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Die Kinder gehen an der Hand ihrer Eltern.
The children are holding their parents' hands.
Indicates physical contact where one person is holding another's hand, often used literally in contexts like walking together or guiding someone.
Sie führte das Kind an der Hand durch die Menschenmenge.
She led the child by the hand through the crowd.
Er nahm ihre Hand an der Hand und lächelte.
He took her hand and smiled.
Commonly used in family contexts, especially with children or elderly people. Can also appear in idiomatic expressions like 'jemanden an der Hand nehmen' (to guide someone closely).
Remember that 'an der Hand' uses the dative case because 'an' is a two-way preposition that takes the dative when indicating location. The hand is the location where the action occurs.
'an der Hand' is always literal in modern German. Do not confuse it with idiomatic expressions like 'jemanden an der Hand nehmen' (to guide someone), which is a separate phrase.
The phrase combines the preposition 'an' (at/on) with the dative feminine article 'der' and the noun 'Hand' (hand). 'Hand' derives from Old High German 'hant', related to English 'hand' and Latin 'manus'. The construction 'an der Hand' has been used in German since Old High German times to describe physical contact involving the hand.
This phrase is always used literally in modern German. It does not carry idiomatic meaning in standard usage. The preposition 'an' requires the dative case ('der Hand'), which is marked by the article 'der'.