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A89305 Horlogiographia optica. Dialling universall and particular: speculative and practicall. In a threefold præcognita, viz. geometricall, philosophicall, and astronomicall: and a threefold practise, viz. arithmeticall, geometricall, and instrumentall. With diverse propositions of the use and benefit of shadows, serving to prick down the signes, declination, and azimuths, on sun-dials, and diverse other benefits. Illustrated by diverse opticall conceits, taken out of Augilonius, Kercherius, Clavius, and others. Lastly, topothesia, or, a feigned description of the court of art. Full of benefit for the making of dials, use of the globes, difference of meridians, and most propositions of astronomie. Together with many usefull instruments and dials in brasse, made by Walter Hayes, at the Crosse Daggers in More Fields. / Written by Silvanus Morgan. Morgan, Sylvanus, 1620-1693.; Goddard, John, fl. 1645-1671, engraver. 1652 (1652) Wing M2741; Thomason E652_16; ESTC R202919 57,946 133

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ponderosity or a center of rotundity if it be a seeming point that is increased or diminished according to the ocular aspect as being somtime neerer and somtime farther from the thing in the visuall line the thing is made more or lesse apparent A center of magnitude is an equal distribution from that point an equality of distribution of the parts giving to each end alike and to each a like vicinity to that point or center A center of ponderosity is such a point in which an unequall thing hangs in equi libra in an equall distribution of the weight though one end be longer or bigger than the other of the quantity of the ponderosity A center of rotundity is such a center as is the center of a Globe or Circle being equally distant from all places Now the earth is to be understood to be such a center as the center of a Globe or Sphear being equally distant from the concave superficies of the Firmament neither is it to be understood to be a center as a point indivisible but either comparatively or optically comparatively in respect of the superior Orbs Optically by reason of the far distance of the one from the earth as that the fixed Stars being far distant seeme by the weaknesse of the sense to be conceived as a center indivisible when by the force and vigour of reason and demonstration they are found to exceed this Globe of earth much in magnitude so that what our sense cannot apprehend must be comprehended by reason As in the Circles of the Coelestiall Orbs because they cannot be perceived by sense yet must necessarily be imagined to be so Whence it is observable that all Sun Dials though they stand on the surface of the earth doe as truly shew the houre as if they stood in the center CHAP IV. Declaring what reason might move the Philosophers and others to think the Earth to be the center and that the World moves on an axis circa quem convertitur OCular observations are affirmative demonstrations so that what is made plain by sense is apparent to reason hence it so happeneth that we imagine the Earth to move as it were on an axis because both by ocular and Instrumentall observation in respect that by the eye it is observed that one place of the Skie is semper apparens neither making Cosmicall Haeliacall or Achronicall rising or setting but still remaining as a point as it were immoveable about which the whole heavens are turned These yet are necessary to be imagined for the better demonstration of the ground of art for all men know the heavens to be supported only by the providence of God Thus much for the reason shewing why the World may be imagined to be turned on an Axis the demonstration proving that the earth is the center is thus not in maintaining unlikely arguments but verity of observation for all Gnomons casting shadow on the face of the earth cast the like length or equality of shadow they making one the same angle with the earth the Sun being at one and the same angle of height to al the Gnomons As in example let the earth be represented by the small circle within the great circle marked ABCD and let a Gnomon stand at E of the lesser Circle whose horizon is the line AC and let an other gnomon of the same length be set at I whose horizon is represented by the line BD now if the Sun be at equall angles of height above these two Horizons namely at 60 degrees from C to G and 60 from B to F the Gnomons shall give a like equality of shadows as in example is manifest Now from the former appears that the earth is of no other form then round else could it not give equality of shadows neither could it be the center to all the other inferior Orbs For if you grant not the earth to be the middle this must necessarily follow that there is not equality of shadow For example let the great Circle represent the heavens and the lesse the earth out of the center of the greater now the Sunne being above the Horizon AC 60 d. and a gnomon at E casts his shadow from E to F and if the same gnomon of the same length doth stand till the Sun come to the opposite side of the Horizon AC and the Sun being 60 degrees above that Horizon casts the shadow from E to H which are unequall in length the reason of which inequality proves that then it did not stand in the center and the equality of the other proves that it is in the center Hence is also most forceably proved that the earth is compleatly round in the respect of the heavens as is shewed by the equality of shadows for if it were not round one and the same gnomon could not give one and the same shadow the earth being not compleatly round as in the ensuing discourse and demonstration is more plainly handled and made manifest And that the earth is round may appeare first by the Eclipses when the shadow of the earth appeareth on the body of the Moon darkning it in whole or in part and such is the body such is the shadow Again it appears to be round by the orderly appearing of the Stars for as men travell farther North or South they discover new Stars which they saw not before and lose the sight of them they did see As also by the rising or setting of the Sun or Stars which appear not at the same time to all Countries but by difference of Meridians and by the different observations of Eclipses appearing sooner to the Easterly Nations then those that are farther West Neither doe the tops of the highest hils nor the sinking of the lowest valleys though they may seeme to make the earth un-even yet compared with the whole greatnesse doe not at all hinder the roundnesse of it and is no bigger then a point or pins head in comparison of the highest heavens Thus having run over the Systeme of the greater WORLD now let us say somthing of the Compendium thereof that is MAN CHAP V. Of Man or the little World MAn is the perfection of the Creation the glory of the Creator the compendium of the World the Lord of the Creatures He is truly a Cosmus of beauty whose eye is the Sunne of his body by which he beholds the never resting motions of the heavens contemplatively to behold the place of motion the place of his eternall rest Lord what is man that thou shouldest be so mindefull of him or the son of man that thou so regardest him thou hast made a World of wonder in his face Thou hast made him to be a rationall creature endowed him with reason so that his intellect becomes his Primum mobile to set his action at work nevertheles man neither moves nor reigns in himselfe and therefore not for himselfe but is born not to himselfe but for his Countrey therefore he ought to employ
divided into 360 degrees between the open ends and the angle it self is the Center of the Circle The quantity of a Solid consists of length breadth and thickness the form is various regular or irregular The five regular or Platonick Bodies are the Tetrahedron Hexahedron Octohedron Dodecahedron Icosahedron Tetrahedron is a Solid Body consisting of four equall equilaterall Triangles A Hexahedron is a Solid Body consisting of six equal Squares and is right angled every way An Octahedron is a Solid Body consisting of eight equal Equilaterall Triangles A Dodecahedron is a Solid Body consisting of 12 equall Pentagons An Icosahedron is a Solid Body consisting of 20 equal Equilaterall Triangles All which are here described in plano by which they are made in pasteboard Or if you would cut them in Solid it is performed by Mr. Wells in his Art of Shadows where also he hath fitted planes for the same Bodies A Parallel line is a line equidistant in all places from another line which two lines can never meet A Perpendicular is a line rightly elevated to another at right angles and is thus erected Suppose AB be a line and in the point A you would erect a perpendicular set one foot of your Compasses in A extend the other upwards anywhere as at C then keeping the foot fixed in C remove that foot as was in A towards B till it fall again in the line AB then if you lay a Ruler by the feet of your Compasses keep the foot fixed in C and turn the other foot toward D by the side of the Ruler and where that falls make a marke from whence draw the line DA which is perpendicular to AB And so much shall suffice for the Praecognita Geometricall the Philosophicall followeth The end of the Praecognita Geometricall THE ARGVMENT OF THE Praecognita Philosophicall NOt to maintain with nice Philosophie What unto reason seems to be obscure Or shew you things hid in obscurity Whose grounds are nothing sure 'T is not the drift of this my BOOK The world in two to part Nor shew you things whereon to looke But what hath ground by Art If Art confirm what here you read Sure you 'l confirmed be If reason wonte demonstrate it Learn somwhere else for me There 's shew'd to you what shadow is And the Earths proper place How it the middle doth possesse And how heavens run their race Resolving many a Proposition Which are of use and needfull to be known THE PRAECOGNITA PHILOSOPHICAL CHAP I. Of Light and Shadows HE that seeketh Shadow in its predicaments seeketh a reality in an imitation he is rightly answered umbram per se in nullo praedicamento esse the reason is thus rendred as hath been it is not a reality but a confused imitation of a Body arising from the objecting of light So then there can be no other definition then this Shadow is but the imitation of substance not incident to parts caused by the interposition of a substance for Umbra non potest agere sine lumine And And it is twofold caused by a twofold motion of light that is either from a direct beam of light which is primary or from a secondary which is reflective hence it is that Sun Dials are made where the direct beams can never fall as on the seeling of a Chamber or the like But in vain man seeketh after a shadow what then shall we proceed no farther surely not so for qui semper est in suo officio is semper orat for there are no good and lawful actions but doe condescend to the glory of God and especially good and lawfull Arts And that shadow may appear to be but dependant on light it is thus proved Quod est existit in se id non existit in alio that which is and subsisteth in it selfe that subsisteth not in another but shadow subsisteth not in it selfe for take away the cause that is light and you take away the effect that is shadow Hence we also observe the Sun to be the fountain of light whose daily and occurrent motions doth cause an admirable lustre to the glory of God seeing that by him we measure out our Times Seasons and Years Is it not his annuall revolution or his proper motion that limits our Year Is it not his Tropicall distinctions that limits our Seasons Is it not his Diurnall motion that limits out our Dayes and Houres And man truly that arch type of perfection hath limited these motions even in the small type of a Dyall plane as shall be made manifest in things of the second notion that is Demonstration by which all things shall be made plain CHAP II. Of the World proving that the Earth possesseth its own proper place WE have now with the Philosopher found out that common place or place of being that is the World will you know his reason 't is rendred Quia omnia reliqua mundi corpora in se includit I 'le tell you of no plurality not of planetary inhabitants such as the Lunaries lest you grabble in darkness in expecting a shadow from the light without interposition for can the light really without a substance be its own Gnomon surely no neither can we imagine our earth to be a changing Cynthia or a Moon to give light to the Lunary inhabitants For if our Earth be a light as some would have it how comes it to passe that it is a Gnomon also to cast a shadow on the body of the Moon far lesse then it selfe and so by consequence a greater light cannot seem to be darkned on a lesser or duller light and if not darkned no shadow can appear But from this common place the World with all its parts shall we descend to a second grade of distinction and come now to another which is a proprius locus and divide it into proper places considering it as it is divided into Coelum Solum Salum Heaven Earth Sea we need not so far a distinction but to prove that the earth is in its own proper place I thus reason Proprius locus est qui proxime nullo alio interveniente continet locatum but it is certain that nothing can come so between the earth as to dispossesse it of its place therefore it possesseth its proper place furthermore ad quod aliquid movetur id est ejus locus to what any thing moves that is its place but the earth moves not to any other place as being stable in its own proper place And this proper place is the terminus ad quem to which as the place of their rest all heavie things tend in quo motus terminantur in which their motion is ended CHAP III. Shewing how the Earth is to be understood to be the Center A Center is either to be understood Geometrically or Optically either as it is a point or seeming a point If it be a point it is conceived to be either a center of magnitude or a center of
himselfe in such Arts as may be and prove to be profitable for his Countrey Man is the Atlas that supports the Earth A perfect World though in a second birth I know not which the compleat World to call The senslesse World or man the rationall One claims compleat in bignesse and in birth Saith she 's compleat for man was last brought forth Man speaks again and stands in his defence Because he 's rationall hath compleat sense Nature now seeing them to disagree Sought for a means that they united be Concluded man that he should guide the Sphears Limit their motion in Dayes and Moneths and Years He thinking now his Office not in vain Limits the Sun unto a Diall plain Girdles the World in Circles Zones and Climes To shew his Art unto the after times Nature that made him thus compleat in all To please him more him Microcosmus call A little world only in this respect Of quantity and not for his defect Pray Gentle Reader view but well their feature Which being done pray tell me who 's the greater For he hath given me certain knowledge of the things that are namely to know how the World was made and the operations of the Elements the beginning ending and midst of times the alteration of the turning of the Sun and the change of Seasons the circuite of years and position of Stars Wisd. 7. 17. The ende of the Praecognita Philosophicall THE ARGVMENT OF THE Praecognita Astronomicall YOu 'r come to see a sight the World 's the stage Perhaps you 'l sayt's but a Star-gazing age What come you out to see one use an Instrument Can speculation yeild you such content That you can rest in learning but the name Of Pegasus or of swift Charleses Wane And would you learn to know how he doth move About his axis set at work by Jove If you would learn the practice read and then I need not thus intreat you by my pen To tread in Arts fair steps or to attain the way Go on make haste Relinquent do not stay Or will you scale Olympick hils so high Be sure you take fast hold ASTRONOMIE Then in that fair spread Canopie no way From thee is hid no not Galezia They that descend the waters deepe doe see Gods wonders in the deepe and what they be They that contemplate on the starry skie Do see the works that he hath fram'd so high Learn first division of the World and how 'T is seated I doe come to shew you now THE PRAECOGNITA ASTRONOMICAL CHAP I. Of the division of the World by accidentall scituation of the Circles COSMUS the World is divided by Microcosmus the little World into substantiall and imaginary parts Now the substantiall are those materiall parts or substance of which the World is compacted and made a Body by the inter-folding of one Sphear within another as is the Sphear of Saturn Jupiter Mars Sol c. And these of themselves have a gentle and proper motion but by violence of the first mover have a racked motion contrary to their own proper motion whence it appears that the motion of the heavens are two one proper to the Sphears as they are different in themselves the other common to all By Phebus motion plainly doth appear How many dayes doe constitute one yeare Will you know how many days doe constitute a year he telleth you who saith Ter centum ter viginti cum quinque diebus Sex horas neque plus integer Annus habet Three hundred sixty five dayes as appear With six houres added make a compleat Year The just period of the Suns proper revolution Perpetuus Solis distinguit tempora motus The Imaginary part traced out by mans imagination are Circles such is the Horizon the Equator the Meridian these Circles have of themselves no proper motion but by alteration of place have an accidentall division dividing the World into a right Sphear cutting the parallels of the Sun equally or oblique making unequall dayes and nights whence two observations arise First Where the parallels of the Sun are cut equally there is also the dayes and nights equall Secondly Where they are cut oblique there also the dayes and nights are unequall The variety of the heavens are diversly divided into Sphears or severall Orbs and as the Poets have found out a Galazia the milkie way of Juno her brests or the way by which the gods goe to their Palaces so they will assigne to each Sphear his severall god Goddesse of Heralts Caliope in the highest Sphears doth dwell Astrologie Amongst the Stars Urania doth excell Philosophie Polimnia the Sphear of Saturn guides Gladnesse Sterpsicore with Jupiter abides Historie And Clio raigneth in mans fixed Sphear Tragedic Melpomine guides him that gvids the year Solace Yea and Erata doth fair Venus sway Loud Instruments Mercury his Orbe Euturpe doth obey Ditty And horned Cynthia is become the Court Of Thalia to sing and laugh at sport Where they take their places as they come in order The Sphear is said to be right where the Poles have no elevation but lie in the Horizon so that to them the Equinoctiall is in the Zenith that is the point just over their heads The Sphear is oblique in regard of its accidentall division accidentally divided in regard of its orbicular form orbicular in regard of its accidentall equall variation orbicular it appears before in the Praecognita Philosophicall his equall variation is seen by the equall proportion of the earth answering to a Coelestiall degree for Circles are in proportion one to another and parallel one to another are cut equally so is the earth to the heavens having considered them as before we will now consider another sort of Sphear which is called parallel This parallel Sphear is so that the parallels of the Sun are parallel to the Horizon having the Poles in their Zenith being the extream intemperate colde and frozen Zone Ovid in his banishment complaines thus thereof Hard is the fright in Scythia I sustain Over my head heavens Axis doth remain CHAP II. Of the Circles of the Horizon the Equator and the Meridian THe greatest Circle of a Sphear is that which divides it in two equall parts and that because it crosseth diametrically and the diameter is the longest line as can be struck in a Circle and therefore the greatest which great Circles are represented in the following figure representing the Circles of a Sphear in an oblique Latitude according to the Latitude or elevation of the Pole here at London which is 51 deg. 32 min. being North Latitude because the North Pole is elevated The Horizon is a great Circle dividing the part of heauen seen from where we imagine an Antipodes the inhabitants being to us an Antipheristasin our direct opposites so that while the Sun continues visible to us it is above our Horizon and so continues day with us while it is night with our opposites and when the Sun goes down with us it appears to