Why does the Torah write "ba'Yom ha'Shemini", without a prefix 'Vav'?
Succah, 47b: To teach us that Shemini Atzeres is an independent Yom-Tov 1 and requires the recital of 'Shehecheyanu'. 2
Succah (Ibid.): As opposed to the seventh day of Pesach, which is also called 'Atzeres', but by which the Torah wrote - in 28:25 "u'va'Yom ha'Shevi'i".
Other Amora'im learn it from the fact that whereaas in connection with the seventh day of Pesach they also brought the same number of bulls as on the other days of Pesach, here, they brought only one bull; and others again, from the fact that the Torah changes here - in Pasuk 37 - from ke'Mishpatam" - in Pasuk 33 - to "ka'Mishpat". See Torah Temimah, notes 24-26.
What are the connotations of the word "Atzeres"?
Refer to Vayikra, 23:36:1:1-5.
Rashi #2 (citing the Sifri): It means 'Stay behind!' Refrain from leaving Yerushalayim, implying the Mitzvah of 'Linah'. 1
Rashi #2 (citing Succah, 55b): Throughout the seven days of Yom-Tov, Yisrael bring Korbanos on behalf of the nations of the world. Therefore when the time comes to take their leave, Hashem says to them ''Prepare for Me a small Se'udah, so that I should benefit from you!' 2
Targum Yonasan: 'On the eighth day you shall gather joyfully from the Succah into your houses ? a joyful gathering, a Yom-Tov and a holy convocation'.
Chagigah, 9a: We learn via a Gezeirah Shavah "Atzeres" "Atzeres" from the seventh day of Pesach 3 that someone who did not bring his Chagigah beforehand, may bring it on Shemini Atzeres - even though it is not an intrinsic part of Succos. 4
Staying overnight in Yerushalayim.
Refer to Vayikra, 23:36:1.1:1.
See Torah Temimah, note 7.
See Torah Temimah, note 8.
Why here, does the Torah write "Atzeres Tih'yeh lachem", and in Re'eh Devarim, 16:8, "Atzeres la'Hashem"?
Pesachim 68a #1 (according to R. Eliezer): To teach us that it must all be either for Hashem (learning Torah and Tefilah), or all for you (eating and drinking).
Pesachim 68a #2 (according to R. Yehoshua): To teach us to divide it - half la'Hashem, and half 'lachem.
Kol Eliyahu: If one takes half the Gematriya of la'Hashem - 28), and half the Gematriya of lachem - 45, They add up to 73, the Gematriya of Yom Tov.
Maharsha (on Pesachim, 68a): The Pasuk there is discussing the last day of Pesach, the current Pasuk, Shemini Atzeres. 1
Surely we do not distinguish between these Yamim Tovim?
