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The Florentine calendar was used in Italy in the Middle Ages. In this system, the new day begins at sunset. When the reference of a birth was, for example, "two hours into the day", this meant two hours after sunset. This means a birth date of August 12 would, by modern reckoning, be considered to be August 11.
The year also began not on January 1 but rather on March 25, which is why some dates are in apparent one-year discrepancy. For example, a birth date of March 10, 1552 in Florentine reckoning translates to March 10, 1553 in modern reckoning. This was not unusual; before the conversion to the Gregorian calendar in 1583, the French year began on Easter day, the Venetian year on March 1, and the English year on March 25 (until 1752). Italy was one of the few nations to immediately convert from the Julian Calendar to the Gregorian: October 4, 1582 was followed by October 15, 1582 (Gregorian).
The Florentine calendar shares this feature with the Celtic calendar: Celtic days too began at sundown: they keep birthdays and the beginnings of months and years in such an order that the day follows the night, their adversary Julius Caesar observed in his Commentarii de Bello Gallico (Gallic Wars).