And the 51st mitzvah is that we are commanded to bring an offering in addition [to the daily offerings1] on the eighth day of the holiday of Sukkos. This is the musaf Shemini Atzeres offering.
[The source of this commandment is G‑d's statement,2 "And the eighth day shall be a day of rest...You must present a burnt-offering as an appealing fragrance to G‑d one bull, one ram, 14 yearling sheep...and a sin-offering of one goat."]
The reason why we are forced to count this musaf offering separately from those of Sukkos3 is because of the principle,4 "Shemini Atzeres is considered a separate holiday." Our Sages said explicitly,5 "It is considered a separate holiday, with a separate sacrifice." This proves that the sacrifice is counted separately. This is extremely obvious.
