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Origin and history of -th
-th(1)
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.
Physicists coined zeroth by 1896, in describing functions, "coming before the first."
-th(2)
suffix forming nouns of action, state, or quality from verbs or adjectives (such as birth, bath, depth, death, growth, strength, truth, math (n.2)), from Old English -ðu, -ð, from Proto-Germanic *-itho (cognates: Old Norse -þ, Old High German -ida, Gothic -iþa), abstract noun suffix, from PIE *-ita (cognates: Sanskrit -tati-; Greek -tet-; Latin -tati-, as in libertatem "liberty" from liber "free"). Sometimes in English reduced to -t, especially after -h- (as in height).
Formerly more widespread (Middle English had stilþe "silence," c. 1200; wrengthe "wrongness, crookedness, distortion," c. 1300), and in recent centuries often tempting to new coinages (17c. swelth "swelling;" Ruskin's illth).
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