An Etymological Dictionary of the German Language/Ball
Ball, (1.) m., ‘challenge (of hounds),’ belongs to the stem of bellen.
Ball (2.), m.. ‘ball,’ from the equiv. MHG. bal (gen. balles) or balle, ballen, m. OHG. ballo, m., balla, f.; AS. *bealla is wanting; E. ball (MidE. balle) is borrowed from the Rom. word Fr. balle, which was obtained from German. OIc. bǫllr, ‘ball,’ presupposes Goth. *ballus. The root bal- appears also with a further gradation in Bolle (in Bolster too?); comp. further Bellen.
Ball (3.), m., ‘dancing entertainment,’ from Fr. bal, ‘ball’; OFr. baller, ‘to dance,’ and its Rom. cognates have been derived from Gr. βαλλίξω, ‘I dance.’