An Etymological Dictionary of the German Language/Sprosse
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Sprosse, f., ‘shoot, sprout; rung,’ from MidHG. sproȥȥe, OHG. sproȥȥo, m., ‘rung.’ This meaning is probably derived from an older signification (‘twig’); comp. OIc. sprote, ‘twig, rod, staff,’ AS. sprota, ‘twig.’ These terms are connected with the Teut. root sprū̆t in sprietzen, of which Sproß, ‘sprout,’ is a ModHG. derivative; from the latter Sprößling is derived.