Etymology
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-ance 

word-forming element attached to verbs to form abstract nouns of process or fact (convergence from converge), or of state or quality (absence from absent); ultimately from Latin -antia and -entia, which depended on the vowel in the stem word, from PIE *-nt-, adjectival suffix.

Latin present-participle endings for verbs stems in -a- were distinguished from those in -i- and -e-. Hence Modern English protestant, opponent, obedient from Latin protestare, opponere, obedire.

As Old French evolved from Latin, these were leveled to -ance, but later French borrowings from Latin (some of them subsequently passed to English) used the appropriate Latin form of the ending, as did words borrowed by English directly from Latin (diligence,absence).

English thus inherited a confused mass of words from French (crescent/croissant), and further confused it since c. 1500 by restoring -ence selectively in some forms of these words to conform with Latin. Thus dependant, but independence, etc.

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-re 

word-ending that sometimes distinguish British from American English. In the U.S., the change from -re to -er (to match pronunciation) in words such as fibre, centre, theatre began in late 18c. and became standard there over the next 25 years at the urging of Noah Webster (the 1804 edition of his speller, and especially his 1806 dictionary). The -re spelling, like -our, however, had the authority of Johnson's dictionary behind it and was unmoved in Britain, where it came to be a point of national pride, contra the Yankees.

Despite Webster's efforts, -re was retained in words with -c- or -g- (such as ogre, acre, the latter of which Webster insisted to the end of his days ought to be aker, and it was so printed in editions of the dictionary during his lifetime). The -re spelling generally is more justified by conservative etymology, based on French antecedents. It is met today in the U.S. only in Theatre as an element in the proper names of entertainment showplaces, where it is perhaps felt to inspire a perception of bon ton.

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