and Circle of Latitude passing by any Star, is called, The Lon- Fig. gitude of that Star: And the Ark, which in the faid Circle of XXV. • Latitude, is between the Ecliptick and the Star, is the Stars Latitude: And all this is to be understood of the Cæleftial Globe. But upon the Terrestrial Globe, the Longitude and Latitude of any Place are referred to the Equinoctial and Meridian: So the Longitude of an Earthly Place is an Ark of the Æquinostial, intercepted between the First Meridian, and the Meridian paffing by the fame Place. And the Latitude of the fame Place is, an Ark of the Meridian, to be reckoned from the Equinoctial 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 faid Amplitude is either North or South, according to the Beaming of the Sun or Star, in respect of the true Eaft or West Points. The Altitude of the Sun or a Star, is taken in the Vertical Circle, paffing by the fame, between the Horizon and the faid Star: So the Depreffion of the Star is, An Arch of the Vertical Circle, between the Horizon and the faid Star.

ANCILLA

ANCILLA MATHEMATICA.

VEL,

Trigonometria Practica.

SECTION III.

Fig.

XXVI.

T

OF

GEOGRAPHY.

HE following Geographical Problems being first to be performed upon the Terrestrial Globe; upon which the Spherical Triangle, that resolves any Question is discovered, in order to the Trigonometrical Calculation : I conceive it neceffary, in the first place, to infert this General

PROBLEM.

How to Measure the Sides and Angles, of all Spherical Triangles, upon the Convex Superficies of the Globe.

T

are

HE Sides of all Spherical Triangles upon the Globe, 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 fuch Great Circles as are actually divided into Degrees upon the Globe, or its Appendants; as the Equinoctial, 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 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 fuch Side in a Pair of Calliper Compasses, and apply it to any of the forementioned Great Circles (as the EquinoFial, &c.) it shall thereupon shew you the Quantity of that Side in Degrees. -Or, the Quadrant of Altitude (but rather, a thin Plate of Brafs 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, shall 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 counting (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.

PROB. Ι.

To find the Longitude of any Place, described upon the Terreftrial
Globe.

Longitude

is the Distance of a Place from the first Meridian reckoned in the Degrees of the Equator, beginning, as was faid, 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) suppose London, to the Brazen Meridian; then count how many Degrees of the Equator are contained between the first Meridian, and that of London cut 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