In the direction of a gate or gates; toward the gate.
From 'gateward' plus '-s,' an adverbial suffix. The '-wards' ending (also seen in 'afterwards,' 'towards') creates directional adverbs from Old English origins.
'Gatewards' is a rare adverb that shows how Old English had a rich system for creating directional words—we still use this system today with words like 'homeward,' 'seaward,' and 'forward.'
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