with the other and from the point D an other circle that will meet if you have been exact in the working the straight line QOP and the circle also that you have drawn about the point D and both in one point as for example in the point B which will inable you to discern well the point B in the straight line POQ mark this point B in the line POQ whether you find it united with the point O and so both of them making but one and the same point as it falls out when the days and nights are equal or whether you find it divided from the point O as it falls out in other seasons and as you see in this example Then draw with the rule by these two points B and D a straight line BD which you shall stretch out sufficiently beyond the point D. When the days and nights are equal as in Autumne and in the Spring and that the point B is found to be united with the point O the line BD comes likewise to be united with the line OD and both together make but one line But at any other time as the two points B and O are two several points and divided one from the other so the two lines BD and OD are two several lines and divided one from the other This being done go to the figure above meaâ—ure with your Compasse the space from B to C and with this space go to the figure below set one foot of the Compasse upon the line BD to the point B and set the other foot in any place of the same line BD where it may light upon as for example in the point C by this means you shall make the portion BC of the line BD of the lower figure equal with the portion BC of the line BD of the higher figure make after the same manner with the Compasse the portion BF of the line BD of the lower figure equal to the Portion BF of the line BD of the figure above Finally in the same figure below and in the line QOP mark at your discretion another point I of one side or other of the point B according as you shall find it most convenient for the place of the Dyal and as far from this point B as occasion will permit the further the better and so you have found the four spaces that you wanted for the perfect placing of the Axeltree of your Dyal For in so doing you have found in this figure below the distances that are from every one of the four points BDF C to one and the same point I that is to say the space from B to I the space from D to I the space from F to I and the space from C to I which distances BI DI FI and CI will serve you to place the Axeltree of the Dyal in the manner following Figure 10 To all sorts of People CUt as you see in the lower figure three sticks sharp it both ends one CI of the length of the point C to the point I otherwise of the space CI of the figure above The other FI of the length of the space FI of the higher figure and take with your Compasses the space BI of the figure above and being so open see both feet at once upon a straight line along the Axeltree rod of the lower figure for example in two points as B and I and mark these two points B I in the Axeltree rod 10 11 Figure 11 To all sorts of People THat being done go to the place of the Dyal the which to avoid the confusion or multiplicity of lines I have set below in the lower figure set in this lower figure one of the ends of the stick CI to the point of shadow C one of the ends F of the stick FI to the point of shadow F and one of the ends D of the stick DI to the point of shadow D and one of the points B of the Axeltree rod set it to the point B of the pin AB And holding thus the three ends CDF of the three sticks to the points of shadow CDF every one respectively to his own and the point B of the Axeltree rod to the point of the pin B bring together the three other ends I of the three sticks or rods CI DI FI into one point in the air I for they must meet there then bring the point I of the Axeltree rod also to the point in the air I with the three ends I of the sticks for it must come and meet there exactly if you have done right or if the straightnesse of the place hath not hindered you If the straightnesse of the place of the Dyal hinders the three ends I of the sticks from meeting together in one point in the air I take the point I in the figure below in
your Dyal is the shadow of the pin comes to be of such a length and the extremity or end thereof so weakned and so diminished in strength and so confuse in the superficies of the Dyal that it is very hard to find out Figure 13 To all sorts of People I come now to the next and second thing that you are to do which is to trace out the lines of the hours IN this example I suppose that the Axeltree rod doth not meet the superficies of the Dyal about the place that you work in and therefore I represent it suspended in the air with two or three supporters as you see I suppose also that the superficies of the Dyal is not smooth but rough and uneven as I have said When you have placed the Rod BI which is the Axeltree of the Dyal as you see both in the higher and lower figure you have made an end then of the first of those two things that you were to do for the making of your Dyal Now there remains but the second to be done which is the finding and the tracing out of the lines of the hours in the Dyal and for that purpose Consider in your higher figure that the superficies and the axeltree of your Dyal are two divers things and differing one from an other and there is no such communication from the one to the other as that with them alone you may find out directly the place of the lines of the hours without making use of a third thing that may be a means betwixt those two The meanest and the least thing that you can have to be a means betwixt the superficies and the axeltree of the Dyal is a Ruler 13 To the end that this middle rule may serve you alike in all occasions it must have all the conditions that you see represented in the figure below First it must be as long as the place will give you leave and it must crosse over if need be the whole superficies of the Dyal and reach over on both sides if it be possible Secondly it must be in the air and suspended between the superficies and the axeltree of the Dyal Thirdly it must be placed as far from the axeltree rod as possible may be Fourthly it must be placed like a crosse in regard of the same axeltree rod Figure 14 To all sorts of People TO place this middle rule well and as it ought to be betwixt the superficies and the axeltree of the Dyal Chuse along the axeltree rod BI of the higher figure some fit or convenient place as in the point O and make a round and fixed stay in that place by winding or tying some strong thing about this axeltree rod as the figure doth shew Tye a string to the axeltree rod BI by the means of a ring that may be so big that you may turn the string with it about the axeltree rod easily as the lower figure shews you Then with the corner of a squire ED in the lower figure thrust on the ring where the string is and put it close to this stay O and holding the string fast between the stay O and the squire ED set the back of one of the sides OE of this squires length to the axeltree rod BI and by this means the other side DO of this squire will shoot out into the air like a wing from the axeltree rod BI then stretch out the string in a straight line from the stay O of the axeltree along the back of the other side OD of the squire And holding still in this manner the ring close to the stay of the axeltree by means of the squire and the back of one of the sides joyned at length to the axeltree rod and the other side of the squire like a wing and the string stretcht out in a straight line along this wing turn both the squire and the string altogether still in this same manner about the axeltree rod as the lower figure doth shew 14 When you have found out those two places that are farthest one from another in which this string turning in this manner with the squire along the side like a wing may go and meet the superficies of the Dyal as here the places G and H. Make with mastick or plaster or cement or such like stuff a little knob flat at the top in each of these places as for example one in G and another as in H which two knobs may shoot out of the superficies of the Dyal in such sort that you may lay a Ruler on the top of them going from one of the knobs to the other as you see here in the lower figure 15 Figure 15 To all sorts of People VVHen you have thus made those two knobbs G H in the lower figure take the squire again and the string and set them again close to the stay O of the axeltree rod as you know they were And make them go about again as before both together about the axeltree BI and while you are turning about the string will fall right over against the two knobs shorten or lengthen it so that it may go and touch a point at the top of each one of the two knobs one after another viz. a point as P at the top of the knob G and a point as Q at the top of the knob H and mark these two points Q and P upon these two knobs When you have mark'd two points in this manner set a Ruler in the lower figure upon these two knobs and place it so that it may passe from one to the other by those two points Q and P and make the Ruler fast in this place with cement or plaster or the like in such wise that it may not stir any way And this rule so placed is the third and middle piece between the superficies and the axeltree of the Dyal by means whereof you shall cause as I shall say hereafter this superficies and this axeltree to have what communication soever you please one with another After you have placed this middle rule in this manner between the superficies and the axeltree of the Dyal Consider that in France now they reckon 34 hours for one day and a night and that these 24 hours are divided in twice twelve hours and that every one of these 12 hours is subdivided in twice 6 hours So that in the 24 hours of one day and one night as they are now reckoned in France there are two hours that are each of them of 12 that is to say one hour of 12 in the middest of the night and another hour of twelve in the middest of the day these two hours of 12 are called midnight and midday then there are two other hours each of them of 6. viz. an hour of 6 in the evening and another of 6 in the morning Where you must note that both the two hours of 12 and the two hours of 6 come alwayes to meet together in
it is the point of one of the hours of 6 as the point 6 〈◊〉 you shall go on in finding out the points of the other hours which may be found in your Dyal in this manner following Figure 17 To all sorts of People MArk at your discretion in the rule PQ two several points MN and consider the point in the middle of the body of the axeltree close by the stay O that is the Point about which you have turned the string with the corner of the squire You see there three several points unmoveable and fixed viz. the point M and the point N in the middle rule and the point O in the middle of the body of the axeltree rod close to the stay And so having those three points fixed M N O you have by this means the three several distances viz. the measures of the distances that are from one of these three points to the two others viz. the space or distance from the point M to the point N the distance from the point M to the point O and the space from the point N to the point O. Remember two things one is that the point O is in the middle of the body that is to say of the bignesse and not in the out side of the axeltree rod The other is that these two points MN that you have mark'd at discretion in the middle rule are not for all that certainly the points of hour and that they are to serve you to find out the points of hour and perhaps they may chance to be some of them and may be not and perhaps you must blot them out after you have found out the points of hour This being done so take with your Compasse upon the middle rule the distance from the point M to the point N and with this space go to some place that is flat or smooth and set both the feet of your Compasse therein at once as in the figure below in the points M and N and by these two points draw a straight line MN as long at either end as the rule PQ Then go back to the Dyal above take with the Compasse the distance which is from the posnt M to the middle of the bigness of the axeltree close by the stay O or else otherwise take the distance which is from the point M to the axeltree towards the stay O and adde unto it half of the bigness of the Axeltree and with this space MO come back to the figure below set one of the feet of the Compasse to the point M and turning this foot about upon this point M trace with the other foot a line crooked like a bow O go back to the figure above take again with your Compass the distance which is from the point N to the middle of the bigness of the axeltree close by the stay O and with this space come back to the lower figure set one of the feet of the Compass to the point N and turning this foot upon this point N trace with the other foot another crooked line that may meet with the other in one point as O for it must meet with it Then open yout Compass at discretion rather more than lesse and set one of the feet of the Compass so open at discretion to the point O and turning this foot of the Compass upon this point O trace with the other foot a round RGSH Go back to the Dyal in the figure above take with your Compass upon the rule QP the distance which is from one of the points M or N to the point of 6 hours and with this space for example of M6 come back to the lower figure set one of the points or feet of the Compass upon this point M go and mark with the other foot in the line M a point as 6 of the same side upon the rule And so you have in the line MN one and the same thing as you have in the Dyal in the middle rule viz. the three points MN and 6 of the same distance in each of these two straight lines This being done draw in the figure below by the two points O and 6 a straight line O 6 which may divide the round RGSH in two halfs RGS and RHS. Open the Compass at your discretion and as much as the space will give you leave and keeping your Compass so open at discretion set one of the feet to the point S and turning this foot upon this point S trace with the other foot two crooked lines L and D then with the same space remove your Compass out of his place and set one of the feet to the point R and turning this foot about upon this point R trace with the other foot two other crooked lines that may meet in two points L and D the two crooked lines that you have drawn about the point S and mark those two points L and D and draw by those two points a straight line LD which may passe by the point O if you have been exact in your operations So you have divided this round into four quarters of a round with the two straight lines SOR LOD and if the straight line LOD drawn in length comes to meet the line MN in a point as 12 it shews that there is also the point of the hours of 12 in your Dyal viz. in the middle rule between the superficies and the axeltree now divide with your Compass every one of these quarters of the round into six parts equal as you see in the points that are upon the brim of the round RGSH and by the center or middle point of this round O and by every one of the points of these divisions of the edge or brim of the round draw some lines or beams as you see some drawn already that may go and meet the straight line MN as in the points 5 4 3 2 1 11. and these points are the points of the other hours that are to be found in your Dyal 18 17 Figure 18 To all sorts of People NOw take with the Compass in the figure above the space from 6 to 5 and with this space go to the Dyal in the figure below set one of the feet of the Compass to the point 6 and keeping this foot of the Compass upon this point 6 go and mark with the other foot in the middle rule another point 5 and by this means you shall transport with your Compass the space 6 5 â—â—rom the line of the figure above which represents your table or the flat place in the Dyal of the figure below upon the middle rule MN so accordingly take with your Compass every one of the other spaces 5 4 4 3 3 2 2 1 1â— 12 11 from the higher figure and bring them in this manner to the Dyal upon the middle rule in the lower figure and so you have done in this middle rule in the Dyal of the lower figure all and the same spaces