"cut off or clip an animal's tail," late 14c., from dok (n.) "fleshy part of an animal's tail" (mid-14c.), which is from Old English -docca "muscle" or an Old Norse equivalent, from Proto-Germanic *dokko "something round, bundle" (source also of Old Norse dokka "bundle; girl," Danish dukke "a bundle, bunch, ball of twine, straw, etc.," also "doll," German Docke "small column, bundle; doll, smart girl").
The general meaning "deduct a part from," especially "to reduce (someone's) pay for some infraction" is recorded by 1815. Related: Docked; docking.
1816, "patterned wooden flooring," from French parquet "wooden flooring; enclosed portion of a park," from Old French parchet (14c.) "small compartment, enclosed space; part of a park or theater," diminutive of parc (see park (n.)).
Meaning "part of a theater auditorium at the front of the ground floor" is recorded by 1754 in a French context. The noun use in English has been influenced by the verb meaning "provide with a floor of parquet work" (attested from 1640s, from French parqueter. Related: Parquetry "inlaid flooring in which a pattern is formed by different types of wood" (1842).
1670s, in botany, "rootlet, part of the embryo of a plant which develops into the primary root," from Latin radicula, diminutive of radix "root" (from PIE root *wrād- "branch, root"). Anatomical sense of "branch of a nerve, vein, etc. resembling a root" is by 1830.