"Since -torium is a productive suffix only after verbal stems, the rise of terri-torium is unexplained" [Michiel de Vaan, "Etymological Dictionary of Latin and the other Italic Languages"]. An alternative theory, somewhat supported by the vowels of the original Latin word, suggests derivation from terrere "to frighten" (see terrible); thus territorium would mean "a place from which people are warned off."
It forms all or part of: inter; Mediterranean; metatarsal; parterre; subterranean; tarsal; tarsus; Tartuffe; terra; terrace; terra-cotta; terrain; terran; terraqueous; terrarium; terrene; terrestrial; terrier; territory; thirst; toast; torrent; torrid; turmeric; tureen.
It is the hypothetical source of/evidence for its existence is provided by: Sanskrit tarsayati "dries up;" Avestan tarshu- "dry, solid;" Greek teresesthai "to become or be dry," tersainein "to make dry;" Latin torrere "dry up, parch," terra "earth, land;" Gothic þaursus "dry, barren," Old High German thurri, German dürr, Old English þyrre "dry;" Old English þurstig "thirsty."
mid-14c., "territory ruled by a duke or duchess," from Old French duché (12c.), from Medieval Latin ducatus "territory of a duke," from Latin dux "leader" (see duke (n.)).
county name, Old English Defena(scir) "(territory of the) Dumnonii," a Celtic people-name. As a type of cattle, from 1798.