2 And Abraham said unto his eldest servant of his house, that ruled over all that he had, Put, I pray thee, thy hand under my thigh:
[AD 373] Ephrem the Syrian on Genesis 24:2
Abraham made him swear by the covenant of circumcision. Because God saw that the two heads of the world had dishonored this member, he set the sign of the covenant on it so that this member, which was the most despised of all the limbs, would now be the most honored of all the limbs. The sign of the covenant that was set on it bestowed such great honor that those who take oaths now swear by it and all those who administer oaths make them swear by it.

[AD 407] John Chrysostom on Genesis 24:2
You see, since he had reached extreme old age, the text says, he wished to preserve Isaac from association with the Canaanites, lest he take a wife from among them. So he summoned the more prudent of his servants, the text says, and gave him the following instructions: “Place your hand under my thigh.” In Greek the verse is written this way: “under my thigh”; whereas in Hebrew it says “under my loins.” Why did he speak in this fashion? It was an idiom of people in the past. But on other grounds it was also because the birth of Isaac takes its origin from there.For you to learn that the action was done according to a certain custom, notice that when he was ordering him to put his hand there, he immediately added, “and I will make you swear by the Lord, the God of heaven and the God of earth.” See how he teaches the servant to recognize the Creator of all things. By saying, “the God of heaven and the God of earth,” he encompassed all creation.

[AD 430] Augustine of Hippo on Genesis 24:2
For an important thing was being done when a spouse was being sought for the seed of Abraham. But that the servant might learn this which Abraham knew, that he did not desire grandchildren carnally and that he did not have any carnal conception about his progeny, he said to his slave whom he was sending, “Put your hand under my thigh and swear by the God of heaven.” What does the God of heaven want to signify in respect to the thigh of Abraham? Already you understand the hidden meaning: by the thigh, his progeny. Therefore what was that swearing but a signifying that the God of heaven would come in the flesh from the progeny of Abraham?

[AD 430] Augustine of Hippo on Genesis 24:2
For, putting the hand under the thigh of a man and swearing by the God of heaven, what else did that signify except that in that flesh, which took its origin from that thigh, the God of heaven would come?Marriage therefore is a good in which the married are better in proportion as they fear God more chastely and more faithfully, especially if they also nourish spiritually the children whom they desire carnally.

[AD 430] Augustine of Hippo on Genesis 24:2
This surely was prophetic of the fact that the Lord God of heaven and the Lord of the earth would one day come in flesh fashioned from that thigh.

[AD 542] Caesarius of Arles on Genesis 24:2
When the sacred lesson was read a little while ago, we heard that blessed Abraham called his servant and said to him, “Put your hand under my thigh that I may adjure you by the God of heaven and of earth, not to obtain a wife for my son from the daughters of this region.” And [the servant] obediently placed his hand under his thigh and swore to him. Indeed, brothers, all these things that are read in the Old Testament, if we are willing to accept them only according to the letter, will bring us little or no profit of soul. For of what benefit is it to us who assemble in church with devotion to hear the Word of God, if it is mentioned that Abraham sent his servant to bring his son a wife from a distant country, when we see this happen frequently also in this land? However, brothers, following the blessed apostle Paul, we should believe that all things which were written for the Jews “happened to them as a type” but in reality were fulfilled for us. Therefore Abraham said to his servant, “Put your hand under my thigh and swear by the God of heaven and of earth.” Thus blessed Abraham said, “Put your hand under my thigh,” as if he were saying, put your hand upon the altar, or put your hand upon the ark of the testament, or stretch forth your hand to God’s temple, and swear to me. He touched his thigh and swore by the God of heaven and earth. For blessed Abraham did not err when he commanded that this be done but because he was filled with the spirit of prophecy and knew that from his own seed Christ the Lord of heaven and earth would be born. Therefore, when his servant touched his thigh, he did not utter an oath by any carnal member but by the living and true God, because “Abraham begot Isaac, Isaac begot Jacob, and Jacob begot Judah,” of whose seed Christ the Lord was born.