Selected quad for the lemma: heaven_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
heaven_n	east_n	motion_n	west_n	1,864	5	9.5519	5	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A80170	Navigation by the mariners plain scale new plain'd: or, A treatise of geometrical and arithmetical navigation; wherein sayling is performed in all the three kindes by a right line, and a circle divided into equal parts. Containing 1. New ways of keeping of a reckoning, or platting of a traverse, both upon the plain and mercators chart ... 2. New rules for estimating the ships way through currents, and for correcting the dead reckoning. 3. The refutation of divers errors, and of the plain chart, and how to remove the error committed thereby ... as also a table thereof made to every other centesm. 4. A new easie method of calculation for great circle-sayling, with new projections, schemes and charts ... 5. Arithmetical navigation, or navigation performed by the pen, if tables were wanting ... By John Collins of London, Pen-man, accomptant, philomathet.	Collins, John, 1625-1683.	1659 (1659)	Wing C5378A; Thomason E1002_1; ESTC R207824	177,819	300

a parallel of Altitude called an Almicanterath The prickt Arches Z ⊙ and Z G K being Ellipses represent the Azimuths or Vertical Circles And the other prick't Arches Represent Meridans or hour Circles which are also Ellipses the drawing whereof would be troublesome and therefore is not mentioned and how to shun them in the resolution of any Proposition of the Sphaere by Chords shall afterwards be shewed Any line drawn parallel to AE E as is f p F D R Q will represent parallels of Declination And any Line drawn parallel to F Y will represent a parallel of Latitude in the Heavens Fifthly divers Arches relating to the Suns Motion such as are commonly found by rhe Globes or Calculation are in the same Scheme represented in right Lines 1. The Suns Amplitude or Coast of rising and setting from the East or West is there represented C W in North Signes and by C g in South Signes 2. His Ascensional difference or time of rising from six in Summer by G W in Winter by g h. 3. His Altitude at six in Summer by H C his Depression at six in Winter by C b. 4. His Azimuth at the hour of six by H G in Summer equal to h b in Winter 5. His Vertical Altitude or Altitude of East and West by I C his Depression therein in Winter by C q. 6. His hour from six being East or West in Summer by G I in Winter by h q. 7. His Azimuth from the East and West upon any Altitude is represented in the parallel of Altitude where it intersects the parallel of Declination here by M ⊙ 8. The hour of the day from six to any Altitude is represented in the said point of Intersection but in the parallel of Declination here by G ⊙ and all these Arches thus represented in right Lines are the Sines of those Arches to the Radius of the parallel in which they happen being accounted from the midst of the said parallel Now how to measure the quantities of these respective Arches by a Line of Chords and consequently thereby to resolve all the cases of Sphaerical Triangles is the intended subject of some following Pages The former Arches thus represented in right Lines many whereof fall in parallels or lesser Circles when Calculation is used are all represented by Arches of great Circles namely such as bisect the Sphaere and the former Scheme doth represent the Triangles commonly used in Calculation Thus the right angled Triangle C d y right angled at d supposing the Sun at y is made of C y The Suns place or distance from the nearest Equinoctial point C d his right Ascension Y d his Declination d C y the angle of the Ecliptick and Equinoctial C y d the angle of the Suns Meridian and Ecliptick In the right angled Triangle W O P right angled at O supposing the Sun at W. O P is the poles Elevation P W the complement of the Suns Declination W O the Suns Azimuth from the North. W P O the hour from Midnight or complement of the Ascensional difference P W O the angle of Position that is of the Suns Meridian with the Horizon and of the like parts or their complements is made the Triangle C m W. In the right angled Triangle C K G right angled at K supposing the Sun at G. C G is his Declination G K his height at the hour of six C K the Suns Azimuth from the East or West at the hour of six K C G the angle of the Poles Elevation C G K the angle of the Suns position In the right angled Triangle C k I right angled at k supposing the Sun at I. I k is the Suns Declination C k his hour from six C I his height being East or West k C I the Latitude k I C the Angle of the Suns position In the oblique Angled Triangle Z ⊙ P if the Sun be at ⊙ Z P is the Complement of the Latitude P ⊙ his distance from the elevated Pole in this Case the complement of his Declination Z ⊙ the Complement of his Altitude or height Z P ⊙ the Angle of the hour from Noon P Z ⊙ the Suns Azimuth from the North or midnight Meridian Z ⊙ P the Angle of the Suns Position Thus we have shewed how the former Scheme represents the Sphaerical Triangles used in Calculation whereby of the six parts in each Triangle if any three are given the rest may be found by Calculation from the Proportions and that either by Multiplication and Division when the natural Tables of Sines and Tangents are used or by Addition and Substraction when the Logarithmical are used and what is performed by either of those sorts of Tables we shall here perform by Scale and Compass from which performances the like measure of exactness is not attainable as from the Tables CHAP. III. Shewing how to know upon what day of the Week any day of any Moneth happens upon for ever 1 TO perform this Proposition there must be a general Rule prescribed to find on what day of the Week the first of March will happen upon for ever which take in the following Verses To number two adde year of our Lord God And a fourth part thereof neglect the odd Remainder if such be the sum divide By seven lay your quotient aside The Rest when your Divisions finished Will number shew day of the Week you need On which the first of March doth chance to be Still counting Lords day first if you do see That nothing do remain then you may say The day you seek's the seventh and Saturns day Example Let it be required to find on what day of the Week the first of March will happen in the year of our Lord 1687. Operation Divisor 7 2 The even fourth of the Year The remainder neglected 301 Quotient 1687 421 2100 21 10 7 3 remains Because three remains the first of March in that Year happens on a Tuesday in the Year 1679 nothing remains therefore it happens on a Saturday Proposition 2. The day of the Week on which the first of March happens on any Year being known and remembred To find on what day of the Week any day of any Moneth in the said Year hapneth To perform this Proposition the following Verse being in effect a perpetual Almanack is to be recorded laid up in Memory All evil chances grievous evils bring Fierce death attends foul chances governing In this Verse are twelve words relating to the number of the twelve Moneths of the Year accounting March the first wherefore the word proper to that Moneth is All and so in order Fierce is the seventh word and therefore belongs to the seventh Moneth or September That which is to be observed from these Words is what letter the word beginneth withal and to count the number of that letter in the order of the Alphabet which will never exceed seven and the number of the said letter shews what day of the Moneth proper

Instrument to be cut in Brass with Paper Prints fitted up for Sale which will be of excellent use to Seamen Surveyors and all that are Mathematically Studious I remain thy freind desirous of the Advancement of Knowledge JOHN COLLINS THE CONTENTS A Double Scale of Chords used in this Book and described Page 1 2. Sphaerical Definitions from page 2 to 9. All the Points Arks and Circles defined represented to the view in a Scheme of the Analemma p. 10 to 14 A general Almanack in two Verses p. 15 The manner of measuring and proportioning out Sines by a Line of Chords p. 18 19 A general Rule in two Verses for finding the Suns place 21 To finde the Suns Declination and right Ascension 23 24 To finde the Suns amplitude height at Six Vertical height time of rising c. 25 26 The sixteen right angled Cases resolved by proportions of four several kindes p. 27 to 32 To finde the Suns height without Instrument 32 To finde the Hour Azimuth and Angle of Position p. 33 to 39 To finde the Suns Altitudes on all Hours 40 41 To finde the Distances of Places c. 42 43 All the Oblique Cases solved p. 46. p. 53 To finde the Altitudes on all Azimuths p. 46 to 52 All the sixteen Cases of right angled Sphaerical Triangles projected and otherwise resolved p. 57 to 63 The Longitude and Latitude of a Star given to finde its Declination and right Ascension p. 64 Two Azimuths and two Altitudes given to finde the Latitude and Declination by Projection p. 65 With Proportions to finde the same by Calculation p. 66 67 Page 2. Line 17. Obliterate Superficies OF THE SCALE Used in this Book THough this Treatise bears the name of the Mariners Plain Scale new Plain'd yet the Scale intended thereby is cut in the Frontis-piece of the first Book Nothing more is necessarily required in the performances of this Book then from the commonly known Division of a Circle into 360 equal parts called Degrees to prick down any number of Degrees less then 180d and a quadrant divided into nine equal parts and one of those parts for convenience below the Diamater into 10 Sub-divisions called Degrees may very well serve the turn which the Readers ingenuity will furnish himself withal in any place if he have but Compasses yet for expedition a line of Sines is often made use of In the following Diagram the equal Divisions of the Semicircle are transferred into the line of Chords in the Diameter by setting one foot of the Compasses in A which is called the lesser Chord Those Chords being numbred by the half Arches to which they belong become a line of Sines of the same Radius with the Diameter of the Semicircle and are called the greater Sines To that Radius there is fitted a Chord of 60d called the greater Chord that the Reader might be supplyed with both for the lesser Chord will not serve to prick off an Arch in a Circle of twice the Radius whereto it is fitted unless the said Chord be doubled in a right line before it be pircked into the Circumference The Sines to the Chord in the Diameter are graduated on the Radius or line C B by drawing lines thorough each degree of the quadrants AB DB and are called the lesser Sines There is also added a Scale of equal parts and Rumbes for other Protractions but we use neither of them in this Book The Schemes in the Book are fitted either to the lesser or greater Chord here described Every degree of a Line of Sines or Chords we suppose to be divided into 60 parts which we call minutes which in the following Operations are guessed at for a small Instrument will not admit of so many Sub-divisions CHAP. I. Sphaerical Definitions BEfore we proceed to the Resolution of any particular questions it will be necessary to premise the common Spherical Definitions and to shew how the Analemma repesents them The word Sphere though as Herigonius sheweth it be taken in a fourfold sense yet I think it not necessary to define above two of them 1. Therefore a Sphere may according to Theodosius be understood to be a solid Superficies or round Body contained under one Surface in the middle whereof there is a point whence all right lines drawn unto the Circumference are equal and is made by the turning round of half a Circle till it end where it began 2. It is taken for a certain round Instrument consisting of divers Circles whereby the motions of the Heavens and the Scituation of the whole World is most conveniently represented For the better explanation whereof Astronomers do imagine 10 Principal points and 10 Circles to be in the hollow inside of the first moveable Sphere which are commonly drawn upon any Globe or Sphere besides divers other Circles which are not delineated but onely apprehended in the fancy The Points are the two Poles of the World the two Poles of the Zodiack the two Equinoctial points the two Solstitial points and the Zenith and Nadir The Poles of the World are two points which are Diametrically or directly opposite to one another about which the whole frame of Heaven moveth from the East into the West whereof one is perpetually seen by us and is called the Arctick or North Pole The other being hid from us and directly opposite to the former is called the Antarctick or South pole a right line imagined to be drawn from the one Pole to the other is called the Axis or Axeltree of the World The Axis differs from the Diameter because that every right line drawn through the Center of the Sphere and limited on each side of the Surface of the Sphere is a Diameter but not an Axis unless the Sphere move round about it The Poles of the Zodiack are two points Diametrically opposite upon which the Heavens move from the West into the East one of them is towards the North distant from the Arctick or North Pole 23 degrees 31 minutes the other is towards the South and is as much distant from the South Pole A Degree is the 360th part of any whole Circle and a Minute is the 60th part of a Degree but of late some divide a Degree into 100 parts which are called Centesmes or Centesimal Minutes in defining some of the Points we must refer to Circles afterwards to be defined The Equinoctial Points are in the beginnings of Aries and Libra to which when the Sun cometh he makes the day and night of an equal length throughout the whole World to wit in the beginning of Aries about the 11th of March which is accounted the beginning of the Spring and in the beginning of Libra about the 13 of September which is the beginning of Autumn The Point of the Summer Solstice is in the beginning of Cancer to which when the Sun cometh as about the 12th of June is the beginning of Summer and the longest day in the year The Point of the Winter Solstice is

in the beginning of Capricorn to which when the Sun cometh as about the 11th of December is the shortest day in the year and in the Astronomical account the beginning of Winter The Zenith is an imaginary point in the Heavens right over our heads 90d from the Horizon The Nadir is a point or prick in the Heavens under our feet opposite to the Zenith Of the Circles of the Sphere The 10 Circles are the Horizon the Meridian the Equinoctial the Zodiack the Colure of the Equinoxes the Colure of the Solstices the Tropick of Cancer the Tropick of Capricorn and the two Polar Circles The first six are called great Circles and the other four lesser Circles By the Center of a Circle is meant a Point or Prick in the middle of the Circle from whence all Lines drawn to the Circumference are equal and are known by the name of Radius resembling the spoak of a Cart-wheel That is said to be a great Circle which hath the same Center as the Sphere and divides it into two equal halfs called Hemispheres and that is called a lesser Circle which hath a different Center from the Center of the Sphere and divides the Sphere into two unequal Portions or Segments 1. Of the Horizon The Horizon is distinguished by the names of Rational or Sensible the Rational Horizon is a great Circle every where equidistant from the Zenith and divides the upper Hemisphere from the lower and by accident or chance is distinguished by the names of a right Oblique and parallel Horizon A right Horizon is such a Horizon as passeth through each Pole of the World and cuts the Equinoctial at right Angles whence the Inhabitants under the Equinoctial are said to have a right Horizon and a right Sphere An Oblique Horizon is such a one as cuts the Equinoctial obliquely or aslope A parallel Horizon is not such a one as cuts the Equinoctial but is coincident and is the same therewith and such is the Horizon under the Poles The sensible Horizon is a Circle dividing that part of the Heavens which we see from that part which see not thence called Finitor From the Accidental Scituation of the Horizon follows many consequences 1. Those that live in a right Horizon that is under the Equinoctial have their days and nights always of an equal length to them all the Stars both rise and set twice in a year the Sun passeth through their Zenith consequently they have two Summers and two Winters to wit Summers when the Sun passeth through their Zenith and Winters when he is in or near the Tropicks 2. In any right or Oblique Sphere the length of the day when the Sun is in the Equinoctial is equal to the length of the night 3. In any Oblique Sphere the nearer the Sun approacheth to the Visible Pole the longer are the Days more then the Nights some Stars always appear others never appear and the more remote from the Equinoctial the greater is the number of such Stars and the more inequality is there between the Days and Nights 4. To those that live under the Polar Circles their day once a year is 24 hours long and their Night nothing 5. Under the Pole one half of the Sphere doth always appear and the other half not appear and one half of the year is well nigh continually Day and the other half continually Night because the Equinoctial lies in the Horizon 'T is said well nigh for by reason of the Suns Excentricity the day under the North Pole is longer then the Night about eight days and on the contrary under the South Pole is shorter then the night as many days 2. Of the Meridian The Meridian is a great Circle which passeth through the Poles of the World the Zenith and Nadir and the North and South points of the Horizon and is so called because that at all times and places when the Sun by his daily motion cometh unto that Circle twice every 24 hours maketh the middle of the day and middle of the night all places that lie under the same Meridian bear North and South but places that lie East and West from one another have each of them a several Meridian 3. Of the Equinoctial It is a great Circle imagined in the Heavens dividing them into two equal parts or halfs called the North and South Hemisphere lying just in the middle between the two Poles being every where equi-distant from them and is called the Equator because when the Sun cometh unto it which is twice in the year at his entrance into Aries and Libra the days and nights are of an equal length throughout the whole World 4. Of the Zodiack The Zodiack alias Signifer is another great Circle that divides the Equinoctial into two equal parts the Points of Intersection being called Aries and Libra the one half of it doth decline into the North the other half into the South as much as the Poles thereof are distant from the Poles of the World namely 23d 31′ and likewise passeth through the two Solstitial Points it 's ordinary Breadth or Latitude is 12 degrees but late Writers make it 14 or 16d by reason of the wandrings of Mars and Venus A Line dividing the breadth thereof into two halfs is called the Ecliptick Line because the Eclipses of the Sun and Moon are always under that Line it 's Circumference is divided into 12 parts called the 12 Signs whereof each containeth 30d. The Names and Characters of the 12 Signs are Aries ♈ Taurus ♉ Gemini ♊ Cancer ♋ Leo ♌ Virgo ♍ Libra ♎ Scorpius ♏ Sagittarius ♐ Capricornus ♑ Aquarius ♒ Pisces ♓ The six former are the Northern and the six latter the Southern Signs Of the Colures These are two great Circles and are no other then two Meridians passing through both the Poles of the World crossing one another therein at right Angles and divide the Equinoctial and the Zodiack into four equal parts making thereby the four Seasons of the year The Colure of the Equinoxes is so called because it passeth through the Equinoctial points of Aries and Libra shewing thereby the beginning of the Spring and Autumn when the days and nights are equal The other Colure passeth through the two Solstitial or Tropical Points of Cancer and Capricorn shewing the beginning of the Summer and Winter at which two times the days are longest and shortest The very beginning of Cancer where the Colure crosseth the Ecliptick line is called the Point of the Summer Solstice to which place when the Sun cometh he can approach no nearer the Zenith but returneth towards the Equinoctial again the Arch of the Meridian or Colure contained betwixt the Summer Solstice and the Equator is called the greatest Declination of the Sun Of the four Lesser Circles The Tropicks are two lesser Circles parallel to the Equinoctial limiting the Suns greatest Declination towards both the Poles that towards the North Pole is called the Tropick of Cancer because the