Rif Brachot 18b

18b

{Brachot 26b continued}
For the daily afternoon sacrifice could be offered until the evening. Rabbi Yehuda said: until the middle of the afternoon {Plag HaMincha} daily afternoon sacrifice could be offered until Plag HaMincha. And why did they {the Sages} say that Maariv has no fixed time? For the limbs and the fats which were not consumed during the day could be brought the entire night. And why did they {the Sages} say one can say Musaf the entire day? For the Musaf {additional} sacrifice could be offered the entire day. Rabbi Yehuda says {one may say Mussaf} until 7 hours, for the Musaf sacrifice could be offered until 7 hours.

What is Mincha Gedolah {greater afternoon}? From 6 and 1/2 hours and onward.
And what is Mincha Ketana {smaller afternoon}? From 9 and 1/2 hours and onward.
The middle of the later Mincha {=afternoon} {that is, from 6 and 1/2 until 12 hours which is night} is 11 hours minus 1/4. {That is, 10 and 3/4 hours. The calculation is as follows. From 9 and 1/2 hours until 12 hours is a time period of 2 and 1/2 hours. Half of this time period, of 2 and 1/2 hours, is 1 and 1/4 hour. 9 and 1/2 hours + 1 and 1/4 hour = 10 and 3/4 hour, so that is the midpoint of the Mincha Ketana.}

It was asked, according to Rabbi Yehuda, is the time limit he gives inclusive, or not inclusive?
{As an example, Rabbi Yehuda says until 4 hours. Does that include the entirety of the 4th hour, or once the 3rd hour has terminated, one may no longer pray? And the same for Plag HaMincha.}

{Brachot 27a}
And we conclude that the time limit he gives is inclusive {of his end point}, for we learnt that Rabbi Yehuda ben Bava testified on the daily morning sacrifice that it was offered during the 4th hour. We derive from this that the time limit is inclusive, and so we derive.
Rav Kahana said: the halacha is like Rabbi Yehuda {about praying Shacharit until the 4th hour} since we learn {in the Mishna} in Bechirta {=Eduyot, Testimonies} like him.

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{The Mishna had said:}
"THE AFTERNOON PRAYER {Mincha} [CAN BE SAID] TILL EVENING {Erev};
Rabbi JUDAH SAYS, UNTIL THE MIDDLE OF THE AFTERNOON. {Plag HaMincha}"
Rav Chisda said to Rabbi Yitzchak: There {by Shacharit} Rav Kahana said that the halacha is like Rabbi Yehuda since we learn in a Mishna in Bechirta {Eduyot} like him. Here {regarding Mincha} what? He was silent, and told him nothing. And we conclude here that we don't rule that the halacha is like this one {the Sages} nor like that one {Rabbi Yehuda}, and if he does like this one he has accomplished, and if he does like that one he has accomplished.

Rabbi Yehoshua ben Levi said: It is forbidden to pass opposite the people praying.
Is this so?
But Rav Ami and Rav Asi passed?
Rav Ami and Rav Asi passed outside of a range of 4 cubits.

Rav Yehuda cited Rav: A student should never pray in front of his teacher, or behind his teacher, or opposite {=next to} his teacher . {Our gemara seems to lack this last "opposite his teacher."}

{Brachot 27b}
The learnt {in a brayta}: Rabbi Eleazar ben Chosma {our Gemara: Rabbi Eleazar} says: One who prays opposite his teacher, and one who prays behind his teacher, and one who gives greeting {Shalom} to his teacher {perhaps an ordinary greeting rather than one of more respect, or perhaps because he should wait for his teacher to greet him first}, and one who contradicts the school of his teacher, and one who says a matter that he did not hear from his teacher, causes the Divine Presence to remove itself from {the nation of} Israel.

Rav Chiyya bar Avin said: Rav prayed {Maariv} of Shabbat on Erev Shabbat and Rabbi Yoshiya prayed {Maariv} of Motzaei Shabbat on Shabbat.

The question was asked: "Rav prayed {Maariv} of Shabbat on Erev Shabbat" - does he say kedusha {sanctification of the day} over a cup {presumably as opposed to saying it in Shemoneh Esrei - just as we saw earlier, and are about to see again, the idea of making havdala over a cup if he skipped Ata Chonantanu}, or did he not say kedusha over a cup?

Come and hear: For Rav Yehuda cited Shmuel: A man may pray {Maariv} of Shabbat on Erev Shabbat, and says kedusha over the cup.

"And Rabbi Yoshiya prayed {Maariv} of Motzaei Shabbat on Shabbat" - does he say havdala over the cup, or does he not say havdala over the cup?

Come and hear: For Rav Tachlifa bar Avimi cited Shmuel: A man may pray {Maariv} of Motzaei Shabbat on Shabbat, and says havdala over the cup.

{The Mishna said:} "THE EVENING PRAYER {Maariv} HAS NO FIXED LIMIT."
What does it mean it has no fixed limit? It has no fixed limit according to the one who says [that Maariv is optional.]