Etymology
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Words related to flourish

*bhel- (3)
Proto-Indo-European root meaning "to thrive, bloom," possibly a variant of PIE root *bhel- (2) "to blow, swell."

It forms all or part of: blade; bleed; bless; blood; blow (v.2) "to bloom, blossom;" bloom (n.1) "blossom of a plant;" bloom (n.2) "rough mass of wrought iron;" blossom; cauliflower; chervil; cinquefoil; deflower; defoliation; effloresce; exfoliate; feuilleton; flora; floral; floret; florid; florin; florist; flour; flourish; flower; foil (n.) "very thin sheet of metal;" foliage; folio; folium; gillyflower; Phyllis; phyllo-; portfolio; trefoil.

It is the hypothetical source of/evidence for its existence is provided by: Greek phyllon "leaf;" Latin flos "flower," folio, folium "leaf;" Middle Irish blath, Welsh blawd "blossom, flower;" Gaelic bile "leaflet, blossom;" Old English blowan "to flower, bloom."
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flourishing (adj.)
late 14c., "prospering, thriving;" c. 1400, "full of flowers," present-participle adjective from flourish (v.). Related: Flourishingly.
Florence 
chief city of Tuscany, also a fem. proper name, both from Latin Florentia, fem. of Florentius, literally "blooming," from florens (genitive florentis), present participle of florere "to flower" (see flourish). The city name is from Roman Colonia Florentia, "flowering colony," either literal or figurative, and became Old Italian Fiorenze, modern Italian Firenze.
florescence (n.)
"process of flowering," 1764, from Modern Latin florescentia, from Latin florescentem (nominative florescens) "blooming," present participle of florescere "to begin to bloom," inceptive of florere "to blossom" (see flourish (v.)).
floruit 
"period during which a historical person's life work was done," 1843, Latin, literally "he flourished," third person singular perfect indicative of florere "to flourish, to bloom" (see flourish (v.)). Usually in abbreviation fl. The third person singular present subjunctive of the verb, floreat, sometimes is attached to proper names "to indicate the hope that the named person, institution, etc., may prosper" [OED].
inflorescence (n.)
1760, "arrangement of flowers on a stem in relation to one another," from Modern Latin inflorescentia, from Late Latin inflorescentem (nominative inflorescens) "flowering," present participle of Latin inflorescere "to come to flower," from in- "in" (from PIE root *en "in") + florescere "to begin to bloom" (see flourish (v.)). Meaning "a beginning to bloom" in English is from 1800.