Jesus as the New Eve? Mary as the New Adam?

Ephrem the Syrian (AD 307-373), Saint Ephrem's Commentary on Tatian's Diatessaron, Carmel McCarthy trans., Chapter II, Sections 2-3 (pp. 60-61)(footnotes omitted, brackets and italics are McCarthy's):

§2. [Mary] gave birth without [the assistance of] a man. Just as in the beginning Eve was born of Adam without intercourse, so too [in the case of] Joseph and Mary, his virgin and spouse. Eve gave birth to the murderer, but Mary gave birth to the Life-Giver. The former gave birth to him who shed the blood of his brother, but the latter to him whose blood was shed by his brothers. The former saw him who was trembling and fleeing because of the curse of the earth, the latter [saw] him who bore the curse and nailed it on his cross. The virgin's conception teaches that he, who begot Adam without intercourse from the virgin earth, also fashioned the Second Adam without intercourse in the virgin's womb. Whereas the First [Adam] returned back into the womb of his mother, [it was] by means of the Second [Adam], who did not return back into the womb of his mother, that the former, who had been buried in the womb of his mother, was brought back [from it]. 

§3. Mary was trying to convince Joseph that her conception was from the Spirit, but he did not accept [it] because it was an unwonted thing. When he saw however that her countenance was serene, although her womb was heavy, he was not willing to put her to shame, being a just man, but neither [was he willing] to receive her as husband, for he thought that she had intercourse with another man. In his uprightness therefore he judged that he should not take her, but also that he should not denounce her. Therefore, the angel appeared to him and said, Joseph, son of David. It was a wonderful thing that [the angel] also called him, Son of David, to remind him of David, the head of his ancestors, to whom God had made a promise that from his descendants according to the flesh he would raise up the Messiah. Do not be afraid to take Mary your spouse, because what is in her is from the Holy Spirit. If you are in doubt as to whether the virgin's conception was without intercourse, listen to Isaiah who said, Behold the virgin will conceive, and to Daniel, A stone was cut off, but not with [human] hands. This not like that [other passage], Look at the mountain and the well; since that [passage implies] a man and woman, whereas here it is [written], Not with [human] hands. Just as Adam fills the role of father and mother for Eve, so too does Mary for our Lord.  

I bring up this odd usage by Ephrem to encourage folks not to get overly excited by patristic-era use of comparisons between the New Testament and the Old.  These are fun comparisons, but they lack Scriptural warrant in terms of being the meaning of Scripture.