1 “O sing unto the Lord a new song”. The new man knows this, the old man knows it not. The old man is the old life, and the new man the new life: the old life is derived from Adam, the new life is formed in Christ. But in this Psalm, the whole world is enjoined to sing a new song. More openly elsewhere the words are these: “O sing unto the Lord a new song; sing unto the Lord, all the whole earth;” that they who cut themselves off from the communion of the whole earth, may understand that they cannot sing the new song, because it is sung in the whole, and not in a part of it. Attend here also, and see that this is said. And when the whole earth is enjoined to sing a new song, it is meant, that peace sings a new song. “For He has done marvelous things.” What marvelous things? Behold, the Gospel was just now being read, and we heard the marvellous things of the Lord. The only son of his mother, who was a widow, was being carried out dead: the Lord, in compassion, made them stand still; they laid him down, and the Lord said, “Young man, I say unto you, Arise.”...“The Lord has done marvellous things.” What marvellous things? Hear: “His own right hand, and His holy arm, has healed for Him.” What is the Lord's holy Arm? Our Lord Jesus Christ. Hear Isaiah: “Who has believed our report, and to whom is the arm of the Lord revealed?” His holy arm then, and His own right hand, is Himself. Our Lord Jesus Christ is therefore the arm of God, and the right hand of God; for this reason is it said, “has He healed for Him.” It is not said only, “His right hand has healed the world,” but “has healed for Him.” For many are healed for themselves, not for Him. Behold how many long for that bodily health, and receive it from Him: they are healed by Him, but not for Him. How are they healed by Him, and not for Him? When they have received health, they become wanton: they who when sick were chaste, when cured become adulterers: they who when in illness injured no man, on the recovery of their strength attack and crush the innocent: they are healed, but not unto Him. Who is he who is healed unto Him? He who is healed inwardly. Who is he that is healed inwardly? He who trusts in Him, that when he shall have been healed inwardly, reformed into a new man, afterwards this mortal flesh too, which does languish for a time, may in the end itself even recover its most perfect health. Let us therefore be healed for Him. But that we may be healed for Him, let us believe in His right hand.
2. “The Lord has made known His salvation”. This very right hand, this very arm, this very salvation, is our Lord Jesus Christ of whom it is said, “And all flesh shall see the salvation of God;” of whom also that Simeon who embraced the Infant in his arms, spoke, “Lord, now let Your servant depart in peace; for my eyes have seen Your salvation.” “The Lord has made known His salvation.” To whom did He make it known? To a part, or to the whole? Not to any part specially. Let no man betray, no man deceive, no man say, “Lo, here is Christ, or there:” the man who says, Lo, He is here, or there, points to some particular spots. To whom “has the Lord declared His salvation”? Hear what follows: “His righteousness has He openly showed in the sight of the heathen.” Our Lord and Saviour Jesus Christ is the right hand of God, the arm of God, the salvation of God, and the righteousness of God.
3. “He has remembered His mercy to Jacob, and His truth unto the house of Israel”. What means this, “He has remembered His mercy and truth”? He has pitied, so that He promised; because He promised and showed His mercy, truth has followed: mercy has gone before promise, promise has been fulfilled in truth....
“And His truth unto the house of Israel.” Who is this Israel? That ye may not perchance think of one nation of the Jews, hear what follows: “All the ends of the world have seen the salvation of our God.” It is not said, all the earth: but, “all the ends of the world:” as it is said, from one end to the other. Let no man cut this down, let no man scatter it abroad; strong is the unity of Christ. He who gave so great a price, has bought the whole: “All the ends of the world.”
Source: The Enarrations, or Expositions, on the Psalms (New Advent)