(R. Tanchuma citing R. Pinchas citing R. Levi): [Chagai] asked them about a Chamishi in Kodesh;

"Hen Yisa Ish Besar Kodesh bi'Chnaf Bigdo" - the corner is a Rishon. The Kodesh meat is a Sheni. The bread or Tavshil is a Shelishi. The wine or oil is a Revi'i. The food is a Chamishi. Is there a Chamishi in Kodesh?

"Va'Ya'anu ha'Kohanim va'Yomru Lo." They answered him properly, for there is not a Chamishi in Kodesh. (He then asked if the corner was Tamei Mes, so the food is a Revi'i. They answered him properly, that it is Tamei.)

Question: [If so,] why did he curse them?

Answer: This is like one who seeks a pretext against his friend. [He cursed them] because they did not care about the Bayis.

Question: Why did he say "va'Asher Yakrivu Sham Tamei Hu"?

Answer: It is like R. Simon bar Zavdi said - they found the skull of Arnon ha'Yevusi under the Mizbe'ach.

(Beraisa - R. Yosi): What is the source for a Revi'i in Kodesh? We learn from a Kal va'Chomer;

A Mechusar Kipurim (a Zav, Zavah, Yoledes or Metzora who must bring a Korban to complete Taharah) does not disqualify Terumah, but he disqualifies Kodesh. A Shelishi of Terumah is disqualified (one may not eat it). All the more so it is Posel Kodesh (makes a Revi'i)!

We learned a Shelishi from a verse ("veha'Basar Asher Yiga b'Chol Tamei Lo Ye'achel" - even if it touched a Sheni, Kodshim becomes a Shelishi), and a Revi'i from a Kal v'Chomer.

Question (R. Yochanan): A food that touched a Tevul Yom disproves this! It is Pasul in Terumah, and it does not disqualify Kodesh!

(R. Chiyah citing R. Yochanan): R. Yosi holds like R. Akiva, his Rebbi. Just like R. Akiva says "Yitma" - it is Metamei [others] mid'Oraisa, R. Yosi says "v'Chol Mashkeh... Yitma" (Vayikra 11:34) - it is Metamei [others] mid'Oraisa.

(R. Avahu citing R. Yosi bar Chaninah): R. Yosi does not need this Kal v'Chomer. R. Yosi expounds a verse. "Veha'Basar Asher Yiga" - this is a Sheni, which touched a Rishon. "B'Chol Tamei" - this is a Shelishi, which touched a Sheni. The last Tum'ah (the Shelishi touched a Revi'i) "Lo Ye'achel."

Question: [In our Mishnah, R. Akiva expounded a Shelishi for] food that became Tamei from the airspace of a Kli Cheres that became Tamei through a Sheretz. What is the source for food that became Tamei [directly] from a Sheretz?

Answer: A Kal v'Chomer teaches this. Kelim do not become Tamei from the airspace of a Kli Cheres, yet if they became Tamei through a Sheretz, they are Metamei like a Sheretz to be Metamei food. Food itself that became Tamei through a Sheretz, all the more so it is Metamei like a Sheretz to be Metamei food!

Question: This is like R. Akiva. According to R. Yishmael [who does not learn from Yitma, what is the source]?

Answer (Beraisa - R. Yishmael) Question: "Veha'Basar Asher Yiga b'Chol Tamei - this is a Rishon, which touched any Tum'ah. "Lo Ye'achel" includes a Sheni. What is the source for a Shelishi?

Answer: A Kal v'Chomer teaches this. A Tevul Yom does not disqualify Chulin, but he disqualifies Terumah. A Sheni, which is Pasul in Chulin, all the more so it disqualifies Terumah!

Question: What is the source for a Revi'i of Kodesh?

Answer: A Kal v'Chomer teaches this. A Mechusar Kipurim does not disqualify Terumah, but he disqualifies Kodesh. A Shelishi of Terumah is disqualified. All the more so it is Posel Kodesh (makes a Revi'i)!

Question: We learned a Rishon and Sheni from a verse, a Shelishi from a Kal v'Chomer, and a Revi'i from a Kal v'Chomer. Do we learn a Kal v'Chomer from a Kal v'Chomer (in Kodshim)?!

Answer: Everything depends on a Halachah (tradition from Sinai), that a Shelishi is disqualified in Terumah and a Revi'i in Kodesh. (The Kal v'Chomer is a mere Asmachta for the Halachah.)

(Mishnah): On that day, R. Akiva expounded "you will measure 2000 Amos outside the city, to the east..." (and this is part of the Levite city). Another verse says "1000 Amos from the wall of the city"!

Question: You cannot say 1000 Amos, for it says 2000 Amos! You cannot say 2000 Amos, for it says 1000 Amos! Why does it say 1000, and why does it say 2000?

Answer #1 (R. Akiva): We leave 1000 Amos for Migrash (vacant). 2000 Amos is the Techum within which one may walk on Shabbos;

Answer #2 (R. Eliezer, son of R. Yosi ha'Glili): We leave 1000 Amos for Migrash. [The remaining 1000 Amos until] 2000 are for fields and vineyards.

(Gemara): R. Eliezer, son of R. Yosi ha'Glili says, 2000 Amos is the Techum of the Levite cities. Deduct 1000 Amos for Migrash. It turns out that a quarter is Migrash, and the rest is fields and vineyards (this will be explained. To simplify the numbers, every area mentioned is in units of a square of side 1000, i.e. a million square Amos.)

(R. Yirmeyah citing R. Shmuel bar Rav Yitzchak citing Rav): A quarter of the 1000 Amos (the city was a square of side 500 Amos. With the Migrash around, it was a square of side 1000 Amos. Its area (one) was a quarter of the entire area including the fields and vineyards, i.e. a square of side 2000 (its area is four). Or, the area of the Migrash itself without the city (three quarters) was a quarter of the area of the fields and vineyards alone, which was three.)

(R. Yitzchak): You can even say [a full square of 1000 Amos for Migrash] on each side; it is a quarter [of the area for fields and vineyards. I.e. the city is 2000 by 2000; with the Migrash around, it was a square of side 4000. With the fields and vineyards around, it was a square of side 8000. The area of the fields and vineyards was 48; the Migrash's area was 12];

Note: Perhaps the text should be corrected to say "Pi Arba" (four times as much), and not "Ribu'a". (PF)

One who makes a square four measures [bigger, i.e. each side is four times as long] he needs 16 [times as much area to fill it. The city and Migrash are four times as long as according to Rav, and their area is 16 times as much.]

R. Mana gauged like the moon [a crescent; the interior is lacking. Here, the Migrash lacked the place of the city. This is like Abaye in Eruvin 57a. The city was a circle of side 1000, the Migrash was a circle of diameter 3000. Chazal rely on the approximation that the area of a circle is three fourths (precisely, it is Pi divided by four) of the smallest square that fits around it; so the Migrash's area was 6, about a quarter of the entire area (about 24, i.e. 25 less the area of the city).]

R. Avin gauged like a strap [folded around for lashes. The entire Migrash was a square of 2000 Amos on each corner of the city. A quarter of this, i.e. the square of 1000 Amos closest to the city, was for people's needs, and the rest, i.e. the outer square, was for animals. Between the Migrashim (next to the city, on every side) was for fields and vineyards.]

R. Oshaya gauged like round bowls. (Since a circle's area is a fixed portion (about three fourths) of the square around it, whether R. Oshaya holds like Rav (that the city was 500 Amos from one side to the other), with the Migrash it was 1000 Amos, and with the fields and vineyards 2000), or like R. Yitzchak, that these distances were 2000, 4000 and 8000 respectively, the Migrash is a quarter, based on the calculation above.)

(R. Yosi bei R. Bun): Fifty by 50 [Amos] is a Beis Se'ah; 100 by 100 is four Beis Sa'im.

This is like the [case of the] Reish Galusa. The kingdom was imposed on him to fill a hall 40 by 40 [Amos] with wheat. He came to Rav Huna;

Rav Huna: Appease them to take from you [a room] 20 by 20 now, and another 20 by 20 later, and you will profit (save) half [of the demand]!

(R. Ba citing R. Yehudah, and R. Ze'ira citing R. Ukva): We are Mekader (when measuring distance along a slope, one person holds the end of the rope near his feet, and the other holds it near his head, to reduce or cancel the vertical component of the distance) only with a rope of 50 Amos.

(R. Ze'ira citing Rav Chisdai): We are not Mekader when measuring [the area outside] Levite cities, nor the place for Eglah Arufah in a Nachal (valley or river; we must measure to determine the closest city).

Question: This is fine for the opinion (R. Akiva) that [the verse teaches that] 1000 Amos is Migrash, and 2000 Amos is Techum Shabbos;

However, according to the opinion that 1000 Amos is Migrash, and 2000 Amos is fields and vineyards, we learned Techum Shabbos only from the Levite cities. For the primary (Levite cities) we are not Mekader, and for the secondary (Techum Shabbos) we are Mekader (to increase the extent)?!

Question: What is the source that they did not bury people in Levite cities?

Answer (R. Avahu citing R. Yosi bar Chanina): "U'Migresheihem Yihyu li'Vhemtam veli'Rchusham ul'Chol Chayasam" - for their animals and their [needs of] life (CHIZKUNI Bamidbar 35:3); they were not given for burial.

(Mishnah) Question: On that day, R. Akiva expounded "Az Yashir Moshe u'Vnei Yisrael Es ha'Shirah ha'Zos la'Shem va'Yomeru Leimor" - there was no need to say Leimor. Why does it say Leimor?

Answer #1: It teaches that Yisrael answered after Moshe sang each segment, like when they recite Hallel (the Tzibur answers to the Shali'ach Tzibur) - "Ashirah la'Shem Ki Ga'o Ga'ah." Therefore, it says Leimor;

Answer #2 (R. Nechemyah): It was like we recite Shema Yisrael, and not like we recite Hallel.

(Gemara): It was like a minor reciting Hallel in the Beis ha'Keneses. (The Tzibur are not Yotzei through the minor, so) they answer him on every matter;

Moshe said "Ashirah." They answered "Ashirah". Moshe said "Azi". They answered "Azi".

R. Eliezer the son of R. Yosi ha'Glili says, they sang like an adult reciting Hallel in the Beis ha'Keneses. They answer the first matter:

Moshe said "Ashirah." They answered "Ashirah". Moshe said "Azi". They answered "Ashirah".

R. Yosi ha'Glili says, when our ancestors were at the sea, an infant was on his mother's knee and a baby was nursing from his mother. Once they saw the Shechinah, the infant raised his head from his mother's knee and the baby stopped nursing. Even they opened their mouths with song and praise, and said "Zeh Keli v'Anvehu."

R. Meir says, even fetuses in their mother's wombs sang - "b'Makhelos Barchu Elokim Hash-m mi'Mekor Yisrael."

R. Nechemyah says, when our ancestors alighted from the sea, they saw the corpses of the sinners who subjugated them and forced them to do harsh labors, and all of them were corpses cast on the sea shore. They wanted to sing Shirah, and Ru'ach ha'Kodesh rested upon them;

Even the smallest Yisrael sang Shirah like Moshe - "va'Yizkor Yemei Olam Moshe Amo Ayeh ha'Ma'alem mi'Yam" - it does not say 'Es Ro'eh ha'Tzon', rather, "Es Ro'ei Tzono" - this teaches that [Hash-m] made all of them like shepherds (they had Ru'ach ha'Kodesh, like Moshe).

Question: Why does it say Leimor? (Since everyone had Ru'ach ha'Kodesh, they did not need to answer to Moshe, like we answered in our Mishnah.)

Answer: We should say [Shirah over miracles done for us] all generations.

(R. Avahu citing R. Yosi bei R. Chanina): It was like a [Rebbi begins a verse, and his Talmidim complete the] verse - Moshe said "Ashirah", and they answered to him "Ashirah la'Shem Ki Ga'o Ga'ah Sus v'Rachbo Ramah va'Yam." Moshe said "Azi v'Zimras". They answered "Azi v'Zimras Kah."

It says "bi'Fro'a Pera'os b'Yisrael b'Hisnadev Am" - we read this like Isnadvu Roshei Am - when Ha'Kadosh Baruch Hu does miracles for them, [the heads of the nation] should [volunteer and] say Shirah. (PNEI MOSHE)

Question: When they were redeemed from Mitzrayim [they did not say Shirah, until Keri'as Yam Suf, which was six days later]!

Answer: That is different, for it was the beginning of their redemption. (It was completed only when their oppressors died at Keri'as Yam Suf.)

Question: When they were redeemed [from Haman, through] Mordechai and Esther (they did not say Shirah)!

Answer #1: That is different, for they were in Chutz la'Aretz. (After Yisrael came to Eretz Yisrael, we say Shirah only for miracles in Eretz Yisrael.)

Answer #2: Mordechai and Esther redeemed them from those who hated them, but they were not redeemed from the kingdom (they were still subjects of Achashverosh).

(Mishnah): On that day, R. Yehoshua ben Hurkenos expounded that Iyov served Hash-m out of love - "if Hash-m would kill me, Lo (to Him) I will hope";

This is not decisive. It can mean 'to Him I will hope', or 'I do not hope to Him'!

"Until I expire, my purity will not veer from me" teaches that he served from love.

(Gemara - Beraisa, in the name of R. Yehudah): "Chai Kel Hesir Mishpati v'Shakai Hemar Nafshi" - one vows in the King's life only if he loves Him.

In the name of R. Nasan, they said "Gam Hu Li li'Yshu'ah Ki Lo Lefanav Chanef Yavo" [shows that he hoped to Him].

Contradiction: One verse says "v'Ahavta Es Hash-m Elokecha", and one verse says "Es Hash-m Elokecha Tira v'Oso Sa'avod"!

Answer: Do amidst love, and do amidst fear;

Do amidst love so if you come to hate, know that you love, and a lover does not hate;

Do amidst fear, so if you come to rebel, know that you fear, and one who fears does not rebel.

(Beraisa): There are seven types of Perushim (ascetics, most of which are improper; they will be explained) - Shichmi, Nikfi, Kizi, Nachiyah, Eda Chovasi v'E'esenah, from love, and from fear.

A Parush Shichmi carries [items needed for] Mitzvos on his Shechem (shoulder, to publicize the matter);

A Parush Nikfi says Akif [lend to] me, and I will do a Mitzvah (to publicize it);

A Parush Kizai does one Aveirah, and one Mitzvah, and [does not repent, for he thinks that] one cancels one.

A Parush Nachiyah - what I have, I Menachi (deduct) from it and do a Mitzvah;

A Parush Eda Chovasi v'E'esenah - [tell me] what is my liability (what Aveirah I did), and I will do a Mitzvah corresponding to [offset] it;

A Parush [who serves from] fear is like Iyov;

A Parush [who serves amidst] love is like Avraham. The dearest of all of them is a Parush amidst love, like Avraham.

Avraham Avinu made [his] Yetzer ha'Ra good- "u'Matzasa Es Levavo Ne'eman Lefanecha." (The letter 'Beis' is doubled in Levavo, to allude to both Yetzers. Even actions that require physical Hana'ah, Avraham did amidst love of Hash-m, and not for his pleasure.)

(R. Acha): [The Yetzer ha'Ra] compromised with [Avraham, and agreed not to make him sin] - "v'Charas Imo ha'Bris veha'Chesed..."

However, David could not [control it so much], and killed it in his heart. What is the source? "V'Libi Chalal b'Kirbi."

R. Akiva was being judged (suffering an excruciating execution) in front of Turnusrufus the Rasha. The time for Keri'as Shma came. He began to recite Keri'as Shma, and laughed.

Turnusrufus: Elder, elder - either you are a witch [and through witchcraft, you do not feel the pain], or you rebel at afflictions (pretend not to feel them, to anger me)!

R. Akiva: That man's Ru'ach should leave (you should die)! I am not a witch, nor do I rebel at afflictions. Rather, all my life I read this verse - "v'Ahavta Es Hash-m Elokecha b'Chol Levavcha uv'Chol Nafshecha uv'Chol Me'odecha" (and I was not in a situation to fulfill all of them);

" I loved Him with all my heart, and I loved Him with all my money. With all my life, I was not tested;

And now that came [the opportunity to fulfill] b'Chol Nafshi, and the time for Keri'as Shma came, and I did not divert my mind [from fulfilling amidst love], therefore I recite Shma and laugh!

Nechemyah Imsoni served R. Akiva 22 years. [R. Akiva] used to say that "Es" and "Gam" are inclusions, and "Ach" and "Rak" are exclusions.

Question (Nechemyah): What [can we include] from "Es Hash-m Elokecha Tira" (that we should fear it like Hash-m)?!

Answer (R. Akiva): [Fear] Him and His Torah.