Astronomy, Book I.

CHAPTER 14.

Concerning other circles, such as those of Declination and Latitude: including Right Ascension and the Longitude of the Stars.

The circles called Declination and Latitude are especially necessary to understand.
The circles of Declination are those drawn through the poles of the world The poles of the world are the two points in the sky around which the stars appear to rotate, aligned with the Earth's axis of rotation. that intersect the Equator at right angles. Since the Declination of stars is measured from the Equator toward either pole of the world, it is clear that the Declination of any star or celestial point is simply the arc of one of these circles intercepted between the Equator and that star or point.
It is established that Declination is therefore of two types: one Northern original: "Borealem" and the other Southern original: "Australem", depending on whether the point or star is to the north or south of the Equator.
As seen in the diagram below: when A-B is the Equator; C is the North Pole and D is the South Pole; C-A-D-B is the Solstitial Colure, and C-E-D is the Equinoctial Colure The Colures are two great circles that intersect at the celestial poles; one passes through the equinoxes and the other through the solstices.; then the Colures themselves, as well as the circles C-F-D, C-G-D, C-H-D, and C-I-D, are circles of Declination. The Declination of star K (which is Northern) is the arc H-K. The Declination of star L (which is Southern) is the arc I-L. In the same way, the Declination of the solstitial points M and N will be B-M for the Northern and A-N for the Southern.

A circular astronomical diagram representing the celestial sphere. It features a central circle with various intersecting lines and arcs labeled with letters A, B, C, D, E, F, G, H, I, K, L, M, N, O, P, Q, R, S, T. The vertical axis connects poles C and D, while the horizontal axis A-B represents the Equator. Several longitudinal arcs, representing meridians or declination circles, converge at the poles. Symbols for the zodiac signs of Cancer and Capricorn are visible near points M and N. A secondary tilted axis O-P represents the poles of the Ecliptic, the path the Sun follows through the sky.

It should be noted that Right Ascension is paired with Declination. This is the name given to the arc of the Equator from the beginning of Aries symbol: ♈︎ to the point where the specified circle of Declination intersects the Equator. This point rises or ascends at the same time as the designated celestial point or star on a "right" horizon. What constitutes a right or an oblique horizon will be explained more fully in the following chapter.
Thus, the Right Ascension of star K is the arc of the Equator E-H; for star L, it is the arc E-I. For the beginning of Cancer (M), it is the arc E-B, which is a quadrant, or 90 degrees. For the beginning of Capricorn, it is the arc E-B along with the entire remaining hemisphere up to A, which is three-quarters of a circle, or 270 degrees.
It is called "Right" Ascension because when the horizon is oblique An oblique horizon is one where the celestial equator meets the horizon at an angle other than 90 degrees, which occurs everywhere except at the Earth's equator., the Ascension is also Oblique. In that case, the same point on the Equator no longer rises at the same time as the designated star, but rather some other point rises earlier or later. From this, the arc of the Equator intercepted between these two points is called the Ascensional Difference.
In this City Gassendi is likely referring to Paris, where he worked., for example, the Ascensional Difference for the beginnings of Cancer symbol: ♋︎ and Capricorn symbol: ♑︎ is 30 degrees. Because the start of Cancer rises later, and the start of Capricorn rises earlier, than the point of Right Ascension, it follows that the Oblique Ascension of the start of Cancer in Paris is 120 degrees, and for Capricorn it is 240 degrees. This same proportion is understood to apply to the stars.

Circles of Latitude are those drawn through the poles of the Zodiac, or Ecliptic, which intersect the Ecliptic at right angles. Since the Latitude of stars is measured from the Ecliptic, it is clear that Latitude is nothing other than the arc of one of these circles intercepted between the Ecliptic and the designated star or celestial point.
It is similarly established that Latitude is of two types, Northern and Southern, depending on whether the star is north or south of the Ecliptic.
In the previous diagram, where N-M is the Ecliptic, O is the Northern pole of the Ecliptic, and P is the Southern pole; O-N-P-M is the same Solstitial Colure. Both this Colure and the dotted circles O-Q-P, O-R-P, O-S-P, O-T-P, and O-V-P are circles of Latitude. The Latitude of star K (and its Northern...