Luke 2:13-14: "And suddenly there was with the angel a multitude of the heavenly host praising God and saying, 'Glory to God in the highest, and on earth peace among those with whom he is pleased!'"
Isaiah 9:4-5: "For the yoke of his burden, and the staff for his shoulder, the rod of his oppressor, you have broken as on the day of Midian. For every boot of the tramping warrior in battle tumult and every garment rolled in blood will be burned as fuel for the fire."
Genesis 11:9: "Therefore its name was called Babel, because there the LORD confused the language of all the earth. And from there the LORD dispersed them over the face of all the earth."
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The text is public domain:
It came upon the midnight clear,
That glorious song of old,
From angels bending near the earth
To touch their harps of gold:
"Peace on the earth, goodwill to all,
From heav'n's all-gracious king."
The world in solemn stillness lay
To hear the angels sing.
Still through the cloven skies they come
With peaceful wings unfurled,
And still their heav'nly music floats
O'er all the weary world.
Above its sad and lowly plains
They bend on hov'ring wing,
And ever o'er its babel sounds
The blessed angels sing.
All you, beneath your heavy load,
By care and guilt bent low,
Who toil along a dreary way
With painful steps and slow;
Look up, for golden is the hour,
Come swiftly on the wing,
The Prince was born to bring you peace;
Of Him the angels sing.
For lo, the days have come to pass
By prophets seen of old,
When down into the circling years
Came Christ as was foretold.
His word of peace shall to the earth
God's ancient promise bring,
And all who take this gift will hear
The song the angels sing.
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The text from Luke is the main Biblical referent in the hymn, although it appears primarily in the first verse (and it's not in the third at all). In the text, the angels say, "Glory to God in the highest, and on earth peace...." While the hymn has the speech more or less the same, it changes the angels' "saying" to singing.
The Genesis text appears in the second verse, but it's not a very involved reference. It's just "the weary world['s]... babel sounds."
Instead of Luke, the third verse comes from the Isaiah text. The hymn renders "the yoke of his burden, and the staff for his shoulder, the rod of his oppressor," as the more prosaic "heavy load" and "care and guilt." The citation should extend to include verse six too: "For to us a child is born, to us a son is given; and the government shall be upon his shoulder, and his name shall be called Wonderful Counselor, Mighty God, Everlasting Father, Prince of Peace." It's only the first half of the hymn verse that's "dreary" and "painful." The second half is "golden" because of Jesus' birth, and Isaiah 9:6 speaks about this too. The hymn even calls Him "The Prince [who] was born to bring you peace," which is the same appellation ("Prince of Peace") given in Isaiah 9:6.