Gemara

9b (Mishnah): The following are forbidden from shortly before the time of Minchah, until praying:

To begin a haircut from a barber, to enter the bathhouse or a tannery, to eat, or to judge;

If one began, he need not stop.

Opinion #1: They are forbidden before Minchah Gedolah.

Objection: Why are these forbidden? There is plenty of time (to pray afterwards)!

Opinion #2: They are forbidden before Minchah Ketanah.

(Mishnah): If one began, he need not stop.

Suggestion: This refutes R. Yehoshua ben Levi!

(R. Yehoshua ben Levi): One may not eat anything once the time of Minchah arrives.

Rejection: Really, they are forbidden before Minchah Gedolah;

Answer #1 (to Objection): The Mishnah discusses the haircut of Ben El'asa, a big tannery, the full works in the bathhouse, eating a big meal, and the beginning of judgment.

Answer #2 (Rav Acha bar Yakov): The Mishnah discusses a normal haircut, bath, tannery, meal, or end of judgment. Even a small meal (and these other matters) can get drawn out [or lead to Ones], and he will miss praying.

(Abaye): In Bavel, according to the opinion that Tefilas Ma'ariv is optional, if one untied his belt, since it would be a toil to tie it again, he may eat before praying.

Inference: The opinion that Ma'ariv is obligatory requires him to retie it and pray Ma'ariv before eating.

Question: All agree that Minchah is obligatory. The Mishnah permits one to finish eating if he began, and R. Chanina taught that this is once he untied the belt!

Answers: We are more stringent about Ma'ariv, for people often get drunk at night. Alternatively, since one may pray Ma'ariv the entire night, people do not fear missing it, and they are prone to delay it.

Berachos 28b: The Halachah does not follow R. Yehoshua ben Levi.

Sukah 38a (Mishnah): If one who came from the road and did not have a Lulav, when he gets home he takes it on his table.

Inference: He must interrupt (eating to take it).

Question (Mishnah): If one began, he need not interrupt (for Minchah).

Answer (Rav Safra): There, time will remain afterwards. Here, time will not remain.

Rishonim

Rif (4a): We conclude that the Mishnah discusses before Minchah Gedolah. One may not begin even a small meal, lest it get drawn out.

Rambam (Hilchos Shabbos 6:5): From the time of Minchah Gedolah, one may not eat, even Arai (haphazardly), lest he eat extensively.

Rosh (1:18): R. Tam rules like the first version, which forbids a big meal or the beginning of judgment before Minchah Gedolah. Therefore, one may begin a small meal close to Minchah Gedolah. If one began a big meal, he need not interrupt, even when the time of Minchah Ketanah comes. The Halachah does not follow R. Yehoshua ben Levi, who forbids tasting anything from the time of Minchah Ketanah. In Berachos, we rule unlike him.

Question: Since the Halachah does not follow R. Yehoshua ben Levi, why don't we establish the Mishnah to discuss Minchah Ketanah, but one may begin even a big meal before Minchah Gedolah? We established the Mishnah to discuss a big meal before Minchah Gedolah only due to R. Yehoshua ben Levi!

Answer (Rosh): Even though we rule unlike him, this means that we may eat Peros beforehand. However, we hold like him regarding that one who began eating close to Minchah Ketanah must interrupt, since the Gemara did not answer that we rule unlike him. A big meal is of a wedding, Bris Milah, or Pidyon ha'Ben. A small meal is what a normal person eats. R. Tam holds like this. The Ri permits beginning a small meal close to Minchah Ketanah. If one began a big meal, he need not interrupt, even if the time for Minchah Ketanah came, as long as time will remain to pray after he finishes the meal. If he began to eat close to Minchah Ketanah, he interrupts when the time for Minchah comes. The Rif rules like the latter version, which forbids even a small meal close to Minchah Gedolah. R. Yonah agrees. The first answer is weak. Rav Acha bar Yakov gave a good answer. Also, the Gemara says that people do not often get drunk at Minchah. We understand this is if our Mishnah discusses a common meal. People very often get drunk at big meals!

Rosh (1:18): The Mishnah says that if he began one of these activities, he need not stop. This is when he will have time to pray during the day after finishing his Melachah. The Gemara said that it is not common to get drunk at (the time for) Minchah. I.e. he will not get drunk, and he can pray after finishing his meal. Therefore, he need not interrupt. If he would not need to interrupt even if Minchah will pass, what difference does it make that it is not common to get drunk? Even if it were common to get drunk, he need not interrupt even if no time remains! Rather, we discuss when time remains. Since it is not common to get drunk, he will finish his meal and pray. Sukah 38a explicitly says so about one who came from the road without a Lulav. The Gemara asked from our Mishnah, and answered that here time will remain afterwards; there, time will not remain. Our Mishnah discusses even when he began b'Isur. This is clear from the Gemara, which says regarding Ma'ariv that if one untied his belt, we do not exert him (to tie it again and pray before eating). We learn from Minchah, about which it says that if he began, he need not interrupt. We must say that this refers to one who began b'Isur, like regarding Ma'ariv. Also, since we do not answer regarding Sukah that Lulav is different because he began b'Isur, this shows that our Mishnah permits before Minchah even if he began b'Isur.

Poskim

Shulchan Aruch (OC 232:2): One may not begin to eat even a small meal, close to Minchah Gedolah.

Beis Yosef (DH u'Mah she'Chasav d'Ein): The Rashba (Berachos 28a DH v'Lo) says that the Halachah does not follow R. Yehoshua ben Levi only regarding interrupting. If one began to eat, he need not interrupt. L'Chatchilah, it is forbidden, like it says in Shabbos. In a Teshuvah (1:268) he explained that R. Yehoshua ben Levi forbids only a Seudah. He calls this "tasting".

Beis Yosef (DH veha'Rif): The Tur (CM 5) says that the Rosh concludes like the Rif. I say that this is not necessary true. The Rambam rules like the Rif, therefore we rule like him.

Shulchan Aruch (ibid.): If he began one of all these, he does not interrupt, even though he began b'Isur.

Beis Yosef (DH v'Im): Tosfos, the Rosh, the Ran and the Mordechai proved from our Gemara and in Sukah that even if one began b'Isur, he need not interrupt.

Magen Avraham (9): If one began to eat close to Minchah Ketanah, he must interrupt even if time remains.

R. Akiva Eiger: In OC 652:2 (regarding Lulav), we say that even if he began b'Isur, he need not interrupt if time will remain! We must say that here is different, for the primary time for Minchah is then (nine and a half hours), for this is when they used to offer the afternoon Tamid.

Magen Avraham (9): If one need not interrupt, and he interrupts, he is called a Hedyot (commoner).

Shnos Eliyahu (of the Gra, Berachos 1:3): Sometimes we say that one who is exempt and fulfills is called a Hedyot. Sometimes we say that it is the ideal Mitzvah, even though he is not obligated. I say that this is when it is intrinsically a Mitzvah, just Chachamim did not obligate him, e.g. to interrupt a meal to pray.

Bi'ur Halachah (DH v'Im): Surely, the Magen Avraham agrees that he is not called a Hedyot if according to letter of the law he must interrupt, e.g. he started after Minchah Ketanah, just we rely on people who call to come to pray. Whenever we say that he need not interrupt, this is even if he will lose Tefilah b'Tzibur and pray alone later.

Rema: Some disagree, and permit a small meal.

Beis Yosef (DH d'Tanan): Tosfos says that we rule like the first version, which is the Stam Gemara of Rav Ashi, who is Basra. The Rosh says that based on this, one may begin a small meal close to Minchah Gedolah. As long as time will remain to pray after the meal. If he began eating before Minchah Ketanah, he interrupts when the time for Minchah comes.

Gra (DH v'Yesh Cholkim): This opinion is primary.

Bi'ur Halachah (DH v'Yesh): The Gra says that this opinion is primary. Therefore, even one who does not want to rely on the custom to be lenient brought below, he should be stringent only for this opinion, but he should not be as stringent as the first opinion.

Rema (ibid.): Some permit even a big meal close to Minchah Gedolah. Some permit a small meal close to Minchah Ketanah.

Beis Yosef (DH v'Chasav ha'Ran): The Ran says that the Ba'al ha'Ma'or is even more lenient. Since the Halachah does not follow R. Yehoshua ben Levi, we leave the Mishnah like the simple reading, which is before Minchah Ketanah. One may not begin even a small meal then.

Mishnah Berurah (25): These two opinions are more lenient. Each forbids in only one case. The first of these two forbids only close to Minchah Ketanah, and even a small meal is forbidden. The latter of these two forbids a big meal even close to Minchah Gedolah.

Mishnah Berurah (26): Hagahos Mordechai is lenient even about this. He forbids only a big meal close to Minchah Ketanah. Also R. Yerucham connotes that people are lenient [about a small meal] even after the time for Minchah Ketanah came.

Rema (ibid.): The custom is to be lenient like both opinions, i.e. a big meal close to Minchah Gedolah and a small meal close to Minchah Ketanah. Perhaps this is because nowadays people call when it is time to pray in the Beis ha'Keneses, so we are not concerned lest one be negligent and not pray. However, one should be stringent about a big meal close to Minchah Gedolah, and even if he began beforehand, when Minchah Ketanah comes and time is running out, he must get up to pray.

Mishnah Berurah (25): This discusses one who prays b'Tzibur. It does not help for one who prays alone.