RAV DIMI, WHILE IN ERETZ YISRAEL
Rav Nachman bar Yitzchak gives an answer, but it is immediately rejected.
Answer: It is true that R. Akiva derived this from this verse, but R. Yishmael interpets the verse entirely different (he says it is taking about Shabbos, not Shemitah). According to R. Yishmael, then, the additional periods are Halachah l'Moshe mi'Sinai. R. Asi's statement was in accordance with R. Yishmael's view.
R. Yochanan disagrees with the above, and says that Raban Gamliel abolished the entire additional period, all the way down to Rosh Ha'Shanah. This is because he (R. Gamliel) derived from a Gezeirah Shavah that there is no such thing as an additional period to Shemitah.
Question: How can a Gezeirah Shavah uproot an explicit Halachah l'Moshe mi'Sinai?
Answer: R. Ashi revises R. Yochanan's statement: The reason R. Gamliel abolished the entire additional period down to Rosh ha'Shanah is that he held like R. Yishmael, that the additional period is a Halachah l'Moshe mi'Sinai, and he also held that this Halachah l'Moshe mi'Sinai was explicitly limited to Temple times, and is inoperative nowadays.
WHY IS COLLECTED RAIN WATER FORBIDDEN?
Question: The Mishnah prohibits watering from collected rain water and from a Kilon (a deep well requiring much exertion). Why is collected rain water forbidden?
Answer (R. Ila'a): It is a Gezeirah - if we allow rainwater, people will also use a Kilon.
Answer (R. Ashi): Rainwater itself is often as much exertion as a Kilon - when its surface level begins to go down.
[The following (until (e)) is based on Rashi MS, Kupfer, Mekitzei Nirdamim 5721.] The Gemara says that these two Amora'im would disagree about R. Zeira's ruling: Rivulets that flow from pools of water (and never become depleted) are permitted on Chol ha'Mo'ed; we do not make a Gezeirah that people will use a Kilon. R' Ila'a would disagree with this ruling; R. Ashi would agree (because the water in these rivulets can never end up being a cause of exertion).
In regard to R. Zeira's ruling, R. Yirmeyah asks, Isn't this against the Mishnah, which forbids "Rainwater," seemingly including these rivulets that are rainwater?
Answer: The reason for the Mishnah's general prohibition of rainwater is that this rainwater could run dry, requiring exertion to draw further water (as R. Ashi said above, 9b). R. Zeira, however, was referring to the rivulets of Bavel, which never run dry, and this concern therefore does not apply to them.
WATERING A FIELD FROM A POOL OF WATER (1)
Beraisa: One may not water a field from pools that are full of water (because they might dry up). But if there is a channel that runs between them, it is permitted (because then he can always use the channel water if the pools dry out).
(R. Papa): This is only true if there is enough water in the channel to water most of the field. If not, he might run out of water in the middle and exert himself to bring more water from a distant place.
(R. Ashi): Even if there is not enough water in the channel to water most of the field it is alright. This is because the water in the channel comes and goes, and if there is no water one day, there will be in another day or two, so he will not go fetching faraway water now.
WATERING A FIELD FROM A POOL OF WATER (2)
(Beraisa): A pool that gets water from the drippings of a Beis ha'Shalchin further uphill can be used to water a lower Beis ha'Shalchin.
Question: Might not the pool run out of water (leading to exertion to find other sources of water)?
Answer: The Beraisa permits it only while the dripping continues; in this case the pool will certainly not run out of water.
(Abaye): The Beraisa applies only when the spring which supplies the upper Beis ha'Shalchin is still flowing.
MOVING WATER FROM ONE PATCH TO ANOTHER
(R. Shimon ben Menasya): One should not take water from a lower patch and carry it up to a higher patch.
(R. Elazar bar Shimon): This applies even to a single two-leveled patch - one should not take water from the lower to the upper part.
(Beraisa): One may do "Madlin" to his vegetables to enable their eating on Chol ha'Mo'ed (even though it involves exertion, it is permitted because it is an immediate need for the holiday - Ritva), but not to make them grow better (for after Chol ha'Mo'ed - Ritva).
Rava Tosfa'a thought "Madlin" means pruning branches, but watering is never permitted except for Beis ha'Shalchin and without exertion.
Ravina corrected him: "Madlin" means drawing water.
THE MISHNAH FORBADE MAKING UGIYOS UNDER VINES
"Ugiyos" refers to what is called Bankei in Aramaic, and Bedidin in a Beraisa - namely, digging circles in the ground around the bases of vines (to hold water).
Question: Rav Yehudah permitted people to make these Bankei in their vineyards on Chol ha'Mo'ed
Answer: The Mishnah only forbids making new Ugiyos; repairing old ones is permitted, and this is what R. Yehudah did.
R. ELAZAR BEN AZARYAH FORBADE DIGGING A WATER CHANNEL ON CHOL HA'MO'ED AND ON SHEMITAH (SEE ABOVE 1:A:4)
Question: We understand Chol ha'Mo'ed, because it involves exertion. But what could possibly be wrong with digging a channel on Shemitah? Two Amora'im suggest two approaches:
Approach #1: It appears to others that he is hoeing his land for agricultural purposes.
Approach #2: It appears to others that he is preparing the banks of the channel for planting crops.
What is the Nafka Minah between the two approaches?
In a case where water runs into the channel immediately as it is being dug. This does not appear like hoeing, but it still looks like he is preparing the banks for planting.
This Nafka Minah is rejected, because in fact both Amora'im agree to Approach #2; the argument is over whether there ALSO exists Approach #1. The real Nafka Minah is in a case where he takes the dirt being dug and throws it far away, not on the banks. This does not look like preparation of the banks for planting, but it can look like hoeing.
Ameimar held Approach #1 and asked this question accordingly: R. Elazar ben Azaryah says one may not pile up manure for storage in his field on Shemitah (it looks like he's fertilizing his field), unless he puts it on a rock 3 Tefachim high - or digs a 3-Tefach hole. We see that he was not concerned that digging (for non-agricultural purposes) might appear to others to be hoeing.
Answer: R. Elazar ben Azaryah didn't mean that he should dig a hole during Shemitah, but that if he had a hole already dug he could use it for manure.
THE MISHNAH PERMITTED REPAIRING AN EXISTING CHANNEL ON CHOL HA'MO'ED IF IT GOT CLOGGED
What is the definition of "fixing a clog"? If it was originally 6 Tefachim deep and is clogged until it is only 1 Tefach deep (i.e., 5 Tefachim need to be cleared).
Given: A 3 Tefach channel clogged until it is 1/2 Tefach can't be cleared (because it is essentially useless anyway). A 12-Tefach channel clogged until it is 2 Tefachim can't be cleared (because 10 Tefachim is too much exertion to clear).
Question: What about a 7-Tefach channel that is clogged until it is 2 Tefachim? Is it permitted because it too involves a 5-Tefach clearing, or is it forbidden because he has to bend down an extra Tefach to clean it out, and this is too much exertion? No decision is reached (Teiku).
Abaye permitted removal of tree branches growing in the river.
R. Yirmeyah permitted to clear out the blocked source of the river.
R. Ashi permitted clearing out silt from the river, because this is a public need, which is permitted in the Mishnah (above, 1b).