2 Moses my servant is dead; now therefore arise, go over this Jordan, thou, and all this people, unto the land which I do give to them, even to the children of Israel.
[AD 253] Origen of Alexandria on Joshua 1:1-2
The book does not so much indicate to us the deeds of the son of Nun as it represents for us the mysteries of Jesus my Lord. For he himself is the one who assumes power after the death of Moses; he is the one who leads the army and fights against Amalek. What was foreshadowed there on the mountain by lifted hands was the time when “he attaches [them] to his cross, triumphing over the principalities and powers on it.”2Thus Moses is dead; for the law has ceased, because “the law and the prophets extend only up to John.” Do you want me to bring forth proofs from the Scriptures that the law is called Moses? Hear what he says in the Gospel: “They have Moses and the prophets, let them listen to them.” Here, without any doubt, he calls the law Moses.
Therefore “Moses, the servant of God, is dead”; for the law is dead, and the legal precepts are now invalid.

[AD 325] Lucius Caecilius Firmianus Lactantius on Joshua 1:1-2
For the prophet does not speak this way: “And the Lord said to me,” but to Jesus [Joshua], in order to show that he was not speaking of himself but of Christ to whom God was then speaking. For that Jesus [Joshua] was a figure of Christ. Although he was first called Hoshea, Moses, foreseeing the future, ordered him to be called Joshua (or Jesus), so that, since he was selected leader of the soldiery against Amalek who was attacking the children of Israel, he might overcome the adversary through the figure of his name and lead the people into the land of promise. And for this reason also he succeeded Moses, to show that the new law given through Jesus Christ would succeed the old law which was given through Moses.

[AD 397] Ambrose of Milan on Joshua 1:1-2
Joshua the son of Nun became so great, because his union with Moses was the means not only of instructing him in a knowledge of the law but also of sanctifying him to receive grace. When in his tabernacle the majesty of the Lord was seen to shine forth in its divine Presence, Joshua alone was in the tabernacle. When Moses spoke with God, Joshua too was covered by the sacred cloud. The priests and people stood below, and Joshua and Moses went up the mount to receive the law. All the people were within the camp; Joshua was without the camp in the tabernacle of witness. When the pillar of a cloud came down and God spoke with Moses, Joshua stood as a trusty servant beside him. He, a young man, did not go out of the tabernacle, though the old men who stood far off trembled at these divine wonders.

[AD 407] John Chrysostom on Joshua 1:1-2
The name of Jesus [Joshua] was a type. For this reason then, and because of the very name, the creation reverenced him. What then! Was no other person called Jesus [Joshua]? But this man was on this account so called as a type; for he used to be called Hoshea. Therefore the name was changed: for it was a prediction and a prophecy. He brought in the people into the promised land, as Jesus into heaven; not the law; since neither did Moses [enter the promised land] but remained outside. The law has not power to bring in, but grace.