Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	divide_v	equal_a	line_n	1,364	5	9.1106	5	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A80180	The lighting colomne or sea-mirrour containing the sea-coasts of the northern, eastern and western navigation: setting forth in divers necessarie sea-cards all the ports, rivers, bayes, roads, depths and sands ... With the discoveries of the chief countries, and on what cours and distance they lay one from another ... As also the situation of the northernly countries, as islands, the strate Davids, the isle of Ian-Mayen, Bear-Island, Old-Greenland, Spitsbergen and Nova Zembla ... Gathered out of the experience and practice of divers pilots and lovers of the famous art of navigation. By Jan van Loon. Whereunto is added a brief instruction of the art of navigation, together vvith nevv tables of the suns declination, also an almanack extending untill the yeare 1661.	Colom, Jacob Aertsz, 1599-1673.	1654 (1654)	Wing C5401A; ESTC R230954	549,120	428

the world right over our heads and crosse wise through the Equinoctiall and to cut right through the Horizon North and South The Sun touching this Circle is at the highest and then it is just noone or the middle time of the day and likewise the stars when they come upon this Circle they are like the Sun at the highest of the Horizon and right South and as soone as they have past it they begin to goe downeward againe The 21 Point Of the height of the Sunne or Starres and what it is THe height of the sunne or Starres is nothing else but the distance or space that is between the Horizon and the Sun or Starre it selfe which to understand perfectly you must make that we suppose a point or prick to be right above our heads in the Heavens that is equally distant from the Horizon in all places which point is called the Zenith or the head point now seeing that the whole circuit of the heavens containeth 360 degrees and that the just halfe thereof is seen above the Horizon it is certaine that this point called the Zenith in all places is above the Horizon 90 degr whether you turn cast west north or south or any other way now when the Sun riseth above the Horizon and ascendeth higher and higher from it and commeth toward this point or Zenith we say that as many degrees as it ascended from the Horizon towards the aforesaid point or Zenith that the same is the height thereof as by example when he is risen halfe up from the Horizon towards the Zenith then he is 45 degrees and if he be risen a third part from the Horizon then he is 30 degr high and so forth the like is also to be understood of the height of the Stars The 22 Point How to measure or find the height of the Sun or of the Starres TO find the height the Mathematicians have devised divers fit Instruments whereof there are two that are most used at sea which are the Astrolabium and the common Crosse-staffe the use of the Astrolabium is plaine and well known unto all men for holding the instrument by the ring let the Sun shine through the holes of the eares the uttermost part of the Diall counting from below upwards sheweth how many degrees the Sun is risen above the Horizon as the former figure plainly sheweth The Crosse-staffe is used thus you must place the end of the Staffe underneath the eye then you must remove the Crosse too and fro untill the upper end of the Crosse standeth even upon halfe the Sun or Star and the under end just with the Horizon and then the Crosse will shew you upon the staffe how many degrees they are in height so you account after those numbers whereof ninety stand that the end of the staffe that is next to your eye the computation going backward from the other end of the staffe for otherwise if you reckon by those numbers that proceed forward from the end next your eye then it will shew you how many degrees the Sun or Star standeth from the Zenith or Head point of the Horizon as you may see by the figure ensuing The 23 Point How you must make a perfect Crosse-staffe and how you shall marke it THe Crosse staves are oftentimes made the one after the other by imitation or patterns and that many times without judgement or knowledge whether the pattern bee good or not whereof notwithstanding a man ought to bee very certaine for it is a matter of great importance and therfore I have here set downe two severall wayes easie to be understood how to make the same exquisitely and perfectly upon good reason good ground Make an even smooth board and paste good paper upon it then draw a strait line upon one edge or side thereof as you see in this figure a ●ine marked C A D then marke another line as you see it marked B C that B C A bee a right and just halfe square then take a good paire of Compasses and set one foot thereof in the angle marked C and compas therewith as you see B E A so that A E B may bee a right quadrant or fourth part of a Circle then devide it into two parts to E and then devide the other halfe which is A E into 90 parts or degrees as thus first devide it into 3 parts and then devide each 3 parts again into 3 and then it wil be divided into 9 parts which done devide each of them into two parts and those divisions or parts divide into 5 parts and then it will bee divided into 90 parts then take a straight line and lay the one end thereof upon the Center C and so forth upon every severall point which you have divided in the Quadrant and then draw lines from the Center C through all the foresaid points as long as the board will containe them as you may see in this figure which done then your instrument is fully made and prepared to marke your staves there upon Which to doe with your compasses take just the half length of your Crosse and set the one foot thereof in the Center and put the other at F and doe the like from D right to G which two points or pricks draw with a straight line unto each other as you see in the line F and G and then mark where the line F G is cut through by the lines that come out of the Center through the degrees or points of the quadrant for those cuttings through shew upon the said line the right marking of your Crosse-staffe that is you must marke your Staffe just as you see that these lines in F G are marked by the lines that come out of the center and passe through it whether the Crosse bee long or short you must follow the same order that you are taught in the figure the line H I is drawne for a shorter Crosse then the former and K L for one that is shorter then that viz whos 's halfe is just so long as the Line C K. The second manner of Framing your Crosse-staffe much excelleth the ftrst in perfection and curiosity so you divide it perfectly with your Compasses which is done in this manner Upon an hard even board which is pasted with paper draw a straight line as long as your staffe is and with point compasse take the just halfe or the length of your Crosse whereunto you mean to mark your staffe and prick it many times along in the said line as you can divide each of the said lengths into 11000 equall parts then look upon the table here after insuing which shewed you how many of those points or parts you shall marke for each degree and that you must doe in manner following from the end of the staffe which you will make the eye-end pricke just the halfe length of the Crosse and there make a Crosse stroke from whence prick for every degree so many

of the Globe wee see the Starres as well on the one side as on the other in whatsoever part of the Heaven that it is alwayes of one greatenesse and it is found by experience that wee alwayes see the one half of the Heaven and the other halfe is hidden from our eyes from thence it appeares plainly according to the expression in the third Figure That the earth stands in the middle of the World From thence is likewise to bee marked that the Globe of the earth is no more to bee likened by the Heavens then a point without thicknesse for if the earth had any thicknesse in respect of Heaven wee should standing upon the earth by that reason not see halfe of the Heaven according to Demonstration of the 4 Figure The fourth Point Of the greatnesse of the Earth ALthough the Globe of the Earth as is sayd in respect of the extraordinary widenesse of the Heaven is no more then a point neverthelesse in respect of its selfe it is a greate body having in its Compasse 5400 dutch Miles And that is knowne by this meanes If you devide the whole Circkle of the Compasse of the earth into 360 parts or degrees and wee find as well by Navigation as by measuring of Land that such a Degree or part containeth fifteene such Dutch Miles 360 such part beeing multiplyed by fifteene make out 5400 Duth miles The fifth Point Of the Axis and Poles or Axepoints of the World IN the Globe of the World is imagined to bee a Line going from one Point on the side of the Spheare as a Diameter through the Center to another Point right against it on the other side That Line is called the Axis and the outermost-outermost-ends thereof or the foresayd Points the Poles or Axepoints of the World the one towards the North and is called the Northerne Pole and the other towards the South called the Southerne Pole Upon whichs Poles it is imagined that the Spheare is upon its Axeltree daily turned The Demonstrastion THE Line A.G.B. in this Figure going from the Point A through the Center G as a Diameter to the Point B right against it sheweth the Axel of the World and the Points A and B the Poles A to the North the Northerne and B to the South the Southerne Poles The Sixth Point Of the Aequinoctiall Line IN the middest of the Heavens every where equally distant from both the Poles is imagined a greate Circle dividing the whole Spheare into two equall parts which is called the Aequinoctial because when the Sonne commeth to or under that Cirkle which commeth to passe the 21 of March and the 23 of September the day and night are in all places of the Earth of an equall length The knowledge of this Cirkle is proffitable above all things in Navigation to know thereby how farr wee goe either to the Northwards or Southwards upon Earth thereby also is reckoned the time and hower of the day the Declination of the Sonn and Starrs and more other proffitable things Demonstration IN the foregoing Figure A and B the Poles of the World C D E F is the Equinoctiall Line in the middest of the Heaven equally distant from both the Poles A and B dividing the whole Spheare A C B E into two equall parts as C A E the Northerne and C B E the Southerne part from hence is to bee noted Seeing that the whole Compasse of the Heavens is divided into 360 degrees that the Poles stand from one another 180 degrees and betweene the Poles and the Aequinoctiall remaineth every where on both sides 90 degrees This Line is marked in the Sea-cards with a red Line from east to west through the beginning of the degrees according as they are reckoned as well towards the North as to the South The Seventh Point Of the Ecliptique Line THE Ecliptique Line lyeth awry over the Equinoctiall deviding it in two points right over against one another in two equall parts and is also devided by it in two equall parts the one lyeth betweene the Equinoctiall and the North Pole the other betweene the Equinoctiall and the South Pole It s greatest Declination on both sides of the Equinoctaill towards both the Poles is 23 degree 31½ minutes and is devided into twelve equall parts and to each of them a severall signe applyed The Sonne goeth alongst this Circkle without ever going out of it and runneth through it with its owne naturall course every yeare once and even as the Poles of the World stand every where alike distant from the Equinoctiall even soo hath the Ecliptique alsoo its two Poles every were alike distant from the same Demonstration IN this Figure as before is sayd A B are the Poles of the World C D E F the Equinoctiall G D H F the Ecliptique Line cutting and dividing the Equinoctiall and its selfe alsoo into two equall parts in the points D and F which wee call the Equinoctiall the one at D the Spring Equinoctiall the other at F the Autumne Equinoctiall The one halfe D H F the northern part lyeth betweene the Equinoctiall D E F and A the North Pole at most declined towards F H 23 degrees and 31 2 minutes The other halfe F G D the Southern part lyeth betweene the Equinoctiall F C D and the South Pole B likewise at most declined as C G 23 degrees 31½ minutes The North part is devided into six signes which wee call the Northerly beginning at D with the Kimbug signes towards the North. Aries Taurus Gemini unto H. the point of the farthest declination From thence with the descending signes of the North Cancer Leo Virgo to the Equinoctiall Line in F. the Autumne Equinoctiall the southern part is also divided into six signes which wee call the Southerly beginning at F with the discending signes towards the South Libra Virgo Saggitarius untill G the Point of the sartkest Declination towards the South from thence further with klimbing signes towards the North Capricornus Aquarius Pisces as farr as till you come to the Equinoctiall line in the Spring Equinoctiall D. The Sunne runneth through the three first Northerly signes from the 21 of March new style to the 21 of June New styl the other from the 21 of Iune to the 23 of September The first 3 Southerly signes from the 23 of September to the 23 of December and the other from the 23 December till the 21 of March againe The Poles of the Ecliptique are M and N both of them standing every where alike distant from the Ecliptique G H and soo farre from the Poles of the World A and B as the Ecliptique is farthest declining from the Equinoctiall at H E and C G. The eighth Point Of the Coluri THe Coluri are two Circkles going Croswayes through both the Poles of the World dividing each other into two parts in the Poles and together with them the whole Globe Equinoctiall Zodiack or Ecliptique and all the Paralels in 4 equall parts the

of the aforesaid parts as the table ensuing sheweth you As for example for the first degree prick 176 parts for the second 355 parts for the third 538 parts for the fourth 724 parts and so forth Remembring that you must prick all the lengths of pricks or parts aforesaid from the aforesaid crosse stroke which is marked upon the halfe length of the Crosse into 11000 parts then devide the whole Crosse so and then take for every degree halfe so many as the Table sheweth unto you And if you cannot doe so devide halfe the Crosse into a 1000 parts and then leave the hindermost letter of the table out as where you should for the first degree take an 176 parts take but 17 parts leaving the last figure out but if your crosses be so smal that you can devide the halfe of them into no smaller then an hundred parts then leave out the two last figures in the table But you must understand that the more parts that you devide the crosses into your markes will fall out so much the better perfec●er de parts de parts de parts de parts de parts 1 176 19 4019 37 10057 55 21716 73 756612 2 355 20 4281 38 10503 56 22708 74 61154 3 538 21 4550 39 10965 57 23759 75 65958 4 72● 22 4826 40 11445 58 24874 76 71445 5 913 23 5108 41 11943 59 26059 77 77769 6 1106 24 5399 42 12460 60 27321 78 85144 7 1303 25 5697 43 12998 61 28667 79 93854 8 1504 26 6003 44 13558 62 30108 80 104301 9 1708 27 6318 45 14142 63 31663 81 117062 10 1918 28 6643 46 14751 64 33315 82 133007 11 2131 29 6976 47 15386 65 35107 83 153469 12 2349 30 7320 48 16051 66 37046 84 180811 13 2572 31 7675 49 16746 67 39152 85 219038 14 2799 32 8040 50 17475 68 41445 86 276362 15 3032 33 8418 51 18239 69 43955 87 371885 16 3270 34 8807 52 19042 70 46713 88 561810 17 3514 35 9210 53 19887 71 49758 89 1139891 18 3764 36 9626 54 20777 72 53137 90 infinit The 24 Point Of the cutting of the Crosse-staffe and how a man may helpe and prevent all the defects of the staffe Set the great Crosse with the middlemost upon like degrees to wit each upon such as for that purpose are marked upon the staffe then apply the staffe the Crosses so firmely remaining unto your eye in such manner whether it bee on the innermost or outermost corner it is all one as that you discerne the ends of the Crosses both above and beneath just over each other in forme as this figure specifieth If then you draw strait lines by the ends of of the Crosses A B and D C they shall meet just in the middle point of your sight And in asmuch as the Crosses are placed upon like degrees the lines aforesaid shall meet just upon the end of the staffe seeing that the end of the staffe representeth the center of the quadrant whereby your staffe is marked So then the aforesaid lines or ends of the Crosses answer both just upon the end of the staffe also upon the sight so that it followeth necessarily and appeareth evidently that the end of the staffe and the sight meet in one or to speake properly both of them stand just in the center of the quadrant Therefore whensoever with the Crosse staffe you will take the height of the Sun or of any Star then observe diligently how many degrees it is elevated above the Horizon and place the two Crosses upon so many degrees then apply the staffe to your eye in such manner as that you may see the ends of the Crosses just over each other according as is taught before in such forme then as you finde the staffe to stand to your eye shall you place the staffe taking away one of the Crosses when you desire to measure according to such height this is a sure rule which will never fayle neither can you possibly misse if you follow it N o 1 The 25 Point How to finde the height of the Sun by the shadow N o 2 That being done the preparation is made to marke the peece take first the just widenesse with a paire of Compasses that is betweene EG the foremost edge of the long crosse and A B the outermost edge of the eare in the little crosse as in the figure No. 2. and put that on the peece of the point D on the left roundell inward toward C on that point draw a thwart line from thence you shall begin to marke that the widenesse betweene the middle line of the staffe and the under edge of the eare which is in the uppermost crosse as in the foresaid figure No. 2. from F tot A prick that on the quadrant from A toward F in H and from C to G in I and draw the line H I. Then observe how all the lines comming from A the center of the quadrant cutting through this line even so must the peece bee marked beginning at the point C with 90 80 70 c. But if so doing you cannot get so many degrees on the staffe as you desire to have for your use then set the little crosse a third or fourth part lower toward the great crosse at your pleasere so that the under edge of the eare AB in the figure No. 2. may come to stand at MN then in the place of the length F A take F M and thrust it in the quadrant of A toward F into K and from C unto L and draw the line K L that then will bee marked as it ought by cutting the lines comming from the center through the devision of the quadrant but you must take a certaine marke in the long crosse for to set the little crosse in such manner as you would use both marking But if you would make more markes on the same peece you must slide that little crosse more netherward and then doe as was said before but you may not forget to make certaine markes in the long crosse for to set the little crosse wel according to the marking which you desire to use To marke this crosse staffe from tables more perfectly draw on an even board pasted with paper a right or straight line as long or longer then the staffe that you desire to marke You shall with the compasse take the widenesse of the staffe between the middle line and the nethermost edge of the eare at the little crosse as it is in the figure No. 2. F A or F M or also F O what marking soever you desire to follow set that widenesse taken as often alongst that foresaid line as you can and each of these lengths you shall divide in 10000 parts this table in this place shewes how many of these parts you shall appoint for a degree or a fourth part of a degree beginning as is the figure a foresayd No. 2. from the point C. The first Columne

reckoned upon the Meridian or length of the earth from the westend of England Those which are more easterly from thence have the lesser declination when the Sun departeth from the Line and increaseth in declination either towards the North or South as wel betweene the 20 of March and the 22 of Iune as betweene the 23 of September and the 22 of December and the greater declination when the Sun returneth againe towards the Line whether it bee by north or by south the Line as wel betweene the 22 of December and the 20 of March as betweene the 22 of Iune and the 23 of December On the contrary those which are more westerly from thence have the waxing declination that is when the Sun runneth from the Line either by North or by South the Line the greater declination and the falling declination that is when the Sunne runneth againe towards the Line either by North or by South the Line maketh the lesse That commeth to passe by reason of time thus Those which are more easterly have the Sunne sooner in the south or in their Meridian and therefore is the waxing declination lesse and the falling greater on the contrary those which are more westerly have the Sonne later in the South and therefore have they the increasing declination more the decreasing lesse The first Example Concerning those which are more easterly with rising declination upon the 25 of March in the second yeare following the Leap-yeare I desire to know ●he Sonnes declination at noone at Bantam in the East-Indies First I seeke upon a Globe or any other Table how much more Easterly Bantam lyeth then the Lands end of England and I find it to bee about 120 degrees herein wee reckon not so neare upon a degree or two because such a difference is but little in this respect whilst then the Sonne must have 24 houres to run about the heaven or the whole earth which is 360 degrees I seeke how much time hee must have to run 120 degrees and I say thus 360 degrees ma●● 24 houres what maketh then 120 facit 8 houres 〈◊〉 thence I find that the Sunne commeth 8 houres sooner to the South at Bantam then at the Lands end of England that is That the Sunne is fall South at Bantam when it is but 4 a clock after midnight at Englands Lands end Then I looke in these Tables upon the abovewritten 25 of March for the declination of the Sun and I find it to bee 1 degree 57 minutes and out of the declination on the day following 2 degrees 21 minutes that the declination of the Sun at that time in 24 houres increaseth 24 minutes therefore say I if the declination increase 24 minutes in 24 houres how much in 8 houres facit 8 minutes from thence it is cleare that seeing the Sun runneth from the Meridian over Bantam to the Meridian of Englands end and the declination riseth or increaseth 8 minutes that it at Bantam is 8 minutes lesse as these Tables declare The Suns declination is that day at Bantam no more then 1 degree and 49 minutes by north the Line The Second Example With falling Declination Upon the 16 of the same yeare I desire to know the Suns declination at noone at Bantam and I find in these Tables upon that day for the length of England Lands end 2 degrees 40 minutes that it decreaseth every day at that time of the yeare 24 minutes Seeing then the Sun as is sayd in the first example cometh 8 houres sooner to the South at Bantam then at Englands end I say doth the declination decrease 24 minutes in 24 houres how much maketh it in 8 houres it maketh 8 minutes from thence it is knowne that seeing the Sonne runneth from the Meridian of Bantam to that of Englands End and the declination falleth 8 minutes and therefore at Bantam is it 8 minutes more even as these Tables declare The declination of the Sonne on that day is at Bantam 2 degrees and 48 minutes Observation From hence it followeth That one and the same Steer-man sayling eastwards to the Indies comming upon two such divers times before the Straite of Sunda and would take the height of the Pole according to the Sun of one and the same corner of Land and should use these Tables without such caution hee should though hee thought it wel done thereby taking one time 8 minutes soo much and the other time 8 minutes too little declination hee should find it to differ 16 minutes in his height therefore in long voyages you must thinke wel upon this The third Example Concerning those which are more Westerly with rising declination A certaine Ship comming upon the 9 of October in the third yeare after Leape-yeare upon the greate South Sea neare the Coast of Peru the Steerman desireth to know the Suns declination there at noone hee findeth out of a Globe or any other Table that that Coast lyeth full 80 degrees more Westerly then Englands Lands End The Sun must then run from the South over Englands end to the South of the foresaid Coast of Peru full 80 degrees to which hee requireth about 5 houres and an halfe so that when the Sun standeth there in the South it is then from Englands end halfe an houre past 5 in the afternone Hee findeth in these Tables the declination of that day 6 degrees 13 minutes by South the Line and out of that of the following day which is 6 degrees 36 minutes that at that time in 24 houres the declination riseth 23 min. therefore shall hee say the declination riseth in 24 houres 33 minutes how much then in 5 houres and a ½ facit full 5 minutes and from thence wee find that seeing the Sun running from the Meridian of Englands end to hert of the Coast of Peru riseth full 5 minutes and thereupon the declination on that day is there 5 minutes more even as the tables demonstrate The declination then on that day on the Coast of Peru is 6 degrees 18 minutes The fourth Example Concerning the falling declination Suppose that such commeth to passe on the foresaid Coast of Peru on the 8 of September the same yeare these tables point at the declination of that day 5 degrees 46 minutes and the day following 5 degrees 23 minutes so as upon that time of the yeare in 24 houres time the declination lesseneth 23 minutes The Steerman shal then reckon thus if in 24 houres the declination lesseneth 23 minutes how much is that in 5 houres and a halfe facit full 5 minutes and shall from thence find that his declination is there 5 minutes lesse as these Tables instruct the Sonnes declination then upon that day is upon the Coast of Peru 5 degrees 42 minutes from hence may bee understood what it is which before is said in the example of the more easterly that a Steereman whe would looke after the Sun on the Coast of Peru upon such two divers times in the same place and