Sabbath a synonym of midnight-to-midnight "Saturday" (literally, Saturn's day in at least a dozen languages): this is a simplification of the use of "Sabbath" in other religious contexts, where the two do not coincide. (Using midnight instead of sundown as delimiter dates back to the Roman Empire.) In over thirty other languages, the common name for this day in the seven-day week is a cognate of "Sabbath". "Sabbatini", originally "Sabbadini", often "Sabatini", etc., is a very frequent Italian name form ("Sabbatos" is the Greek form), indicating a family whose ancestor was born on Saturday, Italian "sabato"; "Domenico" indicated birth on Sunday.
Determination of the day of the week day of the week begins by starting from an ‘anchor date’: a known pair (such as January 1, 1800 as a Wednesday), determining the number of days between the known day and the day that you are trying to determine, and using arithmetic modulo 7 to find a new numerical day of the week. One standard approach is to look up (or calculate, using a known rule) the value of the first day of the week of a given century, look up (or calculate, using a method of congruence) an adjustment for the month, calculate the number of leap years