"inlay of some thin material in the surface of a piece of furniture or other object," 1560s, from French marqueterie "inlaid work," from marqueter "to checker" (14c.), frequentative of marquer, from marque "mark," which is probably from a Germanic source (see mark (n.1)).
c. 1400, "process of making patterns of inlaid work in hard materials," from Old French mosaicq "mosaic work," from Italian mosaico, from Medieval Latin musaicum "mosaic work, work of the Muses," noun use of neuter of musaicus "of the Muses," from Latin Musa (see Muse). Medieval mosaics often were dedicated to the Muses.
The word was formed in Medieval Latin as though from Greek, but the (late) Greek word for "mosaic work" was mouseion (and Klein says this sense in Greek was borrowed from Latin). Meaning "a piece of mosaic work" is from 1690s. Figurative meaning "anything resembling a mosaic work in composition" is by 1640s. As an adjective in English, "made of small pieces inlaid to form a pattern," from 1580s. Related: Mosaicist.
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).