Etymology
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petro- (1)

before vowels petr-, word-forming element used from 19c., indicating "rock, stone" (in anatomy it refers to the petrous parts of certain bones), from Greek petros "stone, boulder," petra "rock, rocky mountain range, cliff" (see petrous).

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di- (2)

word-forming element of Latin origin meaning "apart, asunder," the form of dis- before certain voiced consonants. As des- was a form of dis- in Old French, some Middle English words have forms in both de- and di-; compare devise, which really belongs to di- and is related to divide.

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em- 
word-forming element meaning "put in or into, bring to a certain state," sometimes intensive, from French assimilation of en- "in, into" (see en- (1)) to following labial stop (-b-, -p-, and often -m-), or from the same development in later Latin in- (to im-). "This rule was not fully established in spelling before the 17th c." [OED], but it is likely the pronunciation shift was in Old French and Middle English and spelling was slow to conform. Also a living prefix in English used to form verbs from adjectives and nouns (embitter, embody). In words such as emancipate, emerge, emit, emotion the e- is a reduced form of Latin ex- (see ex-) before -m-.
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un- (1)

prefix of negation, Old English un-, from Proto-Germanic *un- (source also of Old Saxon, Old Frisian, Old High German, German un-, Gothic un-, Dutch on-), from PIE *n- (source of Sanskrit a-, an- "not," Greek a-, an-, Old Irish an-, Latin in-), combining form of PIE root *ne- "not." Often euphemistic (such as untruth for "lie").

The most prolific of English prefixes, freely and widely used in Old English, where it forms more than 1,000 compounds. It underwent a mass extinction in early Middle English, but emerged with renewed vigor 16c. to form compounds with native and imported words. It disputes with Latin-derived cognate in- (1) the right to form the negation of certain words (indigestable/undigestable, etc.), and though both might be deployed in cooperation to indicate shades of meaning (unfamous/infamous), typically they are not.

It also makes words from phrases (such as uncalled-for, c. 1600; undreamed-of, 1630s; uncome-at-able, 1690s; unputdownable, 1947, of a book; un-in-one-breath-utterable, Ben Jonson; etc., but the habit is not restricted to un-; such as put-up-able-with, 1812). As a prefix in telegramese to replace not and save the cost of a word, it is attested by 1936.

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