Rosh Hashana

MISHNA: They are four days in the year that serve as the New Year, each for a different purpose: On the first of Nisan is the New Year for kings; it is from this date that the years of a king’s rule are counted. And the first of Nisan is also the New Year for the order of the Festivals, as it determines which is considered the first Festival of the year and which the last.
On the first of Elul is the New Year for animal tithes; all the animals born prior to that date belong to the previous tithe year and are tithed as a single unit, whereas those born after that date belong to the next tithe year. Rabbi Elazar and Rabbi Shimon say: The New Year for animal tithes is on the first of Tishrei.
On the first of Tishrei is the New Year for counting years, as will be explained in the Gemara; for calculating Sabbatical Years and Jubilee Years, i.e., from the first of Tishrei there is a biblical prohibition to work the land during these years; for planting, for determining the years of orla, the three-year period from when a tree has been planted during which time its fruit is forbidden; and for tithing vegetables, as vegetables picked prior to that date cannot be tithed together with vegetables picked after that date.
On the first of Shevat is the New Year for the tree; the fruit of a tree that was formed prior to that date belong to the previous tithe year and cannot be tithed together with fruit that was formed after that date; this ruling is in accordance with the statement of Beit Shammai. But Beit Hillel say: The New Year for trees is on the fifteenth of Shevat.
GEMARA: The New Year for kings; with regard to what halakha is it mentioned in the mishna? Why is it necessary to set a specific date to count the years of a king’s rule, rather than counting them from the day that he ascends to the throne? Rav Ḥisda said: It is for determining the validity of documents.
It was the common practice to date documents in accordance with the years of the king’s rule; therefore, it was important that these years begin at a fixed time, so that one knows whether a particular document was antedated or postdated, as we learned in a mishna: Antedated promissory notes, i.e., promissory notes dated prior to the date on which the loan actually took place, are invalid because a loan document creates a lien on the borrower’s property. By dating the document earlier than the loan itself, the lender has a fraudulent mortgage on the property, which can be used against any future purchaser. Therefore, the Sages ordained that an antedated promissory note does not establish a lien, even from the true date of the loan. But postdated promissory notes bearing a date that is later than the date when the loan actually took place are valid, as postdating the note presents no opportunity for defrauding a purchaser.
The Sages taught in a baraita: If a king ascended to the throne on the twenty-ninth of Adar, the month preceding Nisan, once the first of Nisan arrives, although he reigned for only one day, a year is counted toward his reign; his first year of rule is completed from the first of Nisan. But if he ascended to the throne only on the first of Nisan, one counts an additional year toward his reign only when the next Nisan arrives.
The Master said, citing the baraita: If a king ascended to the throne on the twenty-ninth of Adar, once the first of Nisan arrives a year is counted toward his reign. The Gemara comments: This