The Order of Ancestors

Gradum, quem Mattheaus in ordine regiae successionis ediderat, Lucas in sacerdotali origine computat. Quem dum uterque dinumerat, cognationem in Domino utriusque tribus uterque significat. Recteque generationis gradus ponitur: quia sacerdotalis et regiae tribus societas per Dvid ex conjugio inita, jam a Salathiel in Zorobabel confirmetur ex genere. Atque ita dum Matthaeus paternam originem, quae ex Juda proficiscebatur, recenset, Lucas vero acceptum per Natham ex tribu Levi genus edocet; suis quibusque partibus Domino nostro Jesu Christo, qui est aeternus et rex et sacerdos, etiam in carnali ortu utriusque generis gloriam probaverunt. Quod vero Joseph potiusquam Mariae nativitas recensetur, nihil refert: eadem enim est totius tribus atque una cognatio. Sanctus Hilarius Pictaviensis, In Evangelium Matthaei Commentarius, Cap I

The order which Matthew gives by the royal succession, Luke reckons according to the priestly origin. One reckons by the bloodline of the Lord and the other by His tribe. It is quite right to present the sequence of the Lord's generation in this way since the association of the priestly and royal ancestry begun by David in his marriage is thereafter confirmed through the lineage of Shealtiel to Zerubbabel. And so while Matthew attends to His paternal origin which stemmed from Judah, Luke speaks of the lineage proceeding through Nathan from the tribe of Levi. By both of these ways then is demonstrated the glory of the double genealogy of our Lord Jesus Christ, who is eternal king and priest, even in his corporeal birth. That his nativity is traced from Joseph rather than Mary does not matter, for there is one and the same bloodline for the entire ancestry. Saint Hilary of Poitiers, Commentary on the Gospel of Matthew, Chapter 1