- עצים for private korbanos are funded משל ציבור
A Baraisa teaches the source that wood for private korbanos is funded משל ציבור – from communal funds. One would think that someone who accepts to bring an עולה should bring his own wood, just likes he brings his own נסכים. Therefore, the passuk says: על העצים אשר על האש אשר על המזבח – on the wood which is on the fire which is on the מזבח. This compares the wood to the מזבח, and Rebbe Elazar bar Rebbe Shimon says it teaches: מה מזבח משל ציבור אף עצים ואש משל ציבור – just as the מזבח was funded from communal funds, so too the wood and fire for personal korbanos come from communal funds. Rebbe Elazar ben Shamua says the comparison teaches: מה מזבח שלא נשתמש בו הדיוט – just as the מזבח required that no commoner had ever used its materials, the wood for a korban must also be from unused materials. The Gemara explains they disagree whether חדתי – new [wood] must be used. Although we find that Aravnah offered Dovid to use his wooden farming tools for firewood for korbanos, the Gemara explains they were unused.
- If a minchah’s kometz became mixed with another minchah of a different consistency
The next Mishnah states: נתערב קומצה בקומץ חבירתה – if [a minchah’s] kometz became mixed with the kometz of another [minchah], or with the minchah of a Kohen, the daily minchah of the Kohen Gadol, or a מנחת נסכים (which is brought with korbanos), all of which are entirely burned on the מזבח, the Tanna Kamma rules them all valid to be offered. Rebbe Yehudah says that where the kometz was mixed into a Kohen Gadol’s minchah or מנחת נסכים, it is invalid, שזו בלילתה עבה – because this [kometz’s] mixture of flour and oil is thick (being one לוג of oil per עשרון of flour), וזו בלילתה רכה – whereas this [מנחת כהן משיח and מנחת נסכים’s] mixture is thin (being three לוגין of oil per עשרון of flour), והן בולעות זו מזו – and they absorb one from the other. Meaning, the thick kometz mixture will absorb some oil from the thinner minchah mixture, resulting in the kometz having too much oil, and the minchah having too little oil, both of which are invalid.
- Mixing the blood of the פר and שעיר proves עולין אין מבטלין זה את זה, or מין במינו אינו בטל
A Mishnah teaches that if blood of a korban became mixed with water, if it still has the appearance of blood, it is valid. If it became mixed with (red) wine, רואין אותו כאילו הוא מים – we view it as if it were water, and if the blood in this amount of water would appear as blood, it is valid. The Tanna Kamma says the same applies if it became mixed with blood of chullin animals, but Rebbe Yehudah says: אין דם מבטל דם – blood does not nullify blood. Rebbe Yochanan says these Tannaim derive their different opinions from the requirement to mix the blood of the פר and שעיר of Yom Kippur, and then sprinkle the mixed blood. Since the פר’s blood greatly exceeds the שעיר’s blood, and the mixed sprinkling is still valid, the Rabbonon say: מכאן לעולין שאין מבטלין זה את זה – from here we see that things which go up on the מזבח do not nullify one another, so the שעיר’s blood is not בטל. Rebbe Yehudah says: מכאן למין במינו שאינו בטל – from here we see that a kind mixed with its own kind is not nullified, and that is why the שעיר’s blood is not בטל. These derivations are further analyzed.