I first encountered the sentences below on p 121, The Words We Live By: Your Annotated Guide to the Constitution (2004; but the newest edition dates at 2015) by Linda Monk. I rewrote the numerals using digits to ease reading.
[ Source: ] The Ratification of the Conventions of nine States, shall be sufficient for the Establishment of this Constitution between the States so ratifying the Same.
Done in Convention by the Unanimous Consent of the States present the 17th Day of September in the Year of our Lord 1787 and of the Independence of the United States of America the Twelfth In witness whereof We have hereunto subscribed our Names, [...]
The date is already stated as September 17 1787. So to what does the bolded refer?