Etymology
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*leu- 
Proto-Indo-European root meaning "to loosen, divide, cut apart."

It forms all or part of: absolute; absolution; absolve; analysis; analytic; catalysis; catalyst; catalytic; dialysis; dissolve; electrolysis; electrolyte; forlorn; Hippolytus; hydrolysis; -less; loess; loose; lorn; lose; loss; Lysander; lysergic; lysis; -lysis; lyso-; lysol; lytic; -lytic; palsy; paralysis; pyrolusite; resolute; resolution; resolve; soluble; solute; solution; solve; solvent.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit lunati "cuts, cuts off," lavitram "sickle;" Greek lyein "to loosen, untie, slacken," lysus "a loosening;" Latin luere "to loose, release, atone for, expiate;" Old Norse lauss "loose, free, unencumbered; vacant; dissolute;" Old English losian "be lost, perish."
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*sleubh- 

Proto-Indo-European root meaning "to slide, slip." 

It forms all or part of: cowslip; lubric; lubricant; lubricate; lubricity; lubricous; sleeve; slip (n.3) "potter's clay;" sloop; slop (n.1) "semiliquid refuse;" slop (n.2) "loose outer garment;" sloven.

It is the hypothetical source of/evidence for its existence is provided by: Latin lubricus "slippery, slimy, smooth," lubricare "make slippery or smooth;" Middle Dutch slupen "to glide;" Gothic sliupan "to creep, slide;" Old English slyppe "dung."

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*‌‌lē- 

Proto-Indo-European root meaning "to let go, slacken." 

It forms all or part of: alas; allegiance; lassitude; last (adj.) "following all others;" late; latter; lenient; lenitive; lenity; let (v.) "allow;" let (n.) "stoppage, obstruction;" liege.

It is the hypothetical source of/evidence for its existence is provided by: Greek ledein "to be weary;" Latin lenis "mild, gentle, calm," lassus "faint, weary;" Lithuanian lėnas "quiet, tranquil, tame, slow," leisti "to let, to let loose;" Old Church Slavonic lena "lazy," Old English læt "sluggish, slow," lætan "to leave behind."  

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*mele- 

*melə-, Proto-Indo-European root meaning "to crush, grind," with derivatives referring to ground or crumbling substances and crushing or grinding instruments.

It forms all or part of: amyl; amyloid; blintz; emmer; emolument; immolate; maelstrom; mall; malleable; malleolus; mallet; malleus; maul; meal (n.2) "edible ground grain;" mill (n.1) "building fitted to grind grain;" millet; mola; molar (n.); mold (n.3) "loose earth;" molder; ormolu; pall-mall.

It is the hypothetical source of/evidence for its existence is provided by: Hittite mallanzi "they grind;" Armenian malem "I crush, bruise;" Greek mylos "millstone," myle "mill;" Latin molere "to grind," mola "millstone, mill," milium "millet;" Old English melu "meal, flour;" Albanian miel "meal, flour;" Old Church Slavonic meljo, Lithuanian malu, malti "to grind;" Old Church Slavonic mlatu, Russian molotu "hammer."

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