Rambam - 1 Chapter a Day

I.e., because the elements of the produce that are sacred have been removed from it [the Rambam’s Commentary to the Mishnah (Demai 7:7)]. Terumat ma’aser should not be separated before the tithes themselves. Nevertheless, if one made such a separation, it is acceptable (Chapter 9, Halachah 5).

In this instance, the term tevel refers to produce from which the tithes and terumat ma’aser have not been separated. Although the term has a more inclusive meaning, from the continuation of the Rambam’s words, this appears to be the intent here.

I.e., were the tevel to be of another type of produce than the ordinary produce, the question of whether or not it is considered insignificant would depend on whether its flavor is detectable. In this situation, however, the two collections of produce are of the same species, so taste is not a factor and the tevel cannot be considered as insignificant.
When tevel is mixed with its own species, it is never nullified even if it is mixed with far more than its own size. The rationale is that it is a devar sheyeish lo matirin, i.e., the prohibition can be corrected by making the appropriate separations (Hilchot Issurei Ma’achalot 15:6).

I.e., if he knows how much produce was mixed in, he can make the appropriate separations even if the produce itself is not distinct.

I.e., one hundredth of the tevel. The Rambam explains what he means by forfeiting this amount and why one must do so in the following halachah.

I.e., it is considered as if the se’ah of terumat ma’aser fell into the ordinary produce in which instance, it would be necessary to remove one se’ah from the mixture [the Rambam’s Commentary to the Mishnah (Demai 7:7)].

I.e., three se’ah: two se’ah for the great terumah and one se’ah for the terumat ma’aser.

For the se’ah that will ultimately be separated from the tevel can be considered as the se’ah that must be removed from the ordinary produce (ibid.).

For the opposite is true, the produce that remains is the ordinary produce (ibid.).

I.e., produce that had been separated as the tithes. Beforehand, terumah had been separated.

I.e., a person separated tithes and gave them to a Levite who did not separate terumat ma'aser from them as of yet.

Setting aside one tenth of the quantity of the tithes. This is the desired approach, because then the necessary separations are being made without losing anything.

And thus cannot exercise the above option.

I.e., one tenth of the tithes.

In his Commentary to the Mishnah (op. cit.), the Rambam explains that this ruling is given because the situation at hand is an intermediate level between an instance where terumat ma’aser becomes mixed with ordinary produce (in which instance 101 times the amount of terumat ma’aser would be necessary) and a situation where the terumat ma’aser need not be considered at all. There is a basis for such leniency, since ultimately, no separation had been made and terumat ma’aser was never mixed with the produce. On the other hand, since a tenth of the tithes is fit to be separated as terumat ma’aser, some recognition should be made. Hence our Sages arrived at the above compromise.

I.e., 11100th of the tevel.

The se’ah of terumat ma’aser from the tevel that is added is considered as mixed in with the tithes (ordinary) produce and therefore betal, subsumed, in it. Hence the person can make use of the produce in the ordinary manner.

The Ra’avad differs with the Rambam. The commentaries justify the Rambam’s view.

And thus separate an additional amount.

A mixture of terumah and ordinary produce. An ordinary person cannot benefit from such a mixture. Instead, it must be sold to a priest at the price of terumah with the exception of the price of the portion that is terumat ma’aser, as the Rambam continues to explain. The tithes would be meduma, because there would not be enough ordinary produce for the terumat ma’aser to be subsumed within them.

Which are ordinary produce.

In this way, he is forfeiting from the tithes the amount of terumat ma’aser in the tithes and the amount of terumat ma’aser in the tevel. The Ra’avad differs with the Rambam and the commentaries support the Rambam’s decision.

The commentaries explain that we are not speaking about an instance where he actually set aside the barrel as tithes, for the Rambam concludes the halachah by saying that he should set aside the tithes. Instead, he merely pledged to separate a barrel from that surface for ten barrels of other wine.

I.e., one of the external surfaces of the cube that is the pile [the Rambam's Commentary to the Mishnah (Demai 7:8)].

The Rambam mentions this point, because otherwise, one could rightly ask: Why does the Mishnah (ibid.) speak about only one barrel of wine as tithes for 100 barrels (Radbaz)?

Our translation is taken from the Rambam’s Commentary to the Mishnah (ibid.). The intent is that each of the barrels on the comers is part of two outer rows. Since he is taking a barrel from opposite comers, he will have certainly taken a barrel from the outer row he intended. Nevertheless, since he does not know which one of the two is appropriate, he should ‘mix them together.

Preferably, he should also use the remaining amount as tithes for other produce. Thus the barrel separated will be used entirely as tithes (Kin ‘at Eliyahu).

These and the following bracketed additions are made on the basis of the Rambam’s Commentary to the Mishnah (loc. cit.).

Each of the barrels is part of two outer half rows, so that the barrel he intended to allocate is certainly among these four barrels.

By doing so, he will have taken a barrel from every row.

In a criss-cross as depicted in the accompanying diagram.