arrow-root n.

"slender, pointed missile weapon, made to be shot from a bow," early 14c., from Old English arwan, earlier earh "arrow," possibly borrowed from Old Norse ör (genitive örvar), from Proto-Germanic *arkhwo (source also of Gothic arhwanza), from PIE root *arku-, source of Latin arcus (see arc (n.)). The etymological sense would be "the thing belonging to the bow." The meaning "a mark like an arrow" in cartography, etc. is from 1834.

It was a rare word in Old English. More common words for "arrow" were stræl (which is cognate with the word still common in Slavic and once prevalent in Germanic, related to words meaning "flash, streak") and fla, flan (the -n perhaps mistaken for a plural inflection), from Old Norse, a North Germanic word, perhaps originally with the sense of "splinter." Stræl disappeared by 1200; fla became flo in early Middle English and lingered in Scottish until after 1500.

Robyn bent his joly bowe,

Therein he set a flo.

["Robyn and Gandelyn," in a minstrel book from c. 1450 in the British Museum]

"underground, downward-growing part of a plant," late Old English rōt and in part from a Scandinavian cognate akin to Old Norse rot "root," figuratively "cause, origin," from Proto-Germanic *wrot (source also of Old English wyrt "root, herb, plant," Old High German wurz, German Wurz "a plant," Gothic waurts "a root," with characteristic Scandinavian loss of -w- before -r-), from PIE root *wrād- "branch, root" (source of wort and radical). The usual Old English words for "root" were wyrttruma and wyrtwala.

Figurative use, "source of a quality or condition," is from late 12c. Of the base parts of teeth, hair, etc., from early 13c. Mathematical sense is from 1550s. Philological sense from 1520s. Slang meaning "penis" is recorded from 1846. In African-American vernacular use, "a spell effected by magical properties of roots," by 1935. The sense of "person considered as the source or offspring of a family or clan" is by early 14c., chiefly biblical.

For coveteousnes is the rote of all evylle, which whill some lusted after, they erde from the feyth, and tanglyd themselves with many sorowes. [I Timothy vi in Tyndale, 1526]

To take root is from mid-15c. as "settle in the ground," hence figurative use (by 1530s). Root beer, made from the extracts of various roots (sarsaparilla, sassafras, etc.), is recorded by 1841, American English; root doctor is from 1821. Roots "established ties with a locality or region; one's background or cultural origins" is by 1921.