On a similar note, the Sages taught in a baraita: One who erred and did not recite the afternoon prayer on the eve of Shabbat, prays in the evening prayer two Amida prayers on Shabbat evening. One who erred and did not recite the afternoon prayer on Shabbat, recites two weekday Amida prayers in the evening prayer at the conclusion of Shabbat. He recites havdala [the prayer of distinction] between the sanctity of Shabbat and the profanity of the week by reciting: You have graced us, etc., in the fourth blessing of the Amida, which is: Who graciously grants knowledge, in the first prayer, as it is the actual evening prayer, but he does not recite havdala in the second prayer, which is in place of the afternoon prayer. Moreover, if he recited havdala in the second prayer and did not recite havdala in the first, the second prayer fulfilled his obligation, the first one did not fulfill his obligation.

The Gemara comments: Is that to say that since he did not recite havdala in the first prayer, he is as one who did not pray and we require him to return to the beginning of the prayer and repeat it? If so, the conclusion is that one who fails to recite havdala in the prayer must repeat that prayer.

The Gemara raises a contradiction to the above conclusion from the Tosefta: One who erred and did not mention the might of the rains: He makes the wind blow and rain fall in the second blessing of the Amida, the blessing on the revival of the dead, and one who erred and failed to recite the request for rain in the ninth blessing of the Amida, the blessing of the years, we require him to return to the beginning of the prayer and repeat it. However, one who erred and failed to recite havdala in the blessing: Who graciously grants knowledge, we do not require him to return to the beginning of the prayer and repeat it, as he can recite havdala over the cup of wine, independent of his prayer. This contradiction was not resolved and remains difficult.

The dispute between the Rabbis and Rabbi Yehuda with regard to the times beyond which the different prayers may not be recited is rooted in a profound disagreement, also manifest in a later amoraic dispute. It was stated: Rabbi Yosei, son of Rabbi Ḥanina, said: The practice of praying three times daily is ancient, albeit not in its present form; 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.

The Gemara comments: 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. The Gemara elaborates: It was taught in a baraita in accordance with the opinion of Rabbi Yosei, son of Rabbi Ḥanina: Abraham instituted the morning prayer, 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 before the Lord” (Genesis 19:27), and from the context as well as the language utilized in the verse, the verb standing 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 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, 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, 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 may be recited until noon? Because, although the daily morning offering 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 is sacrificed until four hours.

And why did the Rabbis say that the afternoon prayer may be recited until the evening? Because the daily afternoon offering is sacrificed until the evening. Rabbi Yehuda says that the afternoon prayer may be recited only until the midpoint of the afternoon because, according to his opinion, the daily afternoon offering is sacrificed until the midpoint of the afternoon.

And why did they say that the evening prayer 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 may be recited all day? Because the additional offering is brought throughout the entire day. However, Rabbi Yehuda says that the additional prayer may be recited until the seventh hour of the day, because the additional offering is sacrificed until the seventh hour.

The baraita continues and states that there are two times for the afternoon prayer. Greater, earlier minḥa [minḥa gedola] and lesser, later minḥa [minḥa ketana]. The Gemara clarifies the difference between them: Which is minḥa gedola? 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 may be sacrificed, as in the case on the eve of Passover that occurs on Shabbat. Which is minḥa ketana? From nine-and-a-half hours and on, which is the standard time that the daily afternoon offering is sacrificed.

On that note, a dilemma was raised before them: Rabbi Yehuda, who holds that the afternoon prayer may be recited only until the midpoint of the afternoon, does he say the midpoint of the first minḥa, minḥa gedola? Or, does he say the midpoint of the last minḥa? Come and hear an explicit resolution to this dilemma: As it was taught in a baraita, Rabbi Yehuda says: They said the midpoint of the last minḥa, 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. The Gemara suggests: Let us say that this is a conclusive refutation of the opinion of Rabbi Yosei, son of Rabbi Ḥanina, who held that the forefathers instituted the prayers. Rabbi Yosei, 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. As, if you do not say so, that even Rabbi Yosei, son of Rabbi Ḥanina, would agree that the laws of offerings and those of prayers are related, then, according to Rabbi Yosei, 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.

We learned in the mishna that Rabbi Yehuda says: The morning prayer may be recited until four hours of the day. A dilemma was raised before the yeshiva students: When Rabbi Yehuda says until, does he mean until and including the fourth hour, or, perhaps when he says “until” he means until and not including, in which case one may not pray during the fourth hour? Come and hear a resolution to this dilemma based on the mishna. Rabbi Yehuda says: The afternoon prayer may be recited only until the midpoint of the afternoon. Now, granted, if you say that until means until and not including, then there is a difference between the opinion of Rabbi Yehuda and the opinion of the Rabbis. However, if you say that until means until and including, then the opinion of Rabbi Yehuda