Parah 1:3 - 1:4

מיום ליום – if it was born on the first of Elul, it didn’t complete a full year until the first of Elul of the second year. For we follow after the its year, but not after the years of the counting of the world. But if the year were intercalated, it was intercalated for it. And similarly, with rams that are two years old.

אינו כשר לא לאיל – for it is not considered a ram until it enters thirty days from the second year for it.

פלגס (a sheep beyond the age of a כבש and below that of an איל ; a youth in the intermediate stage between boyhood and maturity) – It is the language of פלג/part, middle, meaning to say average between this and that, it has exited from the category of כבש but has not entered the category of איל (i.e., a כבש is a sheep at least one year of age; the איל is at least two years old).

נוקד (shepherd) – it is the language of (Amos 1:1): "[דברי עמוס] אשר-היה בנקדים מתקוע"/[The words of Amos] a sheep breeder from Tekoa,” whose explanation is the owners of sheet. (Also, possibly the word נוקד (NUKAD) – a stamped, distinct coin).

פרכדיגמא (false coin, counterfeit) -to a coin that is invalid that they call it PARCHADIGMA in the Greek language. Even this is invalid from the designation/definition of an איל or of a כבש.

מביא עליו נכסי אלי – one-third of a Hin. And we derive it from the fact that it is written (Numbers 7:6-7): “the case of a ram, [you shall present as a grain offering: two-thirds of a measure of choice flour with a third of a Hin of oil mixed in] and a third of a Hin of wine as a libation – [as an offering of pleasing odor to the LORD],” to include the פלגס/sheep beyond the age of a כבש and below that of an איל.

חטאות הצבור (see Leviticus 4:14) – as for example the goats of the New Moons and the Festivals and their burnt offerings (see Numbers 28:3 and following) , all of them are a year old.

חטאת היחיד (see Leviticus 4:28, 32 and 5:6) – a female sheep or a female goat.

ואם הקריבום שיום השמיני כשרים – as it is written (Leviticus 22:27): “and from the eighth day on it shall be acceptable [as a gift to the LORD},” and it is stated regarding a firstborn (Exodus 22:29): “[You shall do the same with your cattle and your flocks: seven days it shall remain with its mother;] on the eighth day you shall give it to Me,” just as the firstborn that he made the eighth day like the eighth [day] and beyond, so also with the rest of the sacrifices he made the eighth day like the eighth [day] and beyond. However, with a matter that is an obligation of the most preferable way of performing a Mitzvah is to bring it from the thirtieth day onward.

והפסח – even though it is an obligation, the Sages were not quiet/silent, because they take it according to the number of souls, so that they don’t come to a case of left over (i.e., part of the offering left over after time permitted for it to be eat. One who eats the leftover portions of an offering is punishable by extirpation – see Tractate Zevahim, Chapter 5, Mishnah 8 which states that the Passover offering an only be consumed until midnight) since it is not eaten [other] than for one fellowship.