Etymology
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seldom (adv.)

"rarely, not often, infrequently," late Old English and early Middle English seldum, an alteration of seldan "infrequently, rarely," from Proto-Germanic *selda- "strange, rare" (source also of Old Norse sjaldan, Old Frisian selden, Dutch zelden, Old High German seltan, German selten), a word of uncertain etymology. Perhaps ultimately from the base of self (q.v.).

The form shifted apparently on analogy of adverbial dative plurals in -um (as in whilom "at one time," from Old English hwilum, from the source of while). The same development also created litlum from little, miclum from mickle. Also compare random, ransom. The forms in -n decreased from 14c. and faded out in 16c.

Old English seldan had comparative seldor, superlative seldost; in early Middle English, as seldan changed form and lost its connection with these, selde was back-formed as a positive. Shakespeare uses seld-shown "rarely exhibited." Some compounds using the old form survived through Middle English, such as selcouth "rarely or little-known, unusual, strange, wonderful," from Old English selcuð, seld-cuð, from seldan + cuð (see couth). 

 German seltsam "strange, odd," Dutch zeldzaam are cognates of seldom, but with the second element conformed to their cognates of -some. Related: Seldomness.

Seldom-times "rarely, hardly ever" is from mid-15c. (earlier was seld-when, Old English seldhwanne "rarely," which lasted until 16c.). Seldom-seen "rarely encountered" is from mid-15c.; older was seld-seen (Middle English seld-sen, from Old English seldsiene), which lasted long enough to appear in Marlowe (seildsene, 1590s).

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often (adv.)

"repeatedly, again and again, many times, under many circumstances," mid-13c., an extended form of oft, in Middle English typically before vowels and h-, probably by influence of its opposite, seldom (Middle English selden). In common use from 16c., replacing oft. Related: Oftener; oftenest.

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ransom (n.)

13c., raunsoun, "sum paid for the release of a prisoner or captured man," also "redemption from damnation," from Old French ranson (Modern French rançon), earlier raenson "ransom, redemption," from Latin redemptionem (nominative redemptio) "a redeeming," from redimere "to redeem, buy back," from red- "back" (see re-) + emere "to take, buy, gain, procure" (from PIE root *em- "to take, distribute"). A doublet of redemption. A faded word somewhat revived by Scott early 19c. Spelling with -m appears by late 14c., but the reason for it is unclear (compare seldom, random).

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random (adj.)

1650s, "having no definite aim or purpose, haphazard, not sent in a special direction," from phrase at random (1560s), "at great speed" (thus, "carelessly, haphazardly"), from an alteration of the Middle English noun randon, randoun "impetuosity; speed" (c. 1300). This is from Old French randon "rush, disorder, force, impetuosity," from randir "to run fast," from Frankish *rant "a running" or some other Germanic source, from Proto-Germanic *randa (source also of Old High German rennen "to run," Old English rinnan "to flow, to run;" see run (v.)). For spelling shift of -n to -m, compare seldom, ransom.

In 1980s U.S. college student slang it began to acquire a sense of "inferior, undesirable." (A 1980 William Safire column describes it as a college slang noun meaning "person who does not belong on our dormitory floor.") Random access in reference to computer memory that need not be read sequentially is recorded from 1953. Related: Randomly; randomness.

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rarely (adv.)

1520s, "thinly, scantily," from rare (adj.1) + -ly (2). From 1550s as "seldom, not often;" the sense of "finely, excellently" is by 1580s.

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fib (v.)
"tell trifling lies," 1680s, from fib (n.). Seldom, if ever, transitive. Related: Fibbed; fibbing; fibbery.
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illy (adv.)
"in an ill manner," 1540s, from ill (adj.) + -ly (2). Correctly formed but seldom used; simple ill generally serving as the adverb.
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blameless (adj.)
"not meriting disapprobation or censure, without fault," late 14c., from blame (n.) + -less. Related: Blamelessly; blamelessness. Seldom-used blameful is recorded from late 14c.
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satiety (n.)

"state of being glutted, feeling of disgust caused by eating too much," 1530s, from French satiété, from Latin satietatem (nominative satietas) "abundance, sufficiency, fullness," from satis "enough" (from PIE root *sa- "to satisfy"). The English word is seldom used in a good sense.

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encouragement (n.)

1560s, from encourage + -ment, or from French encoragement.

As a general rule, Providence seldom vouchsafes to mortals any more than just that degree of encouragement which suffices to keep them at a reasonably full exertion of their powers. [Hawthorne, "House of Seven Gables"]
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