Gemara

(R. Elazar): Hash-m was not angry for a moment during the entire time that Bilam was trying to curse us. He been angry, (Bilam would have succeeded to curse us, and) there would be no remnant of us.

(R. Yochanan): From Bil'am's blessings, we can infer what he wanted to curse. "Mah Tovu Ohalecha" - he wanted that we not have Batei Keneses and Batei Medrash. "Mishkenosecha Yisrael" - he wanted that the Shechinah should not rest on them...

Berachos 7a: A certain heretic used to bother R. Yehoshua ben Levi. R. Yehoshua set a rooster between the legs of his bed, intending to curse him when the mane turned all white (this is a sign of Hash-m's moment of anger).

(Beraisa): "V'Kel Zo'em b'Chol Yom" -- Hash-m's fury is for a Rega (moment). This is one part in 58,888 parts of an hour (about 1/15th of a second).

(R. Avin or R. Avina): This is the time needed to say "Rega."

Rishonim

Tosfos (Avodah Zarah 4b): What curse could Bilam have said in a moment? He could have said 'Kalem' (finish them off). Hash-m reversed his intent, and forced him to say (this word backwards) "u'Sru'as Melech Bo." R. Eliyahu says that he only needed to start his curse at that moment. We find that he wanted to give many curses, like it says in Sanhedrin that from his Berachos, we see what he intended (to curse).

Toldos Yitzchak (Bamidbar 22:2): Everything depends on the conclusion. Bilam intended to answer Amen to all the curses at the moment of Hash-m's anger.

Da'as Zekenim mi'Ba'alei ha'Tosfos (Bamidbar 23:8): Bilam could have said 'Kalem' in a moment. However, what could R. Yehoshua ben Levi have said in a moment to harm the heretic? Rather, it suffices to begin at the moment of anger. We learn also from Bilam's Berachos, which reflect all the curses that he intended to give.

Tosfos Yom Tov (Berachos 5:4): We do not learn Halachah from Agados. Bereishis Rabah (Sof Parshah 8) rules like the opinion that women are commanded to have children, but the Halachah does not follow this. Also the Yerushalmi (Pe'ah 2:6) says that we do not learn Halachah from Agados or Toseftos. We learn only from the Gemara.

Rebuttal (Pri Chodosh (Mayim Chayim, cited in R. Akiva Eiger [36])): IF the Gemara discusses something, we do not learn the Halachah from Agados. If something is not explicit in the Gemara, surely we rely on Medrashim! In many places, Rishonim bring proofs from Medrashim.

Poskim

Shulchan Aruch (OC 89:1): The time for Shacharis extends until four hours. If one transgressed and prayed after four hours, he gets reward for Tefilah, but not for Tefilah in its time.

Mishnah Berurah (5): One must finish within the time.

Eshel Avraham (4, cited in Mishnah Berurah 58:5 and Kaf ha'Chayim 89:9): Likewise, one must finish Kri'as Shema within its time (three hours).

Shulchan Aruch (110:1): In pressed circumstances, e.g. he is on the road or in a place where he fears lest he be interrupted, or he cannot pray with intent a long Tefilah, he prays the first three Berachos, Havinenu (a condensed text of the 13 middle Berachos), and the last three Berachos. One may not do so in winter (for one must request rain).

Mishnah Berurah (1): If one sees that there is no time for a full Tefilah, he prays Havinenu.

Rebuttal (Aruch ha'Shulchan 5): This is based on the Magen Avraham. He holds that if Tefilah will not finish within the time, it is not considered that he prayed within the time. I say that we learn from Tosfos that it all depends on the beginning. If one begins within the time to pray, even if he finishes afterwards, this is called Tefilah in the time.

Gilyonei ha'Shas (Yerushalmi Berachos (after Zera'im), 54): The Yerushalmi (Berachos 4:1) says that if one began Tefilah before the time, and during his Tefilah the time came, this is fine. Tosfos says oppositely! In any case we see that the entire Tefilah need not be within the time. It suffices that part is within the time, or the beginning or the end.

Yabi'a Omer (7 OC 34:4): I disagree with his proof from the Yerushalmi. The proof from Tosfos is not solid, for Tosfos gave another answer. Ya'aros Devash (9:54:4) rejected the other answer, for 'Kalem' does not specify which nation. However, Berachos 34a learns from Moshe's Tefilah for Miryam that one who prays for another need not mention his name. However, the Maharil (161, brought in Magen Avraham 199:1) says that this is only if the one for whom he prays is in front of him. This is why Balak brought Bilam to a place where he could see all of Yisrael. I agree with the Aruch ha'Shulchan, that if it is within the time, but one knows that he will finish after the time, he may pray a full Shemoneh Esre, and not Havinenu, especially since Sefer ha'Itim says that one who prays Havinenu when it is not pressed circumstances was not Yotzei.

Kaf ha'Chayim (1): Many say like the Magen Avraham. Batei Kenesiyos was unsure about this.

Rema (124:2): In pressed circumstances, e.g. he fears lest the time for Tefilah elapse, one may pray immediately aloud, and the Tzibur prays silently word for word with him until after ha'Kel ha'Kadosh.

Magen Avraham (4): 'He fears lest the time for Tefilah elapse' means that he will not finish the 18 Berachos within the time. The Shulchan Aruch says similarly in Siman 232.

Rebuttal (Aruch ha'Shulchan 6): He holds that Tefilah must finish within the time. I wrote differently above. It seems that the Rema means 'if there will be no time for the Shali'ach Tzibur to begin within four hours', but if he begins in time we are not concerned that he finish within the time.

Mishnah Berurah (7): At Shacharis, the Shali'ach Tzibur must finish within four hours, for after this one does not get reward for Tefilah in its time. At Minchah, it is absolutely essential that the Shali'ach Tzibur finish within the time.

Bi'ur Halachah (DH she'Ya'avor): What I wrote in the Mishnah Berurah is from the Eshel Avraham. Granted, regarding Minchah it is better to skip Chazaras ha'Shatz in order to pray within the time. However, this is not clear regarding Shacharis. Perhaps Chachamim did not uproot the enactment of Chazaras ha'Shatz, for it is possible for Chazaras ha'Shatz to end after four hours, since the obligation for Shacharis extends until midday.

Shulchan Aruch (232:1): If time is pressed, they pray Minchah silently, and afterwards the Shali'ach Tzibur says the first two Berachos and answers Kedushah and concludes ha'Kel ha'Kadosh, if there is not time in the day to finish the 18 Berachos.

Beis Yosef (DH Kasuv): Shibolei ha'Leket (47) says in the name of Rav Hai Gaon that if the Tzibur does not have time Bein ha'Shemashos, they pray silently, and afterwards the Shali'ach Tzibur prays. The Shali'ach Tzibur should not say Shemoneh Esre aloud to be Motzi them, for the Mitzvah of Tefilah is silent, for an individual or a Tzibur. The solution if that everyone prays silemntly, and then the Shali'ach Tzibur says the first two Berachos and they answer Kedushah and he concludes ha'Kel ha'Kadosh, if there is not time in the day to finish the 18 Berachos. This is the custom of Rabanan in the Yeshiva, and it is proper.

Question (Magen Avraham 1): In 124:2, it says that people are Yotzei through Tefilah aloud! We must say that there, there is no alternative.

Rema: Some say that the Shali'ach Tzibur prays aloud with the Tzibur. This is the custom. See above 124:2.

Mishnah Berurah (234:6): It is good to say Parshas ha'Tamid and the Ketores before Minchah. However, if there is concern lest the time for Tefilah pass (l'Chatchilah, one must finish before sundown - Mishnah Berurah 233:14), one should skip even Ashrei (to enable finishing it is not time).

Machatzis ha'Shekel (6:6): Beis Yakov (127) brings from the Ari Zal that whatever a person engages in after Tefilah (e.g. Tehilim) before leaving the Beis ha'Keneses, it is included with that influence (of Tefilas ha'Tzibur) and ascends with it. He brings a proof from the latter answer in Tosfos. Since Midah Tovah is greater than the Midah for punishment, all the more so a Tefilah that began at a time of Ratzon (when prayer is accepted) is included in that Ratzon even if it finishes later.

Magen Avraham (426:1): If one began to bless Kidush Levanah and the moon became covered, he may finish the Berachah (Radvaz 1:157). This connotes that if he knows that it will become covered, he may not begin to bless.

Yabi'a Omer (ibid.): Perhaps tl is different, for it is a request for mercy. It would be great if people prayed the entire day! I say that the Radvaz only meant that l'Chatchilah one should not begin if he can be Mekadesh the moon later without clouds.