Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	north_n	south_n	west_n	5,452	5	9.2249	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A01089	The art of dialling by a new, easie, and most speedy way. Shewing, how to describe the houre-lines upon all sorts of plaines, howsoever, or in what latitude soever scituated: as also, to find the suns azimuth, whereby the sight of any plaine is examined. Performed by a quadrant, fitted with lines necessary to the purpose. Invented and published by Samuel Foster, professor of astronomie in Gresham Colledge.	Foster, Samuel, d. 1652.	1638 (1638)	STC 11201; ESTC S102472	16,930	55

cut the line TV at a upon the Quadrant take T a in your Compasses and pricke it downe here from V to 12 and from R to 6. Here by the way observe that because this plaine is an Eeast-incliner the face of it looketh toward the West and then if you imagine the true scituation of this Diall upon the plaine whereon it must stand you will easily conceive that the line of 12 is to stand on the right hand from the line AV. and so the line of 6 on the left hand whereas if this plaine had faced toward the East the line of 12 must have stood on the left hand and 6 on the right hand Your owne conceit together with the precepts of the chapter following must helpe in this and in other things concerning the right scituating of the lineaments of your Diall To proceed then In the same manner must you apply the Bead to every houre line as in the next place I remove it to the line y m in the Quadrant and then I see it to cut the line TV in b I take 1 b in my Compasses and with it doe pricke downe from V to 1 and from R to 7. Againe the Bead being applyed to the lines nr sb the threed will cut the line TV upon the Quadrant in c and d I take the points TC Td in my Compasses and pricke them downe from V to 2 and 3 and from R to 8 and 9. Then againe the Bead applyed to the lines ei Va the threed will cut the line TV in the points e and o I take then Te and Tf and pricke them downe from U ●o 11 and 10 and from R to 5 and 4. 5. Lastly lay your rule to A and draw A10 A11 A12 A1 A2 A3 A4 A5 A6 A7 A8 A9 Thus have you twelve houres and if you extend these beyond the Center you shall have the whole 24 houres of which number you may take those that shall bee fit for the Plaine in this scituation The halfe houres may thus bee pricked on and drawne also by applying the Bead to the halfe houres pricked downe in Vcb T the upper limbe of the Quadrant for so the threed will give you the halfe houre points upon the line TV which may be taken off and set downe upon the Diall as the houres themselves were CHAP. XII How to place the Diall in a right Scituation upon the Plaine AFter the houre-lines are drawne by the last Chapter they are to be placed in a right scituation upon their Plaine Which to doe upon some Plaines is more difficult than the Description of the Diall it selfe To give some directions herein I have added this Chapter where you have 9 Questions with their Answers giving light sufficient to what is here intended and required but first be admonished of three things 1. That the inclination mentioned Chap. 8. is the very same in Use with the Prosthaphaereticall arke mentioned Chapter 9. And therefore when I mention the Prosthaphaereticall arke because it is of most frequent use you must remember I meane both the Prosthaph arke Chap. 9 and the Inclination Chap. 8. 2. That these rules though given primarily for places of North-latitude lying within the Temperate Torrid and Frigid Zones yet are also as true and may bee applyed to all places of South-latitude if we exchange the names of North and South for South and North. Here by the way note that the North part of the Torrid Zone extendeth from 0 degrees of latitude to 23 gr 30 min. the Temperate Zone reacheth from 23 gr 30 min. to 66 gr 30 min. the Frigid Zone extendeth from 66 gr 30 min. to 90 gr of latitude And so I come to the 9 Questions 1. What Pole is elevated above the Plaine Upon all Upright plaines declining from the North Upon the upper faces of all East or West incliners Upon the upper faces of all North-incliners whose Prosthaph arke is lesse than the latitude of the place On the under faces of all North-incliners whose Prosthaph arke is greater then the Latitude of the place and on the upper faces of all South-incliners The North pole is elevated And therefore contrarily Upon all upright Plaines declining from the South On the under faces of all East and West and South incliners On the under faces of all North-incliners whose Prosthaphaereticall arke is lesse than the Latitude of the place On the upper faces of all North-incliners whose Prosthaph arke is greater than the Latitude of the place The South pole is elevated 2. What part of the Meridian ascendeth or descendeth from the Horizontall line of the Plaine In all Upright plaines the Meridian lyeth in the Verticall line and if they decline from the South it descendeth if from the North it ascendeth Upon both faces of East and West Incliners the Meridian lyeth in the Horizontall line In all North-incliners the North part of the Meridian ascendeth the South part descendeth in all South incliners the South part of the Meridian ascendeth the North part descendeth upon both upper and under faces And if these North and South incliners be direct then the Meridian lyeth in the Verticall line and so maketh a right angle with the Horizontall line but if they decline then the Meridian on the one side maketh an acute angle with the horizontall line 3. To which part of the Meridian is the style with the substyle to be referred as making with it an acute angle The style is the cocke of the Diall the substyle is the line whereon it standeth signed out in the former descriptions by the letters AV. In all Plaines whereon the North pole is elevated it is referred to the North part of the Meridian and maketh an acute angle therewith In all Plaines whereon the South pole is elevated it is referred to the South part of the Meridian and is to make an acute Angle therewith Except here only those South-incliners whose Prosthaph arke is more than the complement of your Latitude for on these plaines the substyle standeth on that part of the Meridian whose denomination is contrary to the Pole elevated above the Plaine For on the upper faces the North pole is elevated but the substyle standeth toward the South end of the Meridian and on the under 〈◊〉 the South pole is elevated but the substyle lyeth toward the North end of the Meridian Note here that in South-incliners whose Prosthaphaereticall arke is equall to the complement of your Latitude the substyle lyeth square to the Meridian upon the line of 6 a clocke which line in such plaines alwayes lyeth perpendicular to the Meridian line Amongst these falleth the Equinoctiall plaine 4. On which side of the Meridian lyeth the substyle In all direct plaines it lyeth in the Meridian In all Decliners it goeth from the Meridian toward that coast which is contrary to the coast of the plaines declination And so doe all houres also goe upon the Plaine to that coast which is contrary to

the coast whereon they are As all the morning or Easterne houres goe to the Westerne coast of the Plaine and all the Evening or Westerne houres goe to the Easterne coast of the Plaine Which being observed will bee a great helpe to place them aright 5. What plaines have the line of 12 upon them and which not All upright Plaines in all latitudes whatsoever declining from the South have the line of 12 and decliners from the North in the temperate Zone have it not but in the other Zones they also have it The upper faces of East and West incliners in all Latitudes have it the underfaces have it not The upper faces of all North incliners whatsoever have it their under faces in the Temperate Zone want it in the Frigid Zone have it and in the Torrid Zone likewise if the Prosthaph arke bee greater than the Sunnes least North Meridian altitude but if it be lesse they want it also For South incliners consider the Sunnes greatest and least Meridian altitude upon the South coast For if the Prosthaphaereticall arke bee such as falleth betweene them that is if it be greater than the least or lesse than the greatest then have bothsides the line of 12 upon them but if it be lesse than the least then doth the Underface want it universally and the upper face alone hath it if greater than the greatest then doth the Upper face want it and the under face alone hath it Except in the Frigid Zone where the upper face hath it also by reason of the Sunnes not setting there for a time 6. Whether the North or South part of the Meridian serveth for the line of 12 In those Plaines that have the line of 12 where the North pole is elevated there the North part of the Meridian serveth for 12. and where the South pole is elevated there the South part of the Meridian serveth for the line of 12 or mid-day Except in all Latitudes the under faces of those South incliners whose Prosthaphaereticall arke falleth betweene the Sunnes greatest and least Meridian altitudes for in them the South pole is elevated but the North part of the Meridian serveth for the line of 12. Except in speciall those Upright Plaines in the Torrid-zone which looke toward the North and the Under faces of North-incliners also whose Prosthaphaereticall arke is greater than the least North-meridian-altitude for these have the South or lower part of the Meridian serving for 12 though the North pole be elevated 7. Which way the style pointeth and how it is to bee placed In Plaines where the North pole is elevated it pointeth up towards it and where the South pole is elevated it pointeth downe towards it The style lyeth perpendicularly over the substyle noted in the former figures with AV and is to be elevated above it to such an angle as the Elevation of the pole above the Plaine shall be found to be by the 6 7 8 and 9 Chapters 8. When is it that that part of the Meridian next the substyle and the line of twelve doe goe contrary wayes In all Latitudes Upon the upper faces of South-incliners whose Prosthaphaereticall arke is greater than the complement of the Latitude but lesse than the Sunnes greatest South Meridian altitude And on the Under faces of those South-incliners also whos 's Prosthaph is lesse than the complement of the Latitude but greater than the Sunnes least South meridian altitude In the Torrid-Zone alone you must adde hither also North upright Plaines and those North-incliners on the Under-face whose Prosthaphaereticall-arke is greater than the least North-meridian altitude of the Sun for these have the line of midday standing on that coast which is contrary to the coast of that part of the Meridian next the substyle and none else The line of 12. I call herethe line of midday because in the Frigid-zone where the Sunne setteth not in many dayes together there are two twelves the one answering to our midday and the other to our midnight and so all Upper faces of South-incliners whose Prosthaphaereticall arke falleth betweene the least and greatest South meridian altitudes have there two 12 a clockelines upon them 9. How much the Meridian line ascendeth or descendeth from the Horizontall line The quantity of the Angle is to be found upon the circle on the back-side of your Quadrant in this manner Extend the threed from the complement of the Plaines inclination taken in the lower Quadrant to the complement of the Plaines declination counted in the Semicircle and the threed will shew you upon the Diameter the degrees and minutes of the Meridians Ascension or Descension In the example of the 9. Chapt. taking the Upper face of that Plaine I find the Meridian to ascend above the Horizontall line 33 gr 41 minutes ¶ These directions are sufficient for the bestowing of every line into its proper place and coast As may bee seene in the Example of the ninth Chapter For First upon the upper face of that North incliner because his Prosthaph arke 16 gr 6 min. is lesse than 52 gr 30 min. the Latitude of the place therefore the North pole is elevated above it by the Answer to the first Quest. 2. Because it is a North-incliner therefore the North part of the Meridian ascendeth above the Horizontall line by the answer to the second Question 3. Because the North pole is elevated therefore the Style with the substyle maketh an acute angle with the North end of the Meridian by the Answer to the third Question 4. Because this Plaine declineth toward the West therefore the substyle lyeth on the East-side of the Meridian and so doe the houres of the afternoone by the Answer to the fourth Question 5. This Plaine being the Upper face of the North-incliner will have the line of 12 to bee drawne upon it by the Answer to the fifth Question 6. Because the North Pole is elevated therefore the North part of the Meridian serveth for the line of 12 by the Answer to the sixt Question 7. Because the North pole is elevated therefore the style pointeth upward toward the North pole by the Answer to the seventh Question 8. That part of the Meridian next the Substyle and the line of 12 are both one and so therefore goe both one way by the Answer to the eight Question 9. By the second the Meridian line ascendeth and the quantity of the ascent is 33 gr 41 min. above the Horizontall line by the Answer of the ninth Question Thus you see every doubt cleared in this example the like may be done in all others CHAP. XIII The making and placing of Polar Plaines Place this Diagram betweene folio 32. and 33. The horizontall line of the Plaine These Plaines may have Dialls described upon them by this Quadrant but the better way is the common way to protract them by an equinoctiall circle for otherwise the style will be alway of one distance from the Plaine be the Diall greater or

lesser The Polar plaines that decline before they can be described must have their New-inclination known and then their delineation will be easie the manner of it may be seene in this Example Suppose the upper face of a North-inclining Plaine lying in the Latitude of 52 gr 30 min. to decline from the South toward the East 68 gr and to incline towards the North 73 gr 57 min. you shall find by the ninth Chapter the Prosthaph arke to be 52 gr 30 min. the same with the Latitude of the place and therefore you may conclude this plaine to be Polar By the same Chapter you shall find the New inclination to be 63 degrees When you have these you may draw your Semicircle AB4 and divide it into 12 equall parts for the houres so signing the new-inclination 63 degrees from A to B draw CB and supposing the altitude of your style to be CD through D draw the perpendicular D 12 and where the lines drawne from C through the divisions of the semicircle doe cut the line D 12 there raise perpendiculars for the houres and so finish it up as the manner is The style lyeth directly over and parallel to the substyle CB the distance of it from the plain is CD and in this Example the substyle CB standeth from the line of 12 Westward because the plaine declineth Eastward according to the rules in the former Chapter and so doe the morning houres also For the placing of the Diall in a true site upon the Plaine you shall find by the answer to the 9 Quest. in the former Chapter that the Meridian ascendeth 55 gr 38 min. for other necessaries the precepts of the former Chapter will direct you Onely observe that in Upright East and West plaine the line of 6 is alwayes the substyle and it ascendeth above the North end of the Horizontall line as much as the Latitude of the place commeth to FINIS AN APPENDIX Shewing a ready way to find out the Latitude of any place by the Sunne BEcause in the third Chapter and quite through this Treatise the Latitude of the place is supposed to bee knowne when as every one perhaps cannot tell which way to find it out I thought good therefore to adde this Appendix as a ready helpe to shew how it may bee attained sufficiently for our purpose Know then that for the finding out of the Latitude of a place by the Sunne these things are required 1. To find the Meridian line The readiest way to find the Meridian line is by the North-starre This starre is within 2 degr 37 min. of the North-pole The North-pole lyes very neere betweene Allioth or the root of the great Beares tayle and this starre You may therefore imagine where the Pole is if you conceive a right line drawne from the Pole-starre to Allioth and by your imagination suppose ⅔ parts of the distance of the next starre of the little Beares taile from the Pole-starre towards Allioth for there is the very Pole-point Now then if you set up two poles aslope and from the tops of them hang two cords with weights at the ends of them and turne them till you standing on the South-side of them may see them both together with the Pole-point as it were all in one line then be sure these two cords doe hang in the Meridian line or very neere it yea so neere it that though you should erre 3 degrees herein wherein you need not to erre one degree yet will not the Meridian altitude in these Climates especially more Northward faile you above 3 minutes which is neere enough to our purpose I have here given you the chiefe starres of the great and little Beares that by them you may come to know the starres used in this observation and so find the very Pole-point it selfe 2. To find the Sunnes Meridian altitude Observe diligently about noone when the shadow of the South cord shall fall upon the North cord for then is the Sun in the Meridian At that instant observe the Suns altitude stedily and carefully for that is the Meridian and greatest altitude of the Sun for that day 3. To find the Sunnes declination For this purpose the limbe hath the characters of the 12 Signes fixed to each 30 degree and a scale of declinations under the limbe noted with MN The Scale is divided by this table for looke what degr and min. of the Eclipt doe answer to the degr of declination in the table the same are to be numbred in the limbe and by a ruler applyed to them the degrees of declination are drawne upon the Scale A Table to make the Scale for the declination of every part of the Eclipticke Degr. of decl Deg. of the ecl Degr. of decl Deg. of the ecl Degr. declin Degr. eclipt Degr. declin Degr. Eclipt Degr. declin Degr. Eclipt Degr. declin Degr. Eclipt 0.0 0.00 4.0 10.04 8.0 20.26 12.0 31.26 16.0 43.44 2.0 59.04 0.15 0.38 4.15 10.43 8.15 21.06 12.15 31.09 16.15 44.34 20.15 60.14 0.30 1.15 4.30 11.21 8.30 21.46 12.30 32.52 16.30 45.25 20.30 61.26 0.45 1.53 4.45 11.59 8.45 22.26 12.45 33.36 16.45 46.17 20.45 62.41 1.0 2.31 5.0 12.37 9.0 23.06 13.0 34.21 17.0 47.09 20.0 46.00 1.15 3.08 5.15 13.16 9.15 23.46 13.15 35.05 17.15 48.03 21.15 65.22 1.30 3.46 5.30 13.54 9.30 24.27 13.30 35.50 17.30 48.57 21.30 66.48 1.45 4.24 5.45 14.33 9.45 25.08 13.45 36.35 17.45 49.52 21.45 68. ●● 2.0 5.01 6.0 15.12 10.0 25.49 14.0 37.21 18.0 50.48 22.0 69.58 2.15 5.39 6.15 15.51 10.15 26.30 14.15 38.07 18.15 51.45 22.15 71.44 2.30 6.16 6.30 16.30 10.30 27.12 14.30 38.54 18.30 52.43 22.30 73.41 2.45 6.55 6.45 17.08 10.45 27.53 14.45 39.41 18.45 53.43 22.45 75.53 3.0 7.33 7.0 17.48 11.0 28.36 15.0 40.28 19.0 54.44 23.0 78.30 3.15 8.10 7.15 18.27 11.15 29.17 15.15 41.16 19.15 55.47 23.15 81.52 3.30 8.48 7.30 19.6 11.30 30.00 15.30 42.05 19.30 56.50 23.30 90.00 3.45 9.26 7.45 19.46 11.45 30.43 15.45 42.54 19.45 57.56 Finis Before you can find the Declination you must know the Sunnes place and for such as know not the use of the Astronomicall tables an Almanacke will serve where for every day at noone you shall find the Sunnes place in signes degrees and minutes The degr and min. must bee numbred in their Signes upon the limbe and the threed applyed thereto will shew the declination answerable As for example September 21. 1637 in the Almanack for this yeare the Sunne is found to be in 8 gr 23 min. of ♎ In the Quadrants limbe I looke for the Signe ♎ and number there 8 gr 23 min. whereto apply the threed I find it to cut in the scale of Declinations 3 gr 20 min. 4. By the Meridian Altitude and declination of the Sun had how to find the Latitude of the place or the Elevation of the Pole above the Horizon Compare the Sunnes Meridian altitude and declination together and if the Sunne be in a North Signe as ♈ ♉ ♊ ♋ ♌ ♍ then substract the declination out of the Meridian altitude so shall the difference give you the height of the Equinoctiall But if the Sun be in the South Signes as ♎ ♏ ♐ ♑ ♒ ♓ then adde the declination to the Meridian altitude so shall the summe give you the height of the Equinoctiall which being taken out of the Quadrant or 90 degrees leaveth the Latitude of your place or the Elevation of the Pole above your Horizen For Example Upon the 21 of September 1637. I observed the Sunnes altitude in the Meridian to be 34 gr 10 min. Upon which day I find the Sunnes place to be as before 8 gr 23 min. of ♎ and the declination 3 gr 20 min. And because the Sun is in a South signe I adde this declination and Meridian altitude together the summe 37 gr 30 min. is the altitude of the Aequator and this taken out of 90 degrees leaveth 52 gr 30 min. for the Latitude of Coventrie