Etymology
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Words related to erosion

ex- 
word-forming element, in English meaning usually "out of, from," but also "upwards, completely, deprive of, without," and "former;" from Latin ex "out of, from within; from which time, since; according to; in regard to," from PIE *eghs "out" (source also of Gaulish ex-, Old Irish ess-, Old Church Slavonic izu, Russian iz). In some cases also from Greek cognate ex, ek. PIE *eghs had comparative form *eks-tero and superlative *eks-t(e)r-emo-. Often reduced to e- before -b-, -d-, -g-, consonantal -i-, -l-, -m-, -n-, -v- (as in elude, emerge, evaporate, etc.).
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rodent (n.)

"a rodent mammal" 1835 (as an adjective 1833), from Modern Latin Rodentia, the order name, from Latin rodentem (nominative rodens), "the gnawers," present participle of rodere "to gnaw, eat away," which is of uncertain etymology, possibly is from an extended form of PIE root *red- "to scrape, scratch, gnaw." Uncertain connection to Old English rætt (see rat (n.)). They are characterized by having no canine teeth and strong incisors.

erode (v.)

1610s, "gnaw or eat away" (transitive), a back-formation from erosion, or else from French éroder, from Latin erodere "to gnaw away, consume," from assimilated form of ex "away" (see ex-) + rodere "to gnaw" (see rodent). Intransitive sense "become worn away" is by 1905. Related: Eroded; eroding. Originally of acids, ulcers, etc.; geological sense is from 1830.

*red- 

*rēd-, Proto-Indo-European root meaning "to scrape, scratch, gnaw."

It forms (possibly) all or part of: abrade; abrasion; corrode; corrosion; erase; erode; erosion; radula; rascal; rase; rash (n.) "eruption of small red spots on skin;" raster; rat; raze; razor; rodent; rostrum; tabula rasa.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit radati "scrapes, gnaws," radanah "tooth;" Latin rodere "to gnaw, eat away," radere "to scrape;" Welsh rhathu "scrape, polish."