Gemara

32a - Mishnah: We do not say less than 10 verses of Malchuyos, 10 of Zichronos, and 10 of Shofaros;

R. Yochanan ben Nuri says, if he said three of each he was Yotzei.

Question: Does R. Yochanan ben Nuri require three verses from Torah, three from Nevi'im and three from Kesuvim, or only one each from Torah, Nevi'im and Kesuvim?

Answer (Beraisa): We do not say less than 10 verses each of Malchuyos, Zichronos, and Shofaros. If one said seven of each he was Yotzei;

R. Yochanan ben Nuri says, one may not say less than seven (of each, l'Chatchilah). If he said three of each, corresponding to Torah, Nevi'im and Kesuvim, he was Yotzei;

Some say that this corresponds to Kohanim, Leviyim and Yisraelim.

Shmuel: The Halachah follows R. Yochanan ben Nuri.

35a - Beraisa - R. Meir: The Shali'ach Tzibur is Motzi the Rabim in the Berachos of Rosh Hashanah and Yom Kipur (of Yovel);

Chachamim say, just like the Shali'ach Tzibur is obligated, every individual is obligated.

Question: Why are the Berachos of Rosh Hashanah and Yom Kipur different?

Suggestion: There are many verses.

Rejection: Rav taught that after saying 'Uv'Sorasecha Chasuv (and it is written in Your Torah)', he need not say anything else!

Answer: There are many Berachos.

Sukah 55a - Question: (In Chutz la'Aretz,) we keep two days of Yom Tov (so there are only five days of Chol ha'Mo'ed Sukos). Which Korbanos do we say?

Answer #1 (Abaye): We omit those of the second day.

Answer #2 (Rava): We omit those of the seventh day.

Ameimar enacted in Neharda'a to repeat (this will be explained).

Rishonim

Rif and Rosh (4:3): The Halachah follows R. Yochanan ben Nuri.

Ran (DH Masnisin): The Rif did not bring the Beraisa in which R. Yochanan ben Nuri says that one may not say less than seven because it argues with our Mishnah. R. Yochanan ben Nuri agrees that l'Chatchilah, one must say 10.

Note: The Gemara proved from the Beraisa that b'Di'eved he holds that three in all suffice. We must assume that the Beraisa agrees with the Mishnah except for where it clearly argues.

Rif: We conclude that after saying 'Uv'Sorasecha Chasuv', he need not say anything else!

Rebuttal (Ba'al ha'Ma'or): Rav refers to verses of Korbanos Musaf, like Rashi explained.

Defense (Milchamos Hash-m): The Ge'onim explain that Rav also refers to Malchuyos, Zichronos and Shofaros. He holds like R. Yochanan ben Nuri. If one says a Torah verse of Malchuyos, and 'Uv'Sorasecha Chasuv, and also in Divrei Kodshecha (Kesuvim), and through Your Nevi'im', he was Yotzei Malchuyos, for it is as if he said a verse of each. The same applies to Zichronos and Shofaros. This is why the Gemara asks why the Shali'ach Tzibur can be Motzi people. According to Rashi, what was the question? Even after Rav's leniency, even if we hold like R. Yochanan ben Nuri, one must say at least nine verses, which is more than the number of verses of Korbanos Musaf! Also, we should have answered that there are many verses of Malchuyos, Zichronos and Shofaros, rather than say that there are many Berachos! And (before this answer) why did we think that Rosh Hashanah and Yom Kipur of Yovel are different than Musaf of any Yom Tov? Rashi changed the text and says that we assumed that there are too many verses, i.e. of Malchuyos,... and Musafim. This is a poor answer. Rav refers to the Mishnah (which does not discuss verses of Musafim). Also, the Mishnah requires saying Malchuyos, Zichronos and Shofaros in Shacharis, when we do not say Musafim. It was a later enactment to say them at Musaf!

Rif and Rosh (Megilah 10b and 4:10): Ameimar enacted in Neharda'a to repeat in Kri'as ha'Torah. A Gaon explained that on the first two days we read only "Uva'Chamishah Asar".

R. Chananel (Sukah 55a DH Anan): The Amora'im discuss Kri'as ha'Torah and Tefilah.

Rashi (Sukah 55a DH Anan and DH Iskin) and Tosfos (DH Iskin): The Amora'im discuss which Korbanos we mention in Musaf. We repeat the Parashiyos in Kri'as ha'Torah, similar to Ameimar's enactment.

Rambam (Hilchos Shofar 3:8): In each Berachah of Malchuyos, Zichronos and Shofaros one must say 10 verses corresponding to the Berachah. He says three from Torah, three from Tehilim, three from Nevi'im, and concludes with one from Torah. If he concluded with Navi he was Yotzei. If he said one each from Torah, Kesuvim, and Nevi'im, he was Yotzei. Even if he said 'Hashem Elokeinu, uv'Sorasecha Chasuv...' and said one verse of Torah and stopped, he need not do more.

Question (Ran DH Kivan): This is difficult, for even R. Yochanan ben Nuri requires three verses!

Answer #1 (Magid Mishnah): The Rambam explains that he requires three verses in all, one each for Malchuyos, Zichronos and Shofaros. Rav explains that a verse of Torah (not of Nevi'im and Kesuvim) is required for each.

Objection (Lechem Mishneh): R. Yochanan ben Nuri says that b'Di'eved one is Yotzei with three verses. If Rav's Heter is only b'Di'eved, surely it is better for the Shali'ach Tzibur to be Motzi people l'Chatchilah. If so, what forced the Gemara to find another reason why one may be Yotzei?

Answer #2 (Lechem Mishneh): L'Chatchilah, one must say 10 verses. We suggested that the Shali'ach Tzibur can be Motzi people because people are prone to err in the verses. Rav's teaching refutes this, for even if one errs he will be Yotzei.

R. Mano'ach: Had Rav discussed verses of Musaf, he would have said 'Kemo she'Chosavta Aleinu v'Sorasecha (like You wrote in Your Torah that we must offer)...', for this is how we preface Korbanos Musaf.

Rambam (Tefilos Kol ha'Shanah, Sof Berachah Emtza'is): The custom is that in all Tefilos Musaf we say 'Kemo she'Chosavta Aleinu v'Sorasecha' and recite the Korbanos for that day like they are written in the Torah. If he does not mention the verses, since he said 'Kemo she'Chosavta Aleinu v'Sorasecha', he need not say more.

Rosh (14): Rashi explains that the 'many verses' in the Berachos of Rosh Hashanah and Yom Kipur are the Korbanos of Musaf. His Rebbi'im explain that they are Malchuyos, Zichronos and Shofaros. Rashi disagrees, for Chachamim and R. Yochanan ben Nuri both require at least three verses. R. Tam answers that once one began to say verses, he shows that he does not want to rely on 'uv'Sorasecha Chasuv'. This is when Chachamim and R. Yochanan ben Nuri argue about how many verses he must say. All agree that if he did not mention any verses, he can exempt himself by saying 'uv'Sorasecha Chasuv'. However, the verses of Korbanos Musaf must always be said. However, regarding Korbanos Rosh Chodesh on Rosh Hashanah, it suffices to say "Milvad Olas ha'Chodesh u'Minchasah" and 'U'Shnei Se'irim Lechaper'.

Rebuttal (Rosh): Many disagree with R. Tam. He says that Malchuyos, Zichronos and Shofaros are not Me'akev, even though the Mishnah explicitly teaches them. The verses of Korbanos Musaf are not mentioned in the Mishnah or Gemara. It is unreasonable that they should be Me'akev! In Sefard the custom is to say them only on Shabbos and Rosh Chodesh. Since these are frequent, people will not err. We do not say the verses of Korbanos Musaf of Mo'adim, lest people err.

Note: If we include the verse of Musaf Rosh Chodesh, there are more verses for Musfei Rosh Hashanah than for other Mo'adim. However, the Musafim for Yom Kipur are not longer, unless we include the verses in Acharei Mos of Avodas ha'Yom. If they are included, we should also include the verses of Korbanos brought with Shtei ha'Lechem on Shavu'os, and if so there are more than on Rosh Hashanah! Perhaps the Gemara could have asked this, but it gave a better answer.

Rashbam (Eruvin 40a DH Zikaron): One need not say verses of Malchuyos, Zichronos and Shofaros. If one began to say verses, he must finish. The same applies to verses of Korbanos Musaf on Yom Tov.

Poskim

Shulchan Aruch (591:2): The custom of Sefardim is not to say verses of Korbanos Musaf at all.

Beis Yosef (DH veha'Minhag): In Sefard the custom is not to say verses of Korbanos Musaf of Rosh Hashanah or Rosh Chodesh. One should not change from his ancestors' custom.

Rema: The custom among Ashkenazim is to say Korbanos Musaf of Rosh Hashanah. We do not say Korbanos Rosh Chodesh on Rosh Hashanah, only "Milvad Olas ha'Chodesh u'Minchasah" and 'U'Shnei Se'irim Lechaper'.

Mishnah Berurah (3): We also do not say Korbanos Rosh Chodesh with 'Eizehu Mekomam' before Shacharis. We are concerned lest people count the month from the second day. Also, the primary attribute of the day is that it is Rosh Hashanah. Also, we expound that Rosh Chodesh is hidden in Rosh Hashanah - "Ba'Keseh l'Yom Chageinu."

Shulchan Aruch (4): We say 10 verses of Malchuyos, 10 of Zichronos and 10 of Shofaros. In each Berachah three are from Torah, three from Kesuvim, three from Nevi'im, and one (more) from Torah.

Rema: If he did not begin any verses, just he said 'uv'Sorasecha Chasuv Leimor', he was Yotzei.

Mishnah Berurah (11): He must also say 'And it is written in Divrei Kodshecha, and through Your Nevi'im.' The Magen Avraham says that nowadays we are obligated to say all the verses (just like Tefilas Ma'ariv became obligatory).