The Gemara discusses how far from the Beis HaMikdash is considered Derech Rechokah. Ulla says it is 15 mil away because a person would not be able to walk that far from the start of the day and arrive by Zman Shechitas Korban Pesach at noon. The Gemara connects Ulla to Rebbi Yochanan who says a person can walk 40 mil from Alos ha'Shachar until Tzeis ha'Kochavim. If we subtract the 5 mil from alos to neitz and the 5 mil from shkia to tzeis, we are left with 30 mil between neitz and shkia, so chatzos would be 15 mil into the day - just like Ulla said.
Is this Gemara a proof for the Vilna Gaon's way of calculating zmanim? Gemara is explicit that chatzos (and all Sha'os Zmanios) are calculated between Netz and Shekiah - and not between Alos and Tzeis as Magen Avraham says.
Is this a proof to Gra?
Yaakov Abramovitz, Flushing
1) The Magen Avraham himself initially suggests that this is a proof for the opinion that later became famous as the opinion of the Gra.
2) This is in Shulchan Aruch Orach Chaim siman 233, which is where the time for davening Minchah is discussed. The MA there #3 writes that there appears to be a proof from Pesachim 93b that the day is calculated from Netz to Shekiah because we learn that the time for slaughtering the korban is only up to the beginning of shekiah. He also cites Tosfos Menachos 20b DH Nifsal (in the first very wide line) who proves from our Gemara that one may not shecht once shekiah (which is 72 minutes before Tzeis) has started. The Gemara reckons the 15 mil from midday until shekiah and does not reckon the 5 mil from shekiah until Tzeis.
[ Tosfos appears not to be discussing a person who starts off at the beginning of the day and wants to reach the Beis Hamikdash before the time for shechitah starts. Rather he is discussing someone who starts at noon and wants to arrive before the time for shechitah has finished].
3) However, Magen Avraham continues and writes that this proof can be rebuffed. This is because there may be a difference between the time for slaughtering a korban and the time for davening Minchah. It may be that the time for davening Minchah depends on when the Mincha flour offering was brought every day in the Beis Hamikdash. This was after the time of slaughtering the korban Tamid. The flour Minchah offering could be brought until Tzeis (see Machatzis HaShekel on the Magen Avraham).
4) Therefore the Magen Avraham can argue that there is not a proof from our Gemara concerning times for all purposes. There is only a proof regarding the latest time that shechitah can be perfomed.
Chodesh Tov
Dovid Bloom