(Mishnah - R. Yehudah): He may pray "Ad" (until) four hours.

Question: Does he mean "Ad v'Ad Bichlal" (up to and including, i.e. until the end of four hours), or "Ad v'Lo Ad Bichlal" (up to but not including, i.e. until the start of the fourth hour)?

Answer (Seifa - R. Yehudah): One may pray [Minchah] "Ad Plag ha'Minchah."

(This is not in Tosfos' text of the Mishnah, Tosfos changes references to the "Seifa" to "Beraisa #2.")

We understand this if he means Ad v'Lo Ad Bichlal -- he permits until the start of Plag ha'Minchah, Chachamim allow until evening;

But if he means Ad v'Ad Bichlal, this is like Chachamim!

Objection: In the Seifa, he means Ad v'Ad Bichlal!

(Mishnah (or a Beraisa)): The time for Musaf is the entire day.

R. Yehudah says, it is "Ad" seven hours of the day.

(Beraisa): If one has an obligation [now] to pray both Minchah and Musaf, he prays Minchah first, for it is more frequent;

R. Yehudah says, he prays Musaf first, for its time will expire soon, Minchah's time will not.

We understand this if he means Ad v'Ad Bichlal -- he permits Musaf until the end of seven hours, at the same time he can be obligated to pray Minchah and Musaf (i.e. between six and a half and seven hours);

But if he means Ad v'Lo Ad Bichlal, he permits Musaf until the end of six hours, which is before the earliest time for Minchah!

Question: But if he holds Ad v'Ad Bichlal, the Reisha is difficult, for he agrees with Chachamim! (In Beraisa #3, he permits "Ad" the latter Plag ha'Minchah.)

Answer: You assumed that R. Yehudah permits until the beginning of the latter Plag -- this is wrong! Rather, he refers to the first Plag, and permits until it ends;

(Either way, he permits until ten and three quarters hours; the only difference is what "Ad" means, which we must clarify in order to understand his opinion regarding Shacharis and Musaf.)

Beraisa #3 means, R. Yehudah permits until the first Plag ends and the latter begins, i.e. ten and three quarters hours.

Support (Rav Nachman - Mishnah): R. Yehudah ben Bava testified about five laws for which he had a tradition:

We instruct minors to do Mi'un;

A woman can remarry based on one witness who says that her husband died;

A chicken was stoned in Yerushalayim because it killed a person;

Wine may be used for Nesachim forty days after the grapes were pressed;

The morning Tamid may be offered during the fourth hour of the day.

[Surely, he holds like R. Yehudah;] this shows that R. Yehudah means Ad v'Ad Bichlal.

(Rav Kahana): The Halachah follows R. Yehudah, because the Mishnah in Eduyos follows him. (The Halachah follows every Mishnah in Eduyos.)

(Mishnah): The morning Tamid is offered at four hours of the day.

Question: Who is the Tana of the following Beraisa?

(Beraisa): "V'Cham ha'Shemesh v'Namas" -- [the manna melted] at four hours of the day.

Question: Perhaps it was at six hours of the day!

Answer: Elsewhere it says "k'Chom ha'Yom," this refers to six hours -- therefore, "v'Cham ha'Shemesh" refers to four hours (this will be explained).

Summation of question: This is not like R. Yehudah, nor like Chachamim! (Bnei Yisrael collected the manna "ba'Boker ba'Boker" -- afterwards, "v'Cham ha'Shemesh"!

R. Yehudah says that four hours is still called morning (he is Machshir the morning Tamid until then, even though it says "ba'Boker"), Chachamim say that until Chatzos is morning!

Answer #1: It is like Chachamim;

Regarding the manna it says "ba'Boker ba'Boker" to teach that there were two periods in the morning (in the first half they gathered manna, it melted during the second half).

Answer #2: It is like R. Yehudah;

The extra "ba'Boker" teaches that they collected it an hour before the end of the morning.

Question: All agree that it melted at four hours of the day -- how do they learn this from the verse?

Answer (Rav Acha bar Yakov): "V'Cham ha'Shemesh" refers to when it is hot only in the sun, not in the shade, i.e. at four hours. (But "k'Chom ha'Yom" is when it is hot even in the shade, at six hours.)

(Mishnah): Minchah is until the evening...

Question (Rav Chisda): Rav Kahana said that the Halachah follows R. Yehudah regarding Shacharis;

Whom does the Halachah follow regarding Minchah?

R. Yitzchak could not answer.

Answer #1 (Rav Chisda): Rav used to pray Ma'ariv of Shabbos on Erev Shabbos before dark -- this shows that the Halachah follows R. Yehudah! (According to Chachamim, it is still the time for Minchah, one may not pray Ma'ariv then!)

Objection and Answer #2: Rav Huna and Rabanan used to wait until dark to pray Ma'ariv -- this shows that the Halachah follows Chachamim!

Conclusion: Since the Halachah was not fixed like either opinion, one may follow either one.

A case occurred, Rav visited Bei Geniva; he was praying Ma'ariv of Shabbos on Erev Shabbos before dark (he had already accepted Kedushas Shabbos), R. Yirmeyah bar Aba was praying in back of him. Rav finished first, he did not [return to his place, for he would have had to] interrupt between R. Yirmeyah and the wall.

We learn three things from this:

One may pray Ma'ariv of Shabbos on Erev Shabbos;

A Talmid may pray in back of his Rebbi;

It is forbidden to pass in front of someone praying.

This supports R. Yehoshua ben Levi.

(R. Yehoshua ben Levi): It is forbidden to pass in front of someone praying.

Question: But R. Ami and R. Asi pass in front of someone praying!

Answer: They do not pass within four Amos.

Question: How could R. Yirmeyah bar Aba pray in back of Rav?

(Rav Yehudah): One may not pray at the side of his Rebbi (for he thereby "equates" himself to his Rebbi), nor in back of his Rebbi (Rashi - this is haughtiness; Tosfos - it looks like he bows to his Rebbi; Yerushalmi - lest he cause his Rebbi to have to wait for him to finish).

(Beraisa - R. Eliezer): The following cause the Shechinah to depart from Yisrael:

One who prays in back of his Rebbi, gives or returns a greeting of Shalom to his Rebbi (like he does to anyone else), argues with his Rebbi's teaching (i.e. sets up his own academy to expound, without his Rebbi's permission), or says (R. Yonah - in his Rebbi's name) something that he did not hear from his Rebbi.

Answer: R. Yirmeyah bar Aba was a Talmid Chaver of Rav (a peer of Rav who had learned from him).

Support: He asked Rav, "Badalta?" ("Have you decided to refrain from Melachah (by accepting Kedushas Shabbos before praying Ma'ariv of Shabbos)?" Rav answered, "Yes";

A Talmid (who is not a Talmid Chaver) may not address his Rebbi this way (in the second person, rather, in the third person, with a title of respect).

Question: Must one indeed accept Shabbos before praying Ma'ariv of Shabbos?!

(R. Avin): Rebbi once prayed Ma'ariv of Shabbos on Erev Shabbos, entered the bathhouse (which is forbidden on Shabbos) and taught to us!

Answer (Rava): Rebbi entered the bathhouse to sweat, before Chachamim prohibited this on Shabbos.

Question: But Abaye permitted Rav Dimi bar Livai to fumigate baskets (after praying Ma'ariv of Shabbos on Erev Shabbos)!

Answer: The case was, Rav Dimi erred. (He had not intended to accept Kedushas Shabbos early. It was a cloudy day, he thought that night had come. When the sun reappeared, Abaye permitted him to do Melachah.)

Question: We do not retract such a mistake!

(Avidan): Once, it was very cloudy, everyone thought that night had come. They prayed Ma'ariv of Motza'ei Shabbos; when the sun reappeared, Rebbi said that they need not pray again.

Answer: [An individual would pray again after such a mistake, but] we do not trouble a Tzibur [to return to synagogue to pray again].

(R. Chiya bar Avin): Rav used to pray Ma'ariv of Shabbos on Erev Shabbos; R. Yoshiyah used to pray Ma'ariv of Motza'i Shabbos on Shabbos.

Question: Rav used to pray Ma'ariv of Shabbos on Erev Shabbos -- would he [wait until evening to] say Kidush on a cup of wine, or not?

Answer: Rav Nachman taught that one may pray Ma'ariv of Shabbos on Erev Shabbos and say Kidush over wine (before evening).

The Halachah follows Rav Nachman.

Question: R. Yoshiyah used to pray Ma'ariv of Motza'i Shabbos on Shabbos -- would he say Havdalah over wine (right away, or would he wait until evening)?

Answer: Rav Yehudah taught that one may pray Ma'ariv of Motza'i Shabbos on Shabbos and say Havdalah over wine.

(R. Zeira): A case occurred, R. Yishmael b'Rebbi Yosi prayed Ma'ariv of Shabbos on Erev Shabbos next to this pillar.

(Ula): No -- the case was, R. Elazar b'Rebbi Yosi prayed Ma'ariv of Motza'i Shabbos on Shabbos next to a date tree.

(Mishnah): Ma'ariv is not Kavu'a (fixed).

Question: What does this mean?

Suggestion: One may pray at any time during the night.

Rejection: If so, the Mishnah should say, "The time for Ma'ariv is the entire night"!

Answer: Our Mishnah follows the opinion that Ma'ariv is Reshus (optional; Tosfos - i.e. one may perform a different Mitzvah that cannot be done later instead of praying Ma'ariv).

(Rav Yehudah): R. Gamliel says that Ma'ariv is Chovah (mandatory), R. Yehoshua says that it is Reshus.

(Abaye): The Halachah follows the opinion that it is Chovah.

(Rava): The Halachah follows the opinion that it is Reshus.

(Beraisa): A case occurred, R. Yehoshua told a certain Talmid (who had asked) that Ma'ariv is Reshus; R. Gamliel answered him that it is Chovah.

The Talmid: But R. Yehoshua said that it is Reshus!

R. Gamliel: Wait until Ba'alei Trisim (Rashi - great Chachamim that wage the "war" of Halachah; Aruch - guards) enter the Beis Medrash.

The Ba'alei Trisim entered the Beis Medrash; the Talmid asked his question, and R. Gamliel answered, "Chovah."

R. Gamliel asked if anyone disagrees; R. Yehoshua said, "No."

R. Gamliel: I heard that you disagree -- stand up, they will testify about what you said!

R. Yehoshua: I cannot contradict the Talmid, for he is alive.

R. Gamliel was sitting and expounding, R. Yehoshua was standing, everyone was murmuring; they told Chutzpis to stop (he was translating and broadcasting for R. Gamliel).

Rabanan: Also before, R. Gamliel pained R. Yehoshua, in a case of establishing which day will be Rosh Hashanah, and in the episode with R. Tzadok -- this cannot continue! We must choose a different Nasi.

We cannot appoint R. Yehoshua, for he was an involved party (this would pain R. Gamliel too much);

We cannot appoint R. Akiva, lest he be punished (for being a cause of pain to R. Gamliel), for his ancestors (who were converts) do not have enough merits to protect him;

Let us pick R. Elazar ben Azaryah -- he is a Chacham, wealthy, and a tenth generation descendant of Ezra.

He is a Chacham -- he can answer questions;

He is wealthy -- if we must bribe the Roman ruler, he can do so;

He is a tenth generation descendant of Ezra -- the merit of his ancestors will shield him from punishment on account of R. Gamliel.