Old English bihaldan (West Saxon behealdan) "give regard to, hold in view," also "keep hold of; belong to," from be- + haldan, healdan (see hold (v.)). Related: Beheld; beholding. A common West Germanic compound, compare Old Saxon bihaldan "hold, keep," Old Frisian bihalda "hold, possess, keep, protect, save," Old High German bihaltan, German behalten, but "[t]he application to watching, looking, is confined to English" [OED]. Related: Beholding.
Middle English holden, earlier halden, from Old English haldan (Anglian), healdan (West Saxon), "to contain; to grasp; to retain (liquid, etc.); to observe, fulfill (a custom, etc.); to have as one's own; to have in mind (of opinions, etc.); to possess, control, rule; to detain, lock up; to foster, cherish, keep watch over; to continue in existence or action; to keep back from action," class VII strong verb (past tense heold, past participle healden), from Proto-Germanic *haldanan (source also of Old Saxon haldan, Old Frisian halda, Old Norse halda, Dutch houden, German halten "to hold," Gothic haldan "to tend").
Based on the Gothic sense (also present as a secondary sense in Old English), the verb is presumed originally in Germanic to have meant "to keep, tend, watch over" (as grazing cattle), later "to have." Ancestral sense is preserved in behold. The original past participle holden was replaced by held beginning 16c., but survives in some legal jargon and in beholden.
The modern use in the sense "lock up, keep in custody" is from 1903. Hold back in the figurative senses is from 1530s (transitive); 1570s (intransitive). To hold off is early 15c. (transitive), c. 1600 (intransitive). Hold on is early 13c. as "to maintain one's course," 1830 as "to keep one's grip on something," 1846 as an order to wait or stop.
To hold (one's) tongue "be silent" is from c. 1300. To hold (one's) own is from early 14c. To hold (someone's) hand in the figurative sense of "give moral support" is from 1935. To hold (one's) horses "be patient" is from 1842, American English; the notion is of keeping a tight grip on the reins. To have and to hold have been paired alliteratively at least since c. 1200, originally of marriage but also of real estate. To hold water in the figurative sense "be sound or consistent throughout" is from 1620s.
"demonstrable proposition in science or mathematics," 1550s, from French théorème (16c.) and directly from Late Latin theorema, from Greek theorema "spectacle, sight," in Euclid "proposition to be proved," literally "that which is looked at," from theorein "to look at, behold" (see theory).
mid-14c., "specially prepared or arranged display," from Old French spectacle "sight, spectacle, Roman games" (13c.), from Latin spectaculum "a public show, spectacle, place from which shows are seen," from spectare "to view, watch, behold," frequentative form of specere "to look at" (from PIE root *spek- "to observe").
Middle English sheuen, from Old English sceawian "to look at, see, gaze, behold, observe; inspect, examine; look for, choose," from Proto-Germanic *skauwojanan (source also of Old Saxon skauwon "to look at," Old Frisian skawia, Dutch schouwen, Old High German scouwon "to look at"), from Proto-Germanic root *skau- "behold, look at," from PIE *skou-, variant of root *keu- "to see, observe, perceive."
The causal meaning "let be seen; put in sight, make known" evolved c. 1200 for unknown reasons, seems to be unique to English (German schauen still means "look at"), and in a century displaced the older meaning. The sense of "explain, make clear" is from c. 1300, as the intransitive sense of "be seen, appear."
The spelling shew, popular 18c. and surviving into early 19c., represents an obsolete pronunciation (rhymes with view). The horse-racing sense of "finish third or in the top three" is by 1903, perhaps from an earlier sense in card-playing.
"perceive or recognize the difference or distinction between (two or more things);" also "distinguish (an object) with the eyes, see distinctly, behold;" also "perceive rationally, understand;" late 14c., from Old French discerner (13c.) "distinguish (between), separate" (by sifting), and directly from Latin discernere "to separate, set apart, divide, distribute; distinguish, perceive," from dis- "off, away" (see dis-) + cernere "distinguish, separate, sift" (from PIE root *krei- "to sieve," thus "discriminate, distinguish"). Related: Discerned; discerning.