Kommentar zu Zevachim 8:10

הניתנין במתנה אחת – In the Gemara (Tractate Zevakhim 81a) as for example, cup of the blood of a firstling that was mixed in a cup of the blood of a tithe.

[If blood] which requires one application [was mixed] with blood [also] requiring one application, it [the mixture] should be presented with one application.
[If blood] which requires four applications [was mixed] with blood requiring four applications, they should be presented with four applications.
[If blood] which requires four applications [was mixed] with blood which requires one application: Rabbi Eliezer says: it [the mixture] should be presented with four applications. Rabbi Joshua says: it should be presented with one application.
Rabbi Eliezer said to him: Behold, he transgresses the [injunction] not to diminish [from God’s commandment]! Rabbi Joshua said to him: Behold, he transgresses the injunction not to add [to God’s commandments].
Rabbi Eliezer said to him: The injunction not to add applies only where it is by itself. Rabbi Joshua said to him: The injunction not to diminish applies only where it is by itself.
Moreover, Rabbi Joshua said: when you make [four] applications you transgress the injunction not to add, and perform an action with your own hands; whereas when you do not make [four] applications you transgress the injunction not to diminish, but do not perform an action with your own hands.
The first-born animal, the tithe and the pesah require only one blood application on the outer altar. Some other sacrifices require two applications that are actually four because they are applied on two corners. The hatat requires four distinct blood applications. Our mishnah deals with a case where blood from animals requiring different numbers of blood applications are mixed up with each other.
Note that unlike the previous cases where the mixture had invalid blood in it, in this case the mixture consists of only valid blood. The problem is not in the blood itself, but what exactly to do with it.
Sections one and two: If blood from animals requiring the same number of applications is mixed up then they can simply make that number of applications with the blood. These two sections are quite obvious and probably serve as an introduction to the more interesting case which arises in the next section.
Section three: Here blood requiring two different numbers of applications is mixed up. Rabbi Eliezer holds that in such a situation, they should apply the maximum number of applications, in this case four, whereas Rabbi Joshua holds that they should apply the minimum number of applications, one.
Section four: Let the battle begin! Rabbi Eliezer says that if they make only one application, they will be transgressing the biblical prohibition against diminishing from God’s commandments. Rabbi Joshua quickly responds that Rabbi Eliezer’s suggestion is also problematic, for by making four blood applications, he will be adding to God’s commandments, and this is also prohibited (see Deuteronomy 4:2).
Section five: Rabbi Eliezer explains that the prohibition against adding to God’s commandments only applies when the blood is alone, meaning it is not mixed in with blood that requires four applications. If someone were to take blood that requires one application and apply it four times, that would be a transgression. But in our case since some of the blood does require four applications, there is no transgression.
Of course, Rabbi Joshua responds accordingly that the same can be said with regard to the prohibition against diminishing from God’s commandments it would only apply if there was only blood requiring four applications and he applied it only once. Since some of the blood requires one application, there is no transgression.
This argument seems to be going nowhere!
Section six: So now we’re all tied up in the bottom of the ninth. Rabbi Eliezer had his arguments and Rabbi Joshua responded to each of them. The winning blow (to mix my metaphor) is delivered by Rabbi Joshua who says that in this situation it is preferable to transgress by omission rather than commission. It is preferable to make only one blood application and thereby omit the other three, than to make four applications, thereby adding on three to the blood which only required one.
Interesting, this becomes a halakhic rule in other situations. Generally, if there is a conflict of mitzvoth or a situation of such nature, it is better to not perform anything, than to potentially actively transgress a commandment. As I stated in my introduction, many rules that originally appear in Seder Kodashim, are adopted to other areas of halakhah. Temple law, while not in practice by the time of the Mishnah, remained a rich source of halakhah.

ינתנו מתנה אחת – from each cup individual cup he gives one gift [of sprinkling] from this cup and another gift [of sprinkling] from that cup.

מתן ארבע במתן ארבע – as, for example, the blood of a burnt-offering with the blood of a peace-offering or the blood of a guilt-offering, for both of them require two gifts which are four and both of them are [sprinkled] below [the red line].

מתן ארבע במתן אחד = as, for example, the [blood of] a burnt-offering with [the blood of] a firstling that both of them are [sprinkled] below [the red line].

רא"א ינתנו במתן ארבע – and I see the extra gifts that are sprinkled from the blood of the firstling as if they are water, and this is not [a violation of] “do not add” (i.e., Deuteronomy 13:1: “[Be careful to observe only that which I enjoin upon you:] neither add to it [nor take away from it.”].

במתנה אחת so that he will not transgress on “do not add” (see above, Deuteronomy 13:1), but regarding the burnt-offering, he has fulfilled it, for all that are given/sprinkled on the outer altar when they are given/sprinkled in one gift, atones.

ולא עשית מעשה בידך – and it is not similar to someone doing an action, to sitting and not doing and the prohibition comes of its own accord. And the Halakha is according to Rabbi Yehoshua.