Etymology
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beech (n.)
type of large forest tree noted for its smooth, silvery bark and its mast, which serves as food for animals, Old English bece "beech," earlier boece, from Proto-Germanic *bokjon (source also of Old Norse bok, Dutch beuk, Flemish boek, Old High German buohha, German Buche, Middle Dutch boeke "beech"), from PIE root *bhago- "beech tree" (cognate with Greek phegos "oak," Latin fagus "beech;" see fagus). Formerly with adjectival form beechen. Also see book (n.).
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buckwheat (n.)
1540s, from Middle Dutch boecweite "beech wheat" (compare Danish boghvede, Swedish bovete, German Buchweizen), so called from resemblance of the grains to the seed of beech trees. Possibly a native formation on the same model as the Dutch word, from a dialectal form of beech. See beech + wheat.
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book (n.)
Origin and meaning of book

Old English boc "book, writing, written document," generally referred (despite phonetic difficulties) to Proto-Germanic *bōk(ō)-, from *bokiz "beech" (source also of German Buch "book" Buche "beech;" see beech), the notion being of beechwood tablets on which runes were inscribed; but it may be from the tree itself (people still carve initials in them).

Latin and Sanskrit also have words for "writing" that are based on tree names ("birch" and "ash," respectively). And compare French livre "book," from Latin librum, originally "the inner bark of trees" (see library). The Old English word originally meant any written document. The sense gradually narrowed by early Middle English to "a written work covering many pages fastened together and bound," also "a literary composition" in any form, of however many volumes. Later also "bound pages," whether written on or not. In 19c. it also could mean "a magazine;" in 20c. a telephone directory.

From c. 1200 as "a main subdivision of a larger work." Meaning "libretto of an opera" is from 1768. A betting book "record of bets made" is from 1812. Meaning "sum of criminal charges" is from 1926, hence slang phrase throw the book at (1932). Book of Life "the roll of those chosen for eternal life" is from mid-14c. Book of the month is from 1926. To do something by the book "according to the rules" is from 1590s.

The use of books or written charters was introduced in Anglo-Saxon times by the ecclesiastics, as affording more permanent and satisfactory evidence of a grant or conveyance of land than the symbolical or actual delivery of possession before witnesses, which was the method then in vogue. [Century Dictionary]
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fagus (n.)

botanical genus of beech trees, from Latin fagus "beech," from PIE root *bhago- "beech tree" (source also of Greek phegos "oak," Latin fagus "beech," Russian buzina "elder," Old English bece, Old Norse bok, German Buche "beech"), perhaps with a ground sense of "edible" (and connected with the root of Greek phagein "to eat," from PIE root *bhag- "to share out, apportion; to get a share"). Beech mast was an ancient food source for agricultural animals across a wide stretch of Europe.

The restriction to western IE languages and the reference to different trees have suggested to some scholars that this word was not PIE, but a later loanword. In the Balkans, from which the beech started to spread after 6000 BC, the [Greek] word means 'oak,' not 'beech.' Yet 'oak' and 'beech' are both 'fruit-bearing trees,' so that a semantic shift from 'oak' to 'beech' appears quite conceivable. The word itself may then have been PIE after all. [de Vaan]
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hardwood (n.)

1560s, from hard (adj.) + wood (n.). That from deciduous trees, as distinguished from that from pines and firs. Bartlett ("Dictionary of Americanisms," 1848) defines it as "A term applied to woods of solid texture that soon decay, including generally, beech, birch, maple, ash, &c. Used by shipwrights and farmers in Maine, in opposition to oak and pine."

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ash (n.2)
popular name of a common type of forest tree of Eurasia, North America, and North Africa, Old English æsc "ash tree," from Proto-Germanic *askaz, *askiz (source also of Old Norse askr, Old Saxon ask, Middle Dutch esce, German Esche), from PIE root *os- "ash tree" (source also of Armenian haci "ash tree," Albanian ah "beech," Greek oxya "beech," Latin ornus "wild mountain ash," Russian jasen, Lithuanian uosis "ash").

The close-grained wood of the ash is tough and elastic, and it was the preferred wood for spear-shafts, so Old English æsc sometimes meant "spear," as in æsc-here "company armed with spears," æsc-plega "war," literally "spear-play." Æsc also was the name of the Old English runic letter that begins the word.
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mast (n.2)

"fallen nuts or acorns serving as food for animals." Old English mæst, the collective name for the fruit of the beech, oak, chestnut, and other forest trees, especially serving as food for swine, from Proto-Germanic *masto (source also of Dutch, Old High German, German mast "mast;" Old English verb mæsten "to fatten, feed"), perhaps from PIE *mad-sta-, from root *mad- "moist, wet," also used of various qualities of food (source also of Sanskrit madati "it bubbles, gladdens," medah "fat, marrow;" Latin madere "be sodden, be drunk;" Middle Persian mast "drunk;" Old English mete "food," Old High German muos "meal, mush-like food," Gothic mats "food").

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