Fig. XXV.

is called Sphæra Parallela. The Sun moving in that part of the Ecliptick, which is above the Horizon, that is on one fide of the Equinoctial, doth never fet, but is turned continually round about, and maketh a Day of Six Months: So likewife, running through the other Six Signs that are under the Horizon, it doth never rife, but maketh a Night of Six Months alfo.

XXV. The Angle which any Degree of the Ecliptick maketh with the Right Horizon, (that is, in Sphæra Resta) is equal to that Angle which the fame. Degree of the Ecliptick, maketh with the Meridian: But whether the Ecliptick make fuch an Argle with the Right or Oblique Horizon, the farne Angle is always called the Angle Orient; that is, of the rifing Degree of the Ecliptick; and its Meafure is in the Circle of the 90th Degree, between the faid goth Degree and the Horizon..

XXVI. The Angle which the Meridian maketh in the Pole of the World with any Circle of Declination, taketh its Measure in the Equinoctial, between the Meridian and the faid Circle of Declinatial, and this they call, The Distance of the Star from the Meridian. So likewife the Angle which the Meridian maketh with the Vertical Circle at the Zenith, taketh its Measure in the Horizon, between the Meridian and the faid Vertical, and this they call, The Azimuth of the Sun or Star..

XXVII. The Arks to be measured in every Principal Great Cir. cle, or its Secondaries, have alfo their proper Appellations: So the Ark of the Equinoctial, which is comprehended between the beginning of r, and the Circle of Declination paffing by any Star, is called the Right Afcenfion of that Star: And the Ark which in the faid Circle of Declination, is between the Aquinoatial and the Star, is called, The Declination of that Star. But the Oblique Afcenfion of a Star, is an Ark of the Equinoctial, reckoned from the beginning of r, to the Point of the Aquinoial Rifing with that Star: So likewife, the Oblique Defcenton of a Star is, the Ark of the Equino&ial reckoned from the beginning of, to that Point of the Equinoctial, which is a fetting together with the Star. Now the Difference that is between the Right and Oblique Afcenfion of the Sun, or any Star, is called, The Afcenfional Difference. Moreover, the Ark of the Ecliptick, which is between the beginning of r

and

Fig.

and Circle of Latitude paffing by any Star, is called, The Longitude 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 Terreftrial 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 Equinoctial, intercepted between the First Meridian, and the Meridian paf fing 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 Eaft or Weft Points, and that Point where the Sun or Star doth Rife or Set: And the faid Amplitude is either North or South, according to the Beaming of the Sun or Star, in refpect of the true Eaft or Weft 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.

OF

GEOGRAPHY.

THE

HE following Geographical Problems being firft to be performed upon the Terreftrial Globe; upon which the Spherical Triangle, that refolves any Queftion is difcovered, in order to the Trigonometrical Calculation: I conceive it neceffary, in the firft place, to infert this General

PROBLEM.

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

HE Sides of all Spherical Triangles upon the Globe, are

Fig, T Measured by the Degrees of thofe Great Circles, that make

XXVI.

(or conftitute) 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 quino&ial, 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