Roshdestwenski W.G.
The subsequent section refers to Moses as the author of the covenant book: And we will take the book of the covenant, and read it in the ears of the people: and they will say, All that the Lord hath spoken, we will do and hear. Later, it is noted that God entrusted the tablets of the Law, inscribed by His divine hand, to Moses, instructing him to document them: and the Lord said unto Moses, Write these words unto thyself: in these words I will give thee a covenant, and to Israel (Ex. 34:27, Num. 21:14). This Law book is identical to the one wherein the Divine commandments were recorded in Exodus, chapters 20-23.
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When the Israelites, after hearing the commandments given by Moses through the Lord, responded: All things whatsoever the Lord hath said shall we do, Scripture confirms that Moses wrote down all the words of the Lord presented to the people. By divine direction, he organized these words into one book and subsequently recited them for all to hear, to which the people reaffirmed, All things whatsoever the Lord hath said shall we do.