Etymology
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cohere (v.)

1590s, "to be consistent, to follow regularly in natural or logical order," from Latin cohaerere "to cleave together," in transferred use, "be coherent or consistent," from assimilated form of com "together" (see co-) + haerere "to adhere, stick" (see hesitation). More literal sense of "to stick, stick together, cleave" is from 1610s. Related: Cohered; cohering.

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fissure (n.)
c. 1400, from Old French fissure (13c.) and directly from Latin fissura "a cleft," from root of findere "to split, cleave, separate, divide," from PIE *bhind-, nasalized form of root *bheid- "to split."
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fissile (adj.)
1660s, from Latin fissilis "that which may be cleft or split," from fissus, past participle of findere "cleave, split, separate, divide" (from PIE root *bheid- "to split").
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psychodectic (adj.)

"soul-destroying," by 1895, from Latinized form of Greek psykhē "understanding, the mind (as the seat of thought), faculty of reason" (see psyche) + daiktēs "destroying," from daizein "to cleave, slay" (from PIE root *da- "to divide"). 

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schizo- 

word-forming element meaning "division; split, cleavage," from Latinized form of Greek skhizo-, combining form ("irregular," says OED) of skhizein "to split, cleave, part, separate" (from PIE root *skei- "to cut, split").

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spool (n.)

early 14c., "wheel for winding thread upon," from Old North French spole, espole "a spool" (13c.), from Middle Dutch spoele "a spool," from Proto-Germanic *spolon (source also of Norwegian and Swedish spole, Old High German spuola, German Spule "a spool, bobbin"), from PIE root *spel- (1) "to cleave, split" (see spoil (v.)).

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petroglyph (n.)

"carving on or in stone, a rock-carving," usually a prehistoric one, 1854, from French pétroglyphe, from Greek petra "rock" (which is of unknown origin) + glyphē "carving" (from PIE root *gleubh- "to tear apart, cleave"). An earlier word was petrograph (1810). Related: Petroglyphic.

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slip (n.1)
mid-15c., "edge of a garment;" 1550s, "narrow strip," probably from Middle Low German or Middle Dutch slippe "cut, slit," possibly related to Old English toslifan "to split, cleave." Sense of "narrow piece of paper" (as in pink slip) in 1680s.
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cohesive (adj.)

"of or causing the quality of adhering together; capable of sticking," 1730, with -ive + Latin cohaes-, past participle stem of cohaerere "to cleave together," in transferred use, "be coherent or consistent," from assimilated form of com "together" (see co-) + haerere "to adhere, stick" (see hesitation). Related: Cohesively; cohesiveness.

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*bheid- 
Proto-Indo-European root meaning "to split," with derivatives in Germanic "referring to biting (hence also to eating and to hunting) and woodworking" [Watkins].

It forms all or part of: abet; bait (n.) "food used to attract prey;" bait (v.) "to torment, persecute;" bateau; beetle (n.1) "type of insect; bit (n.1) "small piece;" bite; bitter; bitter end; boat; boatswain; -fid; fissile; fission; fissure; giblets; pita; pizza; vent (n.).

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit bhinadmi "I cleave," Latin Latin findere "to split, cleave, separate, divide," Old High German bizzan "to bite," Old English bita "a piece bitten off, morsel," Old Norse beita "to hunt with dogs," beita "pasture, food."
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