Etymology
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garrote (n.)

also garrotte, 1620s, "Spanish method of capital punishment by strangulation," from Spanish garrote "stick for twisting cord" (the method used in the execution), of unknown origin. Perhaps from Old French guaroc "club, stick, rod, shaft of a crossbow," probably ultimately Celtic, but possibly from Frankish *wrokkan "to twist" (cognate with Middle Dutch wroken "to twist").

I have no hesitation in pronouncing death by the garrot, at once the most manly, and the least offensive to the eye. [Major John Richardson, "British Legion," 1837]
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gad (n.)
c. 1300, "a goad, sharp pointed stick to drive oxen, etc.;" c. 1400, "sharp-pointed metal spike," from Old Norse gaddr "spike, nail," from Proto-Germanic *gadaz "pointed stick" (see yard (n.2)). Attested earlier as "metal bar or rod, ingot" (mid-13c.) hence also in Middle English a unit of length in land-measure, varying from 10 to 16 feet. Not related to goad (n.), but perhaps influenced by it in sense.
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stick (n.)

Old English sticca "rod, twig, peg; spoon," from Proto-Germanic *stikkon- "pierce, prick" (source also of Old Norse stik, Middle Dutch stecke, stec, Old High German stehho, German Stecken "stick, staff"), from PIE root *steig- "to stick; pointed" (see stick (v.)).

Meaning "staff used in a game" is from 1670s (originally billiards); meaning "manual gearshift lever" is attested by 1914. Alliterative connection of sticks and stones is recorded from mid-15c.; originally "every part of a building." Stick-bug is from 1870, American English; stick-figure is from 1949.

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spit (n.2)
"sharp-pointed rod for roasting meat," late Old English spitu "a spit," from Proto-Germanic *spituz (source also of Middle Dutch and Dutch spit, Swedish spett (which perhaps is from Low German), Old High German spiz, German Spieß "roasting spit," German spitz "pointed"), from PIE *spei- "sharp point" (see spike (n.1)). This is also the source of the word meaning "sandy point" (1670s). Old French espois, Spanish espeto "spit" are Germanic loan-words. The verb meaning "to put on a spit" is recorded from c. 1200.
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gauge (n.)

early 15c., "fixed standard of measure" (surname Gageman is early 14c.), from Old North French gauge "gauging rod" (see gauge (v.)). Meaning "instrument for measuring" is from 1670s; meaning "distance between rails on a railway" is from 1841.

Railway-gage, the distance between perpendiculars on the insides of the heads of the two rails of a track. Standard gage is 4 feet 8 1/2 inches; anything less than this is narrow gage; anything broader is broad gage. The dimension was fixed for the United States by the wheels of the British locomotive imported from the Stephenson Works in 1829. [Century Dictionary]
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wale (n.)

Old English walu "ridge, bank" of earth or stone, later "ridge made on flesh by a lash" (related to weal (n.2)); from Proto-Germanic *walu- (source also of Low German wale "weal," Old Frisian walu "rod," Old Norse völr "round piece of wood," Gothic walus "a staff, stick," Dutch wortel, German wurzel "root"), from PIE root *wel- (3) "to turn, revolve." The common notion perhaps is "raised line." Used in reference to the ridges of textile fabric from 1580s. Wales "horizontal planks which extend along a ship's sides" is attested from late 13c.

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shaft (n.1)

"long, slender rod," originally "staff or pole forming the body of a spear or lance; spear-shaft," also, perhaps by synecdoche, "spear;" Middle English shafte, from Old English sceaft from Proto-Germanic *skaftaz (source also of Old Norse skapt, Old Saxon skaft, Old High German scaft, German schaft, Dutch schacht, not found in Gothic).

OED suggests this might be explained as a Germanic passive past participle of PIE root *(s)kep- "to cut, to scrape" (source of Old English scafan "to shave, scrape, polish") on notion of "tree branch stripped of its bark." But compare Latin scapus "shaft, stem, shank," Greek skeptron "a staff" (see scepter) which appear to be cognates.

Extended generally to any body of long, cylindrical shape; the meaning "beam or ray" (of light, etc.) is attested from c. 1300; that of "arrow" (especially a long one, used with a long bow) is from c. 1400; that of "a long, straight handle of a tool or utensil" from 1520s. The mechanical sense "long rotating rod for transmission of motive power in a machine" is from 1680s.

The vulgar slang meaning "penis" is recorded by 1719 on notion of "columnar part" (late 14c.); hence probably modern slang shaft (v.) and the related noun meaning "act of unfair treatment" (1959), though some early sources insist this is from the notion of a wound.

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gallows (n.)

c. 1300, plural of Middle English galwe "gallows" (mid-13c.), from Old Norse galgi "gallows," or from Old English galga (Mercian), gealga (West Saxon) "gallows;" all from Proto-Germanic *galgon "pole" (source also of Old Frisian galga, Old Saxon galgo, Middle High German galge "gallows, cross," German Galgen "gallows," Gothic galga "cross"), from PIE *ghalgh- "branch, rod" (source also of Lithuanian žalga "pole, perch," Armenian dzalk "pole").

In Old English, also used of the cross of the crucifixion. Plural because made of two poles. Gallows-tree is Old English galg-treow. Gallows humor (1876) translates German Galgenhumor.

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gadfly (n.)
also gad-fly, 1620s, "fly which bites cattle," probably from gad (n.) "goad, metal rod," here in the sense of "stinger;" but the sense is entangled with gad (v.) "rove about" (on the notion, perhaps, of the insect's power of flight or of the restlessness of animals plagued by them), and another early meaning of gadfly was "someone who likes to go about, often stopping here and there" (1610s). Sense of "one who irritates another" is from 1640s (equivalent of Latin oestrus; see estrus). "In strictness, only the females are gadflies, the males being smaller and quite inoffensive, living on juices of plants" [Century Dictionary]. Earlier bot-fly, from bot "skin parasite" (late 15c.).
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divine (v.)

late 14c., divinen, "learn or make out by or as if by divination, foretell" future events (trans.), also intransitive, "use or practice divination;" from Old French deviner, from Vulgar Latin *devinare, a dissimilation of Latin divinare "foresee, foretell, predict," from divinus "of a god," from divus "of or belonging to a god, inspired, prophetic," which is related to deus "god, deity" (from PIE root *dyeu- "to shine," in derivatives "sky, heaven, god").

Latin divinus also meant, as a noun, "soothsayer." English divine (v.) is also attested from late 14c. in the sense of "make out by observations or otherwise; make a guess or conjecture" without reference to supernatural insight. The earliest English sense is "to contrive, plot" (mid-14c.). Related: Divined; divining. Divining rod (or wand) is attested from 1650s.

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