In the same day the LORD made a covenant with Abram, saying,
Unto your descendants have I given this land, from the river of Egypt unto the great river, the river Euphrates:
Read Chapter 15
Ambrose of Milan
Foreign peoples are given to Abraham as though for education and so that the most scrupulous mind of the just person might cut away their vices and correct their errors. But what is most evident here is rather the mystery of the church. Through its apostles, “who are Israelites, to whom belong the patriarchs,” and from whose patriarchs “Christ was born according to the flesh” under the law, the church was to be constituted from the gathering of pagan peoples who would believe. And it is not by accident that these are indicated by the number ten but rather to show that these, at first unbelievers, when they had completed the measure of impiety, would certainly obtain the crown of faith. .
When the torches had passed over the divided animals, the covenant was made. God said to Abraham, “To your descendants I will give this land,” and he described in detail how far the land extended in each direction. But, through an anagogical [mystical] transposition consistent with our above remarks, we must understand that this land is given to the holy man’s spiritual posterity. The Savior too promises it to those who practice gentleness. This is a promise that applies to the true children and not to all who descend from Abraham, for “it is not the children of the flesh who are the children of God, but the children of the promise are reckoned as descendants.” It is “the one who does the works of Abraham” who is in fact his child. The phrase “from the river to the river” is also well put, for the promise that belongs to the posterity of the holy man is virtue, which is placed between flowing things. Flowing things, of course, do not make up virtue but are its very borders, in the sens...
Of Egypt, a branch of the Nile, not far from Pelusium. This was to be the southern limit, and the Euphrates the northern; the two other boundaries are given, Numbers xxxiv.
Perhaps Solomon's empire extended so far. At least, the Jews would have enjoyed these territories, if they had been faithful. (Menochius)