Zevachim 63B

ומקיפין ויורדין דרך שמאל; חוץ מן העולה לשלשה אלו ⁠– שהיו עולין ויורדין על העקב.

and circle the altar until reaching the southwest corner and descend via the left side of the ramp, except for one who ascends for one of these 3 matters, where they would ascend directly to the southwest corner of the altar, and descend by turning on their heels and retracing the path by which they ascended rather than circling the altar.

גמ׳ מנא הני מילי? אמר רבי יהושע, אמר קרא: ״לא ישים עליה שמן ולא יתן עליה לבנה כי חטאת היא״⁠ – חטאת קרויה מנחה, ומנחה קרויה חטאת;

Talmud: The Talmud asks a question about the Mishnah’s statement that the sacrificial rite of a bird sin offering is performed at the southwest corner of the altar: From where are these matters derived? R' Yehoshua says: The verse states with regard to the sin offering of a destitute sinner, which is a meal offering brought in lieu of an animal or bird: “He should put no oil upon it, neither should he put any frankincense on it; for it is a sin offering” (Leviticus 5:11). From this verse it is evident that a sin offering is called a meal offering and a meal offering is called a sin offering, so that their halakhot may be compared.

מה חטאת טעונה צפון ⁠– אף מנחה טעונה צפון, ומה מנחה בקרן מערבית דרומית ⁠– אף חטאת בקרן מערבית דרומית.

Just as a sin offering requires slaughtering in the north section of the Temple courtyard, so too, the handful of a meal offering requires sanctification in a service vessel in the north. And just as a meal offering is brought near to the southwest corner of the altar, so too, the blood of a sin offering is sprinkled on the southwest corner of the altar.

ומנחה גופה מנלן? דתניא: ״לפני ה׳״⁠ – יכול במערב? תלמוד לומר: ״אל פני המזבח״.

The Talmud asks: And with regard to a meal offering itself, from where do we derive that it must be brought near the altar at the southwest corner? As it is taught in a baraita with regard to the verse: “And this is the law of the meal offering…before YHWH, in front of the altar” (Leviticus 6:7). From the phrase: “Before YHWH,” one might have thought that the rite of bringing the meal offering near the altar must be performed at the west side of the altar, which faces the Sanctuary. Therefore, the verse states: “In front of the altar,” which is its south side, from where the priests ascend the ramp.