And so, with your people on earth and the all the company of heaven, we praise your name and join their unending hymn.
What comes next in the Great Thanksgiving are words from Isaiah 6:3:
“Holy, holy, holy is the LORD Almighty; the whole earth is full of his glory.”
On occasion I’ve wondered how these words from Isaiah’s experience of God’s holiness found their way into the communion liturgy. What connection did they have with Holy Communion or with Jesus’ last supper? In reading Robert Louis Wilken’s The Spirit of Early Christian Thought, I had a Homer Simpson moment. I slapped myself on the forehead and said, “Doh.”
In writing about the the early Christian’s Eucharistic acclamation of praise, Wilken quotes Cyril of Jerusalem.
The hymn of the seraphim was given to us, says Cyril of Jerusalem, “that we might be participants with the heavenly hosts in their hymn of praise.” When the people of God lifted their voices to worship the Triune God they joined the hymn that was being sung by the heavenly host. This is made explicit in the prayer leading up to the singing of the “Holy, holy, holy,” immediately prior to the great prayer of thanksgiving over the gifts of bread and wine: “You are attended by thousands upon thousands, and myriads upon myriads of angels and archangels, of thrones and dominions, of principalities and powers. Beside you stand the two august Seraphim with six wings; two to cover their face, two to cover their feet, two with which to fly. They sing your holiness. With their praise, accept also our acclamation of your holiness: Holy, holy, holy is the Lord Sabaoth. Heaven and earth are filled with your glory.” 
Beside the throne stand the seraphim who cry out: Holy, holy, holy. If, in the Lord’s Supper, we experience the real presence of God in Jesus Christ, then we, too, are in the presence of majesty. That’s true whether you locate the presence of God in the consecrated bread and wine or (as I do) in the faithful obedience of the gathered community.
The next time that you are gathered around the table, open your eyes. You might just see angels and archangels and flaming seraphim gathered with you to praise the holy LORD almighty. The whole creation is full of his glory.
 Wilken, pp. 46-47. This pasage from Cyril of Jerusalem can be found in On the Mysteries 5:6. The linked translation [from Schaff] differs from that of Deiss, whom Wilken quotes.