(Beraisa): The first of Nisan is the new year for the following:

Counting months;

Calculating leap years;

Dating the new Terumas Shekalim (bringing Korbanos from the new contributions);

Some add: Defining terms for renting houses.

Question: What is the source of the first of Nisan as the Rosh Hashanah for months?

Answer #1: One verse states that Pesach is in "the first of the months of the year" (Shemos 12,2) and another verse states that Pesach is in the month of Aviv, when the new crops ripen, i.e. Nisan (Devarim 16,1).

Question: Perhaps it is Iyar (in which the crops also ripen)?

Answer: Aviv refers to the first ripening of crops, not to those that ripen late.

Question: Perhaps it is Adar (in which there is new ripening of crops)?

Answer: It must be that the majority of the crop is newly ripening.

Question: It does not state in the Torah that the majority of the crop must be newly ripening!

Answer #2 (R. Chisda): The Torah states that the seventh month is the one in which the produce is gathered in. Since that refers to Tishrei, the first month must be Nisan.

Question: Perhaps it refers to Cheshvan, making Iyar the first month?

Answer: The ingathering does not occur in Cheshvan.

Question: Perhaps it refers to Elul, making Adar the first month?

Answer: It must be the month in which the majority of the ingathering takes place, which is Tishrei.

Question: It does not state in the Torah that the majority of the ingathering must take place!

Answer #3 (Ravina): Nisan as the Rosh Hashanah for months is learned not from the Chumash, but from Nevi'im: "...the eleventh month, Shevat" (Zecharyah 1,7).

Answer #4 (Rabah bar Ulah): It is learned from the verse stating that Esther was taken to Achashverosh in the tenth month, Teves (Esther 2,16).

Answer #5 (R. Kahana): It is learned from the verse stating that Kisleiv is the ninth month (Zecharyah 7,1).

Answer #6 (R. Acha bar Yakov): It is learned from the verse stating that Sivan is the third month (Esther 8,9).

Answer #7 (R. Ashi): It is learned from the verse stating that Adar is the twelfth month (Esther 3,7).

Answer #8 (R. Ashi): It is learned from the verse stating "the first month, Nisan" (Esther 3,7).

Question: Why didn't everyone use this source, which directly mentions Nisan?

Answer: It might mean that Nisan was the first month in the episode of Haman.

The Tana of our Mishnah did not list this Rosh Hashanah because he was discussing years, not months.

Question: Are decisions to make leap years really made in Nisan? Surely we have learned differently in a Beraisa;

It is forbidden to investigate before Rosh Hashanah (Tishrei) as to whether to make a leap year (as the decision will be forgotten in the meantime).

If it was then decided that the year should be a leap year, this decision is invalid.

In times of need, the decision can be taken immediately after Rosh Hashanah.

The only month that can be added to is Adar.

Answer (R. Nachman bar Yitzchak): The "Rosh Hashanah for leap years" refers to the last date on which one can decide to make a leap year (i.e. as soon as Rosh Chodesh Nisan has been consecrated, it cannot be turned into Adar Sheni):

(Mishnah) (R. Yehoshua and R. Papayas testify:) During the entire month of Adar, they can decide to make the year a leap year (but not once Rosh Chodesh Nisan has been consecrated).

(The excluded view of the Chachamim) This decision can only be taken until Purim.

Question: Why can it only be taken until Purim?

Answer: The laws of Pesach are publicly taught thirty days before Pesach; after listening to these lessons, people will not accept that Pesach has been delayed by a month.

R. Yehoshua and R. Papayas would respond: People understand that the calendar depends upon calculations, and they would reason that the Chachamim had not done the necessary calculations until now.

The Tana of our Mishnah did not list this Rosh Hashanah because he is discussing Roshei Shanim that begin processes, not that end them.

Question: What is the source for the first of Nisan being the new year for Terumas Shekalim?

Answer (R. Yeshayah): The Torah states that the new Korbanos should be brought from the Terumos of the new year (Bamidbar 28,14) and we learn (by way of the identical word "year") (Shemos 12,2) that this refers to the new year beginning with Nisan.

Question: Why not learn that it refers to the new year beginning with Tishrei, where it also has the word "year"?

Answer: The verse of the Korbanos uses the phrase "months of the year," and the word "months" is only mentioned in conjunction with the Rosh Hashanah of Nisan, not with the Rosh Hashanah of Tishrei.

(R. Yehudah, citing Shmuel): Communal Korbanos which are brought on the first of Nisan should be brought from the donations of the new year; if they are brought from last year's donations, they are valid, but a mitzvah is lost.

(Another Beraisa): As above. In addition,a communal Korban donated by an individual is valid, provided that he confers it upon the community.

Question: This is obvious!

Answer: One might have thought that he is suspected of not conferring it upon the community with a full heart; thus, we need be told that there is no such concern.

The Tana of our Mishnah did not list this Rosh Hashanah because since the Korbanos are valid if brought from last year's donations, it is not an absolute Rosh Hashanah.

(Beraisa): If one rents out a house for a year, the year is calculated to the same day of the same month.

If the rental term was "this year," then even if it was rented as late as the first of Adar, the year is finished on the first of Nisan.

Even according to the opinion that one day can count as a year, in this case (where it only finishes in Nisan if it started by the beginning of Adar) it is known that people do not bother to rent out their houses for less than thirty days.

Question: Perhaps Tishrei should be the Rosh Hashanah (and a rental by the first of Elul would finish on the first of Tishrei)?

Answer: A rental that takes place at that time of year is usually intended for the entire duration of winter.

The Tana of our Mishnah, and the Tana Kama of the Beraisa (1:a:4 above), did not list this Rosh Hashanah because it often rains in Nisan, too (therefore, the first of Nisan should not end a rental initiated by the beginning of Adar).

Question:

Our Mishnah follows R. Meir, as we find in a Mishnah (Bechoros 57b) that he holds that the first of Elul is Rosh Hashanah for Ma'aser Behemah.

The Mishnah's earlier ruling that the fifteenth of Nisan is the Rosh Hashanah for festivals follows the view of R. Shimon (who required the three festivals to be sequential from Nisan in order for there to be Bal Te'acher).

If so, the first section and the dissenting view in the second section (that the Rosh Hashanah for Ma'aser Behemah is on the first of Tishrei) are according to R. Shimon, and the first view in the second section is according to R. Meir!

Answer (R. Yosef): The Mishnah is all being stated by Rebi; he brought different sections according to different opinions.

Question: If so, the Tana of the Mishnah cited both the fifteenth of Nisan as the Rosh Hashanah for festivals, and the first of Elul as the Rosh Hashanah for Ma'aser Behemah, in which case there are five Roshei Shanim, not four!

Answer (Rava): It is universally agreed upon that there are four Roshei Shanim-the first of Nisan, the first of Tishrei, the first (or fifteenth) of Shevat, and either the first of Elul (according to R. Meir) or the fifteenth of Nisan (according to R. Shimon).

Alternate answer (R. Nachman bar Yitzchak): The Mishnah means that there are four months in which there are Roshei Shanim.(Nisan contains two)

Question: Surely there are additional Roshei Shanim:

(Mishnah): The sixteenth of Nisan is the Rosh Hashanah for the Omer; the sixth of Sivan is the Rosh Hashanah for the two loaves.

Therefore, according to Rava, our Mishnah should have stated that there are six Roshei Shanim!

And according to R. Nachman bar Yitzchak (that it refers to the number of months which contain Roshei Shanim) it should have stated that there are five!

Answer #1 (R. Papa): The Mishnah only lists those Roshei Shanim which take effect from the previous evening.

Question: Surely the Rosh Hashanah for Korbanos, which renders him liable for Bal Te'acher, takes effect only by day (as it is only then that the Korban can be brought)!

Answer: Since he ought to have brought his Korban before the festival began, the sin is counted from when the festival begins at night.

Question: Surely Yovalos, which only take effect with the blowing of the Shofar, will take effect only by day (as it is only then that the Shofar is blown)!

Answer: The Mishnah follows R. Yishmael, son of R. Yochanan ben Beroka, who holds that Yovel begins with the onset of the first of Tishrei at night.

Answer #2 (R. Shisha berei R. Idi): The Mishnah does not list those Roshei Shanim which take effect only by means of an action (such as bringing the Omer and the two loaves).

Question: Surely the Rosh Hashanah for festivals, which renders him liable for Bal Te'acher, takes effect with the action of bringing the Korban Tamid (as he can't bring his Neder-Korban until that has been brought)!

Answer: He is liable for Bal Te'acher as soon as the day begins.

Question: Surely Yovel only takes effect with the action of blowing the Shofar!

Answer: The Mishnah follows R. Yishmael, son of R. Yochanan ben Beroka, who holds that Yovel begins with the onset of the day.

Answer #3 (R. Ashi): The Mishnah means that there are four Roshei Shanim which occur on Rosh Chodesh.

Question: Would the Mishnah have stated this number which is only true according to Beis Shamai (who holds that the Rosh Hashanah for trees is on the first of Shevat)?

Answer: The Mishnah means that three Roshei Shanim are universally agreed upon to occur on Rosh Chodesh, and the fourth is subject to dispute.