Etymology
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hatch (n.2)
"that which has hatched; action of hatching," 1620s, from hatch (v.1).
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hatch (n.3)
"engraved lines or strokes," 1650s, from hatch (v.2).
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hatch (v.1)
early 13c., hachen, "to produce young from eggs by incubation," probably from an unrecorded Old English *hæccan, of unknown origin, related to Middle High German, German hecken "to mate" (used of birds). Meaning "to come forth from an egg," also "cause to come forth from an egg" are late 14c. Figurative use (of plots, etc.) is from early 14c. Related: Hatched; hatching.
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hatch (n.1)
"opening, grated gate, half-door," Old English hæc (genitive hæcce) "fence, grating, gate," from Proto-Germanic *hak- (source also of Middle High German heck, Dutch hek "fence, gate"), a word of uncertain origin. This apparently is the source of many of the Hatcher surnames; "one who lives near a gate." Sense of "opening in a ship's deck" is first recorded mid-13c. Drinking phrase down the hatch attested by 1931 (the image is nautical).
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hatch (v.2)
"engrave, draw fine parallel lines," late 14c., from Old French hachier "chop up, hack" (14c.), from hache "ax" (see hatchet). Related: Hatched; hatching. The noun meaning "an engraved line or stroke" is from 1650s.
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hatchling (n.)
"newly hatched creature," 1854, from hatch (v.1) + diminutive suffix -ling.
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hatchback 
type of rear door of an automobile, 1970, from hatch (n.) + back (n.).
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hatchway (n.)
"square or oblong opening in the deck of a ship," 1620s, from hatch (n.) + way (n.).
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hash (v.)

1650s, "to hack, chop into small pieces," from French hacher "chop up" (14c.), from Old French hache "ax" (see hatchet). Hash browns (1926) is short for hashed browned potatoes (1886), with the -ed omitted, as in mash potatoes. The hash marks on a football field were so called by 1954, from their similarity to hash marks, armed forces slang for "service stripes on the sleeve of a military uniform" (1909), which supposedly were called that because they mark the number of years one has had free food (that is, hash (n.1)) from the Army; but perhaps there is a connection with the noun form of hatch (v.2).

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