Etymology
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folio (n.)
mid-15c., from Late Latin folio "leaf or sheet of paper," from Latin folio, ablative of folium "leaf" (source also of Italian foglia, French feuille, Spanish hoja), from PIE *bhol-yo- "leaf" (source also of Greek phyllon "leaf," Gaelic bile "leaflet, blossom"), suffixed form of root *bhel- (3) "to thrive, bloom." Ablative of location, because this was used in page references. Meaning "volume of the largest size" first attested 1620s.
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foliation (n.)
1620s, from Latin foliat-, stem of folium "a leaf" (see folio).
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foliate (adj.)
1620s, "beaten into thin sheets," from Medieval Latin foliatus "leaved, leafy," from Latin folium "a leaf" (see folio). As "leaf-like" from 1650s.
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foliate (v.)
1660s (implied in foliated), "to apply silver leaf," from Medieval Latin foliatus "leaved, leafy," from Latin folium "a leaf" (see folio). Meaning "put forth leaves" is from 1775. Related: Foliated; foliating.
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folic (adj.)
1941, in folic acid, coined from Latin folium "a leaf" (see folio) + -ic. So called for its abundance in green leaves, such as those of spinach.
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feuillemorte (adj.)
"of the color of a dead leaf," 1640s, fieulamort, from French feuille morte, literally "dead leaf" (see folio + mortal (adj.)). A word of loose spelling, variants include phyllamort, filemot, philomot.
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portfolio (n.)

"movable receptacle for detached papers or prints," 1722, porto folio; 1719 as port folio, from Italian portafoglio "a case for carrying loose papers," from porta, imperative of portare "to carry" (from PIE root *per- (2) "to lead, pass over") + foglio "sheet, leaf," from Latin folium (see folio). Usually something like a book cover with a flexible back, fastened with strings or clasps. Meaning "official documents of a state department" is from 1835, hence figuratively, of a minister of state. A minister without portfolio is one not in charge of a particular department. Meaning "collection of securities held" is from 1930; portfolio investment is from 1955.

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*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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leaf (n.)

Old English leaf "leaf of a plant, foliage; page of a book, sheet of paper," from Proto-Germanic *lauba- (source also of Old Saxon lof, Old Norse lauf, Old Frisian laf, Dutch loof, Old High German loub, German Laub "foliage, leaves," Gothic laufs "leaf, foliage"), perhaps from PIE *leub(h)- "to peel off, strip or break off" ((source also of Old Irish luib, "herb," lub-gort "garden;" Albanian labë "rind, cork;" Lithuanian luba "plank, board;" Russian lob "forehead, brow," Czech leb "skull;" Lithuanian luobas "bast," Latvian luobas "peel," Russian lub "bast;" Old Norse lyf "medicinal herbs," Old English lybb "poison; magic").

Related to lodge and lobby; for another PIE root see folio. Extended late 14c. to very thin sheets of metal (especially gold). Compare Lithuanian lapas "leaf," from a root also in Greek lepos "bark," lepein "to peel off." Also applied to flat and relatively broad surfaces, especially of flexible or mounted attachments; meaning "hinged flap on the side of a table" is from 1550s. To turn over a (new) leaf (1590s; 1570s as turn the leaf) "begin a new and better course of life" is a reference to the book sense. Among insects, leaf-hopper is from 1847; leaf-cutter from 1816.

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