Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	island_n	north_n	south_n	2,551	5	10.0698	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A34005	The sector on a quadrant, or A treatise containing the description and use of four several quadrants two small ones and two great ones, each rendred many wayes, both general and particular. Each of them accomodated for dyalling; for the resolving of all proportions instrumentally; and for the ready finding the hour and azimuth universally in the equal limbe. Of great use to seamen and practitioners in the mathematicks. Written by John Collins accountant philomath. Also An appendix touching reflected dyalling from a glass placed at any reclination.	Collins, John, 1625-1683.; Lyon, John, professor of mathematics. Appendix touching reflective dialling.; Sutton, Henry, mathematical instrument maker.	1659 (1659)	Wing C5382; ESTC R32501	226,510	415

repaire to the Moneth you are in and those figures that stand against it shewes you what dayes of the said moneth the Weeke day shall be the same as it was the first day of March. Example For the yeare 1660 having found that the first day of March hapned upon a Thursday looke into the column against June and February you will find that the 7th 14th 21th and 28th dayes of those Moneths were Thursdayes whence it might be concluded if need were that the quarter day or 24th day of June that yeare hapneth on the Lords day Of the Epact THe Epact is a number carried on in account from yeare to yeare towards a new change and is 11 dayes and some odde time besides caused by reason of the Moons motion which changeth 12 times in a yeare Solar and runnes also this 11 dayes more towards a new change the use of it serves to find the Moones age and thereby the time of high Water To know the Moons age ADde to the day of the Moneth the Epact and so many days more as are moneths from March to the moneth you are in including both moneths the summe if lesse then 30 is the Moones age if more subtract 30 and the residue in the Moons age prope verum Example The Epact for the year 1658 is 6 and let it be required to know the Moons age the 28 of July being the fift moneth from March both inclusive 6 28 5 The summe of these three numbers is 39 Whence rejecting 30 the remainder is 9 for the Moons age sought The former Rule serves when the Moneth hath 31 dayes but if the Moneth hath but 30 Dayes or lesse take away but 29 and the residue is her ages To find the time of the Moones comming to South MUltiply the Moones age by 4 and divide by 5 the quotient shewes it every Unit that remaines is in value twelve minutes of time and because when the Moon is at the full or 15 dayes old shee comes to South at the houre of 12 at midnight for ease in multiplication and Division when her age exceedes 15 dayes reject 15 from it Example So when the Moon is 8 dayes old she comes to South at 24 minutes past six of the clock which being knowne her rising or setting may be rudely guessed at to be six houres more or lesse before her being South and her setting as much after but in regard of the varying of her declination no general certaine rule for the memory can be given Here it may be noted that the first 15 dayes of the Moones age she commeth to the Meridian after the Sun being to the Eastward of him and the later 15 dayes she comes to the Meridian before the Sun being to the Westward of him To find the time of high Water TO the time of the Moones comming to South adde the time of high water on the change day proper to the place to which the question is suited the summe shewes the time of high waters For Example There is added in a Table of the time of high Water at London which any one may cast up by memory according to these Rules it is to be noted that Spring Tides high winds and the Moon in her quarters causes some variation from the time here expressed Moones age Moon South Tide London Dayes Ho. mi. Ho. Mi 0 15 12 3 00 1 16 12 48 3 48 2 17 1 36 4 36 3 18 2 24 5 24 4 19 3 12 6 12 5 20 4   7 00 6 21 4 48 7 48 7 22 5 36 8 36 8 23 6 24 9 24 9 24 7 12 10 12 10 25 8 00 11 00 11 26 8 48 11 48 12 27 9 36 12 36 13 28 10 24 1 24 14 29 11 12 2 12 This Rule may in some measure satisfie and serve for vulgar use for such as have occasion to go by water and but that there was spare roome to grave on the Epacts nothing at all should have been said thereof A Table shewing the houres and Minutes to be added to the time of the Moons comming to South for the places following being the time of high Water on the change day   H. m. Quinborough Southampton Portsmouth Isle of Wight Beachie the Spits Kentish Knocke half tide at Dunkirke 00  00 Rochester Maulden Aberdeen Redban West end of the Nowre Black taile 00  45 Gravesend Downes Rumney Silly half tide Blackness Ramkins Semhead 1  30 Dundee St. Andrewes Lixborne St. Lucas Bel Isle Holy Isle 2  15 London Tinmouth Hartlepoole Whitby Amsterdam Gascoigne Brittaine Galizia 3  00 Barwick Flamborough head Bridlington bay Ostend Flushing Bourdeaux Fountnesse 3  45 Scarborough quarter tide Lawrenas Mountsbay Severne King sale Corke-haven Baltamoor Dungarvan Calice Creeke Bloy seven Isles 4  30 Falmouth Foy Humber Moonles New-castle Dartmouth Torbay Caldy Garnesey St. Mallowes Abrowrath Lizard 5  15 Plymouth Weymouth Hull Lin Lundy Antwerpe Holmes of Bristol St. Davids head Concalo Saint Malo 6  00 Bristol foulnes at the Start 6  45 Milford Bridg-water Exwater Lands end Waterford Cape cleer Abermorick Texel 7  20 Portland Peterperpont Harflew Hague St. Magnus Sound Dublin Lambay Mackuels Castle 8  15 Poole S. Helen Man Isle Catnes Orkney Faire Isles Dunbar Kildien Basse Islands the Casquers Deepe at halfe tide 9   Needles Oxford Laysto South and North Fore-lands 9  45 Yarmouth Dover Harwich in the frith Bullen Saint John de luce Calice road 10  30 Rye Winchelsea Gorend Rivers mouth of Thames Faire Isle Rhodes 11  15 To find the Epact for ever IN Order hereto first find out the Prime Number divide the yeare of the Lord by 19 the residue after the Division is finished being augmented by an Unit is the Prime sought and if nothing remaine the Prime is an Unit. To find the Epact MUltiply the Prime by 11 the product is the Epact sought if lesse then 30 but if it be more the residue of the Product divided by 30 is the Epact sought there note that the Prime changeth the first of January and the Epact the first of March Otherwise Having once obtained the Epact adde 11 so it the Summe if lesse then 30 is the Epact for the next yeare if more reject 30 and the residue is the Epact sought Caution When the Epact is found to be 29 for any yeare the next yeare following it will be 11 and not 10 as the Rule would suggest A Table of the Epacts belonging to the respective Primes Pr. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Ep. 11 22 3 14 25 6 17 28 9 20 1 12 23 4 15 26 7 18 29 The Prime number called the Golden Number is the number of 19 years in which space the Moone makes all variety of her changes as if she change on a certain day of the month on a certain yeare she shall not change the same day of the moneth again till 19 yeares after and then it doth not happen upon the same houre of the day yet the difference doth not cause

C Signifying the Sides of a Cube O Signifying the Sides of a Octohedron T Signifying the Sides of a Tetrahedron And the Letter S Signifieth the Semidiameter of a Sphere the use whereof are to find the Sides of the five Regular Bodies that may be inscribed in a Sphere Example A joyner being to cut the 5 Regular Bodies desires to know the lengths of the sides of the said 5 Regular Bodies that may be inscribed in a Sphere where Diameter is 6 inches Lay the thread over S and take 3 inches out of the line of equal parts or Inches and enter that extent so that one foot resting on the said Scale of inches the other turned about may but just touch the thread the resting point thus found I call the point of entrance from the said point take the nearest distances to the thread laid over the Letters   Inch. Dec. parts D And measure those Extents on the Line of Inches and you will find them to reach to 2.13 I 3.15 C 3.45 O 4.23 T 4.86 Which are the Dimensions of the respective sides of those Bodies to which the Letters belong The uses of the Lines of quadrature Segments Mettals and Equated Bodies I leave to the Disquisition of the Reader when he shall have occasion to put them in practice which I think will be seldome or never and wherein the assistance of the Pen will be more commendable These lines were added to this quadrant to fill up spare room and to shew that what ever can be done on the Sector may be performed by them on a quadrant A TABLE Of the Latitude of the most eminent Places in England Wales Scotland and Ireland   d. m. Bedford 52 8 Barwick 55 54 Bristol 51 27 Buckingham 52   Cambridge 52 12 Canterbury 51 17 Carlisle 55   Chichester 50 48 Chester 53 16 Colchester 51 58 Derby 52 58 Dorchester 50 40 Durham 54 50 Exceter 50 43 Gilford 51 12 Gloucester 51 53 Hartford 51 49 Hereford 52 7 Huntington 52 19 Ipswich 52 8 Kendal 54 23 Lancaster 54 10 Leicester 52 40 Lincolne 53 14 London 51 32 Northampton 52 14 Norwich 52 42 Nottingham 53   Oxford 51 46 Reading 51 28 Salisbury 51 4 Shrewsbery 52 47 Stafford 52 52 Stamford 52 38 Truero 50 30 Warwick 52 20 Winchester 51 3 Worcester 52 14 Yorke 53 58 WALES d. m. Anglezey 53 28 Barmouth 52 50 Brecknock 52 1 Cardigan 52 12 Carmarthen 51 56 Carnarvan 53 16 Denbigh 53 13 Flint 53 17 Llandaffe 51 35 Monmouth 51 51 Montgomeroy 51 56 Pembrooke 51 46 Radnor 52 19 St. David 52 00 The ISLANDS d. m Garnzey 49 30 Jersey 49 12 Lundy 51 22 Man 54 24 Portland 50 33 Wight Isle 50 39 SCOTLAND d. m. Aberdean 57 32 Dunblain 56 21 Dunkel 56 48 Edinburgh 55 56 Glascow 55 52 Kintaile 57 44 Orkney Isle 60 6 St. Andrewes 56 39 Skirassin 58 36 Sterling 56 12 IRELAND d. m. Autrim 54 38 Arglas 54 10 Armach 54 14 Caterlagh 52 41 Clare 52 34 Corke 51 53 Droghedah 53 38 Dublin 53 13 Dundalk 53 52 Galloway 53 2 Youghal 51 53 Kenny 52 27 Kildare 53 00 Kings towne 53 8 Knock fergus 54 37 Kynsale 51 41 Lymerick 52 30 Queens towne 52 52 Waterford 52 9 Wexford 52 18 A Table of the right Ascensions and Declinations of some of the most principal fixed Stars for some yeares to come   R. Ascension Declination Magnitude   H m D. m.   Pole Star 00 31 87 34 N 2 Andromedas Girdle 00 50 33 50 N 2 Whales Belly 01 35 12 S 3 Rams head 1 48 21 49 N 3 Whales mouth 2 44 2 42 N 2 Medusas head 2 46 39 35 N 3 Perseus right side 2 59 48 33 N 2 Buls eye 4 16 15 46 N 1 Goat 4 52 45 37 N 1 Orions left foot 4 58 8 38 S 1 Orions left shoulder 5 6 5 59 N 3 First in Orions girdle 5 15 00 35 S 3 Second in Orions girdle 5 19 1 27 S 3 Third in Orions girdle 5 23 2 9 S 3 Orions right shoulder 5 36 7 18 N 2 The Wagoner 5 39 44 56 N 2 Bright foot of the Twins 6 18 16 39 N 3 Great Dog 6 30 16 13 S 1 Castor or Apollo 7 12 32 30 N 2 The little Dog 7 22 6 6 N 2 Pollux or Hercules 7 24 28 48 N 2 Hidra's heart 9 10 7 10 S 1 Lions heart 9 50 13 39 N 1 Lions Neck 9 50 21 41 N 3 Great Beares rump 10 40 58 43 N 2 Lions back 11 30 22 4 N 2 Lions tail 11 31 16 30 N 1 The Virgins girdle 12 38 5 20 N 3 First in the great Bears taile next the rump 12 38 57 51 N 2 Vindemiatrix 12 44 15 51 N 3 Virgins Spike 13 7 9 19 S 1 Middlemost in the Great Beares tail 13 10 56 45 N 2 Last in the end of the Great Beares tail 13 34 51 05 N 2 Arcturus 14 00 21 03 N 1 South Ballance 14 32 14 33 S 2 Brightest in the Crown 15 24 27 43 N 3 North Ballance 14 58 08 03 S 3 Serpentaries left hand 15 56 02 46 S 3 Scorpions heart 16 08 25 35 S 1 Serpentaries left knee 16 18 09 46 S 3 Serpentaries right knee 16 49 15 12 S 3 Hercules head 16 59 14 51 N 3 Serpentaries head 17 19 12 52 N 3 Dragons head 17 48 51 36 N 3 Brightest in the Harp 18 25 38 30 N 1 Eagle or Vultures heart 19 34 08 00 N 2 Upper horn of Capricorn 19 58 13 32 S 3 Swans tail 20 30 44 05 N 2 Left shoulder of Aquarius 21 13 07 02 S 3 Pegasus mouth 21 27 08 19 N 3 Right shoulder of Aquarius 21 48 01 58 S 3 Fomahant 22 39 31 17 S 1 Pegasus upper Wing or Marchab 22 48 13 21 N 2 Pegasus Lower Wing 23 55 33 25 N 2 Mr. Sutton knowing that some of the Tables of Declination and Right Ascension in our English Books are antiquated and removed forward took the pains to Calculate a new Table of Right Ascensions and Declinations to serve for the future in regard I was not at leisure to accomplish it which followeth Dayes January ☉ R A. ☉ Decl. H. M. D. M. 1 19 35 21 46 2 19 39 21 36 3 19 43 21 25 4 19 47 21 14 5 19 51 21 03 6 19 56 20 52 7 20 00 20 40 8 20 04 20 27 9 20 09 20 15 10 20 13 20 01 11 20 17 19 48 12 20 22 19 34 13 20 26 19 20 14 20 30 19 05 15 20 34 18 50 16 20 38 18 35 17 20 42 18 19 18 20 46 18 03 19 20 50 17 47 20 20 54 17. 30 21 20 58 17 13 22 21 03 16 56 23 21 07 16 39 24 21 11 16 21 25 21 15 16 03 26 21 19 15 44 27 21 23 15 26 28 21 27 15 07 29 21 31 14 48 30 21 35 14 28 31 21

Night and the difference between 90d and either of those Arks is the Ascensional difference or time of rising and setting from 6. To find the Azimuth generally The Proportions for this purpose have been delivered before from which it may be observed that there are no two terms fixed and therefore to every Altitude the containing sides of the Triangle namely the Complements both of the Altitude and Latitude must be summed and differenced when the Proposition is to be performed on this Line solely and the Operation will be after the same manner as for the hour namely with a Parallel entrance and this is all I shall say of the Authors general way and of any other that he used I never heard of those ways that follow being of my own supply By help of this Line to work a Proportion in Sines alone wherein the Radius leads As the Radius Is to the Sine of any Ark So is the Sine of any other Ark To the Sine of a fourth Ark. This fourth Sine as I have said before is demonstrated by M. Gellibrand to be equal to half the difference of the Versed Sines of the Sum and difference of the two middle terms of the Proportion Operation Let the Proportion be As the Radius Is to the Sine of 40d So is the Sine of 27 To a fourth Sine Sum 67 Difference 13 Take the distance between the Versed Sines of the said sum and difference and measure it on the Line of Sines from the Center and it will reach to 17d the fourth Sine sought By help of this Line may the Divisions of the line Sol or Proportional Sines be graduated to any Radius less then half the Radius of the Quadrant the Canon is As the Versed Sine of any Ark added to a Quadrant Is to the Radius or length of the Line Sol So is the Versed Sine of that Arks Complement to 90d To that length which pricked backward from the end of the Radius of the said Line shall graduate the Arch proposed Example Suppose you would graduate 20 of the Line Sol enter the Radius of the said Line upon the Versed Sine of 110d laying the thred to the other foot and from the Versed Sine of 70d take the nearest distance to the thred which prick from the end of the Line Sol towards the beginning and it shall graduate the said 20d. This Line Sol is made use of by M. Foster in his Scale for Dyalling The Line of Versed Sines was placed on the left edge of the foreside of the Quadrant for the ready taking out the difference of the Versed Sines of any two Arks and to measure a difference of two Versed Sines upon it which are the chief uses I shall make of it whereas to Operate singly upon it it would be more convenient for the hand to have it lie on the right edge of the Quadrant An example for finding the Azimuth generally by help of Versed Sines in the Limb and of other Lines on the Quadrant I shall rehearse the Proportion As the Cosine of the Latitude is to the Secant of the Altitude Or As the Cosine of the Altitude is to the Secant of the Latitude So is the difference of the Versed Sines of the Suns distance from the Elevated Pole and of the Ark of difference between the Latititude and Altitude To the Versed Sine of the Azimuth from the midnight meridian And making the latter clause of the third term the Complement of the Sum of the Latitude and Altitude to a Semicircle the Proportion will find the versed Sine of the Azimuth from the noon Meridian Example Altitude 51d 32′ Latitude 34 32 Complement 55d 2● Difference 17 00 ☉ distance from elevated Pole 66 29 Operation in the first Terms of the Proportion On the Line of Versed Sines take the distance between 17d and 66d 29′ and entring it twice down the line of Sines from the Center take the nearest distance to the thread laid over the Secant of 51d 32′ the given Altitude and entring one foot of this Extent at the Sine of 55d 28′ the Complement of the Latitude lay the thred to the other foot according to nearest distance and in the line of Versed Sines in the Limb it will lie over 95d for the Suns Azimuth from the midnight meridian And the Suns declination supposed the same he shall have the like Azimuth from the North in our Latitude of London when his Altitude is 34d 32′ for the sides of the Triangle are the same Another Example To find it in the versed Sine of 90d Latitude 47d 27′ Altitude 51 32 Sum 98 59 Complement 81 1 Polar distance 66 29 Take the distance in the Line of Sines as representing the former half of a Line of Versed Sines between these two Arks counted towards the Center viz. 66d 29′ and 81d 01′ and enter this extent twice down the Line of Sines from the Center and take the nearest distance to the thred lying over the Secant of the Latitude 47d 27′ then enter one foot of this extent at 51d 32′ counted from the end of the Sines towards the Center laying the thred to the other foot according to nearest distance and in the Versed Sine of 90d it shews the Azimuth to be 65d from the South in this our Northern Hemispere Of the fitted Particular Scale and the Line of Entrance thereto belonging THis Scale serves to find both the Hour and Azimuth in the Latitude of London to which it is fitted in the equal Limb by a Lateral or positive Entrance it consists of two Lines of Sines The greater is 62d of a Sine as large as can stand upon the Quadrant the Radius of the lesser Sine is made equal to 51d 32′ of this greater being fitted to the Latitude The Scale of Entrance standing within the Projection and abutting on the Line of Sines is no other but a portion of a Line of Sines whose Radius is made equal to 38d 28′ of the greater Sine of the fitted Scale and this Scale of Entrance is numbred by its Complements up to 62d as much as is the Suns-greatest meridian Altitude in this Latitude The ground of this Scale is derived from the Diagonal Scale the length whereof bears such Proportion to the Line of Sines whereto it is fitted as the Secant of the particular Latitude doth to the Radius which is the same that the Radius bears to the Cosine of the Latitude and consequently making the Line of Sines to represent the fitted Scale the Radius of that Sine whereto it is fitted must be equal to the Cosine of the Latitude and so we needed no particular Scale but this would remove the particular Scale or Scale of Entrance nearer the Center and would not have been so ready as this fitted Scale however hence I might educe a general method for finding the hour and Azimuth in the Limb without Tangents or Secants The first Work would be

Azimuth shall be 9d 28′ from the Vertical at the hour of 6 in our Latitude of London Another Example to find the time when the Sun will be due East or West Extend the thred over the Latitude in the Semicircle and over the Declination on the Diameter and in the Quadrant of Latitudes it shews the Ark sought The Proportion wrought is As the Radius to the Cotangent of the Latitude So is the Tangent of the Declination To the Sine of the Hour from 6. Example So when the Sun hath 15● of North Declination in our Latitude of London the Hour will be found 12d 18′ from 6 in time 49⅕′ past 6 in the morning or before it in the afternoon Another Example to find the Time of Sun rising As the Cotangent of the Latitude to Radius So is the Tangent of the Declination To the Sine of the Hour from 6 before or after it Lay the thred to the Complement of the Latitude in the Semicircle and over the Declination on the Diameter and in the Quadrant of Latitudes it shews the time sought in degrees to be converted into common time by allowing 15● to an hour and 4′ to a degree So in the Latitude of London 51d 32′ when the Sun hath 15● of Declination the ascensional difference or time of rising from 6 will be 19d 42′ to be converted into common time as before By what hath been said it appears that the Hour and Azimuth may be found generally by help of this Circle and Diameter For the performance whereof we must have recourse to the Proportions delivered in page 123. whereby we may alwaies find the two Angle adjacent to the side on which the Perpendicular falleth which may be any side at pleasure for after the first Proportion wholly in Tangents is wrought to find either of those Angles will be agreeable to the second case of right angled Spherical Triangles wherein there will be given the Hypotenusal and one of the Legs to find the adjacent Angle only it must be suggested that when the two sides that subtend the Angle sought are together greater then a Semicircle recourse must be had to the Opposite Triangle if both those Angles are required to be found by this Trigonometry otherwise one of them and the third Angle may be found by those directions by letting fall the perpendicular on another side provided the sum of the sides subtending those Angles be not also greater then a Semicircle or having first found one Angle the rest may be found by Proportions in Sines only IN the Triangle ☉ Z P if it were required to find the angles at Z and ☉ because the sum of the sides ☉ P and Z P are less then a Semicircle they might be both found by making the half of the Base ☉ Z the first Tearm in the Proportion and then because the angles ☉ Z are of a different affection the Perpendicular would fal without on the side ☉ Z continued towards B as would be evinced by the Proportiod for the fourth Ark discovered would be found greater then the half of ☉ Z hence we derived the Cannon in page 124 for finding the Azimuth Whereby might also be found the angle of Position at ☉ so if it were required to find the angles at ☉ and P the sides ☉ Z and Z P being less then a Semicircle the Perpendicular would fall within from Z on the side ☉ P as would also be discovered by the Proportion for the fourth Ark would be found less then the half of ☉ P. But if it were required to find both the angles at Z and P in this Case we must resolve the Opposite Triangle Z B P because the sum of the sides ☉ Z and ☉ P are together greater then a Semicircle and this being the most difficult Case we shall make our present Example The Proportion will be As the Tangent of half Z P Is to the Tangent of the half sum of Z B and P B So is the Tangent of half their difference To a fourth Tangent That is As Tangent 19d 14′ Is to the Tangent of 86d 30′ So is the Tangent of 9d 30′ To a fourth Operation Extend the Thread through 19 d 14′ on the Semicircle and 9 d 30′ on the Diameter and hold it at the Intersection on the opposite side the Semicircle then lay the Thread to 86 d 30′ in the Semicircle and it shews 82 d 44′ on the Diameter for the fourth Ark sought Because this Ark is greater then the half of Z P we may conclude that the Perpendicular B A falls without on the side Z P continued to A. fourth Ark 82d 44′ half of Z P is 19 14 sum 101 58 is Z A difference 63 30 is P A Then in the right angled Triangle B P A right angled at A we have P A and B P the Hypotenusal to find the angle B P A equal to the angle ☉ Z P. The Proportion is As the Radius Is to the Tangent of 13d the Complement of B P So is the Tangent of P A 63d 30′ To the Cosine of the angle at P. Extend the Thread through 13 d on the Diameter and through 63 d 30′ in the Semicircle counted from the other end and in the upper Quadrant it shews 27 d 35′ for the Complement of the angle sought And letting this Example be to find the Hour and Azimuth in our Latitude of London so much is the hour from six in Winter when the Sun hath 13 d of South Declination and 6 d of Altitude in time 1 ho 50⅓ minutes past six in the morning or as much before it in the afternoon To find the Azimuth Again in the Triangle Z A B right angled at A there is given the Leg or Side Z A 101 d 58′ and the Hipotenusal Z B 96 d to find the angle B Z P here noting that the Cosine or Cotangent of an Ark greater then a Quadrant is the Sine or Tangent of that Arks excess above 90 d and the Sine or Tangent of an Ark greater then a Quadrant the Sine or Tangent of that Arks Complement to 180 d it will hold As the Radius To the Tangent of 6d So is the Tangent 78d 2′ To the Sine of 29 d 44′ found by extending the Thread through 78 d 2′ on the Semicircle counted from the other end alias in the small figures and in the Quadaant it will intersect 29 d 44′ now by the second Case of right angled Sphoerical Triangles the angle A Z B will be Acute wherefore the angle ☉ Z B is 119 d 44′ the Suns Azimuth from the North the Complement being 60 d 16′ is the angle A Z B and so much is the Azimuth from the South To work Proportions in Sines alone THat this Circle might be capacitated to try any Case of Sphoerical Triangles there are added Lines to it namely the Line Sol falling perpendicularly on the Diameter from the end of the