Etymology
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*as- 

also *es-, Proto-Indo-European root meaning "to burn, glow." 

It forms all or part of: ardent; ardor; area; arid; aridity; aril; arson; ash (n.1) "powdery remains of fire;" azalea; potash; potassium.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit asah "ashes, dust;" Hittite hat- "to dry up;" Greek azein "to dry up, parch," azaleos "dry;" Latin aridus "parched, dry," ārēre "to be dry," āra "altar, hearth;" Armenian azazem "I dry up;" Old English æsce "ash," Old High German asca, Gothic azgo "ashes." 

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as- 
assimilated form of ad- before -s-.
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as (adv., conj., pron.)

c. 1200, worn-down form of Old English alswa "quite so, wholly so," literally "all so" (see also), fully established by c. 1400. Equivalent to so; any distinction in use is purely idiomatic. Related to German als "as, than," from Middle High German also.

Phrase as well "just as much" is recorded from late 15c.; the phrase also can imply "as well as not," "as well as anything else." Phrase as if, in Kantian metaphysics (translating German als ob), introducing a supposition not to be taken literally, is from 1892; as an interjection of incredulity (as if!; i.e. "as if that really could happen") is attested from 1995. It duplicates Latin quasi. Phrase as it were "as if it were so" is attested from late 14c.

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third (adj., n.)

"next in order after the second; an ordinal numeral; being one of three equal parts into which a whole is regarded as divided;" late Old English metathesis of þridda, from Proto-Germanic *thridja- (source also of Old Frisian thredda, Old Saxon thriddio, Middle Low German drudde, Dutch derde, Old High German dritto, German dritte, Old Norse þriðe, Danish tredie, Swedish tredje, Gothic þridja), from PIE *tri-tyo- (source also of Sanskrit trtiyas, Avestan thritya, Greek tritos, Latin tertius (source of Italian terzo, Spanish tercio, French tiers), Old Church Slavonic tretiji, Lithuanian trečias, Old Irish triss, Welsh tryde), suffixed form of root *trei- (see three).

Metathesis of thrid into third is attested from c. 950 in Northumbrian (compare wright), but overall thrid was prevalent up to 16c. The noun meaning "third part of anything" is recorded from late 14c. Third rail in electric railway sense is recorded from 1890. Third World War as a possibility first recorded 1947. Third-rate "of poor quality" is from 1814, ultimately from classification of ships (1640s); third class in railway travel is from 1839. Third Reich (1930) is a partial translation of German drittes Reich (1923). Third party in law, insurance, etc., is from 1818.

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category (n.)

1580s, in Aristotle's logic, "a highest notion," from French catégorie, from Late Latin categoria, from Greek kategoria "accusation, prediction, category," verbal noun from kategorein "to speak against; to accuse, assert, predicate," from kata "down to" (or perhaps "against;" see cata-) + agoreuein "to harangue, to declaim (in the assembly)," from agora "public assembly" (from PIE root *ger- "to gather").

The verb's original sense of "accuse" had weakened to "assert, name" by the time Aristotle applied kategoria to his 10 classes of "expressions that are in no way composite," perhaps "things that can be named simply." Exactly what he meant by it "has been disputed almost from his own day till the present" [OED].

What, exactly, is meant by the word "category," whether in Aristotle or in Kant and Hegel, I must confess that I have never been able to understand. I do not myself believe that the term "category" is in any way useful in philosophy, as representing any clear idea. [Bertrand Russell, "A History of Western Philosophy"]

The sense of "any very wide and distinctive class, any comprehensive class of persons or things" is from 1660s.

category should be used by no-one who is not prepared to state (1) that he does not mean class, & (2) that he knows the difference between the two .... [Fowler]
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third degree (n.)
"intense interrogation by police," 1900, probably a reference to Third Degree of master mason in Freemasonry (1772), the conferring of which included an interrogation ceremony. Third degree as a measure of severity of burns (most severe) is attested from 1866, from French (1832); in American English, as a definition of the seriousness of a particular type of crime (the least serious type) it is recorded from 1865.
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sub-category (n.)
also subcategory, 1855, from sub- + category (n.).
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Third World (n.)
1963, from French tiers monde, formulated 1952 by French economic historian Alfred Sauvy (1898-1990) on model of the third estate (French tiers état) of Revolutionary France; his first world (The West) and second world (the Soviet bloc) never caught on.
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categorize (v.)

"place in a category," 1705, from category + -ize. Related: Categorized; categorizing.

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demographic (adj.)

1882, "of or pertaining to demography," from demography + -ic. As a noun, by 1998, short for demographic group or category. Related: Demographical; demographically; demographer (1877).

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