The Orient, as a noun, is a generic term used for the Far East. From about 600 AD, Christian cartographers made T-O Maps, which looked roughly like a T inscribed in an O (see teleny's T-O Map writeup).
The Orient went on top of the map (the East was at the top), and from this practice, we gained the English word "Orient" as a verb: to position something, particularly a map, so that it faces the way that the observer faces.

Sources:
Daniel J. Boorstin's wonderful book, "The Discoverers p. 101"

Etymology rocks.

O"ri*ent (?), a. [F., fr. L. oriens, -entis, p. pr. of oriri to rise. See Origin.]

1.

Rising, as the sun.

Moon, that now meet'st the orient sun.
Milton.

2.

Eastern; oriental. "The orient part." Hakluyt.

3.

Bright; lustrous; superior; pure; perfect; pellucid; -- used of gems and also figuratively, because the most perfect jewels are found in the East. "Pearls round and orient." Jer. Taylor. "Orient gems." Wordsworth. "Orient liquor in a crystal glass." Milton.

 

© Webster 1913


O"ri*ent, n.

1.

The part of the horizon where the sun first appears in the morning; the east.

[Morn] came furrowing all the orient into gold.
Tennyson.

2.

The countries of Asia or the East. Chaucer.

Best built city throughout the Orient.
Sir T. Herbert.

3.

A pearl of great luster. [R.] Carlyle.

 

© Webster 1913


O"ri*ent (?), v. t. [F. orienter. Cf. Orientate.]

1.

To define the position of, in relation to the orient or east; hence, to ascertain the bearings of.

2.

Fig.: To correct or set right by recurring to first principles; to arrange in order; to orientate.

 

© Webster 1913


O"ri*ent, v. t.

1.

Same as Orientate, 2.

2.

To place (a map or chart) so that its east side, north side, etc., lie toward the corresponding parts of the horizon; specif. (Surv.),

to rotate (a map attached to a plane table) until the line of direction between any two of its points is parallel to the corresponding direction in nature.

 

© Webster 1913

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