Commentaire sur La Genèse 24:9

על הדבר הזה, concerning the condition stipulated by Avraham.

וישבע לו על הדבר הזה, he accepted all of Avraham’s conditions as part of his oath.

וישבע לו על הדבר. He swore to him concerning the matter. An absolute oath concerning a Canaanite girl, and a conditional oath concerning the need to find the girl in Abraham's birthplace should the girl refuse to move to the land of Canaan.

וישם, the meaning is clear. (verse 2)

תחת ירך אברהם, “under the thigh of Avraham.” Joseph, when asked by his father to swear that he would not bury him in Egypt but with his father and grandfather in Machpelah, did not do so, as he considered such behavior not respectful toward his father, even though he had requested him to swear. (Compare Genesis 47,2931)