ninth (adj., n.)

"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.

"next in order after the sixth, last in order of a series of seven; being one of seven equal parts into which a whole is or may be divided;" c. 1300, a new formation from seven + -th (1).

It replaced earlier sevende, seveth, from Old English seofunda (Anglian, Northumbrian), seofoþa (West Saxon), which is from Proto-Germanic *sebundon, *sebunthon (source also of Old Norse sjaundi, Danish syvende, Old Frisian sigunda, Old Saxon sivondo, Old High German sibunto, German siebente, siebte), from *sebun "seven." Compare Sanskrit septatha "seventh."

Compare Middle English niend, ninde, earlier for "ninth," from late Old English nigende; also earlier Middle English tende, tiende "tenth" (cognate with Old Norse tiundi, Old Frisian tianda, Old Saxon tehando).

Used as a noun from late Old English, "the (man, hour, etc.) next in order after the sixth;" by 1550s as "one of the seven equal parts into which a whole may be divided." Related: Seventhly (Middle English seventhli).

In music, by 1590s as "tone on the 7th degree above or below a given tone," also "interval between any tone and a tone the seventh degree above it.

All kinds of sevenths are classed as dissonances, the minor seventh being the most beautiful and the most useful of dissonant intervals. The seventh produced by taking two octaves downward from the sixth harmonic of the given tone is sometimes called the natural seventh; it is sometimes used in vocal music, and on instruments, like the violin, whose intonation is not fixed. [Century Dictionary]

Seventh-day for "Saturday" (the seventh day of the week) is by 1680s in the depaganized weekday names of the Society of Friends. Also in reference to Saturday as the sabbath of the Jews, hence Seventh-Day Adventist (by 1860), etc.

word-forming element making ordinal numbers (fourth, tenth, etc.), Old English -ða, from Proto-Germanic *-tha- (cognates: Gothic -da, -ta, Old High German -do, -to, Old Norse -di, -ti), from PIE *-to-, also *-eto-, *-oto-, suffix forming adjectives "marking the accomplishment of the notion of the base" [Watkins].

Cognate with Sanskrit thah, Greek -tos, Latin -tus; Sanskrit ta-, Lithuanian and Old Church Slavonic to, Greek to "the," Latin talis "such;" Greek tēlikos "so old, of such an age," Old Church Slavonic toli "so, to such a degree," toliku "so much," Russian toliko "only;" also see -ed.