Etymology
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octagon (n.)

in geometry, "a plane figure having eight angles and eight sides," 1650s, from Latin octagonos, from Greek oktagōnos, literally "eight-angled, eight-cornered," from okta- combining form of okto "eight" (see eight) + gōnia "angle," which is related to gony "knee" (from PIE root *genu- (1) "knee; angle"). Also octogon (1650s), from French octogone.

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octogenarian (n.)

"person 80 years old or 80-odd years of age," 1789, with -an + French octogénaire "aged 80," from Latin octogenarius "containing eighty," from octogeni "eighty each," related to octoginta "eighty," from octo "eight" (see eight) + -genaria "ten times," from PIE *dkm-ta-, from root *dekm- "ten." As an adjective, "eighty years of age," from 1784. An earlier adjective was octogenary (1690s).

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October 

late Old English, from Latin October (mensis), from octo "eight," from PIE root *octo(u)- "eight" (see eight). The eighth month of the old Roman calendar (pre-46 B.C.E.), which began the year in March. For -ber see December. Replaced Old English winterfylleð. In Russian history, the October Revolution (in which the Bolsheviks overthrew the Provisional Government) happened Nov. 7, 1917, but because Russia had not at that time adopted the Gregorian calendar reform, this date was reckoned there (Old Style) as Oct. 25.

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Octavian 

masc. proper name, from Latin, from Octavius, from octavus "eighth," from octo (see eight).

But although we find so marked differences in the use of the numerals as names, it is impossible to believe that this use did not arise in the same way for all; that is, that they were at first used to distinguish children by the order of birth. But when we find them as praenomina in historical times it is evident that they no longer referred to order of birth. [George Davis Chase, "The Origin of Roman Praenomina," in Harvard Studies in Classical Philology, 1897]
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octave (n.)

c. 1300, utaves (plural, via Anglo-French from popular Old French form oitieve, otaves), reformed in early 15c., from Medieval Latin octava, from Latin octava dies "eighth day," fem. of octavus "eighth," from octo (see eight).

Originally "period of eight days after a festival," also "eighth day after a festival" (counting both days, by inclusive reckoning; thus if the festival was on a Sunday, the octaves would be the following Sunday).

Verse sense of "stanza of eight lines" is from 1580s; musical sense of "note eight diatonic degrees above (or below) a given note" is by 1650s, from Latin octava (pars) "eighth part." Formerly English eighth was used in this sense (mid-15c.)

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octopus (n.)

1758, genus name of a type of eight-armed cephalopod mollusks, from Latinized form of Greek oktōpous, literally "eight-foot," from oktō "eight" (see eight) + pous "foot," from PIE root *ped- "foot."

The more usual Greek word seems to have been polypous (also pōlyps), from polys "many" + pous, but for this word Thompson ["Glossary of Greek Fishes," 1947] suggests folk-etymology and a non-Hellenic origin.

The classically correct Greek plural (had the word been used in this sense in ancient Greek) would be octopodes. Octopi (1817) regards the -us in this word as the Latin noun ending that takes -i in plural. Like many modern scientific names of creatures, it was formed in Modern Latin from Greek elements, so it might be allowed to partake of Latin grammar in forming the plural. But it probably is best to let such words follow the grammar of the language that uses them, and octopuses probably works best in English (unless one wishes also to sanction diplodoci for the dinosaurs).

Used figuratively since at least 1882 of powers having far-reaching influence (usually as considered harmful and destructive). To the ancients, the octopus was crafty and dangerous, thrifty (stores food in its nest), and proverbial of clever and adaptable men, based on the animal's instinct of changing color when frightened or for disguise.

It also was thought to be amphibious and to climb trees near shores to steal grapes and olives (the giant ones were said to raid whole warehouses). Thompson writes that "the eggs look remarkably like ripe olives; hence the story." 

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octahedron (n.)

"a solid figure bounded by eight plane faces," 1560s, from Greek oktahedron, neuter of oktahedros "eight-sided," from okta- "eight" (see octa-) + hedra "a seat; face of a geometrical solid," from PIE root *sed- (1) "to sit." Related: Octahedral.

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octopod 

1826 (adj.), "eight-footed or eight-armed;" 1835 (n.) "an eight-footed or eight-armed animal," especially an octopus, from Latinized form of Greek oktōpod-, stem of oktōpous (see octopus).

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octagonal (adj.)

"eight-sided and eight-angled," 1570s, from octagon + -al (1).

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octad (n.)

"a group, system, or series of eight," 1801; see octa- + -ad.

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