Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	draw_v	line_n	perpendicular_a	3,095	5	14.0786	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A08487	A new handling of the planisphere diuided into three sections. In the first is a plaine and sensible explication of the circles of the sphere, and such termes as appertaine vnto the doctrine de primo mobili ... The second sheweth how vpon any plaine ... hauing one circle diuided into degrees, and crossed vvith tvvo diameters at right angles, most conclusions of the astrolabe may for all latitudes or countries be readily and exactly performed onely vvith ruler and compasses. In the third, being a supplement organicall, is contained the making of certaine easie instruments for the perfecter working the former conclusions, as to know what degrees and minutes be in any circumference giuen ... Pleasant and profitable generally for all men, but especially such as vvould get handines in vsing the ruler and compasse ... vvithout being at the charge of costly instruments. Inuented for the most part, and first published in English by Thomas Olyuer.	Oliver, Thomas, d. 1624.	1601 (1601)	STC 18810; ESTC S113509	50,163	103

which cutteth I P in 2 the line G 2 in the Meridian answereth the point Z or is the 45 degrée Now hauing marked these sections for euerie degrée in the quadrant transfer them one after another into your ruler or the side of your quadrant that is at one end of your quadrant take a line equall to that which answereth one degrée adde to it that which answereth the second to that put that which answereth the third and so till you come to the end of that line which not being able to receiue all draw another line and prosecute the like construction in that and so in the third and forth till you haue transferred all the lines answering your degrées If in this transferring your deuisions agrée not iust with the ends of your lines you must take onelie the ouerplus of the last deuision in the beginning of the next line and so procéed as is aforesaid Now hauing your lines thus deuided and another deuided to the same parts that the side of your quadrant is being parallell to them all perpendicular to one right line you may readilie know what equall partes are contained betwéene any two of your degrées taken howsoeuer whereby you may performe all the vses of Mercators Directorium Thus for example The Longitudes and Latitudes of any two places being giuen to finde their direction commonlie called the Rumbe TAke the equall parts contained as well in the difference of the latitudes as in the diffrence of their longitudes and see whether both be lesse then the side of your quadrant or no first suppose they be lesse and let the geater be X G the lesser G M draw the line X M deuide G X into two equall parts in V then opening your Compasse to the distance V G and kéeping one foote in V with the other marke T in M X on T and G laying a ruler it will cut the limbe in 4. Now if the difference of the Latitudes be lesse then the difference of the longitudes 4 Y is the distance of the rumbe from the Meridian but if the difference of the longitudes be lesse then is 4 P the distance of the rumbe from the Meridian But now suppose that one or both the differences be greater then the side of your quadrant then by the rule of proportions you must finde a line vnto which the lesser is as the greater is to the side of the quadrant or make the side of the quadrant to another line as the greater is to the lesser namelie let G Y be vnto G Q as the greater difference is to the lesse and draw the line Q Y deuide G Y into two equall partes in W then opening your Compasse to the distance W G and kéeping one foote in W in Y Q marke R a ruler laid on G and R will cut the limbe in 3 now as before if the difference of the longitudes be the greater then is H 3 the distance of the rumbe from the Meridian South if the place respected be South North if it be North and so likewise East or West CHAP. 5. Of the backe of your plate To inscribe in the backe of your plate the fixed stars according to their Longitudes and Latitudes or declinations and right ascensions as you please LEt the vtter edge of the backe side of your plate be deuided into 360 degrées which you may vse for the Zodiacke or the Equinoctiall the Zodiacke if you inscribe the Starres according to their Longitudes and Latitudes or the Equinoctiall if you will place them according to their declinations and right ascēsions which is the best for those are oftnest in vse both are done after one manner thus From the beginning of Aries reckon the right ascension as from E by B vnto T and draw the line A T then from B to V reckon the declination B V laying a ruler on V and A it will cut the Synicall arch of the limbe A S C in S in the lyne A T take A Q equall to the distance A S and the point Q is the place of the starre according to his right ascension and declination this being done set downe by it the name and S or N to signifie whether it decline North or South This may be done so sleightlie that you may rub it out when you will with a wet pumice and yet déepe enough to continue a great while for your vse To finde the longitude and latitude or the declination and right ascension of such stars as bee placed on the back of the plate VPon the center of the plate and the point of the star lay a ruler where it cutteth the limbe is the right ascension reckoned from the vernall Section or the longitude if they be placed for the Zodiacke As for example Place this figure in steade of the figure in folio 35. lay a ruler on A and Q it will cut the limbe in T the circumference E B T is the right ascension of Q. Now if in A S C the Synicall arch of the limbe you applie from A to S a distance equall to A Q and lay a ruler on A and S it will cut the limbe in V the circumference B V is the declination of the starre placed at Q or the latitude if they were placed according to the longitudes latitudes by the letter S or N you shall know whether it bee North or south And that you may be furnished for these two last problemes I haue set downe on the other side a table out of Clauius contayning certaine fixed starres both with their longitudes and latitudes and their declinations and right ascensions calculated for this yeare 1600. And thus much at this time for the Planisphere which hereafter I meane to increase with more conclusions problemes and could haue now enlarged it with handling mensurations Synicall calculations and dialling but those thinges séemed somewhat farre from my principall purpose and therefore I will intreate the reader to accept thus much onely as now is deliuered and so for this time I end The end of the new handling of the Planisphere A Table of fixed Starres out of Cla●●ius calculated for the yeere 1600. compleat Bignes Names Place in the Zodiacke or Longitude Their Latitude The part The declination The part The righ● Ascension 3 The Rams former horne Aries 28 5 7 20 N 17 39 N 23 20   Medusaes head Taur 21 5 23 0 N 40 5 N 40 55   Bulles eye Gem. 4 5 5 10 S 15 56 N 63 6   Orions right shoulder Gem. 23 25 17 0 S 6 21 N 83 41   The Goate Gem. 16 25 22 30 N 45 9 N 72 6   The great dogge Can. 9 5 39 10 S 15 ●4 S 97 19   Hydraes bright Starre Leo. 21 25 20 30 S 5 4 S 137 19   Lions hart Leo. 23 50 0 10 N 13 44 N 146 19   Lions tayle Virg. 15 55 11 50 N 16 26 N 171 49   The Virgins spike Lib. 18 5 2 0 S 8 58 S 195 55   Arcturus Lib. 18 25 31 30 N 21 49 N 209 23   Scorpions heart Scor. 4 5 4 0 S 24 57 S 241 16   Harpe Cap. 8 45 62 0 N 38 40 N 275 15   Last in Aquarius water Aqu 28 25 23 0 S 33 24 S 339 56   Swannes tayle Pisc 0 35 60 0 N 44 8 N 307 22   Pegasus legge Pisc 23 35 31 0 N 25 44 N 341 0 Errata Page 3. line vlt. Analemma p. 6. l. 6. Maurolycus p. 10. l. 9. Frisius p. 13. l. vlt. Motus raptus p. 14. l. 33. Zenith appearing p. 16. l. 33. from the Zenith which p. 17. l. 2.5.7 for Z make L. p. 22. l. 1. blot out pan and l. 11. N L. p. 23. l 13.25 for Z make L. ibid. l 20 Tropickes p. 24. l. 26. there mak●th angles p. 25. l. 12. and by two of those p. 26. l. 9. setting Ianuarie p. 32 l. 26.27 for Q make 7. p. 33. l. 10. for 3 3 make 8 8. ibid. l. 13. for G make E. p. 34 l. 4.5 for T make V. l. 13 for F make E. l. 27. which let be C 1 1 l and l K. l. 8 29. for B make P. p. 26 l. 2.7 for B make P. l. 5. for 12. make 2. l 8. for 2. and D make P. p. 38. l. 18. and H l cutting p. 40. l. 23. for K make B. in the figure of the 39. page place 3. on the other side of D.

many exquisite arguments which I meane not to prosecute but hoping from the testimonie of sense in such manner to deduce the positions that any meane capacitie may haue so reasonable a conceit of them that with probabilitie they may easily be admitted I will referre their exact and more subtile demonstration with the reproofe of such as impugne them to some others handling or to some other place Therefore requiring first the reader not to cast vntimely doubts nor hastily to iudge of any part by it selfe before he hath considered and in some manner vnderstood the whole discourse I will according to Hippocrates his counsell begin with the notablest and easiest things Whosoeuer doth but cast vp his eyes vnto heauen presently perceiueth that it compasseth him round about in manner of halfe a globe or an Hemisphere and if he stand vpon some high place or be at Sea farre from land where nothing can be séene but water and the Skie his eye if he turne himselfe about will represent vnto him at the lowest bounds or limits which he seeth the fashion of a circle vpon whose plaine as vpon a base this visible Hemisphere seemeth to be placed therefore that Circle was first in Gréeke and is now commonly in English called the Horizon that is to say bounding or limiting vz. the compasse of your sight The largenes of this Circle euen as it falleth vnder view is of so great a compasse as you neede not restraine the center thereof according to the precise Mathematicall definition to one determinate exquisite indiuisible and very poynt or pricke but without sensible error as your eye will plainly testifie any one at pleasure may bee taken in the place where you stand From a center so taken if there be or be imagined a plumbe line or line perpendicular to the plaine of the Horizon extended vnto the heauen the place which there it toucheth is commonly called by an Arabian name the Zenith being in truth the pole of the Horizon and the line it selfe his Axis By this Axis and any lines crossing it if plainnes be euery way extēded reaching vnto heauen they marke out their circumferences or semicircles cutting one another in the Zenith but in the Horizon their sections are right lines cutting one another in his center Those circles are named Azimutes and are imagined by Astronomers to be cut by other circles parallel to the Horizon which they terme Alinicantars and circles of Altitude because the portion of the Azimute which is betwéene the Horizon and the Parallel sheweth how his aboue the Horizon that poynt of the Parallel is by which the Azimute passeth Furthermore in a cléere night beholding the bright shining Starres you shall euidently perceiue how they change their places continually some to rise and shew themselues other to goe downe vnder the Horizon and to be hidden from your sight onely if you place your selfe so that your right hand be towards their rising and your left hand toward their going downe looking right foorth and somewhat vpward you shall behold certen Starres which are all times of the night to bée seene and neuer Charles Wayne pole star Little Beare go down amōgst some of which placed after this fashion there is one commonly called the Pole star which being the last in the tayle of the constellation called the little Beare lyeth in māner directly as it were in a right line with those two in the hindermost whéeles of Charles his wayne This Starre seemeth little or nothing to remoue out of his place and indeede not farre from it there is a poynt or pricke which remaineth in one and the same place alwaies immoueable The Azimute passing by the Horizons Axis and a right line drawne frō this immoueable point or the pole starre is properly called the Meridian circle the common section of it and the Horizon being a right line is the Meridian line or the line of North and South the right line which crosseth this Meridian line at right angles in the center of the Horizon is called the line of true East and true West or simply the line of East and West which poynts the ends thereof extended directly fall vpon The Arimute standing vpon this line Ioannes de Roias others specially such as write of Dyalling as it were for dignitie and preheminence doe call the Verticall circle which name being common to all Azimutes because they passe by the Zenith in Latin called Vertex or punctum eregione verticis for a distinction Gemma Frosius hath named it the Circle of the East The other Azimutes haue no proper names but are measured or determined in the Horizons circumference That and so likewise all other Circles Astronomers doe imagine to be diuided into 360. equall parts which they name degrées that is to say euerie quarter or quadrant into 90. degrees euery degrée they further diuide into 60. minutes euery minute into 60. seconds euery second into 60. thirds and so continue sometimes vnto tenths and may goe further if they will By these degrees minutes c. which are betwéene that point where any Azimute cutteth the Horizon and the Meridian line or the line of East and West the Azimute is determined assigned or said to be giuen Vpon the points where the Verticall circle cutteth the Horizon which poynts are the true poles of the Meridian and the precise East and West if by often and diligent viewing you shall see two Starres the one in the East and the other at the same time right against it in the West in winter time euen in one night you may behold that which is in the East first ascending and then againe descending at length to come into the West and that which was in the West being till that time hidden from your sight then to appeare againe rising in the East all this while continually the like shape of an Hemisphere being still represented to your eye without any chaunge or alteration whereby you may gather the heauen to bee a perfect Globe or Sphere hauing that part vnder the Horizon equall and like to that which you sée aboue it and that the place where you stand is the very center thereof A line drawne from the pole Starre or rather from the poynt immoueable before mentioned called the Articke or North pole a line I say drawne or imagined to be drawne from that poynt to the place of your standing is called the Aris of the world and extended to the other side of the celestiall Sphere which is vnder vs falleth there vpon the South or Antarcticke pole which in these our countries neuer appeareth These things being but a little héedily considered be so manifest and apparant that neither example nor figure is greatly requisite for the perfect vnderstanding of them yet in this beginning to remoue all difficultie and to make euery thing as plaine as may be doe thus much In some plaine ground or rather vpon a poste or stone or some such like thing made

Equinoctiall Colure that which passeth by the poles of the world and the Solstitiall poynts is called the Solstitiall or Tropicall Colure the portion thereof lying betwéene the two Tropickes is the distance of the Tropickes whose halfe is the Sunnes greatest declination otherwise called the Obliquitie of the Zodiacke which by obseruation made with large instruments is in this our age found by great Artes-men to be 23. degrées and 30. minutes whose report it shall be sufficient to accept of and commit to memorie without taking or trying it by any small instrument though some writers of the vse of the Astrolabe haue made that one of their speciall conclusions The Equinoctiall and the Eclipticke are circles of chiefe accompt the first being the rule and measure of the first motion or the motion of Primum mobile otherwise called the Diurnall reuolution and the other as it were the Standard whereby all secondarie motions are examined therefore the degrées of these circles haue peculiar names called in the Equinoctiall Tempora times because they be the first measures of time euery 15. degrées ascending making an houre and so the whole reuolution of 360. which is performed euery naturall day make 24. houres Astronomers begin to accompt the parts or degrées as well in the Equinoctiall as in the Eclipticke from that poynt common to them both which is called the Vernall section and though in the Equinoctiall there be no chaunge of names yet in the Eclipticke or Zodiacke euery thirtie degrées is called a signe and hath a peculiar name The first 30. immedtatly following the Vernall section is called Aries the next 30. Taurus the third 30. Gemini the fourth 30. whose first point begin a new quadrant and toucheth the Summer Tropicke is termed Cancer the fift 30. Leo the sixt Virgo These sixe Signes make vp the semicircle of the Zodiacke which leaneth or declineth from the Equinoctiall toward the North pole The first 30. after this semicircle beginning at the Autumnall section make the seuenth signe named Libra the next or eight 30. is the signe Scorpio the ninth 30. is Sagittarius the tenth 30. beginning a new quadrant with the first poynt which toucheth the winter Tropicke is Capricornus the eleuenth 30. is Aquarius and the twelfth 30. is Pisces There be characters vsed to expresse euery Signe with which are found in euery Almanacke The Sunne passeth in the Ecliptick from poynt to poynt making his continuall reuolution in it without swaruing to the one side or the other other Starres for the most part decline from it but yet haue their places determined by Longitude and Latitude in respect thereof thus By any poynt or Starre a greatest circle being drawne from the pole of the Ecliptick to his circumference the section there made or the portion of the Ecliptick betwéene that section and the Vernall section is the Longitude of the poynt or Starre by which the greatest circle is drawne his Latitude is that portion of the same greatest circle lying betwéene the Starre and the Eclipticke The Sunne being in any poynt of the Eclipticke and the poynt it selfe with all other Starres wheresoeuer placed besides are in like manner compared to the Equinoctiall and in respect therof not onely their declination which hath béen touched before but also their right Ascension is considered A greatest circle being drawne from the Poles of the world to the Equinoctiall by any poynt or Starre his right Ascension is that portion of the Equinoctiall taken betwéen that poynt where the greatest circle cutteth and the Vernall section The declination is the portion of the greatest circle so drawne which lieth betwéene the Equinoctiall and the Starre which as before was noted is also determined by a Parallel to the Equinoctiall passing by the Starre The right Ascension is so called because vnder the Equinoctiall that is in a Situation where the Equinoctiall passeth by the Zenith and the Horizon by the Poles of the world the Horizon by which once in 24. houres euery poynt ascendeth doth the office of any greatest circle so drawne as is appoynted and agréeth with it most exactly This Situation is called Sphaera recta the right Sphere and the Horizon in that Situation Horizon rectus the right Horizon but when the Equinoctiall declineth from the Zenith and the Poles bée one aboue the other beneath the Horizon that Situation is called the Oblique or Declining Sphere and the Horizon the Oblique Horizon which neuer agréeth with the foresayd greatest circle drawne by the Poles of the world and therefore with the Starre there is another poynt of the Equinoctiall in the Horizon betwéene which and the Vernall section is contained that portion of the Equinoctiall that is called the Starres Oblique Ascension and the portion of the Equinoctiall betwéene the ends of the right and Oblique Ascension is called the Difference Ascensionall But for helping the conceit of these things I will vse a linearie example taking the former figure where E C is the Meridian line and the Diameter on which the Horizon standeth now in the middest of winter the Sun being lowest in the Meridian in the point K by the Diurnall reuolution describeth a Parallel standing vpon the Diameter K M which cutteth the Horizon from the East towards the South it continually groweth higher and higher in the Meridian pan riseth in the Horizon néerer and néerer the East till about the 11. of March at noone it commeth to G the section of the Equinoctiall and the Meridian and then by the Diurnall reuolution describeth a circle iust answering the Equinoctiall which passing by the poynts of East and West in the Horizon standeth vpon the Diameter G F from thence a● Summer commeth on it ascendeth in the Meridian and riseth more Northerly vpon the Horizon til about the 12. of our Iune being at the highest in N it describeth a Parallel standing vpon the Diameter N Z in which it riseth vpon the Horizon furthest frō the East to the Northward from thence it descendeth againe by G to K and passeth in the Horizon by the true East to the furthest Southward then it ascendeth againe till it come to N continually returning from the highest to the lowest from the lowest to the highest whereof the two Parallels standing vpon the Diameters K M L N be called Tropickes By these changes it was easily gathered that the Sunne besides the Diurnall reuolution made another proper to it selfe in a circle standing vpon the Diameter K L drawne from Tropicke to Tropick by A the center of the Sphere by reason whereof this circle called the Eclipticke and the Equinoctiall diuide the one the other into two semicircles The Eclipticke is sometimes called the Zodiacke though properly the Zodiacke be a superficies lying on either side of it as you sée the superficies O P Q R parted by the line Z K. The common Diameter of the Equinoctiall and the Ecliptick standing in A perpendicular to the plaine of the circle B C D E