לימד על בכור בעל מום שניתן לכהן שלא מצינו לו בכל התורה כולה
This verse teaches that a blemished firstborn is given to a priest as a gift, and that he may eat its meat. This is a novel concept, as we have not found in the entire Torah another halakha similar to it, where a blemished offering is given to the priests for consumption.
ורבי ישמעאל נפקא ליה מלך יהיה דסיפא
The Gemara asks: And according to Rabbi Yishmael, who interprets this verse differently, from where does he derive this halakha that a blemished firstborn is given to a priest? The Gemara answers: He derives it from the phrase: “As the breast of waving and as the right thigh, it shall be yours” (Numbers 18:18), which is the latter clause of that same verse. The repetition of the phrase “shall be yours” serves to teach that even the meat of a blemished firstborn shall be eaten by the priests.
בשלמא לר' יוסי הגלילי דמוקי ליה נמי במעשר ופסח היינו דכתיב (במדבר יח, יז) לא תפדה (כי) קדש הם הם קריבין ואין תמורתן קריבה
§ The Gemara raises another question: Granted, according to the opinion of Rabbi Yosei HaGelili, who interprets the verse as referring also to an animal tithe offering and a Paschal offering, this is as it is written in the same verse: “You shall not redeem; they are sacred” (Numbers 18:17). The word “they” indicates that only they are sacrificed on the altar, but their substitutes are not sacrificed. In general, if one substitutes a non-sacred animal for one designated as an offering, both the original and the substitute are considered to be consecrated, and they are therefore sacrificed. But if one substitutes a non-sacred animal for a firstborn, an animal tithe offering, or a Paschal offering, the substitute is not sacrificed.
דתנן תמורת בכור ומעשר הן וולדן וולד ולדן עד סוף כל העולם הרי הן כבכור ומעשר ויאכלו במומן לבעלים
This is as we learned in a mishna (Temura 21a): With regard to the substitute of a firstborn and of an animal tithe offering, both they, the substitutes themselves, and their offspring, and the offspring of their offspring, forever, i.e., for all future generations, are as the firstborn and the animal tithe offering, respectively, and therefore they are eaten in their blemished state by the owners; but unlike the firstborn and the animal tithe offering themselves, they are not sacrificed on the altar.
ותנן אמר רבי יהושע שמעתי שתמורת פסח קריבה ותמורת פסח אינה קריבה ואין לי לפרש
And likewise with regard to the substitute of a Paschal offering, we learned in a mishna (Pesaḥim 96b) that Rabbi Yehoshua says: I have heard two rulings from my teachers: One ruling was that the substitute of a Paschal offering is sacrificed as a peace offering after Passover, and another ruling was that the substitute of a Paschal offering is not offered as a peace offering after Passover; and I cannot explain these apparently contradictory rulings, as I do not remember the circumstances to which each ruling applies. And as will be explained, if the substitution took place after the sacrifice of the Paschal offering, the animal is sacrificed, as it is considered the substitute of a peace offering, whereas if the substitution occurred before the sacrifice of the Paschal offering, it is not sacrificed, as it is the substitute of a Paschal offering. This indicates that the substitute of a Paschal offering is not sacrificed, just like the substitute of a firstborn is not sacrificed.
אלא לרבי ישמעאל דמוקי ליה כוליה בבכור מעשר ופסח דלא קריבה תמורתן מנא ליה מעשר גמר עברה עברה מבכור
But according to the opinion of Rabbi Yishmael, who interprets the entire verse as dealing with a firstborn, from where does he derive the halakha that the substitute of an animal tithe offering and of a Paschal offering are not sacrificed? The Gemara answers: With regard to an animal tithe offering, he derives this by means of a verbal analogy between the terms passing, and passing written with regard to a firstborn. Concerning a firstborn it is stated: “And you shall pass [veha’avarta] to the Lord all that opens the womb” (Exodus 13:12), and concerning an animal tithe it is stated: “Of whatever passes [ya’avor] under the rod” (Leviticus 27:32). From this verbal analogy it may be derived that just as the substitute of a firstborn is not sacrificed, so too, the substitute of an animal tithe offering is not sacrificed.
פסח בהדיא כתב ביה כשב מה ת"ל אם כשב לרבות תמורת הפסח אחר הפסח שתקרב שלמים יכול אף לפני הפסח כן ת"ל הוא
With regard to the Paschal offering, this halakha is not derived through a verbal analogy, but rather this halakha is explicitly written concerning it. The verse referring to peace offerings states: “If he offers a lamb for his offering” (Leviticus 3:7). The Torah could simply have stated: A lamb, and proceed from there to teach the halakhot of a lamb peace offering. If so, what is the meaning when the verse states: “If he offers a lamb”? This serves to include the substitute of a Paschal offering that was substituted after the sacrifice of the Paschal offering, teaching that it is sacrificed as a peace offering, since the Paschal offering has the status of a peace offering after that time. One might have thought that even before the sacrifice of the Paschal offering the same should apply, i.e., that the substitute of a Paschal offering is sacrificed as a peace offering. Therefore, the verse states with regard to the Paschal offering: “It is the sacrifice of the Lord’s Passover” (Exodus 12:27), which indicates that it, the Paschal offering itself, is sacrificed, but its substitute is not sacrificed.
וכל הנך תנאי דמפקי ליה להאי דם זבחיך ישפך לדרשא אחרינא האי כל הניתנין על מזבח החיצון שנתנן מתנה אחת שכיפר מנא להו סברי להו כבית הלל דאמרי אף חטאת שנתנה מתנה אחת כיפר וילפינן כולהו מחטאת:
The Gemara asks: And as for all those tanna’im who derive a different exposition from this verse: “And the blood of your offerings shall be poured” (Deuteronomy 12:27), this halakha that is recorded in the mishna, that with regard to all the offerings whose blood is to be placed on the external altar, in a case where the priest placed the blood on the altar with one placement, he facilitated atonement, from where do they derive this? The Gemara answers: Those tanna’im hold in accordance with the opinion of Beit Hillel, who 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. And they derive the halakha applying to all the other offerings from that which applies to a sin offering.
והחטאת שתי מתנות: אמר רב הונא מ"ט דב"ש
§ The mishna teaches that Beit Shammai maintain that in the case of a sin offering, which requires four placements, at least two placements are necessary to facilitate atonement, whereas Beit Hillel hold that even in the case of a sin offering one placement suffices. Rav Huna said: What is the reasoning for the opinion of Beit Shammai?
(ויקרא ד, ז) קרנות קרנות קרנות הרי כאן שש ארבעה למצוה ושתים לעכב
He explains: The verse states: “And the priest shall take of the blood of the sin offering with his finger, and put it upon the corners of the altar” (Leviticus 4:25). Subsequently, the verse states: “The priest shall take of its blood with his finger, and put it on the corners of the altar” (Leviticus 4:30), and an additional verse states: “The priest shall take of the blood of the sin offering with his finger, and put it on the corners of the altar” (Leviticus 4:34). As the mini-mum amount justifying the use of the plural form, i.e., in the word “corners,” is two, one may conclude that there are six references to the corners of the altar here. Four of them are mentioned for a mitzva, meaning that the priest should place the blood on all four corners of the altar ab initio, and the other two are mentioned to invalidate the offering if he did not present the blood on at least two corners.
ובית הלל קרנת קרנת קרנות הרי כאן ארבע שלש למצוה ואחת לעכב
The Gemara asks: And what is the reasononing for the opinion of Beit Hillel? The Gemara answers: The matter should be understood according to the written consonantal text, i.e., the way in which the words are actually spelled. The word “corners” is written plene, i.e., with a vav, in one of the verses, which means that it must be read in the plural form. In the other two verses, “corners” and “corners” are written deficient, i.e., without a vav, in a way that can be vocalized in the singular form, i.e., as karnat. Therefore, there are four references to corners here. Three of these references are written to indicate the placements of blood are performed only as a mitzva, i.e., they are performed ab initio, and the remaining one is written to indicate that its absence invalidates the offering, i.e., the offering is not valid if the blood was not placed against at least one corner of the altar.
ואימא כולהו למצוה כפרה בכדי לא אשכחן
The Gemara asks: But according to this explanation of Beit Hillel, why not say that all of them are written for the mitzva and none are to invalidate, i.e., that the blood must be presented on all four corners ab initio, but the offering atones after the fact even if the blood was not presented at all? The Gemara rejects this possibility: We have not found anywhere in the Torah an example of an offering in which atonement can be achieved with no placement of the blood.
ואיבעית אימא היינו טעמא דבית הלל אהני מקרא ואהני מסורת אהני מקרא לטפויי חדא ואהני מסורת לבצורי חדא
And if you wish, say instead that this is the reason of Beit Hillel: The vocalized text of the Torah, i.e., the way in which the words of the Torah are pronounced based on the tradition of what vowels the words contain, is effective in determining how the verses are to be expounded. And likewise, the consonantal text of the Torah, i.e., the way in which the words are actually written, is also effective in determining how the verses are to be expounded. The Gemara elaborates: The vocalized text is effective in adding one more corner and the consonantal text is effective in subtracting one corner. Consequently, the verse is interpreted as referring to five corners, four of which are necessary for the mitzva ab initio, and one of which is indispensable after the fact.
אלא מעתה (דברים ו, ח) לטטפת (דברים יא, יח) לטטפת (שמות יג, טז) לטוטפות הרי כאן ארבע אהני קרא ואהני מסורת חמשה בתי בעי למיעבד
The Gemara asks: But if that is so, that this is the proper manner of expounding the verses, consider the case of the phylacteries of the head, about which it is stated: “And for frontlets [totafot] between your eyes” (Exodus 13:16), and: “They shall be for frontlets [totafot] between your eyes” (Deuteronomy 6:8), and subsequently: “They shall be for frontlets [totafot] between your eyes” (Deuteronomy 11:18). The word totafot is written once in plene form, i.e., with a vav, indicating the plural form, and twice in a deficient form, i.e., without a vav, indicating the singular. Accordingly, there are four frontlets here, and from here the Sages derive that the phylacteries of the head consist of four compartments, which together form a cube. Why not say that the vocalized text, read in the plural, is effective, i.e., that it requires six compartments, and likewise, the consonantal text, read in the singular, is effective, i.e., it requires four compartments, and therefore one should be required to prepare five compartments for the phylacteries of the head?
סבר לה כר' עקיבא דאמר טט בכתפי שתים פת באפריקי שתים
The Gemara answers that Beit Hillel hold in accordance with the opinion of Rabbi Akiva, who says that the requirement to have four compartments in the phylacteries of the head is not derived from the number of times that the word totafot is mentioned, but rather from an exposition of the word totafot itself: Tot in the Katpi language means two, and pat in the Afriki language means two, for a total of four.
אלא מעתה (ויקרא כג, מב) בסכת בסכת בסוכות אהני מקרא ואהני מסורת חמשא דפנתא בעי למיעבד
The Gemara raises another objection to this method of exposition: If that is so, consider the case of a sukka, about which it is stated: “In sukkot [basukkot] shall you reside seven days; all that are homeborn in Israel shall reside in sukkot [basukkot]. So that your future generations will know that I caused the children of Israel to reside in sukkot [basukkot] when I took them out of the land of Egypt: I am the Lord your God” (Leviticus 23:42–43). Two instances of the word basukkot are written in a deficient manner, i.e., without a vav, indicating the singular, and one instance is written in plene form, i.e., with a vav, indicating the plural form. The Sages derived from here that a sukka must have four walls. Why not say that the vocalized text, read in the plural, is effective, requiring six walls, and likewise, the consonantal text, read in the singular, is effective, requiring four walls, and therefore one should be required to build a sukka with five walls?