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.

Question: Before which Minchah are these forbidden?

Answer #1: They are forbidden before Minchah Gedolah. (It starts half an hour after midday.)

Objection: Why should these be forbidden? There is plenty of time (to finish them and pray afterwards)!

Answer #2: They are forbidden before Minchah Ketanah. (It starts three and a half hours after midday.)

(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 (like of the Kohen Gadol), 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. Chachamim decreed not to start before prayer, lest the scissors break;

A mere steambath is forbidden, lest he faint and be unable to pray;

One may not peruse his skins in a tannery (even in the middle of tanning), lest he see that he will suffer a loss, and will be upset and unable to pray;

One may not begin even a small meal, lest it get drawn out;

One may not even finish judgment before praying, lest he see a reason to change the verdict [and he will start to judge anew].

11a (Mishnah): If one began, he need not stop. We stop to say Shma [but not for prayer].

The Mishnah repeats 'we do not stop for prayer' to teach about Torah;

(Beraisa): If Chachamim were engaging in Torah, they stop to say Shma, but not for prayer.

(R. Yochanan): This applies only to Chachamim like R. Shimon, who engage in Torah and nothing else, but people like us stop even for prayer.

Rishonim

Rif (4a): We conclude that the Mishnah discusses before Minchah Gedolah. Even a normal haircut is forbidden, lest the scissors break. A mere steambath is forbidden, lest he faint. One may not even look in a tannery, lest he see that he will suffer a loss, and will be distracted. One may not begin even a small meal, lest it get drawn out. One may not even finish judgment, lest he see a reason to change the verdict. [and he will start to judge anew].

Rambam (Hilchos Shabbos 6:5): From the time of Minchah Gedolah, one may not enter a bathhouse, even for a mere steambath, until he prays, lest he faint and miss praying. He may not eat, even Arai (haphazardly), lest he eat extensively. He may not judge, even the end of a case, lest he refute the verdict and tarry (to reach the proper verdict), and he will miss praying. One may not sit in front of a barber, even for a commoner's haircut, lest the scissors break. One may not enter a tannery close to Minchah, lest he see a loss in his work, and get involved in it, and delay praying. If one began one of these activities, he need not stop. Rather, he finishes, and then he prays Minchah.

Rosh (1:18): R. Tam rules like the first version, which forbids a big meal or the beginning of judgment before Minchah Gedolah. The Gemara connotes like this below, for it asks what is the beginning of judgment. This shows that we discuss the beginning of judgment. This is not a proof. Perhaps the Gemara discusses the beginning of judgment for the law of "if he began, he need not interrupt", just like it discusses the beginning of bathing and (visiting) a tannery. However, it seems that the Halachah follows the first version because the Stam Gemara said so, i.e. Rav Ashi, who arranged the Gemara. He is Basra. The Halachah follows him against Rav Acha bar Yakov. Also, the Halachah follows the lenient opinion in mid'Rabanan laws. 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.

Rosh: 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. The Mishnah Stam discusses sitting in front of a barber. It is a weak answer to say that this refers to the haircut of Ben El'asa. The Mishnah discusses a Stam meal, and we say that this is a big meal. Rav Ashi did not give the first answer. Rather, the Bnei Yeshivah discussed the matter and had a difficulty, and needed to give a weak answer, until 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! There is more danger that if one eats first, he will miss praying. There is less concern for this regarding Minchah.

Ran (4a DH Hai): Minchah Gedolah is at six and a half hours of the day. Close to Minchah Gedolah is a half-hour before, from the start of the seventh hour.

Poskim

Shulchan Aruch (OC 232:2): One may not sit for a haircut close to Minchah, until he prays. He may not enter a tannery (where they tan hides), nor to judge, nor to eat even a small meal, close to Minchah Gedolah.

Taz (1): The Mechaber rules like the Rif and Rambam, who are stringent like the latter answer. The Rema (below) rules like Tosfos, who is lenient like the first answer.

Magen Avraham (3): Perhaps if the barber has two or three scissors it is permitted. One may not take a child in his lap close to evening, lest the child soil his parent's clothing, and while he looks for water, the time for Minchah Ketanah will pass, or he will be late to the Beis ha'Keneses.

Kaf ha'Chayim (15): The Ari Zal would not cut his hair after Minchah Gedolah, even on Erev Shabbos.

Magen Avraham (6): Any labor or calculation that is prone to cause pain and distraction, and due to this he will not pray, is like a tannery.

Mishnah Berurah (9): Therefore, those who go to fairs and are distracted buying and selling, l'Chatchilah they may not go close to Minchah Gedolah before praying.

Bi'ur Halachah (DH l'Burski): The Me'iri says that some (i.e. the Rashba brought in Beis Yosef 235) forbid only Melachos that people do not normally interrupt them in the middle. One who sees his hides getting ruined and is concerned for them will not abandon them, change to honorable clothes, pray, and return to the hides. One who has his claim in Beis Din and his witnesses available will not leave to pray. One may begin sewing, writing, or other Melachos that people normally stop in the middle. When the time for Minchah comes, he will interrupt. Perhaps the Magen Avraham means like this (and forbids only Melachos that people do not interrupt). The Pri Megadim says so. However, Mahariyo (cited below in Magen Avraham 8) connotes that all Melachos are forbidden. When there is a need, one may be lenient.

Kaf ha'Chayim (17): A Chacham should not learn with Pilpul (deep analysis) within a half-hour before the time of Minchah. He should learn only Halachah that was already decided. However, if he was learning b'Pilpul and the Tzibur started to pray, he prays with them.

Magen Avraham (8): Mahariyo says that one who did not pray Ma'ariv with the Tzibur may not work or learn until he prays (Berachos 4b), but one may learn before Shacharis. Since the Tzibur prays, we are not concerned lest he be negligent. Similarly, the custom is to eat after the time for Minchah Ketanah. Also, they call people to come to pray.

Shulchan Aruch (ibid.): If he began one of all these, he does not interrupt, even though he began b'Isur. This is if time will remain to pray after finishing his meal or Melachah. If time will not remain to pray afterwards, he must interrupt immediately.

Beis Yosef (DH u'Mah she'Chasav u'Chegon): The Meforshim say that it is clear from these Sugyos that we permit (continuing the meal or Melachah) only when time will remain to pray afterwards. Also the Rambam connotes like this. Terumas ha'Deshen (7) says that some Gedolim hold that if one is at a wedding meal and time will not remain to pray afterwards, he does not interrupt to pray, for he is like one who is engaged in a Mitzvah, so he is exempt from Tefilah. This is wrong.

Magen Avraham (10,11): Even if he began b'Heter, he must interrupt immediately, even if much time remains in the day.

Kaf ha'Chayim (23): This means that he must interrupt after the time for Minchah Ketanah comes.

Rema: Some disagree, and permit a small meal.

Mishnah Berurah (22): Even this opinion forbids small matters close to Minchah Ketanah, i.e. from the beginning of the 10th hour. Even if he began, he must interrupt.

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

Beis Yosef (DH v'Hai): Close to Minchah Ketanah is a half hour beforehand, from the start of the 10th hour.

Rema: 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.

Mishnah Berurah (29): This is only he goes to pray when they call. The Acharonim connote that we rely on this for everything in this Sa'if, e.g. a full bath, just like for a small meal. Meticulous people pray before going to the bathhouse on Erev Shabbos after Minchah Ketanah. Some are stringent even from close to Minchah Gedolah. Those who are lenient have whom to rely on if also in the bathhouse they call to pray when enough time remains for people to leave and pray in time. If not, one may not rely on this at all.

Kaf ha'Chayim (29): Maharil says that we bathe and shave on Erev Shabbos close to Minchah. This is because we have a fixed time for Minchah every day. I.e. they have a fixed time for Minchah shortly before evening. However, the Bach explains that they have a fixed time at which they call people to the Beis ha'Keneses.