Matthew 1

2 Abraham begat Isaac, and Isaac begat Jacob. And Jacob begat Judah and his brethren.  3 And Judah begat Perez and Zerah of Tamar. And Perez begat Hezron.  And Hezron begat Ram.  4 And Ram begat Amminadab. And Amminadab begat Nahshon. And Nahshon begat Salmon.  5 And Salmon begat Boaz of Rahab. And Boaz begat Obed of Ruth.   And Obed begat Jesse.  6 And Jesse begat David the King. And David the King begat Solomon of her that was the wife of Uriah.  7 And Solomon begat Rehoboam. And Rehoboam begat Abijah. And Abijah begat Asaph.  8 And Asaph begat Jehoshaphat. And Jehoshaphat begat Joram. And Joram begat Uzziah.  9 And Uzziah begat Jotham. And Jotham begat Ahaz. And Ahaz begat Hezekiah.  10 And Hezekiah begat Manasseh. And Manasseh begat Amos. And Amos begat Josiah.1 And Josiah begat Jechoniah and his brethren in the Transmigration of Babylon.  12 And after the Transmigration of Babylon, Jechoniah begat Shealtiel.  And Shealtiel begat Zerubbabel.  13 And Zerubbabel begat Abiud. And Abiud begat Eliakim. And Eliakim begat Azor.  14 And Azor begat Zadok. And Zadok begat Achim. And Achim begat Eliud.  15 And Eliud begat Eleazar. And Eleazar begat Matthan.  And Matthan begat Jacob.  16 And Jacob begat Joseph the husband of Mary: of whom was born Jesus, who is called Christ.  17 Therefore all the generations from Abraham unto David, fourteen generations.  And from David to the transmigration of Babylon, fourteen generations.  And from the transmigration of Babylon unto Christ, fourteen generations. 

Luke 3

23 And Jesus himself was beginning to be about thirty years old: as it was thought, the son of Joseph, who was of Heli, 24 who was of Matthat, who was of Levi, who was of Melchi, who was of Jannai, who was of Joseph, 25 Who was of Mathathias, who was of Amos, who was of Naum, who was of Esli, who was of Naggai. 26 Who was of Maath, who was of Mathathias, who was of Semein, who was of Joseph, who was of Joda, 27 Who was of Joanan, who was of Rhesa, who was of Zerubbabel, who was of Shealtiel, who was of Neri, 28 Who was of Melchi, who was of Addi, who was of Cosam, who was of Elmadan, who was of Er, 29 Who was of Joshua, who was of Eliezer, who was of Jorim, who was of Matthat, who was of Levi, 30 Who was of Simeon, who was of Judah, who was of Joseph, who was of Jonam, who was of Eliakim, 31 Who was of Melea, who was of Menna, who was of Mattatha, who was of Nathan, who was of David, 32 Who was of Jesse, who was of Obed, who was of Boaz, who was of Sala, who was of Nahshon, 33 Who was of Amminadab, who was of Arni, who was of Hezron, who was of Perez, who was of Judah, 34 Who was of Jacob, who was of Isaac, who was of Abraham, who was of Terah, who was of Nahor, 35 Who was of Serug, who was of Reu, who was of Peleg, who was of Eber, who was of Shelah, 36 Who was of Cainan, who was of Arphaxad, who was of Shem, who was of Noah, who was of Lamech, 37 Who was of Methuselah, who was of Enoch, who was of Jared, who was of Mahalaleel, who was of Cainan, 38 Who was of Enos, who was of Seth, who was of Adam, who was of God.

Lapide St. Matthew gives the genealogy of the Blessed Virgin through her mother St. Anne, while St. Luke gives it through her father Heli, or Joachim, so that Christ may be shown to be descended of the seed of David in both ways. There is no other better way than this of reconciling the genealogies given by SS. Matthew and Luke. Moreover, it is the common opinion of St. Augustine, Denis the Carthusian, Cajetan, Jansenius, and other doctors whom Suarez quotes (pt. iii., quæst. xxvii. a. 1, disp. 3, sect. 2) that St. Luke traces the genealogy of Christ through Heli, or Joachim, the father of the Blessed Virgin. Hence it must follow that St. Matthew’s genealogy is traced through St. Anne, and that she was the daughter of Mathan; for otherwise all her ancestors, whom St. Matthew recounts, belong only to Joseph, and not to the Blessed Virgin and Christ. St. Matthew then traces Christ’s descent through His father Joseph, St. Luke through His mother, the Blessed Virgin; both lines are united in David, but after him separate through his two sons Solomon and Nathan. And again these two lines of Nathan and of Solomon unite in St. Anne, the daughter of Mathan, and sister of Jacob, Joseph’s father. (Cornelius a Lapide Commentary on Luke 3)

18 And the generation of Christ was in this wise. When his mother Mary was espoused to Joseph, before they came together, she was found to be with child by the Holy Ghost.  19 Whereupon Joseph, for that he was a just man, and would not put her to open shame: was minded secretly to dismiss her. 20 But as he was thus thinking, behold the angel of our Lord appeared to him in sleep saying: Joseph son of David, fear not to take Mary your wife, for that which is born in her, is of the Holy Ghost.  21 And she shall bring forth a son: and you shall call his name Jesus. For he shall save his people from their sins.  22 And all this was done that it might be fulfilled which our Lord spoke by the Prophet saying, 23 Behold a Virgin shall be with child, and bring forth a son, and they shall call his name Emmanuel, which being interpreted is, God with us.  24 And Joseph rising up from sleep, did as the angel of our Lord commanded him, and took his wife.  

Matthew 1

25 And he knew her not until she brought forth her firstborn son: and called his name Jesus.

Luke 2

6 And it came to pass, when they were there, her days had fully come that she should be delivered. 7 And she brought forth her first begotten son, and swaddled him in clothes, and laid down in a manger: because there was no place for them in the inn.

McEvilly "Her days were accomplished" that is, fully nine months — the natural period of gestation — commencing with the conception of our Lord, on the 25th of March, and His birth, on the 25th of December, which, "the authority of the Church keeps, taking up the tradition of the ancients on the subject" (St. Augustin de Trinitate, Lib. iv. c. 5).