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and Circle of Latitude pafling by 'any Star, is called, The Lon- Fig. gitude of that Star: And the drk, which in the said Circle of XXV. Latitude, is between the Ecliptick and the Star, is the Stars Latitude: And all this is to be understood of the Cælestial Globe. But upon the Terrestrial Globe, the Longitude and Latitude of any Place are referred to the Aquinoltial and Meridian: So the Longitude of an Earıbly Place is an Ark of the Æquinotial, intercepted between the First Meridian, and the Meridian pafsing by the same Place. And the Latitude of the same Place is, an Ark of the Meridian, to be reckoned from the Æquinoctial to the Place upon the Globe.

XXVIII. In the Horizon we reckon the Amplitude of the Sun or

any Star, between the true East or West Points, and that Point where the Sun or Star doth Rise or Set: And the said Amplitude is either North or South, according to the Beaming of the Sun or Star, in respect of the true East or West Poinis. The Altitude of the Sun or a Star, is taken in the Vertical Circle, passing by the same, between the Horizon, and the said Star: So the Depression of the Star is, An Arch of the Vertical Cir. cle, between the Horizon and the said Star.

ANCILLA

ANCILLA MATHEMATICA.

V EL,

Trigonometria Practica.

SECTION III.

O F

GEOGRAPHY.
TH

HE following Geographical Problems being first to be per

formed upon the Terrestrial Globe ; upon which the Spherical Triangle, that resolves any Question is discovered, in order to the Trigonometrical Calculation : 1 conceive it necessary, in the first place, to insert this General

PROBLE M.

How to Measure the Sides and Angles, of all Spherical Triangles,

upon the Convex Superficies of ihe Globe. Fig.

HE Sides of all Spherical Triangles upon the Globe, are XXVI. Measured by the Degrees of those Great Circles, that make

, (or constitute) the Triangle, contained between the Two Angular Points.

1. If the Side, or Sides, of the Triangle to be measured, do confift of such Great Circles as are actually divided into Degrees upon the Globe, or its Appendants; as the Æquino&tial, the Colures, the Ecliptick, the general Meridian or Horizon : Then, the number of Degrees contained in that Great Circle, contained between the Two Angular Points; is the Quantity of that Side of that Triangle in Degrees. But,

2. If

1

2. If the Side or Sides of the Triangle be composed of Arches Fig. of such Great Circles as are not actually divided (as all Circles XXVI. of Longitude, and other Oblique Great Circles) then, take the Length of such Side in a Pair of Calliper Compasses, and apply it to any of the forementioned Great Circles (as the Aquinotial, &c.) it shall thereupon shew you the Quantity of that Side in Degrees. -Or, the Quadrant of Altitude (but rather, a thin Plute of Brajs longer than the Quadrant of Altitude, divided into Degrees, as the Quadrant is) applied to the Side to be Measured, between the Two Angular Points, Ihall give you the Quantity of the Degrees of that Side of the Triangle.

II. For the Angles. The Angles of Spherical Triangles are Measured upon the Superficies of the Globe; by councing (or setting off) 90 Deg. from the Angular Point, of the Angle to be Measured, upon both the Sides which contains the Angle to be Measured : And at the Terminations of those 90 Deg. on both the Sides, make Two small Marks upon the Globe. Unto these Two Marks, apply the Quadrant of Altitude, or thin Plate of Brass; so the Number of the Degrees thereof, contained between the Two Marks, is the Quantity of that Angle.

Geographical Problems .

PRO B. I.

To find the Longitude of any Place, described upon the Terrestrial

Globe.
L O , i

reckoned in the Degrees of the Fquator, beginning, as was said, in the New Terrestrial Globe, (made by Mr.

Morden) as St. Michael's Ifland in the Azores.

Practice.] Bring the Place, (that is, the Mark of the Place) suppofe London, to the Brazen Meridian; then count how many Degrees of the Equator are contained between the first Meridian, and that of London cur by the Brazen Meridian, which you will find to be 28 Deg. and that is the Longitude required. And in this manner you find

London

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To find the Latitude of any Place, ,
TH

HE Latitude of a Place, is the Distance of the Equator

from the Parallel of that Place, reckoned in the Degrees of the Brass Meridian; and is either North or South, according as it lyes between the North or South Poles of the Equator.

To find the Latitude, bring the Mark of the Place, suppose London, to be the Brazen Meridian; then count the Number of Degrees upon the Meridian, contained between the Equator and the Place o. Thus you shall find the Latitude, by this new Globe, of London, to be 51 Deg. 30 Min. and of

D. M.

D. M. Labor in the Mogul's Country to be ( 31 30

23 30 The South Part of the Caspian Sea to be

By other 37

Globes

141 Astracan on the North Part of the

and Caspian Sea to be

46 0

49 The North Part of China to be

Maps. 42

52 Delli in India to be

28

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PRO B. III.

Two Places, which differ only in Latitude, to find their Distance.

N this there are Two Varieties of Position.
IN

1. If both the Places lye under the fame Meridian, and on one and the same side of the Æquinoctial: Substract the Lesler Latitude from the Greater, the Difference (or Remainder) reduced into Miles, (by allowing 60 Deg. to One Mile) shall give you the Distance.

Exam

Example. London and Ribadio lye both under the fame Me- Fig. ridian, but differ in Latitude: For London hath 51 Deg. 30 Min. XXVI. of Latitude, at L, and Ribadio hath 34 Deg. of Latitude, at R, both North; the Difference of Latitude is 17 Deg. 30 Min. equal to the Arch LR: And that Reduced into Miles, makes 1050 for their Distance.

2. If the Two Places lye under the fame Meridian, but in dif. ferent Hemispheres, i.e. one on the North, and the other on the South Side of the Aquinoctial : Then, Add both the Latitudes together, and the sum of them is their Distance..

Example. London, and the Island Tristan Dacunhu, lye both under One Meridian, bụt London hath 5ı Deg. 30 Min. of North Latitude, at L, and the Island háth 34 Deg. of South Latitude, at D; the Sum of these Two Latitudes is 85 Deg. 30 Min. equal to the Arch of the Meridian LÆD; the which reduced into Miles, (by multiplying the Degrees by 60, and allowing for every Minute One Mile) makes 5130 Miles, for their Distance.

PRO B. IV.

Two Places, which differ in Longitude only; To find their Distance.
N this there are Two Varieties of Position.

1. If the Two Places lve both under the Æquinoctial, and have no Latitude ; in this Cafe, Their Difference of Longitude (if it be less than 180 Deg) is their Distance: But, if the Difference exceed 180 Deg. Subtraĉt it from 360 Deg. and the Remainder is their Distance, in Degrees.

Example. The Island Samarra, and Mand St. Thomas, lye both under the Æquinotial : St. Thomas having 22 Deg. 10 Min. of Longitude at T, and the Island Sumatra 82 Deg. 10 Min. at S. Now, the Leffer Longitude 22 Deg, 10 Min. subltracted from the Greater 82 Deg. 10 Min. leaves 60 Deg. equal to the Arch S T, for their Dif. ference in Degrees: Which converted into Miles, makes 3600, and so many Miles are the Two Islands distant from each other.

2. But if the Two Places differ only in Longitude, and lye not in the Æquino&tial, but under fome other intermediate Parallel of Latitude: As Hierufalem at H, and Baldo at B; both in the Parallel of 31 Deg. 40 Min. of North Latitude, but differing in Longitude 60 D.g. 15 Min. equal to the Angle H PB, to find the Distance of these Two Places.

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