TANA'IM THAT AGREE WITH R. YISHMAEL
Rejection #1: (They need not agree with each other.) R. Yishmael minimizes exertion when this does not entail disgrace of Kodshim. Perhaps regarding Pesach he permits like Chachamim, in order to avoid disgrace to Kodshim (that a Korban be left half-flayed, like a Neveilah, until evening!)
Rejection #2: R. Yishmael ben R. Yochanan forbids exertion not needed for the sake of the Avodah. (After flaying until the chest, the Eimurim can be removed.) Perhaps regarding the Omer he permits like Chachamim, for the sake of the Avodah! (It is better to use five Sa'im.)
Retraction (Rabah): Rather, R. Yishmael and R. Chanina Segan ha'Kohanim agree with each other;
(Mishnah - R. Chanina): On Shabbos, one person reaps it using one sickle and one box. On a weekday, three people reap it, with three sickles and three boxes;
Chachamim say, whether or not it is Shabbos, they (three people) reap it with three sickles and three boxes.
R. Chanina forbids unnecessary exertion on Shabbos. Presumably, he forbids also unnecessary reaping on Shabbos!
Rejection #1: Normally, R. Yishmael minimizes extra exertion. However, Chachamim want to publicize that the reaping is on the 16th (Rashi; R. Gershom - that the reaping is Docheh Shabbos). Perhaps he agrees three people reap it on Shabbos.
Rejection #2: R. Chanina minimizes the number of people reaping, for the Avodah is done just as well. Perhaps he agrees that we reap the same quantity on Shabbos as a weekday, for this is a need of (optimal) Avodah.
(Rav Ashi): R. Yishmael and R. Yosi agree with each other:
(Mishnah): If the new moon was seen on Shabbos, whether or not it was clearly seen by everyone, witnesses desecrate Shabbos in any way necessary (Rashi - in order to come to Yerushalayim to testify; R. Gershom - messengers may desecrate Shabbos to inform distant places that the 30th day was made Rosh Chodesh);
R. Yosi says, if it was clearly seen by everyone, they may not desecrate Shabbos (presumably, Beis Din (Rashi; R. Gershom - everyone) saw it.)
R. Yosi holds that since it is possible (that there is no need), we do not desecrate Shabbos. Likewise, since it is possible to reap only three Sa'im, we do not reap more.
Rejection #1: R. Yishmael minimizes extra exertion when this will not cause people to sin. Regarding Rosh Chodesh, if they do not desecrate Shabbos when it was seen clearly, perhaps they will not desecrate it when (there is a need to, i.e.) it is not seen clearly;
Rejection #2: R. Yosi does not allow desecration of Shabbos due to concern for the future, since there is no need for today's Avodah that is Docheh Shabbos. Perhaps he agrees that when the Avodah is Docheh Shabbos (e.g. reaping the Omer), we do not limit the exertion!
DOING MORE THAN IS PERMITTED ON SHABBOS
(Rabah or R. Ami): If one slaughtered two Chata'os of the Tzibur (on a Shabbos when exactly one is needed, e.g. Rosh Chodesh. He thought that this is permitted), he is liable for the second, he is exempt for the first;
This is true even if (the first was Nifsal and) the Tzibur fulfilled its obligation with the second, or if the first was lean (and the second was fat).
Contradiction: Rabah does not obligate in this case!
(Rabah): If one had two animals available for a Chatas Tzibur (on Shabbos), one lean and one fat:
If he slaughtered the fat one and then the lean one, he is liable;
If he slaughtered the lean one and then the fat one, he is exempt. Further, if he already slaughtered the lean one, l'Chatchilah he should slaughter the fat one (and offer it!)
Answer #1: We must delete (from a:1) the clause 'or if the first was lean.'
Answer #2: We must say that R. Ami taught this, not Rabah.
Question (Ravina): If (after slaughtering the second,) the first was found to be lean in the intestines (R. Gershom - there is no Chelev to offer), what is the law?
If it depends on intent, he is liable. (Since he did not know that the first is lean, he had no permission to slaughter);
If it depends on the action done, he is exempt (since it was a Mitzvah to slaughter the second.)
Version #1 - Answer (Rav Ashi): Rabah and Rava agree that in such a case he is liable!
If (on Shabbos) Reuven heard that a child was drowning in the sea and he set a trap to catch fish and fish were trapped, he is liable;
(Rabah): If the child was saved in the trap and fish were trapped, he is exempt;
(Rava): He is liable.
Rabah assumes that since he heard that a child was drowning, surely he also intended to save the child;
Had he not heard, all agree that he is liable.
Version #2 - Answer (Rav Ashi): Rabah and Rava argue about your question:
If Reuven heard that a child was drowning and he set a trap to catch fish and fish were trapped, he is liable;
(Rabah): If the child was saved and fish were trapped, he is exempt;
(Rava): He is liable.
Rabah exempts, for he says that it depends on the action done. (He saved the child. This is a Mitzvah);
Rava is Mechayev. He says that it depends on intent.
(Rabah): If (on Shabbos) doctors said that a fig is needed to save Shimon's life and 10 people ran and each brought one at the same time, all are exempt (for all the Melachos they had to do);
All are exempt even if they came one after the other, and even if Shimon recovered before they picked the figs.
Question (Rava): If doctors said that two figs are needed to save Shimon's life and one finds two isolated figs on a tree, and one branch with three figs, which should he bring?
Perhaps he should take the two, for he only takes what is necessary;
Perhaps he should take the branch with three, for this minimizes reaping. (One act suffices!)
Answer: Surely, he should take the branch;
R. Shimon forbids reaping a larger quantity only when it entails more acts of reaping. Here, reaping a larger quantity entails less acts. Surely this is better!
FROM WHERE WE BRING THE OMER
(Mishnah): L'Chatchilah, the Omer must be brought from a place close (to Yerushalayim);
If no barley near Yerushalayim is ripe, it may be brought from anywhere (in Eretz Yisrael);
It once occurred that the Omer was brought from (a place called) Gagos Tzerifin, and Shtei ha'Lechem were brought from Ein Socher.
(Gemara) Question: Why must it be brought from a close place?
Answer #1 The Omer must be Karmel (soft. If it were brought from afar, it could dry up);
Answer #2: We do not pass over Mitzvos. (Once we find a suitable place, we do the Mitzvah immediately.)
(Mishnah): It once occurred that the Omer was brought from Gagos Tzerifin...
(Beraisa): When the Chashmonai kings were fighting each other, Hurkanus was inside Yerushalayim, and Aristobelus was besieging it from outside. Every day, they would lower a basket of coins from the wall, and the besiegers would give them lambs Kosher for the daily Korban, which they would lift over the wall.
An old man told the besiegers, in the language of Chachmas Yevanis, that they will not conquer it as long as they are bringing the Korbanos. The next day, the besiegers gave a pig instead of lambs. When the pig was halfway up, it stuck its claws into the wall; Eretz Yisrael shook 400 Parsah.
Chachamim imposed a curse on anyone who will raise pigs or teach his son Chachmas Yevanis.
Regarding that period we learned that the Omer was brought from barley from Gagos Tzrifin and Shtei ha'Lechem were brought from wheat of Ein Socher.
When it was time to bring the Omer, they did not know where to get it. They announced that anyone who knows should tell.
A mute man came and put one hand on the Gag (roof) and the other on a Tzerif (hut).
Mordechai: Is there a place called Gagos Tzerifin or Tzerifin Gagos? (Rashi - this is the Mordechai who defeated Haman. Tosfos - that Mordechai died long before this. The appointee over the box with money for Kinim (a Ken is two birds for Korbanos) was called 'Mordechai'.)
They found that there was such a place.
The same occurred when it was time to bring Shtei ha'Lechem. The mute came and put one hand on his eye and the other on the Sichra (the hole for the door bolt).
Mordechai: Is there a place called Ein Socher or Socher Ayin?
They found that there was such a place.
Three women came. Each had a Ken to offer. One said 'this is for Zivasi', one said 'for Yamasi', and one said 'For Onasi', People assumed that each Ken was (Chovah,) one Chatas and one Olah. (Rashi - each was for Zivah. Yamasi means 'my Yam (sea of blood).' Onasi means 'my time (to bring a Korban, after seven consecutive days without blood).
Mordechai: Perhaps each Ken is Nedavah (two Olos), in appreciation of salvation from Zivasi (heavy bleeding), Yamasi (danger at sea) and Onasi (a dangerous eye illness).
They asked the women. It was exactly like Mordechai said.