Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	point_n	south_n	west_n	1,337	5	9.1289	5	false

Text snippets containing the quad

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

N W 67 30 E by N 78 45 W by N 78 45 East 90 00 West 90 00 By which it appeareth that every point of the Compasse is distant from the Meridian 11 degrees 15 minutes The third sort of planes are inclining or rather reclining whose upper face beholds the Zenith and in that respect is called Reclining but if a Diall be made on the nether side and thereby respect the Horizon it is then called an incliner so that the one is the opposite to the other These planes are likewise accidentally divided for they are either direct recliners reclining from the direct points of East West North and South and in this sort happens the direct Polar and Aequinoctiall planes as infinite more according to the inclination or reclination of the plane or they are as erect planes doe become declining recliners which looke oblique to the Cardinall parts of the World and obtusely to the parts they respect Suppose a plane to fall backward from the Zenith and by consequence it falls towards the Horizon then that represents a Reclining plane such you shall you suppose the Aequinoctiall Circle in the figure to represent reclining from the North Southwards 51 degrees from the Zenith or suppose the Axis to represent a plane lying parallel to it which falls from the Zenith Northward reclining 38 degrees one being Aequinoctiall the other a Polar plane But for the inclining decliners you shall know them thus forasmuch as the Horizon is the limiter of our sight and being cut at right angles representeth the East West North and South points it may happen so that a plane may lie between two of these quarters in an accidentall Azimuth and so not beholding one of the Cardinall Quarters is said to decline Again the said plain may happen not to stand Verticall which is either Inclining or Reclining and so are said to be Inclining Decliners First because they make no right angle with the Cardinal Quarters Secondly because they are not Verticall or upright There are other Polar planes which lie parallel to the Poles under the Meridian which may justly be called Meridian plains and these are erect direct East and West Dials where the poles of the plane remain which planes if they recline are called Position planes cutting the Horizon in the North and South points for Circles of position are nothing but Circles crossing the Horizon in those points CHAP IV. Shewing the finding out of a Meridian Line after many wayes and the Declination of a Plane A Meridian Line is nothing else but a line whose outmost ends point due North and South and consequently lying under the Meridian Circle and the Sun comming to the Meridian doth then cast the shadow of all things Northward in our Latitude so that a line drawn through the shadow of any thing perpendicularly eraised the Sun being in the Meridian that line so drawn is a Meridian line the use whereof is to place planes in a due scituation to their points respective as in the definition of this Circle I shewed there was accidentall Meridians as many as can be imagined between place and place which difference of Meridians is the Longitude or rather difference of Longitude which is the space of two Meridians which shews why noon is sooner to some then others The Meridian may be found divers wayes as most commonly by the Mariners compasse but by reason the needle hath a point attractive subject to errour and so overthroweth the labour I cease to speake any further It may be found in the night for when the starre called Aliot seems to be over the Pole-starre they are then true North the manner of finding it Mr. Foster hath plainly laid down in his book of Dyalling performed by a Quadrant which is the fourth part of a circle being parted into 90 degrees It may also be fouhd as Master Blundevile in his Booke for the Sea teacheth being indeed a thing very necessary for the Sea which way is thus Strike a Circle on a plain Superficies and raise a wire or such like in the center to cast a shadow then observe in the forenoon when the shadow is so that it just touches the circumference or edge of the Circle and there make a mark doe so again in the afternoon and at the edge where the shadow goes out make another mark between which two marks draw a line which part in halfe then from that middle point to the center draw a line which is a true Meridian Or thus Draw a great many Circles concentricall one within another then observe by the Circles about noone when the Sun casts the shortest shadow and that then shall represent a true Meridian the reason why you must observe the length of the shadow by circles not by lines is because if the Sun have not attained to the true Meridian it wil cast its shadow from a line and so my eye may deceive me when as by Circles the Sun casting shadow round about still meetes with one circumference or other and so we may observe diligently Secondly it is proved that the shadow in the Meridian is the shortest because the Sun is neerest the Verticall point Thirdly it is proved that it is a true Meridian for this cause the Sun as all other Luminous bodies casts his shadow diametrically and so being in the South part casts his shadow northward and is therefore a true Meridian But now to finde the declination of a wall if it be an erect wall draw a perpendicular line but if it be a declining reclining plane draw first an horizontall line and then draw a perpendicular to that and in the perpendicular line strike a Style or small Wyre to make right angles with the plane then note when the shadow of the Style falleth in one line with the perpendicular and at that instant take the altitude of the Sun and so get the Azimuthe reckoned from the South for that is the true declination of the wall from the South The distance of the Azimuthes from the South or other points are mentioned in degrees and minutes in the third Chapter in the definition of the severall sorts of planes or by holding the streight side of any thing against the wall as is the long Square ABCD whose edge AB suppose to be held to a wall and suppose again that you hold a thrid and plummet in your hand at E the Sun shining and it cast shadow the line EF and at the same instant take the altitude of the Sun thereby getting the Azimuthe as is taught following then from the point F as the center of the Horizon and from the line FE reckon the distance of the South which suppose I finde the Azimuthe to be 60 degrees from the East or West by the propositions that are delivered in the end of this Booke and because there is a Quadrant of a Circle between the South and the East or West points I substract the distance of the Azimuthe from 90

the morning houres and 6 7 8 the evening And because the North pole is elevated above this plane 38 deg. 30 min. the Axis must be from the center according to that elevation pointing upward as the South doth downward so as A is the Zenith of the South C must be in the North The Arithmeticall calculation is the same with the former also a North plane may shew all the houres of the South by consideration of reflection For by Opticall demonstration it is proved that the angles of incidence is all one to that of reflection if any be ignorant thereof I purposely remit to teach it to whet the ingenious Reader in labouring to finde it The Figure of a direct East and West Diall for the Latitude of London 51 deg. 30 min. East Diall West Diall CHAP IV. Shewing the making of the Prime Verticall planes that is a direct East or West Diall FOr the effecting of this Diall first draw the line AD on one end thereof draw the circle in the figure representing the Equator then draw two touch lines to the Equator parallel to the line AD these are they on which the houres are marked divide the Equator in the lower semicircle in 12 equall parts then apply a ruler to the center through each part and where it touches the lines of contingence make marks from each touch point draw lines to the opposite touch point which are the parallels of the houres and at the end of those lines mark the Easterly houres from 6 to 11 and of the West from 1 to 6. These planes as I told you want the Meridian houre because it is parallel to the Meridian Now for the placing of the East Diall number the elevation of the Axis to wit the arch DC from the line of the Equator to wit the line AD and in the West Diall number the elevation to B fasten a plummet and thrid in the center A and hold it so that the plummet may fall on the line AC for the East Diall and AB for the West Diall and then the line AD is parallel to the Equator and the Dial in its right position And thus the West as well as East for according to the saying Contrariorum eadem est doctrina contraries have one manner of doctrine Here you may perceive the use of Tangent line for it is evident that every houres distance is ●●t the Tangent of the Aequinoctiall distance The Arithmeticall Calculation 1 Having drawn a line for the houre of 6 whether East or West As the tangent of the houre distance is to the Radius so is the distance of the houre from 6 to the height of the Style 2 As the Radius is to the height of the Style so is the tangent of the houre distance from 6 to the distance of the same houre from the substyle The style must be equall in height to the semidiameter of the Equator and fixed on the line of 6. CHAP V. Shewing the making a direct parallel Polar plane or opposite Aequinoctiall I Call this a direct parallel Polar plane for this cause because all planes may be called by their scituation of their Poles and so an Aequinoctiall parallel plane may be called a Polar plane because the Poles thereof lie in the poles of the World The Gnomon must be a quadrangled Parallelogram whose height is equall to the semidiameter of the Equator as in the East and West Dials so likewise these houres are Tangents to the Equator Arithmeticall calculation Draw first a line representing the Meridian or 12 a clock line and another parallel to the said line for some houre which may have place on the line say As the tangent of that houre is to the Radius so is the distance of that houre from the Meridian to the height of the Style 2 As the Radius is to the height of the style so the tangent of any houre to the distance of that houre from the Meridian CHAP VI Shewing the making of a direct opposite polar plane or parallel Aequinoctiall Diall AN Aequinoctiall plane lyeth parallel to the Aequinoctiall Circle making an angle at the Horizon equal to the elevation of the said Circle the poles of which plane lie in the poles of the world The making of this plane requires little instruction for by drawing a Circle and divide it into 24 parts the plane is prepared all fixing a style in the center at right angles to the plane As the Radins is to the sine of declination so is the co-tangent of the Poles height to the tangent of the distance of the sub-stile from the Meridian If you draw lines from 7 to 5 on each side those lines so cut shall be the places of the houre lines of a parallel polar plane now if you draw to each opposite from the pricked lines those lines shall be the houre lines of the former plane CHAP VII Shewing the making of an erect Verticall declining Diall IF you will work by the fundamentall Diagram you shall first draw a line such is the line AB representing the Meridian then shall you take out of the fundamentall diagram the Secant of the Latitude viz. AC and prick it down from A to B and at B you shall draw a horizontall line at right angles such is the line CD then you shall continue the line AB toward i and from that line and where the line AB crosseth in CD describe an arch equall to the angle of Declination toward F if it decline Eastward and toward G if the plane decline Westward Then shall you prick down on the line BF if it bean Easterly declining plane or from B to G if contrary the Secant complement of the Latitude viz. AG in the fundamentall Diagram and the Sine of 51 degrees viz. DA which is all one with the semidiameter of the Equator and therewithall prick it down at right angles to the line of declination viz. BF from B to H and G and from F towards K and L then draw the long square KIKL and from B toward H and G prick down the severall tangents of 15 30 45 and prick the same distance from K and L towards H and G lastly draw lines through each of those points from F to the horizontall line CD and where they end on that line to each point draw the houre lines from the point A which plane in our example is a Verticall declining eastward 45 degrees and it is finished But because the contingent line will run out so far before it be intersected I shall give you one following Geometricall example to prick down a declining Diall in a right angled parallelogram Now for the Arithmeticall calculation the first operation shall be thus As the Radius to the co-tangent of the elevation so is the sine of the declination to the tangent of the substiles distance from the meridian of the place then II Operation Having the complement of the declination and elevation finde the

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

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

from the point M into whatsoever part let the proper elevation of the pole be numbered or the distance of the axis from the meridian of the plane 8 de 51 3m and by the term of the numeration I let the axis LI be drawn to be extolled or lifted up on the meridian of the plane LM to the angle MLN The third case of the third probleme of Pitiscus his liber Gnomonicorum Si denique arcus BN repertus fuerit major c. Lastly if the arke BN be found greater then the complement of the poles elevation BG it is a token the plane to be inclined beyond the pole artique and moreover the pole artique should be extolled above such a plane to so great an angle as the angle GLO which the arke GO measureth which arke together with the arke ON in the end you may find in such sort as in the precedent case Example Let there be a meridian plane declining to the right hand 35 de 54 m. inclining towards the pole artique 75 de 43 m. and let the elevation of the pole be 49 de 35½ m. but there is sought the meridian of the plane and place together with the elevation of the pole above the plane the calculation shall be thus to 133874 tangent of the arke KN the distance of the meridian of the place from the verticall of the plane 53 de 14½ m by axi. 2. The sine of the arke NC 8 de 29● m. whose complement is BN 81 de 30½ m. from whence if you substract BG 40 de 25 m. there remaineth the arke GN 41 de 5½ m. to 97982 the sine of the angle BNK or ONG by axi. 3. to 64399 the sine of the arch OG the distance of the axis from the meridian of the plane 40 de 51 3 m. by axi. 3. to 17483 the sine of the arke O N the distance of the meridian of the plane from the meridian of the place 10 de 4 m. by axi. comp. 2. The calculation being finished let the horizon of the place be AC the verticall of the plane KD the horizon of the plane AKCD in which let be numbered from the vertical point K toward C the distance of the meridian of the place from the vertical of the plane 53 de 14½ m. and by the end of the numeration let be drawn the meridian of the place LN then from the meridian of the place to wit from the point N backward let the distance of the meridian of the plane 10 de 4m be numbred and by O the end of the numeration let LO the meridian of the plane be drawn from which afterwards let the proper elevation of the pole be numbred or the distance of the axis from the meridian of the plane 48d 5½m and by the term of the numeration G let the axis LG be drawn being extolled above the plane BO to the angle GLO CHAP X. In which is shewed the drawing of the houre-lines in these last planes not there mentioned being also part of Pitiscus his example in the fourth Probleme of his liber Gnom SO then saith he Si axis c. If the axis be oblique to the plane as the foregoing are as in any plane oblique to the Equator many of the houre-lines doe concur at the axis with equal angles but they are easily found thus But because Pitiscus is mute in defining which part he takes for the right hand and which the left we must search his meaning Pitiscus was a Divine is evident by his own words in his dedication Celsitudini tuae tota vita mea prolixe me excusarem quod ego homo Theologus c. If we take him as hee was a Divine we imagine his face to be towards the East then the South is his right hand and the North is his left hand That he was an Astronomer too appeareth by his Books both of proper and common motion then we must imagine his face representing the South the East on his left hand which cannot be as shall appear Neither must we take him according to the Poets whose face must be imagined toward the West In short take him according to Geographie representing the Pole and this shews the right hand was the East and left the West as is evident by the Diall before going for it is a plane declining from the South to the right hand 30 degrees that is the East because it hath the morning houres not the evening because the Sun shines but part of the afternoon on the plane Thus in briefe I have run throngh all planes and proceed to shew you farther conclusions But I desire the Reader to take notice that in these examples of Pitiscus I have followed his own steps and made use of the Naturall Sines and Tangents CHAP XI Shewing how by the helpe of a Horizontall Diall or other to make any Diall in any position how ever HAving prepared a Horizontall Diall as is taught before on the 12 houre as far distant as you please from the foot of the style draw a line perpendicular to the line of 12 on that describe a Semicircle plasing the foot of the Compasses in the crossing of the lines this Semicircle divide into 180 parts each Quadrant into 90 to number the declination thereon let the arch of the Semicircle be toward the North part of the Diall Then prepare a plane slate such as will blot out what hath been formerly made thereon and make it to move perpendicularly on the horizontal plane on the center of the semicircle which wil represent any declining plane by moving it on the semicircle Now knowing the declination of the plane turn this slate towards the easterly part if it decline towards the East if contrary to the West if toward the West and set it on the semicircle to the degree of declination then taking a candle and moving the Diall till the shadow fall on all the houres of the horizontall plane mark also where the shadow falls on the declining plane that also is the same houre on the plane so scituated drawn from the joyning of the style with the plane It is so plain it needs no figure So may you doe in all manner of declining reclining or reclining and inclining Dials by framing your instrument to represent the position of the plane Note also that the same angle the axis of the Horizontal Dial makes with the plane the same elevation must the axis of that plane have and where it shadows on the representing plane when the shadow of the horizontal axis is on 12 that is the meridian of the place By the same also may you describe all the conclusions Astronomicall the Almicanthers circles of height the parallels of the Sun shewing the declination the Azimuthes shewing the point of the Compasse the Sun is in and all the propositions of the Sphere Seeing this is so plain and evident nay a delightful conclusion I will not give

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