Quadrant

In stellar cartography, a quadrant is a major region of space encompassing a portion of a galaxy.

Major quadrants
The Milky Way Galaxy was commonly divided into four equally sized, cubic quadrants, defined by one meridian passing through the galactic core and a second one perpendicular to the first, that also passes through the galactic core. These four quadrants are referred to as the Alpha Quadrant, Beta Quadrant, Gamma Quadrant and Delta Quadrant. The United Federation of Planets and its neighboring powers, including the Klingon and Romulan Empires were located in the Alpha and Beta Quadrants, whereas the Borg Collective was located in the Delta Quadrant, and the Dominion in the Gamma Quadrant. The division into four quadrants was used by United Earth and the Vulcans as early as the mid-22nd century. In 2152, after less than a year into the mission of, it was remarked by Vulcan Ambassador Soval, that he considered the ship to be a danger to the quadrant. By that time, the Enterprise had involved itself in several armed conflicts and escalated the conflict between the Vulcans and the Andorians. In 2154, the subspace message sent by the Borg was determined to have a destination deep inside the Delta Quadrant. 

In 2267, when Lazarus and anti-Lazarus began changing places between each other, the physical laws of the universe were distorted for a brief moment. Captain Kirk noted in his log, that the effects were felt throughout the entire quadrant of space. According to Commodore Barstow of Starfleet Command, the effect occurred in every quadrant of the Galaxy and far beyond. 

Minor quadrants
Smaller areas of space in the Galaxy were also referred to as a quadrants during the 23rd and 24th centuries. These included: Quadrant 9, Quadrant 448, Quadrant 904, the Morgana Quadrant, and the Drema Quadrant. 

In 2266, the Federation starship USS Enterprise (NCC-1701) conducted a survey of a quadrant in which the ship was located. According to Spock, there were no disturbances in this region. 

In 2267, following the loss of the shuttlecraft Galileo in the Murasaki Effect, the Enterprise shuttlecraft Columbus conducted a search of quadrant 779X by 534M. After reporting negative results, the shuttle was ordered by Captain Kirk to proceed to the next quadrant. During that year, negotiations to build a treaty port on Vendikar for the quadrant where the planet was located, were conducted by Federation Ambassador Robert Fox. During the same year, unit XY-75847 reported a fleet of Klingon ships in their sector, which was located in the same quadrant as the planet Organia. Also during the same year, the planet Argelius was of strategic importance as a space port to the Federation. At the time, it was the only port in that quadrant. 

By 2268, the quadrant of space that included such notables as Deep Space Station K-7, Donatu V, and Sherman's Planet, had been under dispute between the Federation and Klingon Empire since initial contact. In that year Nilz Baris served as the Federation Undersecretary in charge of Agricultural Affairs in said quadrant. 

Also in 2268, during the transport mission to Babel, the Enterprise encountered an unidentified vessel that was shadowing their route. Following contact with Starfleet, the Enterprise received acknowledgment which confirmed that there were no other authorized Federation vessels in the quadrant. During the same year, when the Enterprise was exploring an outer quadrant of the Galaxy when it received a distress call from the planet Scalos. 

In 2269, the Enterprise was ordered to respond to a botanical plague that was devastating a planet in the quadrant of the Galaxy where the ship was operating at the time. In 2270, when the Enterprise encountered Kukulkan's starship, it was noted that Starfleet listed no other authorized vessels in that particular quadrant. 

In 2284, when the Enterprise was ordered to Regula I by Starfleet Command, Admiral Kirk informed them that "all we had was a boatload of children," but they were nevertheless diverted because they were the only ship in the quadrant. While en route to Regula, the Enterprise encountered the USS Reliant, under the command of Khan Noonien Singh. Once the two ships were in visual range of each other, it was noted that the Reliant had entered their section of the quadrant. 

In 2364, the planet Aldea was discovered in quadrant 1, mark 9-0, in the Epsilon Mynos system, by the USS Enterprise (NCC-1701-D). Later that year, the Enterprise-D received a communique from Starfleet reporting a battle in Quadrant 9, coordinates 070-mark-3, in the Klingon Neutral Zone. During that year, the Enterprise-D picked up an unusual disturbance in a nearby quadrant, more specifically in Sector 63. The disturbance was caused by the destruction of the USS Horatio. 

As of 2365, the Morgana Quadrant, was a section of the Galaxy that had not yet been visited by a manned Federation vessel. Talos IV was located in the third quadrant of Vernal Galaxy. 

Background information
The term quadrant was first mentioned in "Charlie X".

The minor quadrants were clearly of variable sizes. In some cases a quadrant was an area outside the ship in visual range, such as in Star Trek II: The Wrath of Khan and "When The Bough Breaks" or an area that could still be quickly explored with sublight shuttlecraft, such as those mentioned in "The Galileo Seven". In other cases quadrants were composed of multiple sectors, such as the ones mentioned in "Errand of Mercy" and "Conspiracy". In "Heart of Glory", "Quadrant 9, coordinates 070-mark-3" was also shortened as "Quadrant 907-mark-3".

According to the Star Trek Encyclopedia, the reason for splitting the Federation between Alpha and Beta Quadrants was to rationalize Kirk's line in Star Trek II: The Wrath of Khan that the Enterprise was the only starship in the Quadrant. Quadrants and sectors have been used inconsistently in various Star Trek episodes and films. During The Original Series, the term quadrant was used rather freely, as was the term sector. At times, quadrant seems to refer to a fourth of the entire galaxy, while at others it seems to be a portion of a smaller region. It was not until the episode  of Star Trek: The Next Generation that the current system of Alpha, Beta, Delta, and Gamma quadrants was firmly established. Retroactively, Star Trek VI: The Undiscovered Country adhered to this system as well, as did Star Trek: Enterprise.

Furthermore, according to the Encyclopedia, Earth marks the border between Alpha and Beta Quadrants. The display graphic on a PADD in would seem to confirm this. Dialogue in Star Trek: Voyager and Star Trek: Deep Space Nine however firmly establish that Earth is located on the Alpha Quadrant side of the border.

Additionally, Bjo Trimble explained in the Star Trek Concordance that a quadrant is "an area of space (a misnomer, as it should be called an octant)."

Quadrant Квадрант Kvadrant