The Burnt Offering
ויקרא ו,ב: זֹאת תּוֹרַת הָּעֹלָּה הִוא הָּעֹלָּה
The Sforno explains that there are three parts of the burnt offering (עולה) the disposition of which are indicated in these verses. The principal part is that which is totally consumed and goes up, hence the term עולה, literally going up.
The second part consists of the ashes which still retain some fat of the animal and are burnt together with the first part. Thus, the words את העולה (verse 3) are to be translated “with the olah.”
The third part consists of the ashes carried out of the camp by the Kohen after he changed his regular priestly garments for clothes of lessor quality, since he is now occupied with a non-holy duty. Nonetheless, the ashes are treated with respect and placed in a מקום טהר (a clean place).
The Peace Offering
ויקרא ז, יא: וְזֹאת תּוֹרַת זֶבַח הַשְׁלָּמִים
Nothing leavened is brought on the Altar, with a few special exceptions. One of these exceptions is the ten loaves of leavened bread (out of the forty total loaves) which are brought in conjunction with the thanksgiving offering (one of the categories of the Peace offering). The Sforno explains that this exception is to symbolize what Chaza”l call שְׂאוֹר שֶׁבָּעִסָּה (the leaven in the dough, see Berachos 17a). Rashi explains there that this expression refers to the evil inclination in the heart of a person.
The Thanksgiving offering is brought by someone who was delivered from peril. The very fact that a person was exposed to danger indicates a vulnerability due to spiritual shortcomings. However, HaShem in His mercy saved this person. Thus, the loaves of leavened bread symbolize this concept.
These Breads are Leavened
ויקרא ז,יג: עַל־חַלֹּת לֶחֶם חָּמֵץ יַקְרִיב
This is unique that a portion of the breads for the Korban Todah were leavened. The Sforno explains that one that is required to bring this offering has been saved from a life-threatening situation. It is obvious that this person has fallen short in one’s behavior in some manner which led to the life-threatening situation. The Sforno attributes this to giving it to one’s evil inclination which is known as “s’ore sheb’isah”, the leavening agent in the dough. Thus one brings leaven breads to atone.
The Right Thigh
ויקרא ח,כה: וְאֵת שׁוֹק הַיָּמִין
The Sforno explains the significance of the thigh of the Peace offering that is given to the Kohen, as well as the additional gift of the arm from the Peace offering of the Nazir.
The thigh is connected to the foot while the arm is connected to the hand. Since the Kohen can enter holy places in the Mikdash that the Jew that offers the sacrifice cannot enter, thus, the Kohen is entitled to a part connected to the foot. The Nazir adds a part connected to the hand indicating that until this time the actions of the Nazir were restricted by his vow (given over to the holy) but now the hand of the former Nazir is once again in his domain and control.