Etymology
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Words related to providence

pro- 

word-forming element meaning "forward, forth, toward the front" (as in proclaim, proceed); "beforehand, in advance" (prohibit, provide); "taking care of" (procure); "in place of, on behalf of" (proconsul, pronoun); from Latin pro (adv., prep.) "on behalf of, in place of, before, for, in exchange for, just as," which also was used as a first element in compounds and had a collateral form por-.

Also in some cases from cognate Greek pro "before, in front of, sooner," which also was used in Greek as a prefix (as in problem). Both the Latin and Greek words are from PIE *pro- (source also of Sanskrit pra- "before, forward, forth;" Gothic faura "before," Old English fore "before, for, on account of," fram "forward, from;" Old Irish roar "enough"), extended form of root *per- (1) "forward," hence "in front of, before, toward, near," etc.

The common modern sense of "in favor of, favoring" (pro-independence, pro-fluoridation, pro-Soviet, etc.) was not in classical Latin and is attested in English from early 19c.

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*weid- 
Proto-Indo-European root meaning "to see."

It forms all or part of: advice; advise; belvedere; clairvoyant; deja vu; Druid; eidetic; eidolon; envy; evident; guide; guidon; guise; guy (n.1) "small rope, chain, wire;" Gwendolyn; Hades; history; idea; ideo-; idol; idyll; improvisation; improvise; interview; invidious; kaleidoscope; -oid; penguin; polyhistor; prevision; provide; providence; prudent; purvey; purview; review; revise; Rig Veda; story (n.1) "connected account or narration of some happening;" supervise; survey; twit; unwitting; Veda; vide; view; visa; visage; vision; visit; visor; vista; voyeur; wise (adj.) "learned, sagacious, cunning;" wise (n.) "way of proceeding, manner;" wisdom; wiseacre; wit (n.) "mental capacity;" wit (v.) "to know;" witenagemot; witting; wot.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit veda "I know;" Avestan vaeda "I know;" Greek oida, Doric woida "I know," idein "to see;" Old Irish fis "vision," find "white," i.e. "clearly seen," fiuss "knowledge;" Welsh gwyn, Gaulish vindos, Breton gwenn "white;" Gothic, Old Swedish, Old English witan "to know;" Gothic weitan "to see;" English wise, German wissen "to know;" Lithuanian vysti "to see;" Bulgarian vidya "I see;" Polish widzieć "to see," wiedzieć "to know;" Russian videt' "to see," vest' "news," Old Russian vedat' "to know."
improvidence (n.)
"lack of foresight, rashness," mid-15c., from Late Latin improvidentia, from assimilated form of in- "not" (see in- (1)) + Latin providentia "foresight, precaution" (see providence).
providential (adj.)

1610s, "pertaining to foresight" (implied in providentially); 1640s as "pertaining to divine providence," from Latin providentia "foresight, precaution, foreknowledge" (see providence) + -al (1). Meaning "by divine interposition, effected by the providence of God" is recorded from 1719. Related: Providentially.

prudence (n.)

mid-14c. (c. 1200 as a surname), "intelligence; discretion, foresight; practical wisdom to see what is suitable or profitable;" also one of the four cardinal virtues, "wisdom to see what is virtuous;" from Old French prudence (13c.) and directly from Latin prudentia "a foreseeing, foresight, sagacity, practical judgment," contraction of providentia "foresight" (see providence, which is a doublet). The secondary sense of "knowledge, science" (late 14c.) is preserved in jurisprudence.

purveyance (n.)

c. 1300, purveiaunce, "foresight, foreknowledge, prudence, wisdom" (senses now obsolete), from Anglo-French purveance and directly from Old French porveance, pourveance, from Latin providentia (see providence). From early 14c. as "that which is needed or provided," late 14c. as "act of providing or procuring what is necessary, preliminary arrangement."