The Incarnation and the Consecration

So I'm reading Rev. Nicholas Gihr's The Holy Sacrifice of the Mass as a primary source for Praying the Mass: The Prayers of the Priest.  On pages 530-534, he explains the Offertory prayer (in the Extraordinary Form of the Mass, of course — this book is from 1917) invoking the Holy Spirit, the Veni Sanctificator.

Veni Sanctificator, omnipotens aeterne Deus,
et benedic + hoc sacrificium tuo sancto nomini praeparatum.

Come, O Sanctifier, almighty and eternal God,
and bless this sacrifice prepared for the glory of Your holy Name.

On page 532, he answers the question, "Why is the Holy Spirit invoked (in this prayer and in the epiclesis of other anaphoras) to change the bread and wine into the Eucharist?"  The answer is excellent, and the footnote I've included is too amazing to pass up!

The proximate reason lies in the analogy which the Consecration bears to the Incarnation.  The great similarity and manifold relation between the accomplishment of the Eucharist on the altar and the mystery of the Incarnation of the Son of God in the bosom of the Immaculate Virgin Mary are often commented on by the Fathers, and are expressed also in the liturgy.

The Incarnation is, in a manner, renewed and enlarged in the Eucharistic Consecration — and that at all times as well as in numberless places.*  In like manner and for the same reason is it that the miracles of the Incarnation and Consecration are ascribed to the efficacy of the Holy Ghost.  This happens because both mysteries, being works of divine favor and love, as well as works full of infinite purity and holiness, have a special resemblance to the peculiar character of the Holy Ghost, who is personal love and sanctity.  Therefore, although in reality all the three Divine Persons accomplish the act of Consecration, yet it is most frequently ascribed to the power of the Holy Ghost.  As it is said in the Creed, that the Son of God "became incarnate by the Holy Ghost, of the Virgin Mary," we also acknowledge that the Holy Ghost, by His creative power as "Lord and [Giver] of life," changes the inanimate elements of bread and wine into Christ's Body and Blood.

"How shall this be done," says the holy Virgin, "because I know not man?" The Archangel Gabriel, answering, said to her: "The Holy Ghost shall come upon thee, and the power of the Most High shall overshadow thee."

"And now you ask: How shall the bread become the Body of Christ, and the wine, mingled with water, become the Blood of Christ? And I also answer you: The Holy Ghost shall overshadow each and shall effect that which is beyond language and conception." (St. John Damascene, De fide orthod., IV, 13)

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* St. Chrysostom compares (De beato Philog. hom. 6) altar and crib, remarking that on them the Body of Christ reposes no longer wrapped in swaddling bands, but wholly reclothed by the Holy Ghost.

An instrument customary in the Greek liturgy and known by the name of star (aster, asteriskos) also reminds us of the Incarnation. It consists of two intersecting arcs turned downwards. Assuredly the asterisk serves, in the first place, as a protecting cover for the Eucharistic Bread, that — especially after the Consecration — it may not be touched by the velum spread over it; at the same time it symbolizes by its appearance the star that stood over the place where the Child Jesus lay. When, therefore, the priest has incensed the asterisk, and placed it on the discus under the veil, he says: "and a star came and stood over the place where the child was."