And he came down with them, and stood in the plain, and the company of his disciples, and a great multitude of people out of all Judaea and Jerusalem, and from the seacoast of Tyre and Sidon, who came to hear him, and to be healed of their diseases;
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Ambrose of Milan
Note all things carefully. He ascends with the apostles and descends to the crowds. How would a crowd see Christ, except at a low level? It does not follow him to the heights; it does not climb to majestic places. So when he descends, he finds the weak, for the weak cannot be high up. Thus also Matthew teaches that the weak were healed down below. First each was healed, so that little by little, with increasing virtue, he could ascend to the mountain. On the plain he heals each, that is, he calls them back from recklessness. He turns away the harm of blindness. He descends to heal our wounds, so that in an effective and abundant manner he makes us partakers in his heavenly nature.
But observe all things carefully, how He both ascends with His Apostles and descends to the multitude; for how could the multitude see Christ but in a lowly place. It follows him not to the lofty places, it ascends not the heights. Lastly, when He descends, He finds the sick, for in the high places there can be no sick.
By the sea coast he does not refer to the neighboring sea of Galilee, because this would not be accounted wonderful, but it is so called from the great sea, and therein also Tyre and Sidon may be comprehended, of which it follows, Both of Tyre and Sidon. And these states being Gentile, are purposely named here, to indicate how great was the fame and power of the Savior which had brought even the citizens of the coast to receive His healing and teaching. Hence it follows, Which came to hear him.
You will scarcely find anywhere that the multitudes follow our Lord to the higher places, or that a sick person is healed on a mountain; but having quenched the fever of lust and lit the torch of knowledge each man approaches by degrees to the height of the virtues. But the multitudes which were able to touch the Lord are healed by the virtue of that touch, as formerly the leper is cleansed when our Lord touched him. The touch of the Savior then is the work of salvation, whom to touchis to belie...
When he had appointed the holy apostles, he performed very many wonderful miracles, rebuking demons, delivering from incurable diseases whoever drew near to him, and displaying his own most divine power. He did these works so that both the Jews, who had run together to him, and those from the country of the Greeks might know that Christ was not some ordinary man of those in our degree but, on the contrary, God. He honored these chosen disciples with the dignity of the apostolate. He was the Word that was made man but retained nevertheless his own glory. “For power went forth from him and healed all.” Christ did not borrow strength from some other person, but being himself God by nature, even though he had become flesh, he healed them all, by the demonstration of power over the sick. Commentary on Luke, Homily
But after that the High Priest had made publicly known His choice of Apostles, He did many and great miracles, that the Jews and Gentiles who had assembled might know that these were ere invested by Christ with the dignity of the Apostleship, and that He Himself was not as another man, but rather was God, as being the Incarnate Word. Hence it follows , And, the whole multitude sought to touch him, for there went virtue out of him. For Christ did not receive virtue from others, but since He was as by nature God oaf, sending out His own virtue upon the sick, He healed them all.
To a more extended and even part of the mountain, as we learn from comparing this text with St. Matthew v. 1. as it was from the mountain that Jesus Christ addressed to the people the following discourse. (Bible de Vence)