Dating of jewish calendar
A full calendar system has a different calendar date for every day.
Thus the week cycle is by itself not a full calendar system; neither is a system to name the days within a year without a system for identifying the years.
This was mostly based on observation, but there may have been early attempts to model the pattern of intercalation algorithmically, as evidenced in the fragmentary 2nd-century Coligny calendar.
Latin calendarium meant "account book, register" (as accounts were settled and debts were collected on the calends of each month).
The Latin term was adopted in Old French as calendier and from there in Middle English as calender by the 13th century (the spelling calendar is early modern).
Amongst such calendar systems was the calendar system of the Persian Empire, which in turn gave rise to the Zoroastrian calendar as well as the Hebrew calendar.
A great number of Hellenic calendars developed in Classical Greece, and with the Hellenistic period also influenced calendars outside of the immediate sphere of Greek influence, giving rise to the various Hindu calendars as well as to the ancient Roman calendar.