Lit. 'begotten,' but used for 'born.' In ver. 2 it is the fact of being brought forth -- of course strictly of the mother. It was the actual fact of his being born or brought forth that the magi refer to.
'That that might be,' ch. 1.22; 'so that that should be,' as here; and, 'then was fulfilled,' ver. 17, are never confounded in the quotations of the Old Testament. The first is the object of the prophecy; the second, not simply its object, but an event which was within the scope and intention of the prophecy; the third is merely a case in point, where what happened was an illustration of what was said in the prophecy.
Perhaps a reference to Isa. 11.1, the Hebrew for 'Branch' being Netzer.