Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	arch_n	draw_v	line_n	2,620	5	10.2846	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A53547	Dialling performed instrumentally by our hemisphere in plane projected and first fitted by Mr. William Oughtred and laid down according to his method formerly published for this very subject : together with twentie one several diagrams or schemes demonstratively shewing the reason and ground-work of all dialling as also how to know, distinguish and set down the hour-lines for both faces of all planes at one working / by a practitioner in the same art.	Oughtred, William, 1575-1660.	1652 (1652)	Wing O579A; ESTC R28755	21,881	40

alwaies paralel to som one of the hour-circles in the Instrument For the direct Polar Plane is paralel to the hour-circle of 6 and the Meridian plane is paralel to the hour-circle of 12. The Polar declining Plane BUt the Polar declining Plane is a Plane which is paralel to som one of the hour-circles in the Instrument betwixt 12 and 6 becaus of its Inclination to the Pole and Declination from the prime Vertical or East and West line in the Instrument Next the Substiler and hour-lines in a Meridian Plane make an Arch with the Horizontal line of the plane equal to the Latitude of the place In direct Polar planes they make an Arch of 90 00″ but in Polar declining planes they make an Arch with their Horizontal line of their planes more then the latitude of the place and less then 90 00″ Again in direct Polar planes the Substiler line is the same with the Meridian or 12 a clock line In a Meridian plane it is the same with the hour of 6 but in a Polar declining plane it is betwixt 12 and 6 according to the inclination or distance of the proper Meridian of the plane with or from the Meridian of the place I should now proceed to the setting down those several planes upon the Instrument in their order but becaus som of them are plain regular dials falling under every man's apprehension and som comprehended in what shall bee spoken of the others I will omit these several following The first therefore which I shall omit or pass over is the Horizontal plane whereof the Instrument itself is a perfect pattern as in folio 5 is declared The next following is the due South and North plane which is likewise represented in the Instrument by the line W z E and is fully comprehended and taught in any of the Diagrams no A B or C of the upright declining planes The next following is the Vertical inclining plane which is likewise sufficiently explained in any of the Diagrams of number D E F G of the declining inclining planes there beeing but the same method and order of working for the one as for the other The last which I pass over are the direct Polar and Equinoctial planes beeing very plain regular Dialls and indeed not so proper for the Instrument as aforesaid How to set down upon the Instrument these several Planes following viz. First The upright declining Plane THe first therefore which I will begin withall is how to set down upon the Instrument any upright or upright declining Plane First you must bee very careful which waie your declination tend's for if you mistake herein your work must bee extreme fals This upright declining Plane is proposed to decline 30 00″ to the Eastwards of the South therefore I reckon in the limb of the Instrument 30 00″ to the Northwards of E and 30 00 to the Southwards of W in the greater Diagram number A and so draw the line A z A for the Horizontal line of the Plane Next I cross it at right angles with the line C z E for the perpendicular line thereof for you must know that the Horizontal line of the Plane and the Perpendicular line thereto in all upright planes must bee the two first lines and in all incliners the Horizontal line must bee the first and a line crossing the Horizontal at right angles must bee the second which upon the matter is all one before you can proceed any further This beeing don you perceiv the Southern face of this plane to behold the South-east quarter of the Instrument and the Northern face thereof to behold the North-west quarter of the Instrument which is according to the declination proposed How to set upon the Instrument any Vertical Incliner or any Declining Inclining Plane FOr all sorts of Incliners you must have recours unto the Semidiameter or graduated scale in the Instrument z S. Now this Plane Decline 24 20″ Westerly from S. is proposed to Incline 36 00″ Northerly First becaus this plane decline's to the Southwestwarde therefore in the greater Diagram number D I reckon from W in the limb 24 20″ Northerly and so much from E Southerlie and so I draw the Horizontal line of the Plane A z A which I cross at right angles with the line B z B. Next I consider the Inclination proposed 36 00″ northerlie which I take out of the Scale from S to e and put it over in the northern part of the line B z B from B to T or which is much the better waie I take the complement to 36 00″ beeing 54 00″ out of the Scale from z to e and put it over in the Northern part of the line from z to T becaus the Inclination proposed is northerlie of which you must have asmuch care as to the Declination which point T will bee the highest point in this plane beeing nearest the Zenith z. Now from the two ends of the Horizontal line A and A and through this point T having found a center I draw the Arch of a circle A T A which Arch is the Declining Inclining plane proposed And these two foregoing examples will bee sufficient for setting down or placing upon the Instrument all Planes whatsoëver To finde the place of the Pole of every upright Plane NOw after your Plane is justly set upon your Instrument with its horizontal and perpendicular lines the next thing requisite to know is the place of the Pole of your Plane which must bee carefully placed for from the Pole of every Plane having a center the Substyler and all the hour-lines must be drawn to the limb of the Instrument You are likewise to know that the Pole of every Plane is alwaies 90 00″ from the Plane it self and ever in all upright planes at that end of the perpendicular line in the limb of the Instrument to which the face of your Plane is opposite for which you intend your Diall becaus it is the Semidiameter and therefore the Radius or Sine of 90 00″ which is general Thus in the greater Diagram no A the Southeasterlie face of the plane being proposed therefore at the Southern end of the perpendicular line viz. at C in the limb is the place of the Pole of that face of the plane If the Northwesterlie face which is the contrarie face were intended for principal then the Pole thereof would bee at E in the Northern end thereof To finde the place of the Pole of every Inclining or of every Declining Inclining Plane IF the Plane bee a Vertical Incliner or a Declining inclining Plane as in the greater Diagram no D is proposed then the Pole of the Plane must bee alwaies in the line which crosseth the Horizontal at right angles betwixt the limb and the center z so that you know z T beeing the complement of Inclination 54 00″ if I take 36 00″ out of the Scale from z downwards it will extend to d which beeing put over in the same

line B z B from z it will reach unto m which must bee the place of the Pole of this Plane becaus z T is 54 00″ of the Scale from z and z m is 36 00″ from z which make's the line T z m to bee 90 00″ betwixt the Plane at T and the Pole thereof at m and this is general for all Planes of this nature To draw the Hour-lines upon all Planes with Centers YOu are to mark diligently where the Hour-circles in the Instrument do cross or cut your Plane for if a streight Ruler bee laid to the Pole of the Plane and to those several intersections or crossings of the Hour-circles with the Plane and streight lines drawn from those several intersections or crossings to the limb of the Instrument those streight lines shall bee the Hour-lines for your Plane and by reckoning the degrees in the limb of the Instrument you shall know how much every hour-line is distant either from the Horizontal line of the Plane or from the Perpendicular line thereof or from the Substiler or any one hour-line from another by which you may transfer the same lines upon your Plane by a table made thereby as you pleas To draw the Substiler line upon all Planes with Centers YOu are to mark diligently where the Pole of your Plane fall's to bee either upon an hour-circle or meridian or betwixt any two for if the Pole of the Plane fall upon a Meridian as in the Diagram number D it doth fall just upon the Meridian or hour-circles of one in the point m then this hour-circle of one must bee the proper Meridian of the Plane becaus it passeth through the Pole of the Plane at m. Now if you laie a ruler to the Pole of the Plane m and to the intersection or crossing of this Meridian with the plane it self in the point L and draw the streight line m L K to the limb of the Instrument this line shall bee the Substiler line Furthermore becaus the proper Meridian of the Plane and the hour-circle of one in this Diagram no D bee one and the same therefore the Substiler and hour-line of one must bee one and the same line also and serve for both But if the Pole of the Plane fall betwixt two meridians or hour-circles in the Instrument as in the Diagram no A it doth viz. betwixt the hour circles of 9 and 10 in the Instrument at the point C in the limb becaus it is an upright Plane then for better demonstration sake I will in the Diagrams following where need shall require make or prick one down which in this Diagram no A is C L P E which is the proper meridian of this Plane becaus it passeth through C the Pole thereof Now laying a ruler to the Pole C and to the Intersection of this proper meridian with the Plane it self in the point L and draw the line C L K it must bee the Substiler line for this Plane To finde the height of the Pole above all Planes having Centers THe next and last thing to know is how much the Pole is elevated above your Plane Now the height of the Pole above any Plane is the measure of the arch of the proper meridian of the Plane which is intercepted or included betwixt the Pole in the Instrument and the Plane To know the quantitie of which arch in degrees and minutes first reckon in the limb of the Instrument from either end of the proper meridian 90 00″ mark where this acount end 's and from thence through the center z draw an obscure or occult line to the opposite point in the limb then take the distance betwixt the proper meridian and the center z in the occult line and see how many degrees and minutes it is in the Scale from z downward for the complement thereof beeing taken out of the Scale from z and extended in the occult line on the other side the center shall point out the pole of this proper meridian which had laie a ruler to the Pole of this proper meridian and to the Pole in the Instrument P and make a mark in the limb where the ruler cut 's Again lay the ruler to the Poles of the proper meridian and to the intersection or crossing of this meridian with the Plane and make a second mark in the limb where the ruler cut 's for the degrees and minutes reckoned in the limb betwixt these two marks will bee the exact measure of the arch of the proper meridian of the plane which is intercepted or included betwixt the Pole and the Plane which is the height of the Pole above all planes having centers Thus in the Diagram no A from either end of the proper meridian of the Plane viz. from E or C in the limb I reckon 90 00″ which end 's at A or A beeing in this Diagram the ends of the horizantal line and therefore the same line A z A serv's for the occult line before spoken of and will bee alwaies so in all upright planes Next I finde the distance betwixt the proper meridian and the center z viz. z L to bee in the Scale 21 00″ so that taking 69 00″ the complement thereof out of the Scale from z downwards and extending it in the occult line on the other side the center it will point out the place of the Pole of this proper meridian to bee at h. Now laying a ruler to the Pole of this proper meridian at h and to the Pole in the Instrument P make a mark in the limb where the ruler cut 's viz. n or which is all one draw the obscure line h P n then keeping the ruler at h turn it to the point L where the proper Meridian cut 's the Plane and make the mark o in the limb or the line h L o and you shall finde the degrees and minutes betwixt n and o in the limb to bee 32 40″ which is the measure of the arch of the proper meridian betwixt P and L which is the North-pole's height above the Northern face of the Plane and therefore the South-pole must bee elevated so much above the Southern face thereof Again in the Diagram no D the proper meridian of the Plane which passeth through the Pole of the Plane is the meridian or hour-circle of one viz q m i L q from q therefore either end of this hour-circle which is now the proper meridian of the Plane I reckon 90 00 in the limb which end 's at D from which point D through the center z I draw the occult line D z D Next I finde the distance betwixt the center z and the proper meridian in the obscure line to bee z i 9 00″ of the Scale therefore taking the complement thereof 81 00″ out of the Scale from z downwards it will extend on the other side the center in the occult line from z to h which will bee the place of the Pole of this proper meridian now