The encyclical letter Magnae Dei Matris of Pope Leo XIII was for the month of the Rosary (September 7, 1892). During his long pontificate, this pope dedicated no less than twelve encyclicals to the Most Holy Rosary. He gives us encouragement to recite it with piety and confidence.
When we have recourse to Mary in prayer, we are having recourse to the Mother of mercy, who is so well disposed toward us that, whatever the necessity that presses upon us especially in attaining eternal life, she is instantly at our side of her own accord, even though she has not been invoked. She dispenses grace with a generous hand from that treasure with which from the beginning she was divinely endowed in fullest abundance that she might be worthy to be the Mother of God. By the fullness of grace which confers on her the most illustrious of her many titles, the Blessed Virgin is infinitely superior to all the hierarchies of men and angels, the one creature who is closest of all to Christ. “It is a great thing in any saint to have grace sufficient for the salvation of many souls; but to have enough to suffice for the salvation of everybody in the world, is the greatest of all; and this is found in Christ and in the Blessed Virgin.”
It is impossible to say how pleasing and gratifying to her it is when we greet her with the Angelic Salutation, "full of grace"; and in repeating it, fashion these words of praise into ritual crowns for her. For every time we say them, we recall the memory of her exalted dignity and of the Redemption of the human race which God began through her. We likewise bring to mind the divine and everlasting bond which links her with the joys and sorrows, the humiliations and triumphs of Christ in directing and helping mankind to eternal life.
It pleased Christ to take upon Himself the Son of Man, and to become thereby our Brother, in order that His mercy to us might be shown most openly; for “it behooved him in all things to be made like unto his brethren that he might become a merciful and faithful high priest before God” (Heb. 2:17). Likewise because Mary was chosen to be the Mother of Christ, our Lord and our Brother, the unique prerogative was given her above all other mothers to show her mercy to us and to pour it out upon us.