1610s, "of or pertaining to the Germanic languages and to peoples or tribes who speak or spoke them," from Latin Teutonicus, from Teutones, Teutoni, name of a tribe that inhabited coastal Germany near the mouth of the Elbe and devastated Gaul 113-101 B.C.E., probably via Celtic from Proto-Germanic *theudanoz, from PIE root *teuta- "tribe."
Used in English in anthropology to avoid the modern political association of German; but in this anthropological sense French uses germanique and German uses germanisch, because neither uses its form of German for the narrower national meaning (compare French allemand, for which see Alemanni; and German deutsch, under Dutch). In Finnish, Germany is Saksa "Land of the Saxons."
The Teutonic Knights (founded c.1191) were a military order of German knights formed for service in the Holy Land, but who later crusaded in then-pagan Prussia and Lithuania. The Teutonic cross (1882) was the badge of the order.
It is the hypothetical source of/evidence for its existence is provided by: Old Irish tuoth "people," Old Lithuanian tauta "people," Old Prussian tauto "country," Oscan touto "community," German Deutsch, Gothic þiuda, Old English þeod "people, race, nation," Old English þeodisc "belonging to the people." But Boutkan says it is probably a substratum word.
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Definitions of Teuton from WordNet
someone (especially a German) who speaks a Germanic language;
a member of the ancient Germanic people who migrated from Jutland to southern Gaul and were annihilated by the Romans;