Etymology
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ray (n.1)

"beam of light, light emitted in a given direction from a luminous body," early 14c., rai, from Old French rai (nominative rais) "ray (of the sun), spoke (of a wheel); gush, spurt," from Latin radius "ray, spoke, staff, rod" (see radius). Not common before 17c. [OED]; of the sun, usually in reference to heat (beam being preferred for light).

Ray is usually distinguished from beam, as indicating a smaller amount of light; in scientific use a beam is a collection of parallel rays. In ordinary language ray is the word usually employed when the reference is to the heat rather than the light of the sun .... [OED]

Science fiction's ray-gun is recorded by 1931 (in Amazing Stories; electric ray gun as an imaginary weapon is from 1924; death-ray gun from 1926 as a prop in a vaudeville act), but the Martians had a Heat-Ray weapon in "War of the Worlds" (1898).

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radio (n.)

"wireless transmission of voice signals with radio waves," 1907, abstracted or shortened from earlier combinations such as radio-receiver (1903), radiophone "instrument for the production of sound by radiant energy" (1881), radio-telegraphy "means of sending telegraph messages by radio rather than by wire" (1898), from radio- as a combining form of Latin radius "beam" (see radius). Use for "radio receiver" is attested by 1913; sense of "sound broadcasting as a medium" also is from 1913.

That winter, however—the winter of 1921-22—[radio] came with a rush. Soon everybody was talking, not about wireless telephony, but about radio. A San Francisco paper described the discovery that millions were making: "There is radio music in the air, every night, everywhere. Anybody can hear it at home on a receiving set, which any boy can put up in an hour." In February President Harding had an outfit installed in his study, and the Dixmoor Golf Club announced that it would install a "telephone" to enable golfers to hear church services. [Frederick Lewis Allen, "Only Yesterday: An Informal History of the 1920's," 1931]
It is not a dream, but a probability that the radio will demolish blocs, cut the strings of red tape, actuate the voice "back home," dismantle politics and entrench the nation's executive in a position of power unlike that within the grasp of any executive in the world's history. [The Reading Eagle, Reading, Pa., U.S.A., March 16, 1924]

As late as July 1921 the New York Times was calling it wireless telephony, and wireless remained widespread until World War II, when military preference for radio established it as the word. As an adjective by 1912, "by radio transmission;" meaning "controlled by radio" is from 1974. Radio _______ as the proper name of a particular radio station or service, "radio station or service from _______" is by 1920. A radio shack (1946) was a small outbuilding housing radio equipment.

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spoke (n.)
"radius of a wheel," Old English spaca "spoke of a wheel, radius," related to spicing "large nail," from Proto-Germanic *spaikon (source also of Old Saxon speca, Old Frisian spake, Dutch spaak, Old High German speicha, German speiche "spoke"), of uncertain origin, probably from PIE *spei- "sharp point" (see spike (n.1)).
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-i (2)
plural suffix sometimes preserved in English for words from Latin, it is the Latin plural of nouns of the second declension (such as focus/foci, radius/radii).
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verge (n.)
"edge, rim," mid-15c., from Old French verge "twig, branch; measuring rod; penis; rod or wand of office" (12c.), hence, from the last sense, "scope, territory dominated" (as in estre suz la verge de "be under the authority of"), from Latin virga "shoot, rod, stick, slender green branch," of unknown origin.

Earliest attested sense in English is now-obsolete meaning "male member, penis" (c. 1400). Modern sense is from the notion of within the verge (c. 1500, also as Anglo-French dedeinz la verge), i.e. "subject to the Lord High Steward's authority" (as symbolized by the rod of office), originally a 12-mile radius round the king's court. Sense shifted to "the outermost edge of an expanse or area." Meaning "point at which something happens" (as in on the verge of) is first attested c. 1600. "A very curious sense development." [Weekley]
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compass (n.)

c. 1300, "space, area, extent, circumference," from Old French compas "circle, radius; size, extent; pair of compasses" (12c.), from compasser "to go around, measure (with a compass); divide equally," from Vulgar Latin *compassare "to pace out," from Latin com "with, together" (see com-) + passus "a step" (from PIE root *pete- "to spread").

The mathematical instrument for describing circles was so called in English from mid-14c. The mariners' directional tool (so called since early 15c.) took the name, perhaps, because it's round and has a point like the mathematical instrument.

Meaning "limits, boundary" is from 1550s. Sense of "range of notes which a given voice or instrument can produce" is from 1590s. 

The word is in most European languages, with a mathematical sense in Romance, a nautical sense in Germanic, and both in English. In Middle English it also could mean "ingenuity, subtlety, cunning." Also an adverb in Middle English: to go compass was "go in a circle, go around."

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