In verse 29 Jacob instructed Joseph how to take the oath. In verse 30 Joseph promises to do as Jacob has said, but in this verse Jacob insists that Joseph affirm his promise by taking the oath as given in verse 29.
He said: that is, “Jacob said.”
Swear to me: that is, “Swear an oath to me,” “Take the vow,” or “Promise [in God’s name] that you will do it.”
And he [Joseph] swore to him [Jacob]: we may translate this, for example, “Then Joseph swore an oath [took the vow, made the solemn promise]” or “Then Joseph did as his father commanded him to do.”
Then Israel bowed himself upon the head of his bed: Driver says Jacob “apparently turned himself over on his bed, and bent his head down towards its head—in imitation, as far as possible, of actual prostration.” For the account of David doing something similar in his old age, see 1 Kgs 1.47.
The purpose of bowing in his bed is to give thanks, although translations do not agree on the one being thanked. Therefore some translators do not express the gesture but only its purpose. See Good News Translation. Others retain both the gesture and its function. For example, Bible en français courant says “Then Jacob thanked him by inclining deeply at the head of his bed,” and Revised English Bible says “And Israel bowed in worship by the head of his bed.”
Heb 11.21 records this event as “He leaned on the top of his walking stick and worshiped God” (Good News Translation). The reason for saying “walking stick” is that the Hebrew words for “bed” and “walking stick” are very similar, and the Septuagint, which says “walking stick,” is the basis for the translation in Heb 11.21. However, the Septuagint is not to be translated in this verse.
Quoted with permission from Reyburn, William D. and Fry, Euan McG. A Handbook on Genesis. (UBS Helps for Translators). New York: UBS, 1997. For this and other handbooks for translators see here .
