ONlwSG

bròg f. [b̥ɾɔːɡ̊], gen. bròige [b̥ɾɔːɡ̊ʲə], ‘shoe; boot 

Also bròg mhòr, with the adjective mòr ‘big’.

’ and, by extension, ‘hoof’ is usually derived 

Henderson (1910, 116), who incorrectly cites ON brókr; Bugge (1912, 297); MacBain (1911); MacLennan (1925); Borgstrøm (1937, 237; 1940, 57: ‘probably’); Christiansen (1938, 5: (len.) bhrog; 22: brogh (sic)); Oftedal (1956, 71); Cox (1991, 492); McDonald (2009, 346); Ó Muirithe (2010, 21).

from ON brók f. ‘(usually in the plural) a pair of trousers; (in the singular) one leg of a pair of trousers’ (NO), as is Ir. bróg ‘boot; shoe’ (Ó Dónaill 1977) 

Greene (1978, 121); Mac Mathúna (2001, 76); McDonald (2009, 346); Ó Muirithe (2010, 21).

, Mx braag ‘shoe’ 

Marstrander (1932, 234); de Vries (1962); McDonald (2009, 346). For the vocalism in Mx braag [ɛː], see Jackson 1955, 41–42; Broderick 1984 III, 134.

and EG bróc (brócc, bróg) 

Zimmer (1888, 268–69); Stokes (1892, 122); Craigie (1894, 160–61); Bugge (1912, 297); Marstrander (1915a, 65, 99, 141–43); McDonald (2009, 346); Ó Muirithe (2010, 21).

‘shoe, sandal; greave 

‘A piece of armour to protect the shin’.

(?); pl. greaves, leggings, (long) hose, breeches (?)’ (eDIL^˄).

Pokorny (1921, 123–24), however, points out that EG bróc occurs in Irish literature earlier than the Viking Age 

Specifically in the 8th-century Táin Bó Fraích.

and prefers a derivation from OEng. brōc (cognate with ON brók), which survives in modern English in the forms breek and breech (s.v. briogais).

Hence eDIL^˄ and Sandberg-McGowan (1996, 226–27) suggest a derivation from either Old Norse or Old English.

On this basis, although Bergin (1943, 237) claims that ‘[l]inguistically the question is of minor importance, for the essential part of the vocabulary was common to both languages’, SG bròg is potentially from Old English rather than Old Norse. The semantic development from ‘leg covering’ to ‘foot covering’ is presumably the result of changing modes of attire and the evolution of terms to describe them.

Cf. the metonymic development in SG luirg ‘shin → ankle’ and mugharn etc. ‘(originally) shackle → ankle’ (Ó Maolalaigh 2020, 269–72).