misdivision n.

prefix of Germanic origin affixed to nouns and verbs and meaning "bad, wrong," from Old English mis-, from Proto-Germanic *missa- "divergent, astray" (source also of Old Frisian and Old Saxon mis-, Middle Dutch misse-, Old High German missa-, German miß-, Old Norse mis-, Gothic missa-), perhaps literally "in a changed manner," and with a root sense of "difference, change" (compare Gothic misso "mutually"), and thus possibly from PIE *mit-to-, from root *mei- (1) "to change."

Productive as word-forming element in Old English (as in mislæran "to give bad advice, teach amiss"). In 14c.-16c. in a few verbs its sense began to be felt as "unfavorably," and it came to be used as an intensive prefix with words already expressing negative feeling (as in misdoubt). Practically a separate word in Old and early Middle English (and often written as such). Old English also had an adjective (mislic "diverse, unlike, various") and an adverb (mislice "in various directions, wrongly, astray") derived from it, corresponding to German misslich (adj.). It has become confused with mis- (2).

late 14c., divisioun, "act of separating into parts, portions, or shares; a part separated or distinguished from the rest; state of being at variance in sentiment or interest," from Old French division and directly from Latin divisionem (nominative divisio), noun of action from past-participle stem of dividere "to divide" (see divide (v.)).

Military sense "portion of an army, fleet, or ship's company" is from 1590s. Mathematical sense of "operation inverse to multiplication" is from late 14c. The mathematical division sign supposedly was invented by British mathematician John Pell (1611-1685) who taught at Cambridge and Amsterdam.

fourteenth letter of the English alphabet; in chemistry, the symbol for nitrogen.

In late Middle English a and an commonly were joined to the following noun, if that word began with a vowel, which caused confusion over how such words ought to be divided when written separately. In nickname, newt, and British dialectal naunt, the -n- belongs to a preceding indefinite article an or possessive pronoun mine.

Other examples of this from Middle English manuscripts include a neilond ("an island," early 13c.), a narawe ("an arrow," c. 1400), a nox ("an ox," c. 1400), a noke ("an oak," early 15c.), a nappyle ("an apple," early 15c.), a negge ("an egg," 15c.), a nynche ("an inch," c. 1400), a nostryche ("an ostrich," c. 1500). My naunt for mine aunt is recorded from 13c.-17c. None other could be no noder (mid-15c.). My nown (for mine own) was frequent 15c.-18c. In 16c., an idiot sometimes became a nidiot (1530s), which, with still-common casual pronunciation, became nidget (1570s), now, alas, no longer whinnying with us.

It is "of constant recurrence" in the 15c. vocabularies, according to Thomas Wright, their modern editor. One has, among many others, Hoc alphabetum ... a nabse, from misdivision of an ABC (and pronouncing it as a word), and Hic culus ... a ners. Also compare nonce, pigsney. Even in 19c. provincial English and U.S., noration (from an oration) was "a speech; a rumor."

The process also worked in surnames, from oblique cases of Old English at "by, near," as in Nock/Nokes/Noaks from atten Oke "by the oak;" Nye from atten ye "near the lowland;" and see Nashville. (Elision of the vowel of the definite article also took place and was standard in Chancery English of the 15c.: þarchebisshop for "the archbishop," thorient for "the orient.")

But it is more common for an English word to lose an -n- to a preceding a: apron, auger, adder, umpire, humble pie, etc. By a related error in Elizabethan English, natomy or atomy was common for anatomy, noyance (annoyance) and noying (adj.) turn up 14c.-17c., and Marlowe (1590) has Natolian for Anatolian.  The tendency is not limited to English: compare Luxor, jade (n.1), lute, omelet, and Modern Greek mera for hēmera, the first syllable being confused with the article.

The mathematical use of n for "an indefinite number" is attested by 1717 in phrases such as to the nth power (see nth). In Middle English n. was written in form documents to indicate an unspecified name of a person to be supplied by the speaker or reader.