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Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	let_v	line_n	perpendicular_a	1,964	5	14.8700	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A15752	A short treatise of dialling shewing, the making of all sorts of sun-dials, horizontal, erect, direct, declining, inclining, reclining; vpon any flat or plaine superficies, howsoeuer placed, with ruler and compasse onely, without any arithmeticall calculation. By Edvvard Wright.; Arte of dialing	Wright, Edward, 1558?-1615.	1614 (1614)	STC 26023; ESTC S111551	14,891	53

the Horizon you shall thus know whether it be direct or declining First draw therein a line parallel to the Horizon after this manner holde the Clinatory to the flat in such sort that the plumbline may fall vpon one of the sides of the quadrant then draw a line by the nether side of the Clinatory in recliners or by the vpper side in incliners or by either of those sides in erect flats for that line shall be parallel or aequidistant to the Horizon and may be called the Horizontall line Set the North side of the Cliniatorie to this liue if the North end of the needle looke towards the flat then if the Magnetical Meridian be right vnder the needle it is a direct flat but if it differ from it it is declining and that so much as that difference is and that way which the North end of the needle declineth from the Northend of the Meridian line in the clinatory 4 If the Southend of the needle looke towards the flat made your account contrary wise CHAP. IV. The third diuision of Dials either agreeing with the plaine of the Meridian or disagreeing from the same ALl flats doe either agree with the plaine of the Meridian circle which may therefore bee called meridian flats or else they disagree from the same 2 They are knowne thus If the flat bee erect and declining 90. degrees it is a Meridian flat otherwise it is no Meridian flat and then you must first draw therin the meridian line after this maner 3 If the flat be Horizontal take the clinatory and lay it flat downe thereupon and turning it about till the needle hang precisely ouer the Magneticall meridian by that side thereof that is parallel to the true Meridian line of the Clinatory drawe a right line for that shal be the Meridian line desired 4 In erect flats the Meridian line is perpendicular and therefore laying the Clinatory close to such a flat in such sort that the plumbline hang precisely on either side of the quadrant a line drawne by the side of the clinatory parallel to that side of the quadrant shall be the meridian line 5 In direct flats a line perpendicular to the line aequidistant from the Horizon is the Meridian line we seeke for 6 In flats reclining or inclining declining also 90. degrees which are commonly called East or West reclining or inclining the meridian line is parallel to the horizon 7 For alother inclining or reclining withall declining flats drawe a line vpon some pastbord or paper which shall bee called the horizontal meridian AB wherein settingone foot of your cōpasses with the other draw an arch of a circle therin reckon the complement of the declination FC drawing a right line BC. by the end thereof out of the center B. This right line you shall crosse squire-wise with another as AC which may be called the base of inclination or reclination and must also meet with the horizontall meridian at A. and setting one foot of your compasses in the crossing at C. with the other foote draw an arke counting therein the complement of the reclination or inclination AG. drawing a right line by the end therof out of the center of the foresaid ark CGD from A erect AD. perpendicular to AC which may meet with CGD the line of reclination or inclination at D. Also from A. draw the line AF. perpendicular to the horozontal meridian AB in the point A. and equal to the former perpendicular AD. and from the end therof draw a line to the center of the arke of declination B. Then continuing foorth AC to N. that CN be equall to CD from N. you shall draw a line to B. which if you haue wrought truely must be equall to BE. Now the angle contained betweene the lines NB. and BC. sheweth how much the Meridian line in your Diall ground should be distant from the line which you drew aequidistant to the Horizon heere represented by BC. In this line therefore in the Dial ground set one foote of your compasses and extending the other that way which the Diall declineth drawe an arke of a circle vpwards in recliners but downewards in incliners and therein count the said angle from the line parallel to the Horizon and drawe by the end thereof a line which shall bee the true Meridian in the Dial ground 8 From A draw AH perpendicular to EB make BI equal to BH from I. let IK be drawn perpendicular to BN make CL. equal to CK and drawe a line from L to A. of these three lines AH IK and LA. make the triangle AHM. for then the angle AHM. is the angle which the dial ground maketh with the plain of the meridian CHAP. V. To finde the eleuation of the Meridian line aboue the Horizon THe Meridian line is either parallel to the Horizon or else eleuated the one end higher then the other 2 If the flat bee either horizontal or East or West and inclining or reclining the meridian is parallel to the Horizon 3 In all other flats that disagree from the plaine of the Meridian circle the Meridian line is eleuated the one end higher then the other 4 This eleuation is either vpright as in all erect Dials not declining 90. degrees or else leaning as in all inclining and reclining flats not declining 90 degrees which if they be direct is equall to the complement of reclination or inclination 5 But if they decline then the angle ABE in the former figure is the eleuation of the Meridian line 6 If the meridian line bee not erect it leaueth either Northwards when the eleuated end thereof looketh towards the North or else Southwards when the eleuated end looketh towards the South 7 All flats are either Polar which being continued would goe by the poles of the world as all leaning flats wherein the eleuation of the meridian line is Northwards and equall to the poles eleuation and all erect decliners 90. degrees Otherwise they are no polar flats CHAP. VI. The describing of the figure of the Diall first on paper or pasteboard NOw it shall bee best to take a sheet of paper or rather a pastebord that you may therein describe the figure of your Dial before you draw the Diall it selfe vpon his ground that is vpon the Truncke Stone wall c. 2 This paper or pasteboord therefore you shall place or vnderstand to be placed so as your Dial ground is or must be placed and therein write the names of the parts of the world as they lie in respect of your Dial ground as East West North South Zenith Nadir vpper part nether part c. which you may do by helpe of the magnetical needle for the North end thereof hanging at liberty sheweth the North whereto the South is diametrally opposite and your face being turned towards the North your right hand sheweth the East your left hand the West the Zenith

end of the meridian line as PM PN PO from MNO 5 If the eleuation of the meridian line be Southwards and lesse then the complement of the poles eleuation the eleuation of the stile shal be counted from the vpper ende of the meridian line as DP from D. 6 If the Dial ground looke toward the North the eleuation of the stile from the meridian line shal be reckoned contrariwise in euery kinde CHAP. XII The finding of the substilar line and stile in Dials that be not Polar nor Equinoctiall The stile making oblique angles with the Meridian line HAuing thus found out from whether end of the meridian line the eleuation of the stile is to be reckoned set one foot of your compasses in the meridian line as in A. and stretching foorth the other foot towards that end of the meridian line from which the eleuation of the stile is to bee reckned as towards L. draw an arch of a circle MDLN. and beginning at the Merîdian line reckon and marke therein the eleuation of the stile from the Meridian line LD figure 13. 14. 15. in the rest LO either Eastwards or Westwards in direct Dials as in the 13. 14. 15. fig. but in decliners towards that part of the world which is opposite to the part whereunto the Dial declineth as in the 16. 17. 18. fig. 2 Then in direct Dials a right line ACD fig. 13. 14. 15. drawne out of the center of the said arke by the marke of the stiles eleuation from the meridian line shall be the line representing the stile and therefore the distance of the stile from the substilar line shall be the distance of the stile from the meridian line 3 But in decliners you shall thus finde the substilar line From O the point of the stiles eleuation from the meridian line in the foresaid arke drawe OP a perpendicular to the meridian line AL. and taking the length of this perpendicular with your compasses leaue one foote in P. the concurse therof with the meridian line and with the other describe a quadrant of a circle QRO. beginning from the Meridian line and so proceeding vnto O the other end of the perpendicular line and in that quadrant beginning at the meridian ALQ. reckon and marke QR the complement of the angle conteined betweene the plaines of the diall ground and of the meridian circle and take with your compasses RS. the distance of that marke from the meridian line and setting one foote of the compasses in P. the meeting of that perpendicular with the meridian line with the other make a prick T in the same perpendicular line for then AB a right line drawn by this prick T. out of the center of the foresaid arke MDLN. shall bee the substilar line 4 Then take with your compasses TR. the distance of the foresaid marke in the quadrant QRO. and this pricke and leauing one foote of your compasses in the same pricke T. with the other make another pricke V. in the arke you first described for then a right line AV. drawne thereby out of the arch you first described shall bee the stilar line or line representing the stile 5 In Dials not polar nor aequinoctiall if the distance of the stile from the substilar line be but smal as in the fig. 10. 12. 17. it may bee increased by drawing a paralel CD to the stile already found which for distinctions sake may bee called the stile augmented CHAP. XIII The drawing of the line of Contingence and of the Equinoctiall circle and how it must be diuided NOw in all Dials that be not aequinoctiall draw a right line EHF so long as you can making right angles with the substilar line which is called the line of contingence or touchline 2 Then describe the Equinoctiall circle GHI after this manner Take with your compasses the shortest distance betweene H. the intersection of the line of contingence with the substilar line and the stilar line and leauing one foot in that intersection with the other make a pricke B. in the substilar line whereupon describe a circle GHI which shall be called the equinoctiall circle 3 If the distance of the stile from the substilar be augmented you must draw two touch lines and two aequinoctial circles as in 10. 12. 17. figures 4 The halfe of the aequinoctiall circle next the line of contingence must be deuided into 12. equal parts beginning at H the intersection thereof with the substilar line in all direct dials and erect or meridian polars which are commonly called East or West dials erect as in the 3. 4. 5. 6. 13. 14. 15. figures 5 In polars not meridian nor direct let HK in fig. 7. 8. the complement of the angle which the dial ground maketh with the plaine of the meridian be numbred and marked in the aequinoctial circle beginning at the substilar line and proceeding that way which the diall ground declineth as from H. to K. for at that marke K you must begin to diuide 6 In decliners not polars if the stile make a right angle with the meridian line as in the 9. 10. 11. 12. figu a paralel to the line of contingence drawne by the center of the aequinoctiall shall shew the beginning of the diuision as BK in figu 9. 10. 11. 12. 7 But if the stile make an oblique angle with the meridian line and the line of contingencye cut the meridian line as in the 16. figu your ruler laid to that cutting at X and the center of the Equinoctial B. shal shew in the peripherie thereof the beginning of the diuision K if the distance of the stile from the substilar be not augmented 8 But if it be augmented as in the 17. figure the shortest distance HX betweene H the intersection of the touch line with the substilar line and the stile not augmented AV must bee taken with the compasses and resting one foot in that intersection H with the other make a pricke Y in the substilar line towards B the center of the Equinoctiall by which pricke Y Z the mutuall intersectiō of the next touch line with the meridian line let a right line YZ be drawne for BK and BK paralels to it drawne out of the cenrers of both the Equinoctials towards the meridian line at their crossings with the Equinoctials K K shall shew the beginnings of their diuisions 9 But if the touch line cut not the meridian line as in the figure 18. let a paralel thereto XY bee drawne which may cut the meridian line in Y and take with the compasses the shortest distance ZA betwixt the intersection thereof with the substilar line and the stile not augmented and leauing one foote in that intersection Z with the other make a pricke B in the substilar line towards the center of the Equinoctiall from this pricke drawe a right line BY from B to Y the intersection of the said paralel with the meridian line for BKA paralel to this line drawne out

of the center of the Equinoctiall B. shall shew the beginning of the diuision K. CHAP. XIIII The drawing of the houre lines in all Dials that bee not Equinoctiall HAuing thus deuided the Equinoctial circle lay your ruler to the center thereof B. and to euery one of those prickes 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 by which it is deuided and make marks 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 c. in euery place where it crosseth the line of contingence for then 2 In all polar Dials paralels to the substilar line drawne by those markes shall bee the houre lines as in the 3. 4. 6. 7. 8. figu 3 In Dials not polar in which the height of the stile is not augmented right lines drawne out of the center of the dial by those markes shal be the houre lines as in the 9. 11. 13. 14. 15. 16. 18. figu And if any of the diuisions of the aequinoctiall circle doe fall in to the substilar line a paralel to the line of contingence drawne by the center of the said diall shall shew two opposit houres distant by the space of six houres from the substilar line as for example in direct Dials six in the forenoone and six in the afternoone as in the 13. 14. 15. figure Also if the ruler laid to B. the center of the Equinoctial circle and some diuision thereof as V in the 16. and 18. figu cannot crosse the line of contingence and yet draweth neerer to it draw BY. a right line from the center of the Equinoctial by that diuision and draw AF a paralel to that line which may crosse the substilar and line of contingency in F. then let HA. the other part of the substilar that is betweene the line of contingence and the center of the dial A. be cut in such sort that the segments of the substilar line concurring at the line of contingence AH and HB may keepe the same proportion which the greater segments BH and HA. haue which are contained betweene the center of the Dial and line of contingence and betwixt the center of the Equinoctiall and the line of contingence And let aright line BF bee drawne by that section B and the section of the line of contingence F. For AI a paralel to this right line drawne out of the center of the Diall shall be the houre line that wee seeke for 4 In those dials wherein the distance of the stile from the substilar is augmented right lines drawne by those markes in both lines of contingence which are proportionately distant from the substilar line shall be the houre lines CHAP. XV. What number must be set to the houre lines IN meridian Dials the substilar line is the line of the sixth houre but for the rest we must consider whether it be an oriental or an occidental dial 2 An oriental Dial looketh to the East and the forenoone houres onely must bee set in this Dial and therefore the substilar line sheweth six of the clocke in the morning from which towards the South are the morning houres before sixe viz. 5. 4. 3. c. but towards the North after six 7. 8. 9. 10. 11. as in the 3 figure 3 An occidental Dial looketh directly Westwards and onely the houres after noone can bee set into this dial Therfore the substilar line sheweth the sixt houre after noone from which toward the North are the houres before six in this order 5. 4. 3. 2. 1. but towards the South after six thus 7. 8. 9. c. as in the 4. figure 4 In Dials not Meridian if a ruler laid to the center of the aequinoctial and the beginning of the diuision thereof doe crosse the touchline then the houre line drawne by that crossing is the line of twelue a clocke But if it cannot crosse the touch line imagine notwithstanding that crossing and the twelue a clocke line drawne thereby without the bounds of your Dial whereabouts you thinke it would bee if the ruler and touch line were continued foorth long inough 5 Then in al Dials not meridian imagine the stile to be fastned in his place in aequinoctial Dials perpendicularly erected out of the Center In Dials that be not Equinoctial conceiue it to be placed exactly ouer the substilar line so much raised from the same as the stilar line in your paper or pastbord is distant from the substilar line 6 After this place your paper or pastebord wheron the figure of your Dial is described in the same site or position that the dial ground is or must be placed so that the quarters of the world written thereupon may answer in like position to the quarters of the world as they lie in respect of your dial ground for then if the 12. a clocke line be towards the North from the stile it is the line of the 12. houre of the day From hence therefore towards the West are the forenoone houres 11. 10. 9. 8. 7. c. and toward the East the afternoone houres 1. 2. 3. 4. 5. 6. c. 7 But if the 12. a clocke line bee Southward from the stile it is the line of the twelfth houre in the night from thence therefore on both sides are the night houres toward the West after midnight 1. 2. 3. 4. c. towards the East before midnight 11. 10. 9. 8. c. CHAP. XVI What houre lines are to be expressed in all sorts of Dials IN al Dials those houre lines onely are to be expressed vpon which the shadow of the stile shal fall Therefore the houres of the day onely are to bee expressed 2 In Dials not Polar wherein the height of the stile is not augmented if the stile point vpwards and the eleuation thereof from the substilar line bee not lesse then the complement of the sunnes greatest declination all the houre lines seruing for the longest day are to be expressed therein 3 But if the cleuation of the stile from the substilar be lesse then the complement of the Sunnes greatest declination draw a right line out of the intersection of the line of contingence and substilar perpendicularly ouerthwart the stilar line and setting one foot of your compasses in the center of the dial and extending the other towards the other end of the stilar line draw an arke there from equal to the complement of the Sunnes greatest declination and thereby draw a line out of the center of the Dial and setting one foot of your compasses inthe intersection of this line with the foresaid perpendicular extend the other foot to the stilar line Then keeping this distance set one foote of your compasses in the center of the aequinoctial circle and with the other crosse the line of contingence on both sides the substilar now if you lay your ruler to these crosses and the center of the Dial right lines drawne thereby beyond the center of the Dial shal continue betweene them the space wherein no houre lines are to be expressed 4 This rule holdeth also in meridional Dials inclining when