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Elizabeth, who had been called “barren," is going to be a mother. Gabriel, sent by God, had informed Mary of it. Shortly afterwards, Mary set out in haste for the hill country, to a town of Judah (Lk 1:39).
She is not motivated by curiosity, nor does she make the journey to discover for herself whether the angel's message is true. Humble, filled with charity—a charity that leads her to be more concerned for her elderly cousin than for herself—Mary goes to the home of Elizabeth because she has discerned in the heavenly message a hidden relationship between Elizabeth's child and the Son she carries within her.
It is a long way—nearly a hundred miles—from Nazareth to Ain Karim, the little town in the hills of Judea where, according to tradition, Zachary and Elizabeth lived. Most likely it was Joseph who arranged the trip, looking for a caravan in which the Blessed Virgin could travel safely. He himself may have accompanied her, at least as far as Jerusalem; some commentators even think he went with Mary right to Ain Karim, which is only five miles from the capital. If so, he would have needed to return immediately to his workshop in Nazareth.
Mary entered the house of Zachary and greeted Elizabeth (Lk 1:40). According to a local tradition, the meeting of the two cousins took place, not in the town, but in a country place where Elizabeth—as the sacred text affirms (Lk 1:24)—had secluded herself for five months from the sight of curious relatives and neighbors, to raise up her heart in gratitude to God for such an immense gift.
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As recorded in St. Thomas Aquinas's Catena Aurea (Golden Chain) for Luke 1:
AMBROSE; The Angel, when he announced the hidden mysteries to the Virgin, that he might build up her faith by an example, related to her the conception of a barren woman. When Mary heard it, it was not that she disbelieved the oracle, or was uncertain about the messenger, or doubtful of the example, but rejoicing in the fulfillment of her wish, and conscientious in the observance of her duty, she gladly went forth into the hill country. For what could Mary now, filled with God, but ascend into the higher parts with haste!
ORIGEN; For Jesus who was in her womb hastened to sanctify John, still in the womb of his mother. Whence it follows, with haste.