Why does the Torah not mention Shemini Atzeres?
Oznayim la'Torah #1 (according to Rashi in Pesachim, 71): Because the main objective of the Parshah is the Mitzvah of Simchah and the accompanying Korbanos, which are not applicable of Shemini Atzeres. 1
Oznayim la'Torah #2: The Torah does not mention it because Shemini Atzeres is considered part of Sukos in all regards other than 'Pezer Keshev'.
See Oznayim la'Torah, citing Tosfos there and Rashi himself in Sukah, 48, who maintains that the Mitzvah of Simchah extends to Shemini Atzeres.
What are the implications of "Chag ha'Sukos Ta'aseh l'cha"?
Sukah, 11b: It implies "Ta'aseh", 've'Lo min ha'Asuy' - that one must make the Sukah, and not use what is already made. Consequently, one cannot cover the Sukah with an attached vine or pumpkin and then cut it and places S'chach on top of it. 1 (and by the same token, Beis Hillel rule that, if one's Sukah is covered with planks, one is obligated to loosten rhem or to remove every second plank - Sukah, 15a) in order to avoid 'Ta'aseh, ve'Lo min ha'Asuy'.
See Torah Temimah, note 50.
Why does the Torah add the word "Ta'aseh l'cha"?
Sukah, 27b: To disqualify a Sukah that is stolen. 1
But not a borrowed one, since the Torah wrote in Emor, 23:42 "Kol ha'Ezrach be'Yisrael Yeishvu ba'Sukos - See Torah Temimah, note 52, who elaborates..
What are the implications of "Chag ha'Sukos Ta'aseh l'cha Shiv'as Yamim"?
Sukah, 23a: It implies that a Sukah that cannot last all seven days or that one cannot enter for all seven days of Sukos - is Pasul. 1
Sukah, 27b: It implies a. that one is permitted to move from one Sukah to another on Sukos and b. that one may make a Sukah on Chol ha'Mo'ed Sukos. 2
What is the significance of "be'Osp'cha mi'Gorn'cha u'mi'Yilkvecha."?
Rashi #1 and Targum Yonasan: It comes to teach us that Sukos coincides with (the end of - Targum Yonasan) the ingathering of the summer fruits from the field to the house.
Rashi #2: It teaches us that the S'chach may consist of the residue from the granary and of the wine and olive presses.
Rashbam: Refer to Vayikra, 23:43:2:2**.
Sukos, 12a: It teaches us that a Sukah - with reference to the S'chach - must be made of materials that , like the waste of the granary, and the wine and the oil-presses, are not subject to Tum'ah and that grow from the ground. 1
See Torah Temimah, note 55.
What are the implications of the 'Mem' in "mi'Gorn'cha" and in 'mi'Yikvecha."
Sukah, 12a: It precludes the corn and the grapes and olives themselves - which are subject to Tum'ah.
Why does the Torah give the seasons - 'Aviv', 'Katzir' and 'Asif' in which the Yamim Tovim fall - instead of the dates'?
Oznayim la'Torah: There are three reasons for this: 1. To teach us that the paths of Torah and the paths of Torah are one and the same; 1 2. So that, when we arrange that Pesach coincides with the spring, Shavu'os with the harvest and Sukos, with the ingathering of the produce from the fields, the Simchah on Yom-Tov will merge with the natural joy that one experiences at that time; 2 3. Because Pesach coreponds to the 'spring' of our history - when we left Egypt ... in order to receive the Torah on Shavu'os - the 'harvest'; whereas Sukos corresponds to the ingathering of the exiles in the days of Mashi'ach. 3 Consequently, when the Yamim Tovim fall in the correct times, it reminds us of Mashi'ach and keeps our faith in his coming alive.
