Old English beam, "living tree," but by late 10c. also "rafter, post, ship's timber," from Proto-Germanic *baumaz "tree" (source also of Old Frisian bam "tree, gallows, beam," Middle Dutch boom, Old High German boum, German Baum "tree," and perhaps also (with unexplained sound changes) Old Norse baðmr, Gothic bagms). This is of uncertain etymology (according to Boutkan probably a substrate word). The shift from *-au- to -ea- is regular in Old English.
The meaning "ray of light" developed in Old English, probably because beam was used by Bede to render Latin columna (lucis), the Biblical "pillar of fire." The meaning "directed flow of radiation" is from 1906. To be on the beam "going in the right direction" (1941) originally was an aviator's term for "to follow the course indicated by a radio beam."
The nautical sense of "one of the horizontal transverse timbers holding a ship together" is from early 13c., hence "greatest breadth of a ship," and slang broad in the beam, by 1894 of ships; of persons, "wide-hipped," by 1938.
"emit rays of light," c. 1400, from beam (n.) in the "ray of light" sense. The sense of "shine radiantly" is from 1630s; that of "smile radiantly" is from 1804; that of "to direct radio transmissions" is from 1927. Related: Beamed; beaming.
"the ordinary sound uttered by an ox or cow" [OED], 1540s, from low (v.); ultimately imitative.
"hill, small eminence," obsolete except in place names, from Old English hlaw "hill, mound," especially "barrow," a noun related to hleonian "to lean," from PIE root *klei- "to lean." Compare Latin clivus "hill," Greek klitys "side of a hill," from the same PIE root.
"not high, below the usual level," late 13c., earlier lah (late 12c.), "not rising much, being near the base or ground" (of objects or persons), also "lying on the ground or in a deep place" (late 13c.). This is not found in Old English, so the word is probably from Old Norse lagr "low, low-down, short; humble," or a similar Scandinavian source (compare Swedish låg, Danish lav), from Proto-Germanic *lega- "lying flat, low" (source also of Old Frisian lech, Middle Dutch lage, Dutch laag "low," dialectal German läge "flat"), from PIE root *legh- "to lie down, lay."
In reference to sounds, "not loud," also "having a deep pitch," from c. 1300. Meaning "humble in rank" is from c. 1200; "undignified, not high in character" is from 1550s; meaning "coarse, vulgar" is from 1759. Sense of "dejected, dispirited" is attested from 1737. Of prices, from c. 1400. In geographical usage, low refers to the part of a country near the sea-shore (c. 1300), as in Low Countries "Holland, Belgium, Luxembourg" (1540s). Low German languages (1845) are so called for being spoken in the lower elevations of old Germany.
Abject, low, and mean may have essentially the same meaning, but low is more often used with respect to nature, condition, or rank: mean, to character or conduct: abject, to spirit. [Century Dictionary, 1897]
Low blow in the figurative sense (1940s) is from pugilism. To lie low is from mid-13c. as "get down so as not to be seen," 1880 in the modern slang sense "keep quiet." Low Church in 18c. English history referred to Anglicans laying little stress on church authority (1702); in 19c. it meant evangelical Anglicans.
Old English hlowan "moo, make a noise like a cow," from Proto-Germanic imitative *khlo- (source also of Middle Dutch loeyen, Dutch loeien, Old Low Franconian luon, Old High German hluojen). This is perhaps identical with the imitative PIE root *kele- (2) "to shout."
the low point of anything, the minimum, 1818, originally in card games; general sense by 1911.