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book_n	good_a	work_n	write_v	2,667	5	5.4737	4	true

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ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
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

name will last and be in memory From age to age although for infamie What more abiding Tombe can man invent Then Books which if they 'r good are permanent And monuments of fame the which shall last Till the late evening of the World be past But if erroneous sooth'd with vertues face Their Authors cridit's nothing but disgrace If I should praise thy Book it might be thought Friends will commend although the work be nought But I 'le forbeare lest that my Verses doe Belie that praise that 's only due to you Good Wiue requires no Bush and Books will speak Their Authors credit whether strong or weak W. Leybourn ERRATA REader I having writ this some years since while I was a childe in Art and by this appear to be little more for want of a review hath these faults which I desire thee to mend with thy pen and if there be any errour in Art as in Chap. 17 which is only true at the time of the Equinoctiall take that for an oversight and where thou findest equilibra read equilibrio and in the dedication in some Copies read Robert Bateman for Thomas and side for signe and know that Optima prima cadunt pessimas aeve manent pag. line Correct ● 10 equall lines 18 16 Galaxia 21 1 Galaxia 21 8 Mars 24 12 Scheame 35 1 Hath 38 8 of the Tropicks polar Circles 40 22 AB is 44 31 Artificiall 46 ult heri 49 4 forenoon 63 29 AB 65 11 6 80 16 BD 92 17 Arch CD 9 ult in some copies omit center 126 4 happen 126 6 tovvard B 127 26 before 126 prop. 10 for sine read tang elev   Figure of the Dodicahedron false cut pag. 4 LF omitted at end of Axis 25 For A read D 26 In the East and West Diall A omitted on the top of the middle line C on the left hand B on the right 55 Small arch at B omitted in the first polar plane 58 For E read P on the side of the shadowed line toward the left hand I omitted next to M and L in the center omitted 81 K omitted in figure 85 On the line FC for 01 read 6 for 2 read 12 line MO for 15 read 11 96 A small arch omitted at E F G H omitted at the ende of the line where 9 is 116 I L omitted on the little Epicicle 122 THE ARGVMENT OF THE Praecognita Geometricall and of the Work in generall WHat shall I doe I stand in doubt To shew thee to the light For Momus still will have a flout And like a Satyre bite His Serpentarian tongue will sting His tongue can be no slander He 's one to wards all that hath a fling His fingers ends hath scan'd her But seeing then his tongue can't hurt Fear not my little Book His slanders all last but a spurt And give him leave to look And scan thee thorough and if then This Momus needs must bite At shadows which dependant is Only upon the light Withdraw thy light and be obscure And if he yet can see Faults in the best that ever writ He must finde fault with me How ere proceed in private and deline The time of th' day as oft as sun shall shine And first define a Praecognitiall part Of magnitude as usefull to this art THE PRAECOGNITA GEOMETRICAL THe Arts saith Arnobius are not together with our mindes sent out of the heavenly places but all are found out on earth and are in processe of time soft and fair forged by a continuall meditation our poor and needy life perceiving some casual things to happen prosperously while it doth imitate attempt and try while it doth slip reform and change hath out of these same assiduous apprehensions made up small Sciences of Art the which afterwards by study are brought to some perfection By which we see that Arts are found out by daily practice yet the practice of Art is not manifest but by speculative illustration because by speculation Scimus ut sciamus we know that we may the better know And for this cause I first chose a speculative part that you might the better know the practice and therefore have first chose this speculative part of practicall Geometry which is a Science declaring the nature quantity and quality of Magnitude which proceeds from the least imaginable thing To begin then A Point is an indivisible yet is the first of all dimension it is the Philosophers Atome such a Nothing as that it is the very Energie of all things In God it carryeth its extreams from eternity to eternity in the World it is the same which Moses calls the beginning and is his Genesis 't is the Clotho that gives Clio the matter to work upon and spins it forth from terminus à quo to terminus ad quem in the Alphabet 't is the Alpha and is in the Cuspe of the Ascendant in every Science and the house of Life in every operation Again a Point is either centricall or excentricall both which are considered Geometrically or Optically that is a point or a seeming point a point Geometrically considered is indivisible and being centrall is of magnitude without consideration of form or of rotundity with reference to Figure as a Circle or a Globe c. or of ponderosity with reference to weight and such a point is in those Balances which hang in equilibra yet have one beam longer than the other If it be a seeming point it is increased or diminished Optically that is according to the distance of the object and subject 'T is the birth of any thing and indeed is to be considered as our principall significator which being increased doth produce quantity which is the required to Magnitude for Magnitude is no other then a continuation of Quantity which is either from a Line to a plain Superficies or from a plain Superficies to a Solid Body every of which are considered according to the quantity or form The quantity of a Line is length without breadth or thicknesse the forme either right or curved The quantity of a Superficies consisteth in length and breadth without thicknesse the form is divers either regular or irregular Regular are Triangles Squares Circles Pentagons Hexagons c. An equilaterall Triangle consisteth of three right lines as many angles his inscribed side in a Circle contains 120 degrees A Square of four equall right lines and as many right angles and his inscribed side is 90 degrees A Pentagon consisteth of five equall lines and angles and his inscribed side is 72 degrees of a Circle A Hexagon is of six equall lines and angles and his side within a Circle is 60 degrees which is equall to the Radius or Semidiameter An Angle is the meeting of two lines not in a streight concurring but which being extended will crosse each other but if they will never crosse then they are parallel The quantity of an angle is the measure of the part of a Circle

0 11 1 59 43 56 34 48 12 36 58 25 40 17 6 13 52 10 2 53 45 50 55 43 12 32 37 21 51 13 38 10 30 9 3 45 42 43 6 36 0 26 7 15 58 8 12 5 15 8 4 36 41 34 13 27 31 18 8 8 33 1 15     7 5 27 17 24 56 18 18 9 17 0 6         6 6 18 11 15 40 9 0                 5 7 9 32 6 50                 11 37 4 8 1 32                     21 40 This Table is in Mr. Gunters Book page 240 which if you desire to have the point of the Equinoctiall for a Horizontall plane on the houre of 12 enter the Table of shadows with 38 de 30 m. and you shall finde the length of the shadow to be 15 parts 5 m. of the length of the style divided into 12 which prick down on the line of 12 for the Equinoctiall point from the foot of the style So if I desire the points of the Tropick of Cancer I finde by this Table that at 12 of the clock the Sun is 62 de high with which I enter the Table of shadows finding the length of the shadow which I prick down on the 12 a clock line for the point of the Tropick of Cancer at the houre of 12. If for the houre of 1 I desire the point through which the parallel must pass looke for the houre of 1 and 11 in this last table under Cancer and I finde the Sun to have the height of 59 de 43 m. with which I enter the table of shadows and prick down the length thereof from the bottome of the style reaching till the other foot of the Compasses fall on the houre for which it was intended Doe so in all the other houres till you have pricked down the points of the parallels of declination through which points they must be drawn Hyperbolically Proceed thus in the making of a Horizontall Diall but if it be a direct verticall Diall you shall then take the length of the verticall shadow out of the said Table or work it as an Horizontal plane only accounting the complement of the elevation in stead of the whole elevation For a declining plane you may consider it as a verticall direct in some other place and having found out the Equator of the plane and the substyle you may proceed in the same manner from the foot of the style accounting where the style stands to be no other wayes then the meridian line or line of 12 in a Horizon whose pole is elevated according to the complement height of the style above the substyle and so prick down the length of the shadows from the foot of the style on every one of the Houre lines as if it were a horizontal or Verticall plane But in this you must be wary remembring that you have the height of the sun calculated for every houre of that Latitude in the entrance of the 12 signes in that Place where your Plane is a Horizontall plane or otherwayes by considering of it as a horizontall or Verricallplane in another latitude For the Azimuths or verticall circles shewing one what point of the compasse the sun is in every houre of the day it is performed with a great deale of facility if first when the sun is in the Equator we doe know by the last Table of the height of the sun for every houre of the day and by his meridian altitude with the help of the table of shadows find out the Equinoctiall line whether it be a Horizontall or upright direct plane for having drawn that line at right angles with the meridian and having the place of the Style and length thereof in parts and the parts of shadow to all altitudes of the sun being pricked down from the foot of the Style on the Equinoctiall line through each of those points draw parallel lines to the meridian or 12 a clock line on each side which shall be the Azimuths which you must have a care how you denominate according to the quarter of heaven in which the sun is in for if the Sun be in the easterly points the Azimuths must be on the Western side of the plane so also the morning houres must be on the opposite side There are many other Astronomical conclusions that are used to be put upon planes as the diurnall arches shewing the length of the day and night as also the Jewish or old unequal houres together with the circles of position which with the meridian and horizon distinguisheth the upper hemispheare into 6 parts commonly called the houses of Heaven which if this I have writ beget any desire of the reader I shall endeavour to inlarge my self much more in shewing a demonstrative way in these particulars I have last insisted upon I might heare also shew you the exceeding use of the table of Right and versed shadow in the taking of heights of buildings as it may very wel appear in the severall uses of the quadrant in Diggs his Pantometria in Mr. Gunters quadrant having the parts of right and versed shadow graduated on them to which Books I refer you CHAP XIV Shewing the drawing of the Seeling Diall IT is an Axiom pronounced long since by those who have writ of Opticall conceipts of Light and Shadow that Omnis reflectio Luminis est secundum lineas sensibiles latitudinem habentes And it hath with as great reason bin pronounced by Geometricians that the Angles of Incidence and Reflection is all one as appeareth to us by Euclides Catoptriques and on this foundation is this conceipt of which we are now speaking Wherefore because the direct beams cannot fall on the face of this plane we must by help of a piece of glasse apt to receive and reflect the light placed somwhere horizontally in a window proceed to the work which indeed is no other then a Horizontall Diall reversed to which required a Meridian line which you must endeavour to draw and finde according as you are before taught or by the helpe of the Meridian altitude of the Sun your glasse being fixed marke the spot that reflects upon the seeling just at 12 a clock make that one point and for the other point through which you must draw your meridian line you may finde by holding up a threed and plummet till the plummet fall perpendicular on the glasse and at the other end of the line held on the seeling make another mark through both which draw the Meridian line Now for so much as the center of the Diall is a point without and the distance between the glasse and the seeling is to be considered as the height of the style the glasse it selfe representing the center of the world or the very apex of the style wee must finde out those two Tangents at right angles with the

of the World dare affirmatively reject neither but run after both and submitting my wisdome to the wisest of men must conclude that Cuncta fecit tempestatibus suis pulchra and hath also set the World in their meditation Yet can not Man find out the Work that God hath wrought Sir pardon my boldness in fastning this on your Patronage who indeed are called to this Court of Arts as being Nobly descended whom only it concernes and only whose Vertue hath arrived them to the Temple of Honour who are all invited as appeareth in the conclusion of this imaginary description wherein whilst I seem to be in a dream yet Sir I am certain I know my selfe to be Yours in all that I am able to serve you S. M. TOPOTHESIA OR An IMAGINARY DESCRIPTION of the COVRT of ART COmming into a Librarie of Learning where there was more Languages then I had Tongues that if I had been asked to bring brick I should have brought morter and going gradually along as then but passus Geometricus there I met Minerva which said unto me Vade mecum had not the expression of her gesture be-spoke my company I should have shunned her she then taking me by the hand led me to the end where sat one which was called as I did inquire Clemency the name indeed I understood but the Office I did not whose Inscription was Custos Artis I being touched now with a desire to understand this Inscription began with Desire craving leave used diligence to peruse the Library and found then a Booke intituled the Gate of Languages by that I had perused it I understood the fore-named Inscription and craving leave of Clemency in what respect she might be called the Keeper of Arts who answered with Claudanus thus Principio magni Custos Clementia Mundi Quae Jovis incoluit Zonam quae temper at Aethrum Frigoris flammae mediam quae maxima natu Coelicolum nam prima Chaos Clementia solvit Congeriem miserata rudem vultuque sereno Discussus tenebris in lucem saecula fundit And arising from a Globe which was then her seat she began to discourse of the Nature and Magnitude of the Terrestiall body and propounded to me questions as first If one degree answerable to a Coelestiall degree yield 60 miles what shall 360 degrees yield the proportion was so plainly propounded that I resolved it by the ordinary rule of Proportion she seeing the resolution propounded again and said if this solid Body were cut from the center how many solid obtuse angles might be cut from thence at this I stumbled and desired considering my small practise that she would reduce this Chaos also and turne darknesse into light seeing then my desire and diligence bid me make observation for those three were the wayes to bring me to peace and resolved that as from the center of a Circle but three obtuse angles could be struck so from the center of a Globe but three such angles could be struck and from thence fell to another question asked what I thought of the motion of that body I answered Motion I thought it had none seeing I had such Secretaries of Nature on my side and was loth to joyn my forces with the Copernicans She answered it was part of folly to condemn without knowing the reasons I said it should stil remain a Hypothesis to me but not a firme Axiome for the resolution of which I wil onely sing as sometimes other Poets sang concerning the beginning of the world and invert the sense onely as that in another case so this for our purppse If Tellus winged bee The Earth a motion round Then much deceiv'd are they That it before nere found Solomon was the wisest His wit ner'e this attain'd Cease then Copernicus Thy Hypothesis vain And began to discourse of the longitude of the earth and then I demanded what benefit might incurre from thence to a young Diallist she answered above all one most necessary Probleme which we may finde in Petiscus his example and propounded it thus The difference of meridians given to finde the difference of hours If the place be easterly adde the difference of longitude converted into time to the hours given if it be westerly substract the easterly places whose longitude is greater contra as in Petiscus his example the meridian of Cracovia is 45 deg. 30 min. the longitude of the meridian of Heidelberge is 30 degrees 45 minutes therefore Heidleberg is the more westerly One substracted from 45 30 30 45 the other sheweth the difference of longitude to which degrees and minutes doth answer o ho 59 m. for as Therefore when it is 2 hours post merid. at Cracovia at Neidelberg it is but 1 hour 1 minute past noon For There is left 1 houre 1 minute Thus out of the difference of meridians the divers situation of the heavens is known and from the line of appearances of the heavens the divers hours of divers places is known and this is the foundation of observing the longitude if it be observed what houre an Eclipse appears in one place and what in another the difference of time would shew the longitude and hereby you may make a dyall that together with the proper place of elevation shall shew for any other country for this Proposition I did hartily gratifie Geographia and turning said Astronomy why stand you so sad she answered Art is grown contemptible and every one was ready to say Astrologus est Gastrologus then I said what though vertue was despised yet let them take this answer Thou that contemnest Art And makes it not regarded In Court of Art shal have no part None there but Arts rewarded Gnashing the teeth as if ye strive to blame it Yet know I 'le spare no cost for to obtein it Perceiving your willingnesse said Astronomy I will yet extend my charity and lay down the numbers so that if you add the second and third and substract the first it shall give the fourth the question demanded and then I being careful of the tuition of what she should say took a table-Table-book and writ them as follows 1 The sine comp. elevation pole 38½ sine 90 sine of the decl. of the sun yields the sine of the amplitude ortive which is the distance of the suns rising from due East 2 The sine 90 the sine ele pole 51d½ the sine of decli. yields the sine of the suns height at six a clock 3 Sine comp. of altitude of the sun sine comp. declina sine 90 the sine of the angle of the vertical circle and the meridian for the Azimuth of the sun at the hour of 6 The Azimuth is that point of the compasse the sun is on 4 Sine comp. decli. of the sun sine compl. eleva pole 38d½ sine Altitude of the sun the houre distance from six 5 Sine compl. of decli. sine 90 compl of sine suns amplitude to sine compl. of the