There's another good example of saying the year number fully in the US Constitution (Article VII):
Done in Convention by the Unanimous Consent of the States present the Seventeenth Day of September in the Year of our Lord one thousand seven hundred and Eighty seven and of the Independence of the United States of America the Twelfth In witness whereof We have hereunto subscribed our Names...
The US Constitution would have 1776 as year one, the first year of independence.
I've been a little curious about the usage of the quaint "in the year of the Republic" recently. This sort of epoch is said to be common in Taiwan, based on an East Asian tradition of dating in regnal years, as in contemporary Japan. The French Republican calendar used a similar epoch from 1793, and the positivist calendar had 1789 as the first year. Other examples are a little tricky to Google up, even if it was a common enough phrase. A court document cited here describes 1837 as the second year of the Republic (of Texas). But this system seems to be a source of confusion: 1938 would be the 163rd year of independence, and the 152nd year of the Republic. It's a confusion of cardinal and ordinal numbers; July 4, 1776, marked the completion of two centuries of American independence, even if something that happened in 1976 was "in the 201st year of independence."
So in 2010, we should say "in the 235th year of independence" and "in the 224th year of the Republic".