Ok!

Now let's define some words to clarify the complex ideas that Ibn Khaldoun was trying to explain:

Qutb (plural: Al-Aqtaab) = Pole of either Earth or Celestial Spheres

Da2era 3azimah = Great Circle (opposite to Small Circle in 3D geometry). When you cut a spherical body (a ball) in two 'equal' halves, you've cut it at a "Great Circle". The Equator (latitude 0 of Earth) is a Great Circle. Also all the 'longitudes'. Small Circles are any circle that doesn't cut it in equal halves. All latitudes except Equator are Small Circles. There's no doubt that English and other European languages inherited the term from Arabic (search google with define:great cirlce and you'll see)

Al-Falak (Al-A3la) = Celestial Sphere or Celestial Dome (half sphere) as seen from Earth

Al-Aflaak = Celestial (Bodies/Constellations/Regions not sure?)

Al-Boroug (sgl: Borg) = Constellations (specially Zodiacal)

Mamar = Path (eg, the 'path' of the Sun is "Ecliptic" Circle)

Ofoq = Horizon Circle

Al-Mashreq, Al-Magherb = East and West on BOTH Celestial and Earth spheres

Da2erat Mu3addel Al-Nahar = Celestial Equator Circle. I wasn't sure how to pronounce the word 'm3dl', but I decided that since the 'Equator' that was translated from it is ISM FA3ELL in English, I thought I could use the form of ISM ALFA3ELL in Arabic too. Tell me what you think.

Da2erat Falak Al-Boroug = Ecliptic Circle. I found that very clear to understand since he's mentioned it by its definition and that is how it is divided to the 12 Zodiac constellations and intersecting with the Celestial Equator. I deduced the meaning of Al-Boroug (constellations) from it and also 'Falak' which I am starting to believe it's a general word for Celestial 'regions' or parts of the skies that are neither a certain constellation nor a certain celestial body.

Awal Al-7amal = First of Aries (Vernal Equinox). Do you know that the Ecliptic actually moved from time of Ibn Khaldoun when the intersection of the Ecliptic and C.Equator (Vernal Equinox) were at the Aries??? It's now at Pisces! Even as we speak today the Vernal Equinox located in the far edge of Pisces is called 'First of Aries' in Western Astronomy!

Awal Al-Mizaan = First of Libra (Autumnal Equinox). Same as Awal Al-7amal.

Samt (verb: yusaamet) = Corresponding point in the other sphere (Earth or Celestial Sphere). An observer-person has his 'Samt' point in the Celestial Sphere at the Observer's Zenith. The Sun 'TUSAAMET' a person when it's at the Zenith of this person. Celestial Equator 'YUSAAMET' Earth's Equator. Geometrically, a point is (MUTASAAMETAH) with a star when an imaginary line that passes them could pass too through the Earth's centre. For lines, only Great Circles can be (MUTASAAMETEEN) and are having a plane passing through them that could pass through Earth's centre too. In layman's terms (compromising accuracy indeed), a Celestial point or line are (mutasaameteen) with others on Earth when they're exactly 'above' them. This is wider definition of the simple 'Zenith' word. 'Zenith' is usually the translation of "Noqtat Al-Samt".

Aaaaaall questions/comments are welcome on SSC. Ibn Khaldun deserves all that and more. :)