Gemara

(Mishnah): If a poor person is traveling... if he will stay over Shabbos, we give to him food for three meals.

Shabbos 117b (Beraisa): One must eat three meals on Shabbos;

R. Chidka says, he must eat four meals.

(R. Yochanan): Both of them expound "Ichluhu ha'Yom Ki Shabbos ha'Yom la'Shem ha'Yom Lo Simtza'uhu ba'Sadeh." R. Chidka holds that the three "ha'Yom"s allude to three daytime meals, not including the Shabbos night meal. Chachamim hold that the meal of Shabbos night is included in the three.

118a - Suggestion: The Mishnah is only like Chachamim.

Rejection: It is even like R. Chidka. The case is, he already has a meal with him. He will eat it for the fourth Shabbos meal.

(Mishnah): If a fire erupted, one may save three, two or one meal(s), i.e. if it was Shabbos night, morning or afternoon, respectively.

R. Yosi says, no matter when it was, one may save three meals.

Inference: The first Tana agrees that we eat three meals on Shabbos (but he allows saving only for remaining meals)! This is unlike R. Chidka.

Question (Mishnah): One who has food for 14 meals may not take from the Kupah (money collected and distributed weekly to the poor).

This is not like either Tana! (One eats 15 or 16 meals each week according to Chachamim and R. Chidka, respectively.)

Answer #1: Really, it is like Chachamim. The third Shabbos meal is in place of the meal normally eaten at night on Motzei Shabbos.

Answer #2: It is like R. Akiva, who says that it is better to conduct on Shabbos like on a weekday (and have only two meals) than to take Tzedakah. (Regarding Shabbos meals, it can be like Chachamim or R. Chidka.)

(R. Shimon ben Pazi): We learn the three Shabbos meals from three times it says "Yom". One who fulfills them is saved from three harsh "Yomim": the birth pangs of Moshi'ach, judgment in Gehinom, and the war of Gog and Magog:

Kesuvos 64b (Mishnah #1): One who feeds his wife through an intermediary must supply at least two Kabim of wheat every week.

(Mishnah #2 - R. Yochanan (ben Berokah)): Bread for two meals (for an Eruv) is a loaf costing a 12th of a Dinar when a Se'ah of wheat costs a Dinar;

(R. Shimon): It is two thirds of a loaf of a third of a Kav.

Question: Mishnah #1 cannot be R. Yochanan (if it were, she gets only eight meals per week). It is unlike R. Shimon (she gets 18 meals)!

Answer #1: It is like R. Yochanan. Half the price of bread is the grocer's mark-up. She gets 16 meals each week like R. Chidka.

Answer #2: Our Mishnah is like Chachamim. The extra meal is for guests. (Likewise, our Mishnah can be like R. Shimon.)

Rishonim

Rif and Rosh (Shabbos 43b): The Halachah follows Chachamim.

Ran (DH v'Ika): One may complete the three meals with fruits, just like one can complete the 14 meals that one must eat in the Sukah (according to R. Eliezer) with Targima, which is fruits (Sukah 27a). Rava disagrees, but the Halachah does not follow Rava.

Rambam (Hilchos Shabbos 30:9): One is obligated to eat three Shabbos meals, one at night, one in the morning and one at the time of Minchah. He must be careful about these three meals not to detract from them at all. Even an Oni fed from Tzedakah eats three meals. If one was sick from overeating, or he always fasts, he is exempt from three meals.

Rosh (Sukah 2:13): The Tosefta says that we bless Borei Minei Mezonos on Targima. Perhaps it is more important than meat and fish. Even though Targima must be eaten in a Sukah, we cannot learn from here that one can fulfill Seudah Shlishis through Targima. We learn three Shabbos meals from "ha'Yom" in the verse, and manna was in place of bread!

Poskim

Shulchan Aruch (OC 291:1): One must be very careful to fulfill Seudah Shlishis. Even if he is satiated, he can fulfill it with k'Beitzah. If he cannot eat at all, he need not pain himself. A Chacham plans in advance, and does not fill his stomach at the morning meal, to leave room for Seudah Shlishis.

Magen Avraham: If one has enough bread for two meals, and if he divides it up for three meals he will not have enough for satiation at each meal, it is better to eat two meals to satiation (Sefer Chasidim 861). The Gemara supports this. It says 'it is better to make Shabbos like a weekday (and have only two meals) than to take Tzedakah.' It does not suggest making three meals that will not satiate him. I say that if the morning meal goes past midday, he should divide it into two meals, for he will be satiated when he finishes eating. Chidushei Anshei Shem (on Mordechai Shabbos 397) and Shibolei ha'Leket say so. L'Chatchilah, one should not delay until midday for this, for he annuls Oneg Shabbos. However, some say that one can be Yotzei Seudah Shlishis even before midday, so in any case he should split the morning meal.

Kaf ha'Chayim (1,2): The Zohar says that there is a great punishment for one who omits one of the meals. Therefore, it is better to have three meals, even not to satiation. The Shulchan Aruch (Sa'if 2) does not allow Seudah Shlishis before midday. The Ari Zal requires it to be after Minchah, so it never helps to split the morning meal.

Mishnah Berurah (2): One should eat a bit more than k'Beitzah, for exactly k'Beitzah is Arai (haphazard) (Magen Avraham). Some say that one is Yotzei with a k'Zayis. One should be stringent if possible.

Gra (2): We learn a k'Beitzah from Sukah.

Mishnah Berurah (1): We give three meals to a traveling Oni. One who must borrow for the Shabbos meals should borrow for three meals.

Mishnah Berurah (3,4): The meals are for pleasure, not for pain. If one eats when he is stuffed, this is not considered eating.

Kaf ha'Chayim (3): One normally eats only once during the day, so Seudah Shlishis proves that he ate to honor Shabbos. One who omits Seudah Shlishis proves that he did not eat to honor Shabbos.

Rema: If one did not eat Shabbos night, he eats three meals on Shabbos day.

Mishnah Berurah (5): He says the night Kidush, without "va'Ychulu..." Likewise, if one did not eat on Yom Tov night, he says Kidush and eats two meals on Yom Tov day.

Shulchan Aruch (5): Seudah Shlishis must be with bread. Some allow using any food from the five grains. Some allow accompaniments for bread such as meat and fish, but not fruits. Some allow even fruits. The first opinion is primary, that one must use bread, unless he is too full.

Beis Yosef (DH v'Yesh): The Ran and R. Yonah bring an opinion that one is Yotzei with Targima. Tosfos and the Rosh refuted their proof. Semag requires bread for all three meals.

Mishnah Berurah (24): The second opinion requires food from grain on which we bless Borei Minei Mezonos. The reason for the lenient opinions is because this meal is not normally eaten with appetite.

Beis Yosef (DH Targima): Rashi and the Ran say that Targima is fruits. Tosfos says that it is meat, fish and similar accompaniments for bread; even if one is Yotzei with Targima, he is not Yotzei with fruits, which do not count like a meal for Sukah. The Tur relies on the Rosh (that Targima is Mezonos), for the Tosefta supports him. R. Yerucham, R. Yonah and Shibolei ha'Leket say that one is Yotzei with fruits. Rabbeinu Yehudah was particular to use fruits of the seven species.

Gra (15): Rashi says that Targima is fruits. Tosfos rejected this, based on Rava. The Ran says that the Halachah does not follow Rava.

Mishnah Berurah (22,23): L'Chatchilah, one should have delicacies according to his ability also for Seudah Shlishis. All agree that l'Chatchilah one should have bread (Sa'if 4). They argue about b'Di'eved.

Kaf ha'Chayim (29): One should eat fish at Seudah Shlishis. It is nice to have eggs, for a sign of mourning over Moshe Rabbeinu (who died Shabbos afternoon).

Kaf ha'Chayim (30): It is proper to have bread even when Shabbos is Erev Yom Tov.

Rema: Or, (one has Targima or fruits...) when one cannot use bread, e.g. when Erev Pesach is on Shabbos one cannot eat bread after Minchah.

Mishnah Berurah (25): Therefore, he should fulfill Seudah Shlishis through fried Matzah meal, meat and fish, or fruits.