Gemara

Question: What is the source that we add from Chol onto Kodesh?

Answer #1 (Beraisa #1 - R. Akiva) Question: Why does it say "Be'Charish uva'Katzir Tishbos"? "Sadcha Lo Sizra..." already forbids plowing!

Answer: This forbids plowing in Erev Shemitah for the sake of Shemitah, and to give Kedushas Shemitah to produce which grew a third in Shemitah and was reaped in Motza'ei Shemitah.

R. Yishmael says, the verse equates plowing and reaping (that is forbidden on Shabbos). Just like plowing is Reshus, also reaping. We exclude reaping the Omer, which is a Mitzvah, so it is permitted on Shabbos.

Question: What is R. Yishmael's source that we add from Chol onto Kodesh?

Answer - Beraisa #2 - Suggestion: "V'Inisem Es Nafshoseichem b'Sishah" - perhaps we fast on the ninth!

Rejection: "Ba'Erev".

Suggestion: Perhaps "Ba'Erev" teaches that we need not begin to fast until night!

Rejection: "B'Sishah".

Resolution: We begin to fast before night; this is the source that one must add from Chol onto Kodesh.

Question: This teaches that we add at the beginning of the day. What is the source to add from Chol onto Kodesh at the end?

Answer: "Me'Erev Ad Erev".

Question: This is the source for Yom Kipur - what is the source for Shabbos?

Answer: "Tishbesu".

Question: This is the source for Shabbos - what is the source for other Yomim Tovim?

Answer: "Shabbatchem" - regarding any Shevus (Isur Melachah) we add from Chol to Kodesh.

Question: R. Akiva learns Tosefes (Shabbos, Yom Tov and Yom Kipur) from Shemitah. How does he expound "b'Sishah"?

Answer: This teaches that if one eats and drinks on the ninth, the Torah considers it as if he fasted on the ninth and 10th.

Yoma 81a - Beraisa #3 - Suggestion: "V'Inisem Es Nafshoseichem...; V'Chol Melachah Lo Sa'asu" - perhaps one is liable for Melachah or eating during Tosefes Yom Kipur!

Rejection: "B'Etzem ha'Yom ha'Zeh v''Ha'avadti Es ha'Nefesh ha'Hi", "B'Etzem ha'Yom ha'Zeh v'Nichresah" - there is Kares only for the day itself, not for Tosefes.

Suggestion: Perhaps a Lav forbids Melachah or eating during Tosefes Yom Kipur!

Rejection: "V'Chol Melachah Lo Sa'asu b'Etzem ha'Yom ha'Zeh" - a Lav forbids Melachah only during the day itself. All the more so Inuy, which does not apply to Shabbos or other Yomim Tovim, is only on the day itself!

81b - Question: This Tana learns Tosefes Yom Kipur from "B'Etzem ha'Yom ha'Zeh" (since we need a verse to exempt the Tosefes from Kares, surely it is forbidden). How does he expound "b'Sishah"?

Answer: This teaches that if one eats and drinks on the ninth, the Torah considers it as if he fasted on the ninth and 10th.

Pesachim 54b - Question - Beraisa: The only difference between Tish'ah b'Av and Yom Kipur is that Safek Yom Kipur is forbidden, but Safek Tish'ah b'Av is permitted.

Suggestion: The Safek discussed is Bein ha'Shemashos!

Answer (Rav Shisha brei d'Rav Idi): No, the Safek is which day was fixed to be Rosh Chodesh.

Sukah 28a - Beraisa: "Ha'Ezrach" obligates women in Tosefes Inuy.

Rishonim

The Rif and Rosh (Yoma 2b and 8:8) bring Beraisa #2 and Beraisa #3.

Rambam (Hilchos Shevisas Asor 1:6): One must add from Chol onto Kodesh at the beginning and end of the day - "V'Inisem Es Nafshoseichem b'Sishah la'Chodesh ba'Erev". I.e., one must begin to fast in the evening of the ninth, shortly before the 10th. Similarly, at the end of the day one must continue fasting a bit into the 11th - "Me'Erev Ad Erev Tishbesu Shabatchem".

Magid Mishnah: The Rambam holds that Tosefes is mid'Oraisa only regarding Inuy, but not regarding Melachah, not on Yom Kipur or Shabbos or Yom Tov.

Beis Yosef (OC 261 DH u'Mah she'Chasav u'Zmano): Since the Rambam does not discuss Tosefes regarding Melachah, he must hold that there is no Tosefes even mid'Rabanan.

Support (for Rambam - Rashash Sukah 28a DH Gemara): Sukah 28 expounds "...Te'anu Es Nafshoseichem v'Chol Melachah Lo Sa'asu ha'Ezrach..." to obligate women in Tosefes Inuy. If Tosefes Melachah is mid'Oraisa, why does the Gemara discuss only Tosefes Inuy? The verse also discusses Melachah, and Melachah is closer to "ha'Ezrach" than Inuy!

Rejection (Aruch l'Ner Sukah 28 DH Ela): Tana'im argue about whether or not there is Tosefes Melachah. The Gemara discusses Tosefes Inuy because all agree that it is mid'Oraisa. The Lechem Mishneh (DH v'Tzarich) says that R. Akiva holds that there is no Tosefes mid'Oraisa, even regarding Inuy; the Sha'ar ha'Melech asks, if so the Gemara should have asked how he expounds "ha'Ezrach".

Question: Yoma 81b and Beitzah 30a connote that all agree that Tosefes Inuy is mid'Oraisa, i.e. even what is Vadai Erev Yom Kipur or Motza'ei Yom Kipur. Why does Pesachim 54b suggest that a Beraisa forbids Safek Yom Kipur, i.e. Bein ha'Shemashos? Also Shabbos 34b forbids lighting when it is Safek dark!

Answers (Tosfos DH v'R. Akiva): Perhaps the Gemara forbids Safek because any amount of Tosefes before and after suffices. In the Yerushalmi, R. Gamliel holds that mid'Oraisa there is no Tosefes. R. Akiva learns Tosefes Melachah from Tosefes Shemitah, and Mo'ed Katan (4a) says that Tosefes Shemitah is mid'Oraisa only when the Mikdash stands.

Poskim

Shulchan Aruch (OC 261:2): Some say that one must add from Chol onto Kodesh.

Beis Yosef (ibid.): It is not clear why the Tur does not require Tosefes Shabbos. The Rif and Rosh and all Meforshim other than the Rambam require it. The Tur does not hold like the Rambam, for the Tur requires Tosefes Isur Melachah regarding Yom Kipur.

Taz (608:1): The Tur learns from "B'Etzem ha'Yom ha'Zeh" that there is no Kares for Tosefes, but it is forbidden regarding Melachah and Inuy. However, this is only regarding Yom Kipur, but not for Shabbos and Yom Tov.

Gra (DH Yesh): The Yerushalmi learns from "Sheshes Yomim Ta'avod" that mid'Oraisa there is no Tosefes Melachah. This is also the conclusion in Mo'ed Katan (4a). Tosfos (Rosh Hashanah 9a DH v'R. Akiva) tried to say that there is no Shi'ur Tosefes to resolve Heterim in Shas to do Melachah until just before Shabbos; the Rosh proved that there is a Shi'ur. Tosfos concludes (like the Rambam) that Tosefes Melachah is not obligatory. Nevertheless, Tosefes is a Mitzvah.

Shulchan Aruch (ibid.): The Tosefes must be sometime between the beginning of Sheki'ah, when the sun goes below the horizon, until Bein ha'Shemashos, which begins three Mil and a quarter later.

Rebuttal (Gra DH she'Hu): Shabbos 35b says that Tzeis ha'Kochavim (night) is when three medium-size stars can be seen. Experience testifies that this is long before four Mil after sunset. Rather, Bein ha'Shemashos starts immediately after sundown. After three quarters of a Mil it is night (in Bavel in Nisan or Tishrei). In Pesachim (94a) the Gemara discusses 'Tzeis ha'Kochavim', i.e. when it is totally dark and even the weakest stars can be seen. This is four Mil after sundown.

Magen Avraham (9): The Yere'im, Mordechai and Agudah say that Bein ha'Shemashos ends at sundown, and then it is night. Important people refrain from Melachah two hours before (Tzeis ha'Kochavim).

Mishnah Berurah (23): The Shulchan Aruch holds like R. Tam. Many Rishonim hold like the Gra, that Bein ha'Shemashos starts at sundown. Happy is one who refrains from Melachah (or eating on Erev Yom Kipur) 30 or at least 20 minutes before sundown. This fulfills all the opinions (including the Yere'im), even if the time to walk a Mil is 24 minutes, and it fulfills many opinions regarding Tosefes. One may not end Shabbos until three medium stars are visible. Three quarters of a Mil after sundown suffice for the latitude of Bavel in Nisan or Tishrei; in northern areas one must wait much longer.

Shulchan Aruch (ibid.): One may make Tosefes the entire time between sundown and Bein ha'Shemashos, or just part of this time, as long as he adds to Kodesh some time which is definitely Chol.

Bi'ur Halachah (DH Eizeh): Some say that there is a Shi'ur Tosefes. In any case, it is not more than three quarters of a Mil.