Etymology
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Words related to de

to (prep.)

Old English to "in the direction of, for the purpose of, furthermore," from West Germanic *to (source also of Old Saxon and Old Frisian to, Dutch toe, Old High German zuo, German zu "to"), from PIE pronominal base *do- "to, toward, upward" (source also of Latin donec "as long as," Old Church Slavonic do "as far as, to," Greek suffix -de "to, toward," Old Irish do, Lithuanian da-), from demonstrative *de-. Not found in Scandinavian, where the equivalent of till (prep.) is used.

The nearly universal use of to with infinitives (to sleep, to dream, etc.) arose in Middle English out of the Old English dative use of to, and it helped drive out the Old English inflectional endings (though in this use to itself is a mere sign, without meaning).

Commonly used as a prefix in Middle English (to-hear "listen to," etc.), but few of these survive (to-do, together, and time references such as today, tonight, tomorrow — Chaucer also has to-yeere). To and fro "side to side" is attested from mid-14c. Phrase what's it to you "how does that concern you?" (1819) is a modern form of an old question:

Huæd is ðec ðæs?
[John xxi:22, in Lindisfarne Gospel, c.950]
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auto-da-fe (n.)
"sentence passed by the Inquisition" (plural autos-da-fé), 1723, from Portuguese auto-da-fé "judicial sentence, act of the faith," especially the public burning of a heretic, from Latin actus de fide. The elements are auto "a play," in law, "an order, decree, sentence," from Latin actus (see act (v.)), de "from, of" (see de), fides "faith" (from PIE root *bheidh- "to trust, confide, persuade"). The Spanish form is auto-de-fe, but the Portuguese form took hold in English, perhaps through popular accounts of the executions following the earthquake of 1755.
de- 

active word-forming element in English and in many verbs inherited from French and Latin, from Latin de "down, down from, from, off; concerning" (see de), also used as a prefix in Latin, usually meaning "down, off, away, from among, down from," but also "down to the bottom, totally" hence "completely" (intensive or completive), which is its sense in many English words.

As a Latin prefix it also had the function of undoing or reversing a verb's action, and hence it came to be used as a pure privative — "not, do the opposite of, undo" — which is its primary function as a living prefix in English, as in defrost (1895), defuse (1943), de-escalate (1964), etc. In some cases, a reduced form of dis-.

de facto 

Latin, literally "in fact, in reality," thus, "existing, but not necessarily legally ordained or morally right;" from facto, ablative of factum "deed, act" (see de +  fact).

de jure 

Latin, literally "of law," thus "legitimate, lawful, by right of law, according to law." Jure is ablative of ius "law" (see de +  just (adj.)).

dement (v.)

"drive mad, bring to a state of dementia," now obsolete or archaic but for the past-participle adjective demented, 1540s, probably from French démenter, from Late Latin dementare "to drive out of one's mind," from stem of Latin demens "out of one's senses, insane, raving, foolish; distracting, wild, reckless" (a less technical term than insanitas), from phrase de mente, from de "from, away from" (see de)+ mente, ablative of mens "mind" (from PIE root *men- (1) "to think").

deteriorate (v.)

1640s, transitive, "make worse, reduce in quality," from Late Latin deterioratus, past participle of deteriorare "get worse; make worse," from Latin deterior "worse, lower, inferior, meaner," contrastive of *deter "bad, lower," from PIE *de-tero-, from demonstrative stem *de- (see de). Intransitive sense "grow worse, degenerate" is by 1758. Related: Deteriorated; deteriorating.