"the cardinal number one more than eight or one less than ten; the number which is one more than eight;" Middle English nīn, from Old English nigen, from Proto-Germanic *newun (source also of Old Saxon nigun, Old Frisian niugun, Old Norse niu, Swedish nio, Middle Dutch neghen, Dutch negen, Old High German niun, German neun, Gothic niun "nine").

This is from PIE root *newn "nine" (source also of Sanskrit nava, Avestan nava, Greek ennea (with unetymological initial e-), Albanian nende, Latin novem (with change of -n- to -m- by analogy of septem, decem), Lithuanian devyni, Old Church Slavonic deveti (the Balto-Slavic forms by dissimilation of -n- to -d-), Old Irish noin, Welsh naw).

As "a symbol representing the number nine," late 14c. The proverbial nine lives of a cat are attested from 17c.  Nine-to-five "the average workday" is attested from 1935. Nine days (or nights) has been proverbial since mid-14c. for the time which a wonder or novelty holds attention; the expression nine days' wonder is from 1590s. The Nine "the Muses" is from c. 1600. Also see nines.

word-forming element making cardinal numbers from 13 to 19, meaning "ten more than," from Old English -tene, -tiene, from Proto-Germanic *tekhuniz (cognates: Old Saxon -tein, Dutch -tien, Old High German -zehan, German -zehn, Gothic -taihun), an inflected form of the root of ten; cognate with Latin -decim (source of Italian -dici, Spanish -ce, French -ze).

Proto-Indo-European root meaning "ten."

It forms all or part of: cent; centenarian; centenary; centi-; centime; centurion; century; centennial; cinquecento; dean; deca-; decade; decagon; Decalogue; Decameron; decapod; decathlon; December; decennial; deci-; decile; decimal; decimate; decimation; decuple; decussate; denarius; denier (n.) "French coin;" dicker; dime; dinar; doyen; dozen; duodecimal; duodecimo; eighteen; fifteen; fourteen; hecatomb; hendeca-; hundred; icosahedron; nineteen; nonagenarian; octogenarian; Pentecost; percent; quattrocento; Septuagint; sexagenarian; seventeen; sixteen; ten; tenth; thirteen; thousand; tithe.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit dasa, Avestan dasa, Armenian tasn, Greek deka, Latin decem (source of Spanish diez, French dix), Old Church Slavonic deseti, Lithuanian dešimt, Old Irish deich, Breton dek, Welsh deg, Albanian djetu, Old English ten, Old High German zehan, Gothic taihun "ten."

"next in order or rank after the eighteenth; the ordinal numeral corresponding to nineteen; being one of nineteen equal parts into which a whole is regarded as divided;" late 14c., nyntenthe; from nineteen + -th (1).

It is a replacement or modification (by influence of nineteen) of nigonteoþa, nyenteoþe (c. 1300), from Old English nigon-teoða, which is cognate with Old Frisian niuguntinda, Dutch negentiende, Old High German niuntazehanto, German neunzehnte, Old Norse nitjandi, Danish nittende. Nineteenth hole "bar-room in a golf clubhouse" is attested from 1901.