On Ta'anis 27b, the gemara discusses the Torah reading for the people of the ma'amad who would read daily from Ma'aseh Bereishis during their turn as anshei ma'amad. Within this discussion, the gemara indicates that the Torah portion would be broken up into three parts - one each for the Kohanim, Levi'im and Yisraelim.
The gemara asks - but what about the first day of creation? The Torah portion cannot be broken into three as the first portion of the reading is fiver verses and there is a rule that there can never be less than three verses per aliyah. The gemara offers answers from Rav and Shmuel wherein they suggest that a verse from the first aliyah be repeated in the second portion or that the third pasuk be split in two.
In discussing Rav's proposal of using a pasuk from the first aliyah in the second reading, Tosafos (d'h Rav) observes that this is the system which we use for Rosh Chodesh, wherein we commence the second aliyah with a repetition of the last pasuk from the first aliyah. (This was my thought as well and I wondered why the gemara did not expressly address the question).
Tosafos asks - why do we repeat the verse? Couldn't we just start reading the first aliyah a little further back in the parsha? The question is quite timely as we will read Parshas Pinchas (where the reading for Rosh Chodesh is found) this coming Shabbos.
Tosafos reinforces the question by noting that on Shabbos Chol Hamoed, we being the reading from Parshas Ki Sissa by going back to Moshe's conversation with Hashem in 32:12 wherein he asks Hashem about His direction to take the Jews up. Tosafos opines that the reading related to Chol Hamoed should have started from the discussion of Moshe being told to form new tables which is found in pesukim starting at 33:1.
Toasfos answers by stating that the prior portion in Ki Sissa is connected with the reading for Chol HaMoed as it is the same story. However, the prior pesukim in Parshas Pinchas are unrelated to the Tamid and Rosh Chodesh, therefore there is no option but to start with the proper reading and repeat one verse.
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