7 As then I had begun to say, thus do they cavil. “Matthew,” say they, “is an Evangelist, and you believe him?” Immediately that we acknowledge him to be an Evangelist, we necessarily believe him. Attend then to the generations of Christ, which Matthew has set down. “The book of the generation of Jesus Christ, the Son of David, the son of Abraham.” How the Son of David, and the Son of Abraham? He could not be shown to be so, but by the succession of generations; for certain it is that when the Lord was born of the Virgin Mary, neither Abraham nor David was in this world, and do you say that the same man is both the Son of David, and the Son of Abraham?
Let us, as it were, say to Matthew, Prove your word, for I am waiting for the succession of the generations of Christ. “Abraham begot Isaac; and Isaac begot Jacob; and Jacob begot Judas and his brethren; and Judas begot Phares and Zara of Thamar; and Phares begot Esrom; and Esrom begot Aram; and Aram begot Aminadab; and Aminadab begot Naasson; and Naasson begot Salmon; and Salmon begot Booz of Rachab; and Booz begot Obed of Ruth; and Obed begot Jesse; and Jesse begot David the king.” Now observe how from this point the genealogy is brought down from David to Christ, who is called the Son of Abraham, and the Son of David.
“And David begot Solomon, of her that had been the wife of Urias; and Solomon begot Roboam; and Roboam begot Abia; and Abia begot Asa; and Asa begot Josaphat; and Josaphat begot Joram; and Joram begot Ozias; and Ozias begot Joatham; and Joatham begot Achaz; and Achaz begot Ezekias; and Ezekias begot Manasses; and Manasses begot Amon; and Amon begot Josias; and Josias begot Jechonias and his brethren, about the time they were carried away to Babylon; and after the carrying away into Babylon, Jechonias begot Salathiel; and Salathiel begot Zorobabel; and Zorobabel begot Abiud; and Abiud begot Eliakim; and Eliakim begot Azor; and Azor begot Sadoc; and Sadoc begot Achim; and Achim begot Eliud; and Eliud begot Eleazar; and Eleazar begot Matthan; and Matthan begot Jacob; and Jacob begot Joseph the husband of Mary, of whom was born Jesus, who is called Christ.”
Thus then by the order and succession of fathers and forefathers, Christ is found to be the Son of David, and the Son of Abraham.
Source: Sermons on Selected Lessons of the New Testament (New Advent)