It took me hours to work through Tosafos, so interested or not, here it is!
Summary of Tosafos: Tekufa is counted from Nissan (assuming like R' Yehoshua that world was created in Nissan which is 6 months prior to Tishrei). Molad is counted from Tishrei of Tohu which is 1yr before Adam
Lunar month = 29d 12hrs 793 chalakim (1080 chalakim = 1hr)
6 lunar months = 177d 4hrs 438 chalakim
Solar year = 365d 6hrs
6 solar months = 182d 15hrs
Discrepancy between solar and lunar in 6 months = 5d 10hrs 642 chalakim
Original Kiddush Hachodesh by Adam - Friday in 21hr (9 day hrs), therefore original molad (Tishrei of Yishuv - creation) is 6 hrs prior = Friday after 8am (14hrs)
Every month molad is 1d 12 hrs 793 chalakim earlier in week - 6 months = 9d (or 2d since it will be same day of week) 4hrs 438chal
Nissan of Tohu (6 months before creation) - molad is 2d 4hrs 438chal before Friday 14hrs = wed. 9hrs 642chal
Tishrei of Tohu (12 months before creation) - molad is mon. 5hrs 204chal.
Original Tekufah Nissan of Tohu (for tekufa we follow R' Yehoshua that it was in Nissan) - first hr. of wed. (tues. eve 6pm).
Tishrei of Yishuv (creation) is +15hrs for 6months later = wed. 15hrs.
Discrepancy between tekufa and molad in Tishre of Yishuv (Friday 14hrs and wed. 15hrs) = 1d 23hrs
Add time tekufa preceeded molad in Tishrei (Yishuv) with time tekufa preceeds molad over 6 months from Tishrei of yishuv back to Nissan of Tohu:
1d 23hrs + 5d 10hrs 642chal = 7d 9hrs 642chal
Therefore, in Nissan of Tohu, tekufa preceeded molad by 7d 9hrs 642chal
15 comments:
1st of all, this is great! I tip my cyberspace hat!
when you say molad is counted from tishrei a year before adam, do you mean a year and a half? (since were going like rav yehushua)
As strange as it may seem (rashash already points it out), we only go like r' yehoshua in counting the tekufah (solar), but we go like r' elazar when counting the molad (lunar). therefore,the tekufa count pretends that the world was created in Nissan 6 months before the Tishrei, but for the molad we accept that it was created in Tishrei. Therefore, the Tishrei of tohu is actually a full year before brias ha'olam.
now that i am starting to get the math, can you tell me what tosfos is trying to say?
i haven't quite figured it out! it seems that the system when calculating the leap year and making the solar calendar conform with the lunar, they had a routine of subtracting 7d 9hrs and 643chal from one of the numbers. Tosafos elaborates to explain that this # is the difference between the tekufah and molad in nissan of tohu.
1. "Every month molad is 1d 12 hrs 793 chalakim earlier in week" - I'M MISSING SOMETHING, ISN'T 12 HRS AND CHANGE LATER THAT SAME DAY OF THE WEEK SINCE 28 DAYS ARE DIVISIBLE BY 7? ANSWER: BECAUSE WE ARE GOING BACKWARDS!!!
2. DOES EVERYONE AGREE THAT ADAM WAS CREATED IN TISHREI? (AND IF SO -as it seems- THE LANGUAGE 15 LINES INTO THE TOSFOS IS MISSLEADING)
3. What is the point of the "mechasvei haibur" in tosfos? what are they trying to do?
4. How does the rule of "yom echad b'shana etc" make it that we count the year of tohu?
5. what is the final question of tosfos?
6. what is the number 2:438 in the end of tosfos come from?
Reb Yossie, can I take a stab at # 3 although it seems you have a much better grasp of the tosfos than i do.
i found this in sefer shoshanas yaakov
up until the mechashvei ibur, if one wanted to know the zman hatekufa he would be required to combine all the days from creation until where hes holding and work with the cheshbon of 91 days and 7.5 hrs and the remainder will be where hes holding in the tekufa then.
they found a shorter method. since the tekufa (solar) is greater than the molad (lunar) 10 days 21 hours and 204 chalakim it will emerge that in a cycle of 19 years with the 7 leap years the two cycles will be the same except one hour 485 chalakim that the tekufa will be delayed from the molad.
if you combine all the 19 year cycles since creation and realize the remainder, you can calculate the tekufa.
(this last prat, im not sure about and sad for me, this is the clinching point, but perhaps my beginning can help you and you can repay the favor)
yasherkoach
1 point that might be true.
1. the purpose of the calculators of the ibur is to match up the lunar and solar years (i cant resist, but this is a deep kabalistic concept). in any case, the points tosfos is making is that matching them up means that there will be a 7 plus days diference. since according to the math, in nissan of tohu there was a 7 plus diference.
reb avrumi, thanks, but i couldnt follow your thoughts, where does 10 days and change come from??
thats the 11 days as we know it difference between lunar and solar 365 to 354
as for the last qestion of tosfos. if you make one assumtions it makes sense, that is, that acc to rav yehushua that world was created in nissan it means that 1 day was rosh chodesh, if so molad was fri morning which is 2:4:438 diferent then acc to r"e in nissan of tohu. so q is that we can go figure out which one it is since the moon is only covered for 24 hours.
does this make sense?
only problem is that tosfos seem to say in the begining that acc to r"y world was created in 25 adar, but I saw rav elyashiv clearly say not this way so i am confused.
regarding the last pint acc to rav yehushua if the world was created in 25 adar or 1st of nissan. i searched my computer.
it seems that everyone is quoting tosfos as saying 25 adar. but there is a rashi and ritva that sound like 1st of adar. the ritva is in shabbos 87b regarding the gemara that 1st of nissan had 10 crowns. and the rashi is in the medrash that brings this in pahas breishis. i also found the rebbi of the ramban clearly says that regarding the moon there is no argumetn between r"e and r"y, but if so tosfos last question makes no sense to me!!! tzarich iyun gadol
I suggest you send this to RYGB this is one of his areas
who is RYGB?
for the sake of completion, see pnei yehushua that says the exact oppostie of what i said. oh well, i think this will be all for me for now...
Reb avi, maybe you can rescue us???
i realize the chances of anyone looking at this anymnore is slim, but in case....
the last q of tosfos is simple:
acc to the math the molad of nissan tohu is wed. but acc to r"y if rosh chodesh nissan was when adam was created and a friday then the molad was fri morning just like in r"e it is fri morning. if so there is a 2+ day diference which is dificult, because the moon is covered only 24 hours so we should be able to figure out. the pnei yoshua suggests maybe acc to r"y rosh chodes nissan was the 1st day of creation and if so adam was created on 6st of nissan, if so he was not mekadesh the chodesh and perhaps the molad was the same as r"e.
in my search i noticed that a LOT was written about this and it has ramifications to the year of Yetzias Mitzrayim. This is all i have.
Excellent job on the math!
[RYGB is Rav Yosef Gavriel Bechhofer, a choshuveh talmid chacham and, I am proud to say, a friend.]
Post a Comment