Origins of "Prayer"/the 'Amidah

MISHNA:

According to the Rabbis, the morning prayer [shaḥarit] may be recited until noon.

Rabbi Yehudah says: It may be recited only until four hours after sunrise.

According to the Rabbis, the afternoon prayer [minḥah] may be recited until the evening.

Rabbi Yehudah says: It may be recited only until the midpoint of the afternoon [pelag haminḥah], i.e., the midpoint of the period that begins with the sacrifice of the daily afternoon offering and ends at nightfall, which is the end of the afternoon.

The evening prayer ['aravit] may be recited throughout the night and is not fixed to a specific hour.

According to the Rabbis, the additional prayer [musaf] may be recited all day.

Rabbi Yehudah says: It may be recited only until seven hours after sunrise.

GEMARA:

The Gemara raises a contradiction based on what was taught in a baraita: The mitzvah is to recite the morning Shema' with sunrise so that he will juxtapose redemption, which is mentioned in the blessings following Shema', to the 'Amidah prayer, which is recited immediately after sunrise, and find himself praying in the daytime. Clearly, the time to recite the morning prayer is immediately after sunrise. The Gemara responds: This baraita does not establish a binding halakha. Rather, it taught that rule specifically with regard to those who are scrupulous in fulfillment of mitzvot [vatikin]. As Rabbi Yoḥanan said: Vatikin would finish reciting the morning Shema' with sunrise, but those who are not vatikin may recite their prayers later.

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...It was stated: Rabbi Yosi, son of Rabbi Ḥanina, said: The practice of praying three times daily is ancient; prayers were instituted by the Patriarchs. However, Rabbi Yehoshua ben Levi said that the prayers were instituted based on the daily offerings sacrificed in the Holy Temple, and the prayers parallel the offerings, in terms of both time and characteristics. It was taught in a baraita in accordance with the opinion of Rabbi Yosei, son of Rabbi Ḥanina, and it was taught in a baraita in accordance with the opinion of Rabbi Yehoshua ben Levi. It was taught in a baraita in accordance with the opinion of Rabbi Yosei, son of Rabbi Ḥanina: Abraham instituted the morning prayer [shaḥarit], as it is stated when Abraham came to look out over Sodom the day after he had prayed on its behalf: “And Abraham rose early in the morning to the place where he had stood ['amad] before the Lord” (Genesis 19:27), and from the context as well as the language utilized in the verse, the verb standing ['amidah] means nothing other than prayer, as this language is used to describe Pinehas’ prayer after the plague, as it is stated: “And Pinehas stood up [vaya'amod] and prayed and the plague ended” (Psalms 106:30). Clearly, Abraham was accustomed to stand in prayer in the morning. Isaac instituted the afternoon prayer [minḥah], as it is stated: “And Isaac went out to converse [lasuaḥ] in the field toward evening” (Genesis 24:63), and conversation means nothing other than prayer, as it is stated: “A prayer of the afflicted when he is faint and pours out his complaint [siḥo] before the Lord” (Psalms 102:1). Obviously, Isaac was the first to pray as evening approached, at the time of the afternoon prayer. Jacob instituted the evening prayer ['aravit], as it is stated: “And he encountered [vayifga'] the place and he slept there for the sun had set” (Genesis 28:11). The word encounter means nothing other than prayer, as it is stated when God spoke to Jeremiah: “And you, do not pray on behalf of this nation and do not raise on their behalf song and prayer, and do not encounter [tifga'] Me for I do not hear you” (Jeremiah 7:16). Jacob prayed during the evening, after the sun had set. And it was taught in a baraita in accordance with the opinion of Rabbi Yehoshua ben Levi that the laws of prayer are based on the laws of the daily offerings: Why did the Rabbis say that the morning prayer [shaḥarit] may be recited until noon? Because, although the daily morning offering [shaḥarit] is typically brought early in the morning, it may be sacrificed until noon. And Rabbi Yehuda says: My opinion, that the morning prayer may be recited until four hours into the day, is because the daily morning offering [shaḥarit] is sacrificed until four hours. And why did the Rabbis say that the afternoon prayer [minḥah] may be recited until the evening? Because the daily afternoon [minḥah] offering is sacrificed until the evening. Rabbi Yehuda says that the afternoon prayer [minḥah] may be recited only until the midpoint of the afternoon because, according to his opinion, the daily afternoon offering [minḥah] is sacrificed until the midpoint of the afternoon. And why did they say that the evening prayer ['aravit] is not fixed? Because the burning of the limbs and fats of the offerings that were not consumed by the fire on the altar until the evening. They remained on the altar and were offered continuously throughout the entire night. And why did the Rabbis say that the additional prayer [musaf] may be recited all day? Because the additional offering [musaf] is brought throughout the entire day. However, Rabbi Yehuda says that the additional prayer [musaf] may be recited until the seventh hour of the day, because the additional offering [musaf] is sacrificed until the seventh hour. The baraita continues and states that there are two times for the afternoon prayer. Greater, earlier minḥah [minḥah gedolah] and lesser, later minḥah [minḥah ketanah].

The Gemara clarifies the difference between them: Which is minḥah gedolah? From six-and-a-half hours after sunrise and on, which is a half an hour after noon and on. It is the earliest time that the daily afternoon offering [minḥah] may be sacrificed, as in the case on the eve of Passover that occurs on Shabbat. Which is minḥah ketanah? From nine-and-a-half hours and on, which is the standard time that the daily afternoon offering [minḥah] is sacrificed. On that note, a dilemma was raised before them: Rabbi Yehudah, who holds that the afternoon prayer [minḥah] may be recited only until the midpoint of the afternoon, does he say the midpoint of the first minḥah, minḥah gedolah or, does he say the midpoint of the last minḥah? Come and hear an explicit resolution to this dilemma: As it was taught in a baraita, Rabbi Yehudah says: They said the midpoint of the last minḥah, and that is eleven hours minus a quarter of an hour after sunrise, i.e., an hour-and-a-quarter hours before sunset. In any case, it is clear that according to this baraita the halakhot of prayer are based on the Temple offerings. Let us say that this is a conclusive refutation of the opinion of Rabbi Yosi, son of Rabbi Ḥanina, who held that the forefathers instituted the prayers. Rabbi Yosi, son of Rabbi Ḥanina, could have said to you: Actually, I will say to you that the Patriarchs instituted the prayers and the Sages based the times and characteristics of prayer on the Temple offerings, even though they do not stem from the same source. If you do not say so, then, according to Rabbi Yosi, son of Rabbi Ḥanina, who instituted the additional prayer? It is not one of the prayers instituted by the forefathers. Rather, even according to Rabbi Yosei, son of Rabbi Ḥanina, the prayers were instituted by the Patriarchs and the Sages based them on the laws of the offerings...