An Etymological Dictionary of the German Language/Bär
Bär (1.), m., ‘(paving) beetle,’ from MidHG. bęrn, ‘to strike, beat,’ whence also MidHG. bęr, f., ‘blow, stroke.’ OHG. bęrjan, Goth. *barjan, agrees by the permutation of consonants with Lat. ferio, ‘I strike,’ as well as OBulg. borją, ‘I fight’ (OIc. berjask, ‘to fight’); it is based on the root bher, ‘to strike.’
Bär (2.), m., ‘bear.’ The Lat. name of the animal (ursus) descends from the pre-Aryan period, just as Gr. ἄρκτος and Ind. ṛkša-s (ursus for *urcsus). It is remarkable that the Teutons have abandoned this old Aryan term for ‘bear’ (ṛksós, Teut. orhsa-s), since they have retained other names of animals. In MidHG. we have bër, OHG. bëro, AS. bëra, E. bear, björn, ‘bear’ (Goth. *baíra). The Teut. beron- is a subst. form based upon an Aryan adj. bhero-, equiv. to Lith. bėras, ‘brown’ (Lat. furvus?), from the root of which, bher and ModHG. Biber, braun, may also be derived; in using the adj. as a subst. the Aryan ṛksos is understood. Note that Braun is the name of the bear in the OG. animal fables.
Bär (3.), m., ‘brood-boar,’ from the equiv. MidHG. and OHG. bêr, m., which, with OSax. bêr-swîn, AS. bâr, E. boar, points to Goth. *baira-.