Etymology
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eu- 
word-forming element, in modern use meaning "good, well," from Greek eus "good," eu "well" (adv.), also "luckily, happily" (opposed to kakos), as a noun, "the right, the good cause," from PIE *(e)su- "good" (source also of Sanskrit su- "good," Avestan hu- "good"), originally a suffixed form of root *es- "to be." In compounds the Greek word had more a sense of "greatness, abundance, prosperity," and was opposed to dys-.
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kilo- 
word-forming element meaning "one thousand," introduced in French 1795, when the metric system was officially adopted there; irregularly reduced from Greek khilioi "thousand," from PIE *gheslo- "thousand," source also of Sanskrit sahasra-, Avestan hazanjra "thousand." "It is usually assumed that Lat. mille should be connected too" [Beekes]; see milli-. "In the metric system, kilo- means multiplied, & milli- divided, by 1000" [Fowler].
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nano- 

introduced 1947 (at 14th conference of the Union Internationale de Chimie) as a prefix for units of one thousand-millionth part (now "one-billionth"), from Greek nanos "a dwarf." According to Watkins, this is originally "little old man," from nannos "uncle," masc. of nanna "aunt" (see nana), but Beekes calls it "An onomatopoeic word of unknown origin." Earlier nano- was used as a prefix to mean "dwarf, dwarfish," and still it is used in a non-scientific sense of "very small."

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ap- (1)
form of Latin ad- in compounds with words or stems beginning in -p-; see ad-. In Old French reduced to a-, but scribal re-doubling of ap- to app- in imitation of Latin began 14c. in France, 15c. in England, and was extended to some compounds formed in Old French or Middle English that never had a Latin original (appoint, appall).

In words from Greek, ap- is the form of apo before a vowel (see apo-).
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circum- 

word-forming element meaning "around, round about, all around, on all sides," from Latin adverb and preposition circum "around, round about," literally "in a circle," probably accusative form of circus "ring" (see circus). The Latin word was commonly used in word-formation. In French, the element became circon-; Kitchin points out that con for cum is common even in classical Latin. For sense development, compare German rings "around."

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caco- 
before vowels cac-, word-forming element meaning "bad, ill, poor" (as in cacography, the opposite of calligraphy and orthography), from Latinized form of Greek kakos "bad, evil," considered by etymologists probably to be connected with PIE root *kakka- "to defecate." The ancient Greek word was common in compounds; when added to words already bad, it made them worse; when added to words signifying something good, it often implies too little of it.
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xylo- 
before vowels xyl-, word forming element meaning "wood," from Greek xylon "wood cut and ready for use, firewood, timber; piece of wood; stocks, a plank, beam, or bench," in New Testament, "the Cross," a word of uncertain origin. It seems to correspond with Lithuanian šulas "post, pole, stave," Russian šulo "garden-pole," Serbo-Croatian šulj "block," Old High German sul "style, pole," Gothic sauls "pillar," but the exact relationship is unclear, and Beekes asks, "Was the word taken from a non-IE substrate language?"
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sub- 
word-forming element meaning "under, beneath; behind; from under; resulting from further division," from Latin preposition sub "under, below, beneath, at the foot of," also "close to, up to, towards;" of time, "within, during;" figuratively "subject to, in the power of;" also "a little, somewhat" (as in sub-horridus "somewhat rough"), from PIE *(s)up- (perhaps representing *ex-upo-), a variant form of the root *upo "under," also "up from under." The Latin word also was used as a prefix and in various combinations.

In Latin assimilated to following -c-, -f-, -g-, -p-, and often -r- and -m-. In Old French the prefix appears in the full Latin form only "in learned adoptions of old Latin compounds" [OED], and in popular use it was represented by sous-, sou-; as in French souvenir from Latin subvenire, souscrire (Old French souzescrire) from subscribere, etc.

The original meaning is now obscured in many words from Latin (suggest, suspect, subject, etc.). The prefix is active in Modern English, sometimes meaning "subordinate" (as in subcontractor); "inferior" (17c., as in subhuman); "smaller" (18c.); "a part or division of" (c. 1800, as in subcontinent).
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miso- 

word-forming element of Greek origin meaning "hater, hatred," before vowels, mis-, from Greek misos "hatred," misein "to hate," of uncertain etymology, perhaps from a Pre-Greek word. It was productive as a word-forming element in ancient Greek, for instance misoagathia "hatred of good or goodness;" misoponein "to hate work." In English it formed many compounds now obscure or recherche, but some perhaps still useful, such as  misocapnic (adj.) "hating (tobacco) smoke," misocyny "hatred of dogs," misoneism "hatred of novelty."

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andro- 

word-forming element meaning "man, male, masculine," from Greek andro-, combining form of anēr (genitive andros) "a man, a male" (as opposed to a woman, a youth, or a god), from PIE root *ner- (2) "man," also "vigorous, vital, strong."

Equivalent to Latin vir (see virile). Sometimes in later use equivalent to anthrōpos, Latin homo "a person, a human being," and in compounds it often retain this genderless sense (e.g. androcephalous "having a human head," said of monsters including the Sphinx, which in Greece was female).

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