THE KRI'AH ON ROSH CHODESH
Gemara
21b - Question (Ula bar Rav): How do we split the Kri'ah for Rosh Chodesh among the four Olim?
The first eight verses are a Parashah (a segment of the Torah delineated by spaces. In printed Chumashim a Samech or Pei denotes the end of a Parashah.)
The first two Olim cannot read three verses each, for this would leave two verses in the Parashah, and we do not do this!
Answer #1: Each will read four.
Rejection: If so, how will the last two Olim read the remaining seven verses, which consist of a Parashah of two verses and a Parashah of five?!
The first of the last two Olim cannot read the Parashah of two and one verse from the next Parashah, for we do not begin less than three verses of a Parashah;
If he will read the Parashah of two and three from the next Parashah, only two will remain for the last Oleh!
Answer (Rava): I did not hear this, but I heard the answer to a similar question (from which we can answer your question):
Mishnah: On Sunday, Ma'amados read Parashiyos Bereishis and Yehi Raki'a.
Beraisa: Bereishis is split among two Olim; one Oleh reads Yehi Raki'a.
Question: Bereishis has five verses. How do we divide it? One does not read less than three verses!
Answer #1 (Rav): The second person repeats a verse read by the first.
Answer #2 (Shmuel): Each reads two and a half verses.
Rav didn't say like Shmuel, for he holds that we do not split verses of the Torah.
Question: Does Shmuel permit to split verses of the Torah?! R. Chanina ha'Gadol permitted splitting a verse only to help children learn, because there is no other solution!
Answer: Shmuel says that here also, there is no other solution.
Shmuel didn't say like Rav, because we are concerned lest people who enter or leave in the middle think that the other person read only two verses (they do not know that a verse was repeated).
Rav Yosef: The Halachah is that the middle person repeats.
Rishonim
Rif and Rosh (3:3): Rav Yosef answered that the middle person repeats.
Objection (Ramban DH u'Foshat): The Rif and the Ge'onim explain that Rav Yosef gives the law regarding Rosh Chodesh. The second repeats the third verse and reads two more, leaving three verses in the Parashah. This is difficult! We do not begin less than three verses in a Parashah lest people who enter in the middle will think that he read only two verses. Likewise, if the second Oleh starts from the third verse, people who enter will think that the first read only two verses!
Suggestion: The concern lest people think that the one they hear (they entered during his Kri'ah) reads only two is greater than the concern lest they suspected that the previous Oleh read only two (this requires extrapolation).
Rejection: It is all the same decree. We do not leave less than three verses in a Parashah lest people leave and extrapolate and assume that the next Oleh will read only two, even though they should realize that he might read part of the next Parashah. All the more so we are concerned lest people think that the first read only two verses, since it is unreasonable that he would have started from the previous Parashah (it is unrelated to Rosh Chodesh)!
Ramban (ibid.): It would be better for the second Oleh to finish the Parashah, and for the third to repeat the last three verses of that Parashah and add Parashas "Uva'Yom ha'Shabbos". Rava answered that Rav never allows splitting verses, even though this necessitates repeating, and someone might think that an Olah read less than three; Shmuel allows splitting a verse to avoid this concern. Rav Yosef gave the Halachah regarding the actual argument of Rav and Shmuel, i.e. Ma'amados. The middle Oleh repeats a verse to minimize violations of the decrees not to begin or leave less than three verses in a Parashah. On Rosh Chodesh there are four Olim, so 'the middle' does not specify the second, for the third is equally in the middle. Also, even if the third or fourth would skip we violate only one decree. Even though Ma'amados do not apply nowadays, Rav Yosef's ruling is relevant nowadays, i.e. whether we should repeat verses or split a verse on Rosh Chodesh. However, the custom is like the Ge'onim; and we should not change, especially because it does not entail an Isur.
Ran (DH Hilchesa): There is concern even for people who are there the entire time! If Olim will begin or leave less than three verses in a Parashah, people might think that this is always permitted, and come to do so the entire year, leading others to think that one may read less than three verses. Really, the first Olim should not repeat verses (since they are not forced to), only the last. However, this would entail beginning or leaving less than three verses in a Parashah, which is worse. The same applies if the third repeats verses. Therefore, when Rav Yosef said that the middle repeats, clearly he refers to the second.
Rambam (Hilchos Tefilah 13:4): On Rosh Chodesh the first Oleh reads three verses from "Tzav Es Benei Yisrael..." The second repeats the third verse and reads two more, leaving three verses in the Parashah. The third reads those three verse and Parashas "Uva'Yom ha'Shabbos". The fourth reads "Uv'Roshei Chodsheichem".
Poskim
Shulchan Aruch (OC 423:2): The Kohen reads "Va'Ydaber...", "Tzav..." and "V'Omarta..."; the Levi repeats "V'Omarta..." and adds the next two verses. The Yisrael continues until (but not including) "Uv'Roshei Chodsheichem", and the fourth reads "Uv'Roshei Chodsheichem" until the end.
Shibolei ha'Leket (brought in Beis Yosef DH Kasuv): If the Levi would read three new verses and the Yisrael would repeat a verse, there would be concern for people who leave. It is better (like the Shulchan Aruch says) that the Levi repeat, for now the concern is only for people who enter, and they can ask what happened before.
Rebuttal (Taz 1): The Tana in the Beraisa who is not concerned for people who enter said this (people who enter ask what happened before). The Halachah follows the Tana who is concerned, and he does not distinguish!
Bach (DH uv'Kri'as): It is best that the third Oleh leave Parashas "Uva'Yom ha'Shabbos" for the fourth Oleh. If he reads it, people who enter afterwards may suspect that he read only those two verses.
Note: The Bach is not concerned lest people who leave after the third suspect that the fourth will read only those two verses. Surely, they know that there is only more Aliyah, and surely he will read also "Uv'Roshei Chodsheichem" which is the primary Kri'ah for Rosh Chodesh!
Taz (1): Since Chachamim enacted to repeat a verse on every Rosh Chodesh, the matter becomes known and we need not be concerned lest people think that the first read only two verses. Really, the last Oleh should be the one who repeats a verse, for the first ones are not forced to. However, then it would not look like an enactment. Rather, it would appear that whenever one cannot read three verses he repeats the last verse read. Therefore, if someone mistakenly left less than three verses in a Parashah, the next Oleh should not repeat the last verse, lest people think that this is l'Chatchilah. (However, if the next Oleh is the last he must do so, or else his Berachos will be l'Vatalah.) Also, the primary enactment is that one should not end improperly (less than three verse into a Parashah), for he causes people who enter to think that he did improperly. One who begins with the second or third verse of a Parashah does not bring suspicion on himself. It is clear that he was forced to do so!
Bi'ur Halachah (DH v;Levi): The Gra holds (like the Ramban suggested) that the second Oleh should finish the Parashah, and the third repeats the last three verses of that Parashah and adds "Uva'Yom ha'Shabbos". This was based on his text of Maseches Sofrim. It is best to follow the custom, like the Ramban's conclusion.