Etymology
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either 

Old English ægðer, contraction of æghwæðer (pron., adv., conj.) "each of two, both," from a "always" (see aye (adv.)) + ge- collective prefix + hwæðer "which of two, whether" (see whether). Cognate with Old Frisian eider, Dutch ieder, Old High German eogiwedar, German jeder "either, each, every").

Modern sense of "one or the other of two" is late 13c. Adverbially, for emphasis, "in any case, at all," especially when expressing negation, by 1828. Use of either-or to suggest an unavoidable choice between alternatives (1931) in some cases reflects Danish enten-eller, title of an 1843 book by Kierkegaard.

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whether (conj.)
Old English hwæðer, hweðer "which of two, whether," from Proto-Germanic *gihwatharaz (cognates Old Saxon hwedar, Old Norse hvarr, Gothic huaþar, Old High German hwedar "which of the two," German weder "neither"), from interrogative base *khwa- "who" (from PIE root *kwo-, stem of relative and interrogative pronouns) + comparative suffix *-theraz (cognate compounds in Sanskrit katarah, Avestan katara-, Greek poteros, Latin uter "which of the two, either of two," Lithuanian katras "which of the two," Old Church Slavonic koteru "which"). Its comparative form is either. Also in Old English as a pronoun and adjective. Phrase whether or not (also whether or no) recorded from 1650s.
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or (conj.)

c. 1200, "either, else, otherwise, as an alternative or substitute," from Old English conjunction oþþe "either, or," which is related to Old Frisian ieftha, Middle Dutch ofte, Old Norse eða, Old High German odar, German oder, Gothic aiþþau "or."

This word was extended in early Middle English (and Old High German) with an -r ending, perhaps by analogy with "choice between alternative" words that ended thus (such as either, whether); then it was reduced to oþþr, at first in unstressed positions (commonly thus in Northern and Midlands English by 1300), and finally to or, though other survived in this sense until 16c.

Compare either, which is originally the same word. The contraction took place in the second term of an alternative, such as either ... or, descended from a common construction in Old English, where both words originally were oþþe (see nor). Or else "otherwise" is by c. 1300.

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*kwo- 
also *kwi-, Proto-Indo-European root, stem of relative and interrogative pronouns.

It forms all or part of: cheese (n.2) "a big thing;" cue (n.1) "stage direction;" either; hidalgo; how; kickshaw; neither; neuter; qua; quality; quandary; quantity; quasar; quasi; quasi-; query; quib; quibble; quiddity; quidnunc; quip; quodlibet; quondam; quorum; quote; quotidian; quotient; ubi; ubiquity; what; when; whence; where; whether; which; whither; who; whoever; whom; whose; why.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit kah "who, which;" Avestan ko, Hittite kuish "who;" Latin quis/quid "in what respect, to what extent; how, why," qua "where, which way," qui/quae/quod "who, which;" Lithuanian kas "who;" Old Church Slavonic kuto, Russian kto "who;" Old Irish ce, Welsh pwy "who;" Old English hwa, hwæt, hwær, etc.
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scale-pan (n.)

"either of the dishes of a balance," 1830, from scale (n.2) + pan (n.).

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HIV (n.)
1986, initialism (acronym) from human immunodeficiency virus, name for either of the two viruses that cause AIDS.
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Baja 
in place names (such as Baja California), Spanish baja, literally "lower," either in elevation or geography.
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bronchus (n.)
"either of the two main branches of the trachea" (plural bronchi), 1706, from Latinized form of Greek bronkhos "the wind pipe" (see bronchia).
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interwork (v.)
c. 1600, a hybrid from inter- "between" + work (v.). Related: interworking. Past tense can be either interworked or interwrought.
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cool (n.)

c. 1400, "moderate state of cold, coolness," from cool (adj.). Meaning "one's self-control, composure" (the thing you either keep or lose) is from 1966.

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