Etymology
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Words related to pad

path (n.)

Old English paþ, pæþ "narrow passageway or route across land, a track worn by the feet of people or animals treading it," from West Germanic *patha- (source also of Old Frisian path, Middle Dutch pat, Dutch pad, Old High German pfad, German Pfad "path"), a word of uncertain origin, not attested in Old Norse or Gothic.

The original initial -p- in a Germanic word is an etymological puzzle. Don Ringe ("From Proto-Indo-European to Proto-Germanic," Oxford 2006), reflecting an old theory, describes it as "An obvious loan from Iranian ..., clearly borrowed after Grimm's Law had run its course." Watkins says the word is "probably borrowed (? via Scythian) from Iranian *path-," from PIE root *pent- "to tread, go, pass" (source of Avestan patha "way;" see find (v.)), but this is too much of a stretch for OED and others. In Scotland and Northern England, commonly a steep ascent of a hill or in a road.

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padding (n.)

"material used in stuffing, stuffing used to keep a garment in the desired shape," 1828, verbal noun from pad (v.2).

find (v.)

Old English findan "come upon, meet with; discover; obtain by search or study" (class III strong verb; past tense fand, past participle funden), from Proto-Germanic *findan "to come upon, discover" (source also of Old Saxon findan, Old Frisian finda, Old Norse finna, Middle Dutch vinden, Old High German findan, German finden, Gothic finþan), originally "to come upon."

The Germanic word is from PIE root *pent- "to tread, go" (source also of Old High German fendeo "pedestrian;" Sanskrit panthah "path, way;" Avestan panta "way;" Greek pontos "open sea," patein "to tread, walk;" Latin pons (genitive pontis) "bridge;" Old Church Slavonic pǫti "path," pęta "heel;" Russian put' "path, way;" Armenian hun "ford," Old Prussian pintis "road"). The prehistoric sense development in Germanic would be from "to go" to "to find (out)," but Boutkan has serious doubts about this.

Germanic *-th- in English tends to become -d- after -n-. The change in the Germanic initial consonant is from Grimm's Law. To find out "to discover by scrutiny" is from 1550s (Middle English had a verb, outfinden, "to find out," c. 1300).

footpad (n.)

"highwayman who robs on foot," 1680s, from foot (n.) + pad "pathway, footpath" (1670s), from Middle Dutch pad "way, path," from Proto-Germanic *patha- "way, path" (see pad (v.1), and compare path). Pad was a cant word among thieves and vagabonds, in expressions such as stand pad "stand by the wayside begging." Especially "one of a large class, existing in Europe when police authority was still in an ineffective condition, who made a business of robbing people passing on horseback or in carriages" [Century Dictionary]. 

keypad (n.)
"handheld pad of labelled buttons to work electronics," 1975, from key (n.1) + pad (n.).
kneepad (n.)
also knee-pad, 1858, from knee (n.) + pad (n.).
lily-pad (n.)
"broad leaf of the water-lily," 1834, American English, from lily (n.) + pad (n.).
notepad (n.)

also note-pad, "pad of paper for writing notes," 1907, from note (n.) + pad (n.).

paddle (v.1)

"to dabble, wade in water," 1520s, probably cognate with Low German paddeln "tramp about," frequentative of padjen "to tramp, to run in short steps," from the source of  pad (v.). Related: Paddled; paddling. Meaning "to move in water by means of paddles" is a different word (see paddle (v.3)).