Then Jesus went with them. And when he was now not far from the house, the centurion sent friends to him, saying unto him, Lord, trouble not yourself: for I am not worthy that you should enter under my roof:
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Augustine of Hippo
AD 430
Do not imagine that someone cannot please God while he is engaged in military service. Take as an example holy David to whom the Lord gave such high testimony. Many just men of that time were soldiers. The centurion was the soldier who said to the Lord, “I am not worthy that you should enter under my roof, but only say the word and my servant shall be healed.”
“I am not worthy that you should enter my house. I am not capable of receiving the Sun of Righteousness in its entirety; a little radiance from it is sufficient for me to remove sickness, as it does for the darkness.” When our Lord heard this, he marveled at him. God marveled at a human being. He said to those who were near him, “Truly, I say to you, not even in anyone among the house of Israel have I found this kind of faith.” … The centurion had brought them, and he came so that they would be advocates on his behalf. He rebuked them because they did not possess his faith. To show that the centurion’s faith was the first of the faith of the Gentiles, he said, “Do not imagine that this faith can be limited to the centurion.” For he saw and believed. “Many will believe who have not seen.” “Many will come from the east and from the west and will sit at table with Abraham, Isaac and Jacob in the kingdom of heaven, etc.” Commentary on Tatian’s Diatessaronb.
Jesus Christ went with them, not because he could not cure him, when absent, but that he might set forth the centurion's humility for our imitation. He would not go to the child of the ruler of the synagogue, lest he might appear to be induced by the consideration of his consequence and riches; but he went to the centurion's servant, that he might appear to despise his humble condition. (St. Ambrose)
See how the devout centurion becomes worthier to receive health as he confesses that he is unworthy. In considering his dwelling unacceptable, he has made it the more honorable and acceptable…. The Lord does not go to his house, but the Lord’s healing goes. The Savior does not visit the sick man, but the Savior’s health visits him.