(Gemara) Question: If one roasted an egg [near a kettle heated on a fire], what is the law?

Answer (Rav Yosef): He is Chayav Chatas.

Support (Mar brei d'Ravina - Mishnah): Any food that that was soaked [and fully cooked] in hot water [in a Kli Rishon (a pot that was on the fire)] before Shabbos, one may soak it in hot water on Shabbos;

Any food that that was not soaked in hot water before Shabbos, one may pour hot water over it (Rashbam - from a Kli Rishon; R. Tam - from a Kli Sheni (a Kli into which food was poured from a Kli Rishon)) on Shabbos, except for old salted fish or tuna fish, for rinsing them is their final preparation (and one is liable for this).

(Mishnah): One may not wrap an egg in garments; [R. Yosi permits].

Suggestion: The following Mishnah is like R. Yosi [who permits cooking via the sun], it is unlike Chachamim!

(Mishnah): One may put a Tavshil in a pit [on Shabbos] to guard it; one may put good water [in a Kli] in bad water to cool it, one may put cold water in the sun to warm up.

Rejection (Rav Nachman): No, all permit cooking in the sun; all forbid cooking through something heated by fire;

They argue about cooking through something heated by the sun - Chachamim decree [lest one will come to cook in something heated by fire, R. Yosi does not decree.

(Mishnah): One may not Matmin an egg [in sand or dust to roast].

Question: R. Yosi should also argue about this [and permit it]!

Answer #1 (Rabah): He forbids this, lest one will do Hatmanah in hot ashes [and make them flare up on Shabbos];

Version #1 (Rashi) Answer #2 (Rav Yosef): He forbids this, lest one will uproot dirt [and make a hole].

Version #2 (Tosfos) Answer #2 (Rav Yosef): He forbids this, for one moves [Muktzeh] dirt.

Question: What is the difference between these answers?

Answer: They argue about loose dirt (this is also forbidden on account of hot ashes, but we are not concerned for making a hole (the remaining dirt caves in) or moving Muktzeh (one merely drops the egg, it sinks in itself)).

Question (Beraisa - R. Shimon ben Gamliel): One may roast an egg on a hot roof (heated by the sun), but not in hot plaster (heated by a fire).

If the decree is on account of hot ashes, we understand this - but if the decree is on account of moving dirt, this also applies on a roof!

Answer: Normally, a roof does not have [much] dirt (to warrant a decree).

Question (Mishnah): A case occurred, people in Tiverya brought a pipe of cold water through a hot spring...

If [the previous law,] Hatmanah in sand or dirt is forbidden on account of hot ashes, we understand why Chachamim forbade the water, it also resembles Hatmanah - but if it is on account of moving dirt, why did they forbid?

Answer: This episode does not support the previous law, rather, the Reisha, Chachamim argue with R. Yosi who permits wrapping an egg in garments;

They said, just like [previous] Chachamim forbade water heated through [the spring, which is heated by] the sun, one may not cook in anything heated by the sun;

R. Yosi says, the spring is heated by fire, it passes over the opening to Gehinom.

(Rav Chisda): The episode in Tiverya teaches (Ramban - prompted Chachamim to decree) that Hatmanah in something that adds heat is forbidden, even from Erev Shabbos.

(Ula): No - the Halachah follows the people of Tiverya [who permitted it]!

(Rav Nachman): No - they [accepted Chachamim's words and] broke their pipe.

(Mishnah): The people of Tiverya... [Chachamim said, on Shabbos, it is like water heated on Shabbos, one may not bathe in it or drink it.]

Question: What bathing is discussed?

Suggestion: It discusses bathing the whole body.

Inference: One may not bathing the whole body in water heated on Shabbos, but it is permitted in water heated from before Shabbos;

Rejection (Beraisa #1): On Shabbos, one may wash his face, hands and feet in water heated from before Shabbos, but not his whole body.

Answer #1: It discusses washing one's face, hands and feet.

Objection (Seifa): If it was on Yom Tov, it is like water heated on Yom Tov, one may not bathe in it, one may drink it.

Is our Stam Mishnah like Beis Shamai?!

(Mishnah - Beis Shamai): One may not heat water [on Yom Tov] to wash his feet unless it is fitting to drink (Tosfos - unless he intends to drink some of it);

Beis Hillel permit.

Answer #2 (Rav Ika bar Chananyah): Our Mishnah discusses showering (pouring water on) the whole body - it is like R. Shimon:

(Beraisa #2 - R. Meir): [On Shabbos] one may not shower his entire body in hot or cold water;

R. Shimon permits;

R. Yehudah forbids in hot water, he permits in cold water.

(Rav Chisda): The Tana'im in this Beraisa argue about bathing in a Kli, but all permit bathing in the ground (it does not look like bathing in hot water).

Objection: The episode in Tiverya was in the ground, and Chachamim forbade!

Correction: Rather, Rav Chisda taught that they argue about bathing in the ground, but all forbid bathing in a Kli (onlookers will assume that the water was heated by fire on Shabbos).

(Rabah bar bar Chanah citing R. Yochanan): The Halachah follows R. Yehudah.

Question (Rav Yosef): Did you hear this explicitly, or did you infer it from another teaching?

Question: From which teaching could one infer it?

Answer: R. Yochanan taught that the Halachah always follows the Machri'a (the mediating opinion), except for the case of a rag. (If a rag less than three by three [Tefachim] was designated for a lowly use, e.g. to plug up a bathhouse, R. Eliezer is Metamei whether he hung on a peg or left it in back of the door; R. Yehoshua is Metaher in both cases; R. Akiva is Metamei if he hung it on a peg, he is Metaher if he left it in back of the door.)

Even though R. Eliezer is stringent, R. Yehoshua is lenient and R. Akiva is Machri'a, the Halachah does not follow R. Akiva:

Firstly, R. Akiva was a Talmidim of R. Eliezer and R. Yehoshua;

Also, R. Akiva later retracted and adopted R. Yehoshua's opinion in both cases.

Question: What difference would it make if he inferred it?

Answer: Perhaps R. Yochanan holds that the Halachah always follows the Machri'a in Mishnayos [with just the one exception], but the rule does not apply to Beraisos. (Even if he also said it regarding all Beraisos [that he knew], perhaps he never heard Beraisa #2!)

Answer (Rabah bar bar Chanah): I heard it explicitly.