Gemara

(Beraisa): Ludim (cannibals) eat in the first hour of the day. Bandits eat in the second hour. Heirs eat in the third.

Most people eat in the fourth, workers eat in the fifth, and Chachamim eat in the sixth.

Eating after this (six hours) is like throwing a rock into a pouch [with little wine].

(Abaye): This is only if he did not taste anything all morning. If he ate [even a bit], there is no problem.

68b (Beraisa - R. Eliezer): On Yom Tov a person must eat and drink, or learn;

R. Yehoshua says, one should divide the day - half to eat and drink, and half to learn.

(R. Yochanan): Both of them learn from the same verses:

Contradiction: It says "Atzeres la'Shem Elokecha," and it says "Atzeres Tihyeh Lachem"!

Resolution #1 (R. Eliezer): It must be all for Hash-m (learning), or all for you (eating and drinking)'

Resolution #2 (R. Yehoshua): One must divide the day - half for Hash-m, and half for you.

(R. Elazar): All agree that on Shavu'os [at least] part of the day must be for you.

(Rabah): All agree that on Shabbos [at least] part of the day must be for you.

We learn from "v'Karasa la'Shabos Oneg."

Mar brei d'Ravina used to fast every day, except for Shavu'os, Purim and Erev Yom Kipur:

107b (Beraisa): Even Melech Agripas, who normally ate (began his first meal) at nine hours, may not eat [on Erev Pesach] until dark.

Avodah Zarah 34a (Rabanan of the Beis Medrash): One may fast for part of a day.

Ta'anis 25b (Beraisa - R. Yosi): If a Tzibur was fasting for rain, and rain came before nine hours, they do not finish the fast. If it came after nine hours, they finish it. We find that Achav fasted from nine hours - "Ki Nichna Achav..."

Rishonim

Rif and Rosh (Shabbos 5a and 1:24): The Yerushalmi forbids fasting until six hours on Shabbos. It learns from the Mishnah. If a Tzibur was fasting, and rain came before nine hours, they finish only if it is after midday.

Rashi (25b DH she'Chen): R. Yosi learns from Achav, for after nine hours the fast takes effect on everyone, even princes who rise after three hours, and wait six hours and eat at nine hours, like we say about Agripas. The fast does not take effect on Achav until nine hours. He decided to fast only after this, after Eliyahu rebuked him, and it says "he fasted."

Mordechai (Shabbos 229-230): One may not fast on Shabbos until six hours. Avi ha'Ezri permits to learn and pray [until then], for we hold like R. Eliezer, who says that [Yom Tov must be] all for you, or all for Hash-m." Mar brei d'Ravina used to fast every day [during the day] except for Shavu'os, [Erev Yom Kipur and Purim]. I later saw in Beitzah that he holds like R. Yehoshua. Avi ha'Ezri ruled like him.

Ohr Zaru'a (2:42:7): One must eat before the end of the fifth hour on Shabbos and Yom Tov.

Rashba (614): The Rambam (Hilchos Shevu'os 1:6) says that one who swore to fast on Shabbos is lashed for a vain oath. Perhaps he holds that the Isur to fast on Shabbos is mid'Oraisa.

Poskim

Shulchan Aruch (OC 157:1): One should fix his meal when the fourth hour comes.

Magen Avraham (1): Pesachim 12b connotes that we calculate relative hours from dawn. Chametz depends on relative hours from dawn, like I wrote in 443:3. Ta'anis 25b connotes that we count six hours from when Achav woke up. We must say that in Pesachim we count from dawn, for most people rise then. We can justify lengthy Tefilos on Shabbos and Yom Tov that sometimes finish after six hours, for we count from when people rise.

Note: In the Halachah for Daf 61, I inferred from the Rema (443:1) that Chametz depends on relative hours from sunrise to sunset! He says "in a leap year, one may eat Chametz until four relative hours." I.e. in a regular year, Erev Pesach is often close to Tekufas Nisan, so relative hours are very close to standard hours. In a leap year, Erev Pesach is later after the Tekufah, and relative hours are significantly longer. If we would measure from dawn to Tzeis ha'Kochavim, in every year relative hours are significantly longer!

Kaf ha'Chayim (2): Mateh Yehudah (or Mateh Yosef) says that we always count from dawn.

Eliyahu Rabah (288:2): People rely on Avi ha'Ezri, who permits to learn and pray past midday. Gedulas Mordechai (in Chidushei Anshei Shem, under the Mordechai) says that Avi ha'Ezri rules like R. Yehoshua regarding Yom Tov, but on Shabbos one may learn and pray past midday. What the Shulchan Aruch wrote here is difficult.

Mishnah Berurah (1): This discusses Stam people. Workers eat at five hours.

Shulchan Aruch (ibid.): A Chacham who learns should wait until the sixth hour.

Magen Avraham (2): This refers to the beginning of the sixth hour. One should not delay past [the end of] six hours. See CM 5.

Machatzis ha'Shekel: The Tur wrote there that judges judge until midday. The Beis Yosef asked that Chachamim should eat in the sixth hour! The Shulchan Aruch (5:3) says that they judge five hours. The SMA says that the Tur means almost until midday. The Magen Avraham holds that l'Chatchilah one should do like the Beis Yosef, and in any case he should not delay past midday, like the Tur.

Shulchan Aruch (ibid.): He should not delay past this, for this is like throwing a rock into a pouch, unless he tasted something in the morning.

Magen Avraham (3): Eating after six hours is like throwing a rock into a pouch to fill it. It does not help. It would be better to fill it with wine!

Prishah (1): The pouch is almost full of wine. If he leaves it this way, it will sour. If he throws a rock in, it will not sour, but it will not be as good as if he filled it with wine. This is because when the stomach is empty, harmful fluids enter.

Mishnah Berurah (4): Eating after six hours does not give strength, just like the rock does not add to the wine. One should eat lighter during the day than at night. One should eat twice during the day if he is weak. He should not fill his stomach at once.

Mishnah Berurah (5): If one tasted in the morning, eating after midday is not like throwing a rock into a pouch. In any case, it is proper to fix a meal in the sixth hour even if he tasted in the morning. [In the days of the Gemara] they used to eat a little bread in the morning "like a Talmid eats before going to Kalah (to learn)" (Sukah 26a). Even so, Chachamim ate in the sixth hour.

Note: Perhaps a minority of Talmidim used to eat before going to Kalah! Alternatively, perhaps the Gemara mentioned specifically Kalah, for they used to learn past six hours, therefore Talmidim ate beforehand!

Shulchan Aruch (OC 288:1): One may not fast on Shabbos until six hours.

Kaf ha'Chayim (4, citing Orchos Chayim): The Rashba says that the Isur to fast on Shabbos is mid'Oraisa. Tanchuma Bereishis says so. Kevod Shabbos is 1000 times greater than a fast. This is why Shabbos overrides Ta'anis Esther, which is mid'Rabanan.

Kaf ha'Chayim (5): Even if one fasts the entire year due to his sins, he may not fast on Shabbos, unless the change of routine [eating] would harm him.

Taz (1): Since eating after six hours during the week is like throwing a rock into a pouch, it is considered a fast on Shabbos.

Magen Avraham (1): One may not fast even a small time on Shabbos for the sake of a fast (Maharil Ta'anis 267, Rashi Eruvin 41a DH She'ani, and so connotes Sa'if 4). Some congregations fast until midday on Shabbos due to decrees. This is improper.

Bi'ur Halachah (DH Asur): Poskim argue about whether the Isur to fast on Shabbos is from Navi, or mid'Oraisa (since it says "Ichluhu ha'Yom.") Clearly, all agree that fasting until six hours is forbidden only mid'Rabanan.

Bi'ur Halachah (DH Ad): Since one may not intend to fast at all on Shabbos, the Yerushalmi must forbid until six hours even not for the sake of a fast, for it is a long time. If so, what was the Yerushalmi's proof from people who were fasting until midday? That was for the sake of a fast! The Gra agreed with the Magen Avraham's law.

Kaf ha'Chayim (1): On Shabbos one may not refrain from meat and wine for the sake of a fast, even though there is no obligation to have them.

Mishnah Brurah (1): If one tasted anything before Musaf, Musaf may extend past six hours.

Pninei Tefilah (p.57, in the name of ha'Gaon R. Y.S. Elyashiv Ztz"l): This is even if he drank water before Tefilah, even if he was not thirsty and did not bless.

Kaf ha'Chayim (3): During the week one should eat before midday, for after this is like throwing a rock into a pouch, but there is no Isur. On Shabbos it is forbidden. It is permitted on Rosh Hashanah, for some say that one should fast on Rosh Hashanah. Even though this is not our custom, it is proper to delay until after midday (Bach). Maharshal forbids when Rosh Hashanah is on Shabbos.

Rema: Even if he learns and prays, it is forbidden.

Mishnah Berurah (2): Therefore, it is improper for a Shali'ach Tzibur to sing [at length] and people do not leave the Beis ha'Keneses until after six hours, especially in winter, when the days are short. All the more so this is improper on Yom Tov, except for Rosh Hashanah. Eliyahu Rabah and Bigdei Yesha permit to learn and pray after midday.

Doleh u'Mashke (p. 215, citing ha'Gaon R. C. Kanievsky Shlita) cites an opinion that one should eat before Musaf on Rosh Hashanah if it will finish after midday (but not more than a k'Beitzah of Mezonos, which is forbidden before Musaf - Mishnah Berurah 286:9).