And as concerning - In further proof of this. To show that he actually did it, he proceeds to quote another passage of Scripture.

No more to return to corruption - The word "corruption" is usually employed to denote "putrefaction, or the mouldering away of a body in the grave; its returning to its native dust." But it is certain (Acts 13:35. See the notes on Acts 2:27) that the body of Christ never in this sense saw corruption. The word is therefore used to denote "death, or the grave, the cause and place of corruption." The word is thus used in the Septuagint. It means here simply that he should not die again.

He said on this wise - He said thus ὅυτως houtōs.

I will give you - This quotation is made from Isaiah 55:3. It is quoted from the Septuagint, with a change of but one word, not affecting the sense. In Isaiah the passage does not refer particularly to the resurrection of the Messiah, nor is it the design of Paul to affirm that it does. His object in this verse is not to prove that he would rise from the dead, but that, being risen, he would not again die. That the passage in Isaiah refers to the Messiah there can be no doubt, Acts 13:1, Acts 13:4. The passage here quoted is an address to the people, an assurance to them that the promise made to David would be performed, a solemn declaration that he would make an everlasting covenant with them through the Messiah, the promised descendant of David.

The sure mercies of David - The word "mercies" here refers to the promise made to David; the mercy or favor shown to him by promising to him a successor that should not fail to sit on his throne, 2 Samuel 7:16; Psalm 89:4-5; Psalm 132:11-12. These mercies and promises are called "sure," as being true or unfailing; they would certainly be accomplished. Compare 2 Corinthians 1:20. The word "David" here does not refer, as many have supposed, to the Messiah, but to the King of Israel. God made to David a promise, a certain pledge; he bestowed on him this special mercy, in promising that he should have a successor who should sit forever on his throne. This promise was understood by the Jews, and is often referred to in the New Testament, as relating to the Messiah. Paul here says that that promise is fulfilled. The only question is how it refers to the subject on which he was discoursing. The point was not mainly to prove his resurrection, but to show particularly that he would never die again, or that he would forever live and reign. And the argument is, that as God had promised that David should have a successor who should sit forever on his throne, and as this prediction now terminated in the Messiah, the Lord Jesus, it followed that, as that promise was sure and certain, he would never die again. He must live if the promise was fulfilled. And though he had been put to death, yet under that general promise there was a certainty that he would live again. It was impossible, the meaning is, that the Messiah, the promised successor of David, the perpetual occupier of his throne, should remain under the power of death. Under this assurance the church now reposes its hopes. Zion's King now lives, ever able to vindicate and save his people.

Acts 13:34 Parallel Commentaries

To the Regions Beyond
'Now there were in the church that was at Antioch certain prophets and teachers; as Barnabas, and Simeon that was called Niger, and Lucius of Cyrene, and Manaen, which had been brought up with Herod the tetrarch, and Saul. 2. As they ministered to the Lord, and fasted, the Holy Ghost said, Separate me Barnabas and Saul for the work whereunto I have called them. 3. And when they had fasted and prayed, and laid their hands on them, they sent them away. A. So they, being sent forth by the Holy Ghost, …
Alexander Maclaren—Expositions of Holy Scripture: The Acts

The Man after God's Own Heart
"A man after mine own heart, who shall fulfil all my will."--ACTS xiii. 22. A BIBLE STUDY ON THE IDEAL OF A CHRISTIAN LIFE No man can be making much of his life who has not a very definite conception of what he is living for. And if you ask, at random, a dozen men what is the end of their life, you will be surprised to find how few have formed to themselves more than the most dim idea. The question of the summum bonum has ever been the most difficult for the human mind to grasp. What shall a man …
Henry Drummond—The Ideal Life

Appendix xii. The Baptism of Proselytes
ONLY those who have made study of it can have any idea how large, and sometimes bewildering, is the literature on the subject of Jewish Proselytes and their Baptism. Our present remarks will be confined to the Baptism of Proselytes. 1. Generally, as regards proselytes (Gerim) we have to distinguish between the Ger ha-Shaar (proselyte of the gate) and Ger Toshabh (sojourner,' settled among Israel), and again the Ger hatstsedeq (proselyte of righteousness) and Ger habberith (proselyte of the covenant). …
Alfred Edersheim—The Life and Times of Jesus the Messiah