Beit Shammai say: With regard to all the offerings whose blood is to be placed on the external altar, even those that require that the blood be sprinkled on two opposite corners of the altar so that it will run down each of its four sides, in a case where the priest placed the blood on the altar with only one placement, he facilitated atonement. And in the case of a sin offering, which requires four placements, one on each of the four corners of the altar, at least two placements are necessary to facilitate atonement. And Beit Hillel say: Even with regard to a sin offering, in a case where the priest placed the blood with one placement, he facilitated atonement after the fact. Therefore, since the priest facilitates atonement with one placement in all cases other than a sin offering according to Beit Shammai, and even in the case of a sin offering according to Beit Hillel, if he placed the first placement in its proper manner, and the second with the intent to eat the offering beyond its designated time, he facilitated atonement. Since the second placement is not indispensable with regard to achieving atonement, improper intent while performing that rite does not invalidate the offering. And based on the same reasoning, if he placed the first placement with the intent to eat the offering beyond its designated time and he placed the second placement with the intent to eat the offering outside its designated area, the second of which does not render an offering piggul, the offering is piggul, an offering disqualified by improper intention, and one is liable to receive excision from the World-to-Come [karet] for its consumption. This is because the intent that accompanied the second placement does not supersede the piggul status of the offering.
בֵּית שַׁמַּאי אוֹמְרִים, כָּל הַנִּתָּנִין עַל מִזְבֵּחַ הַחִיצוֹן, שֶׁאִם נְתָנָן מַתָּנָה אַחַת, כִּפֵּר. וּבְחַטָּאת, שְׁתֵּי מַתָּנוֹת. וּבֵית הִלֵּל אוֹמְרִים, אַף חַטָּאת שֶׁנְּתָנָהּ מַתָּנָה אַחַת, כִּפֵּר. לְפִיכָךְ, אִם נָתַן אֶת הָרִאשׁוֹנָה כְתִקְנָהּ וְאֶת הַשְּׁנִיָּה חוּץ לִזְמַנָּהּ, כִּפֵּר. נָתַן אֶת הָרִאשׁוֹנָה חוּץ לִזְמַנָּהּ וְאֶת הַשְּׁנִיָּה חוּץ לִמְקוֹמָהּ, פִּגּוּל, וְחַיָּבִין עָלָיו כָּרֵת:
All this applies to those offerings whose blood is to be placed on the external altar. But with regard to all the offerings whose blood is to be placed on the inner altar, if the priest omitted even one of the placements, it is as though he did not facilitate atonement. Therefore, if he placed all the placements in their proper manner, and one placement in an improper manner, i.e., with the intent to eat the offering beyond its designated time, the offering is disqualified, as it is lacking one placement; but there is no liability for karet for one who partakes of the offering, as the improper intention related to only part of the blood that renders the offering permitted for consumption, and an offering becomes piggul only when the improper intention relates to the entire portion of the offering that renders it permitted for consumption.
And these are the items for which one is not liable to receive karet due to violation of the prohibition of piggul. One is liable to receive karet only if he partakes of an item that was permitted for consumption or for the altar by another item. As for the items listed here, either nothing else renders them permitted for consumption or for the altar, or they themselves render other items permitted. They are as follows: The handful of flour, which permits consumption of the meal offering; the incense, which is burned in its entirety, without another item rendering it permitted for the altar; the frankincense, which is burned together with the handful of the meal offering; the meal offering of priests, from which no handful of flour is removed and which is burned in its entirety (see Leviticus 6:16); the meal offering of the anointed priest, which is sacrificed by the High Priest each day, half in the morning and half in the evening; the blood, which permits all the offerings; and the libations that are brought by themselves as a separate offering and do not accompany an animal offering; this is the statement of Rabbi Meir. And the Rabbis say: The same halakha applies even with regard to libations that are brought with an animal offering. With regard to the log of oil that accompanies the guilt offering of a recovered leper, Rabbi Shimon says: One is not liable for consuming it due to violation of the prohibition of piggul, because it is not permitted by any other item. And Rabbi Meir says: One is liable for consuming it due to violation of the prohibition of piggul, as the blood of the guilt offering of the leper permits its use, as only after the blood’s sacrifice is the oil sprinkled and given to the priests. And the principle is: With regard to any item that has permitting factors, either for consumption by a person or for burning on the altar, one is liable for eating it due to violation of the prohibition of piggul.
אֵלּוּ דְבָרִים שֶׁאֵין חַיָּבִין עֲלֵיהֶם מִשּׁוּם פִּגּוּל. הַקֹּמֶץ, וְהַלְּבוֹנָה, וְהַקְּטֹרֶת, וּמִנְחַת כֹּהֲנִים, וּמִנְחַת כֹּהֵן מָשִׁיחַ, (וּמִנְחַת נְסָכִים), וְהַדָּם, וְהַנְּסָכִים הַבָּאִים בִּפְנֵי עַצְמָן, דִּבְרֵי רַבִּי מֵאִיר. וַחֲכָמִים אוֹמְרִים, אַף הַבָּאִים עִם הַבְּהֵמָה. לֹג שֶׁמֶן שֶׁל מְצֹרָע, רַבִּי שִׁמְעוֹן אוֹמֵר, אֵין חַיָּבִין עָלָיו מִשּׁוּם פִּגּוּל. וְרַבִּי מֵאִיר אוֹמֵר, חַיָּבִין עָלָיו מִשּׁוּם פִּגּוּל, שֶׁדַּם הָאָשָׁם מַתִּירוֹ. וְכֹל שֶׁיֶּשׁ לוֹ מַתִּירִים בֵּין לָאָדָם בֵּין לַמִּזְבֵּחַ, חַיָּבִין עָלָיו מִשּׁוּם פִּגּוּל:
The mishna elaborates: The burnt offering, its blood permits its flesh to be burned on the altar and its hide to be used by the priests. The bird burnt offering, its blood permits its flesh and its skin to be burned on the altar. The bird sin offering, its blood permits its meat for consumption by the priests. Bulls that are burned, e.g., the bull for an unwitting communal sin, and goats that are burned, e.g., the goats sacrificed for an unwitting communal sin of idol worship, their blood permits their sacrificial portions to be sacrificed on the altar. Rabbi Shimon says: Those bulls and goats are not subject to piggul because their blood is presented in the Sanctuary, and in the case of any offering whose blood is not presented on the external altar like that of a peace offering, with regard to which the halakha of piggul was stated in the Torah, one is not liable for eating it due to violation of the prohibition of piggul.
הָעוֹלָה, דָּמָהּ מַתִּיר אֶת בְּשָׂרָהּ לַמִּזְבֵּחַ וְעוֹרָהּ לַכֹּהֲנִים. עוֹלַת הָעוֹף, דָּמָהּ מַתִּיר אֶת בְּשָׂרָהּ לַמִּזְבֵּחַ. חַטַּאת הָעוֹף, דָּמָהּ מַתִּיר אֶת בְּשָׂרָהּ לַכֹּהֲנִים. פָּרִים הַנִּשְׂרָפִים וּשְׂעִירִים הַנִּשְׂרָפִים, דָּמָן מַתִּיר אֶת אֵמוּרֵיהֶן לִקָּרֵב. רַבִּי שִׁמְעוֹן אוֹמֵר, כֹּל שֶׁאֵינוֹ עַל מִזְבֵּחַ הַחִיצוֹן כִּשְׁלָמִים, אֵין חַיָּבִין עָלָיו מִשּׁוּם פִּגּוּל:
With regard to offerings consecrated by gentiles for sacrifice to God, one is not liable for eating them, neither due to violation of the prohibition of piggul if the sacrificial rites were performed with the intent to eat the offering beyond its designated time, nor due to violation of the prohibition of notar, nor due to violation of the prohibition against eating the meat while ritually impure. And one who slaughters them outside the Temple courtyard is exempt; this is the statement of Rabbi Shimon. And Rabbi Yosei deems him liable. Even with regard to those items enumerated in the previous mishna (42b) for which one is not liable for eating them due to violation of the prohibition of piggul, e.g., the handful, the frankincense, and the incense, one is, nevertheless, liable for eating them due to violation of the prohibition of notar, and due to violation of the prohibition against eating consecrated food while ritually impure, except for the blood. Rabbi Shimon deems one liable for an item whose typical manner is such that one eats it. But with regard to the wood, the frankincense, and the incense, one is not liable for eating them due to violation of the prohibition against eating a consecrated item while ritually impure.
קָדְשֵׁי נָכְרִים, אֵין חַיָּבִין עֲלֵיהֶם מִשּׁוּם פִּגּוּל, נוֹתָר וְטָמֵא. וְהַשּׁוֹחֲטָן בַּחוּץ, פָּטוּר, דִּבְרֵי רַבִּי מֵאִיר. רַבִּי יוֹסֵי מְחַיֵּב. דְּבָרִים שֶׁאֵין חַיָּבִין עֲלֵיהֶם מִשּׁוּם פִּגּוּל, חַיָּבִים עֲלֵיהֶם מִשּׁוּם נוֹתָר, מִשּׁוּם טָמֵא, חוּץ מִן הַדָּם. רַבִּי שִׁמְעוֹן אוֹמֵר, בְּדָבָר שֶׁדַּרְכָּן לְהֵאָכֵל. אֲבָל כְּגוֹן הָעֵצִים וְהַלְּבוֹנָה וְהַקְּטֹרֶת, אֵין חַיָּבִין עֲלֵיהֶם מִשּׁוּם טֻמְאָה:
The slaughtered offering is slaughtered for the sake of six matters, and one must have all of these matters in mind: For the sake of the particular type of offering being sacrificed; for the sake of the one who sacrifices the offering; for the sake of God; for the sake of consumption by the fires of the altar; for the sake of the aroma; for the sake of the pleasing of God, i.e., in fulfillment of God’s will; and, in the cases of a sin offering and a guilt offering, for the sake of atonement for the sin. Rabbi Yosei says: Even in the case of one who did not have in mind to slaughter the offering for the sake of any one of these, the offering is valid, as it is a stipulation of the court that he should not state any intent ab initio. This is necessary because the intent follows only the one performing the sacrificial rite, and therefore if the one who slaughters the animal is not careful and states the wrong intent, the offering would be disqualified through his improper intent.
לְשֵׁם שִׁשָּׁה דְבָרִים הַזֶּבַח נִזְבָּח, לְשֵׁם זֶבַח, לְשֵׁם זוֹבֵחַ, לְשֵׁם הַשֵּׁם, לְשֵׁם אִשִּׁים, לְשֵׁם רֵיחַ, לְשֵׁם נִיחוֹחַ. וְהַחַטָּאת וְהָאָשָׁם, לְשֵׁם חֵטְא. אָמַר רַבִּי יוֹסֵי, אַף מִי שֶׁלֹּא הָיָה בְלִבּוֹ לְשֵׁם אַחַד מִכָּל אֵלּוּ, כָּשֵׁר, שֶׁהוּא תְנַאי בֵּית דִּין, שֶׁאֵין הַמַּחֲשָׁבָה הוֹלֶכֶת אֶלָּא אַחַר הָעוֹבֵד: