"I couldn't find anywhere the information about when and how people switched counting the days in a month from the progressive, roman numeral style to the current format? Thanks for your time."This question appears to ask a few different things. Even if I misunderstood the question, which is quite possible, it led to some interesting research that I hope will both help the correspondent and inform other readers of this site. The question appears to ask when we changed (1) from the Roman fasti type of calendar [see the illustration on What Was the Format of the Ancient Roman Calendar? for a typical fasti type calendar] to the modern form and (2) from the Julian calendar to the Gregorian or n.s., for "new style". (3) It almost definitely asks when we switched from Roman numerals to the Arabic system.
From ancient times there have been different forms of calendars. Not even dealing with calendar function (administrative, secular, or religious, used for recording time, movement of celestial bodies, etc.), there have been circular forms, including the apparently zodiacal ancient Hebrew calendars and the wheels of the Mesoamerican, especially the Maya calendar round, and there have been rectangular charts spread out like the Roman fasti. The medieval codex form, replacing the papyrus scroll for the fasti of the Romans, puts one month on a page instead of stringing them along horizontally. We still have perpetual calendars that can be created with wheels. Now we have online calendars that bear a resemblance to but are not identical to the old-fashioned wall calendars and decorative desk diaries still sold at year's end by merchants hoping you'll pick up one for a last-minute gift. All of these are different, yet we can go back and forth from one to the other with relative ease. To the component of the question "when did we switch from Julian to Gregorian?" it depends on where in the world you are, since the change has been going on for five centuries and is still not universal. The British and therefore, the American colonies, did not adopt the calendar until the middle of the 18th century. More information on this process is provided in the next section.
When Was the Change From Roman to Arabic Numerals?
The answer is that it, too, was a process. Not everyone adopted one form and dropped the other. Roman numerals prevailed in Europe until about the middle of the 15th century. This was about a century before the creation of the Gregorian calendar in 1582, a time at which Roman numerals were still common. The Arabic (really Hindu) numerals and the decimal system were, however, probably in Europe by the 10th century. They became better known from about the 12th century, thanks to Latin translations of the works of the Persian founder of algebra, whose name is found in our word algorithm [sound out the last few syllables at the name's end, starting with "al-"], Abū ʿAbdallāh Muḥammad ibn Mūsā al-Khwārizmī (c.780 - c.850).
In summary, the answer to each of the various components of the question is that it didn't happen at one moment, but gradually over centuries.
- "Computation of Time, and Changes of Style in the Calendar," by Spencer Bonsall; The Pennsylvania Magazine of History and Biography, Vol. 3, No. 1 (1879), pp. 65-78.
- On Roman Time: The Codex-Calendar of 354 and the Rhythms of Urban Life in Late Antiquity, by Michele Renee Salzman; University of California Press, 1991.