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Pesachim 23b

{Pesachim 109a}

what use do children have with wine? Rather, one should distribute to them roasted kernels and nuts so that they will ask. {omits "so that they will not sleep. " compare with girsa in our gemara of this entire section}

They learnt {in a brayta}: They said about Rabbi Tarfon {and so too a similar brayta in Yerushalmi. our gemara: Akiva} that he distributed roasted kernels and nuts on erev Pesach to children in order that they should ask.

They learnt {in a brayta}: Rabbi Eliezer the Great says: We are chotef the matzot {eat them hastily -- but see commentaries} to the children so that they do not sleep.

They said about Rabbi Akiva that in all his days, he never said that the time has arrived to stand up from the Bet Midrash except for the night of Pesach and erev Yom Kippur. On the night of Pesach because of the children that they should not sleep {thus one should start the Seder early} and on erev Yom Kippur in order to feed their children.

The Sages learnt {in a brayta}: A man is required to cause his household to rejoice during the festival, for it is stated {Devarim 16}:

Men with what is fitting for them - wine. And women with what is fitting for them - with what?

Rav Yosef taught: In Bavel, with dyed garments. In Eretz Yisrael, with ironed linen garments.

Rabbi Yitzchak said: The xestes {a standard measure, somewhat less than a pint} for muries {fish hash} in Tzippori was equal to the log of the Temple, and with it we measure the reviit {=1/4 of a log} for Pesach.

Rabbi Yochanan said: The ancient tomanta in Teveria was greater than this by 1/4, and with that we measure the reviit for Pesach.

Rav Chisda said: The Biblical reviit is 2 X 2 X 2 7/10 fingerbreadths.

And measured with the thumb, as they learnt {in a brayta}: {Vayikra 15:16}:

mikveh

All of his flesh in water = water into which all of his body may enter.

And how much is that? 1 cubit X 1 cubit X 3 cubits high. {That is, three cubic cubits.} And the Sages gave the measure of the waters of a mikveh to be 40 seah.

To explain: The Biblical reviit is 1 1/2 eggs volumes. And the log is 4 reviit which are 6 eggs. {Since 4 X 1.5 = 6.}

And how do we know that a log is 4 reviit? For they learnt {in the Mishna in Menachot 87b that there are 7 liquid measures in the Temple}: The hin, 1/2 hin, 1/3 hin, 1/4 hin, the log, 1/2 log, 1/3 log, 1/4 log. {The Mishna which lists 7 skips 1/3 log, which for some reason is listed here.}

Thus the log is composed of 4 reviit.

The hin is 12 log, for it is written זה, and זה is in gematria 12 log.

Thus, a hin is 48 reviit {because 12 X 4 = 48}, which are 72 eggs {because 48 X 1.5 = 72}.

A kav is 4 log which is 16 reviit {because 4 log per kav X 4 reviit per log = 16} which are 24 eggs {because 16 X 1.5 = 24}.

And how do we know that the kav is 4 log? For they learnt {in a Mishna}:

Hillel says: A hin full of drawn water invalidates the mikveh - for one is obligated to relate {the teaching} in his teacher's language - and how much is a hin - 12 log.

Shammai says: 9 kav which are 36 log.

Thus, the kav is 4 log {since 9 X 4 = 36}.

The seah is 6 kav which are 2 hin {since 6 kav = 24 log, and there are 12 log to a hin} which are 24 log {since there are 12 log to a hin} which are 96 reviit {since 24 X 4 = 96} which are 144 eggs {since 96 X 1.5 = 144}.

The eifah is 3 seah, which are 18 kav {since there are 6 kav to a seah} which are 6 hin, which are 72 log, which are 288 reviit, which are 432 eggs.

The measure of challah is an omer, which is 1/10th of an eifah, which is 43 eggs. And so too for matzah.

The Biblical reviit is 2 X 2 {X 2 7/10} fingerbreadths.

{How so?}

The Sages measured the water of a mikveh as 40 seah. The seah is 6 kav. The kav is 4 log. The log is 4 reviit.

{Meanwhile,} A cubit is 6 handbreadths. A handbreadths is 4 fingerbreadths, measured with the thumb.

Now, 1 cubit X 1 cubit X 3 cubits high {which is the dimensions of a mikveh} contains 40 seah.

{We can do a simple calculation here, easier than that of the Rif. Since to convert cubits to fingerbreadths, we multiply by 24 (that is, X 6 X 4), we may calculate that:

1 cubic cubit = 24 X 24 X 24 fingers = 13824 cubic fingers.

3 cubic cubits = 3 X 13824 = 41,472 cubic fingers.

This is for 40 seah. Divide by 40, then by 6, then by 4, then by 4 again to get 1 reviit.

Thus, the ratio of 40 seah to 1 reviit is 3840:1.

Thus, 41,472 / 3840 will give us the cubic fingers for 1 reviit.

41,472 / 3840 = 10.8 cubic fingers.

Is this 2 X 2 X 2 7/10 fingers?

2 X 2 X 2.7 = 10.8 exactly.

However, Rif does not have modern geometry, and so he must resort to a more complicated calculation to acheive the same result. Feel free to skip over that, since it is after all just math.

Now, the Yerushalmi gives a different volume measure for a reviit, namely 2 X 2 X 1 + 1/2 + 1/3.

How can we arrive at that amount. I would posit the following - the only obvious room for ambiguity here is in the amah - the cubit. There were two cubit measures. One was composed of 6 handbreadths and the other of 5 handbreadths. The reviit of Bavli is computed using the 6 handbreadth cubit. Let us recalculate assuming a 5 handbreadth cubit, and see if we can arrive at the measure described in the Yerushalmi.

Since to convert cubits to fingerbreadths, we multiply by 20 (that is, X 5 X 4), we may calculate that:

1 cubic cubit = 20 X 20 X 20 fingers = 8000 cubic fingers.

3 cubic cubits = 3 X 8000 = 24,000 cubic fingers.

This is for 40 seah. Divide by 40, then by 6, then by 4, then by 4 again to get 1 reviit.

Thus, the ratio of 40 seah to 1 reviit is 3840:1.

Thus, 24,000 / 3840 will give us the cubic fingers for 1 reviit.

24,000 / 3840 = 6.25 cubic fingers.

How much is that?

That is 2 X 2 X 1.5625 fingerbreadths.

How much is 1.5625 fingerbreadths?

It is 1 + 1/2 + 1/16 fingerbreadths.

This is only slightly less than the Yerushalmi's measure of 1 + 1/2 + 1/3 fingerbreadths.

However, realize first of all that they were not using modern methods of calculation, and so to come to a figure with such precision would be quite difficult. Furthermore, the way these measures seem to work in both Bavli and in Yerushalmi is as the sum of a series of fractions.

Thus, in Bavli, the height is calculated as 2 + 1/2 + 1/5.

And thus, in Yerushalmi, the height is calculated as 1 + 1/2 + 1/3.

In theory, we might have imagined a series of continuously reducing fractions (with zero as the numerator until we reached 1/16), but such precision is unnecessary and overly complicated. Instead, the "good enough" way of describing numbers might be to continuously add smaller fractions until you have the minimum with possibly a bit over. We could not add 0/3 to 1/2 because we would have too little; adding 1/3 takes us over the top, and is thus sufficient.

To repeat where we left off:

}

Now, 1 cubit X 1 cubit X 3 cubits high {which is the dimensions of a mikveh} contains 40 seah.

Half of that is 1 X 1 X 1 1/2 cubits high, which is 9 handbreadths {6 + 3 handbreadths} containing 20 seah.

Half of that is 1 X 1 X 3/4 cubits high, which is 4 1/2 handbreadths, containing 10 seah.

Half of that is 1 X 1/2 cubits X 4 1/2 handbreadths high, containing 5 seah.

Half of that is 1/2 X 1/2 cubits X 4 1/2 handbreadths high, containing 2 1/2 seah, which are 15 kav {since the seah is 6 kav, so 12 kav + 3 kav = 15 kav}

{Recall that there are 6 handbreadths to a cubit, so 1/2 a cubit = 3 handbreadths}

Half of that is 3 handbreadths X 3 handbreadths X 2 1/4 handbreadths high, which are 7 1/2 kav.

Half of that is 3 handbreadths X 1 1/2 handbreadths X 2 1/4 handbreadths high, which are 4 kav - 1/4 of a kav {= 3 3/4 kav}, which are 15 log {since there are 4 log to a kav, and 3.75 X 4 = 15}.

Half of that is 1 1/2 handbreadths X 1 1/2 handbreadths X 2 1/4 handbreadths high, which are 7 1/2 log.

{Recall that there are 4 fingers to a handbreadths, so 1 1/2 handbreadths = 6 fingerbreadths, and 2 1/4 handbreadths = 9 fingerbreadths.}

Thus, 6 fingerbreadths X 6 fingerbreadths X 9 fingerbreadths high are found to be 7 1/2 log.

Half of that is 6 fingers X 3 fingers X 9 fingers high, containing 4 log - 1/4 log {thus, 3 3/4 log}, which are 15 reviit {since there are 4 reviit to a log, and 3 3/4 X 4 = 15}.

And how much are 6 fingers by 3 fingers X 9 fingers high? {We now multiply to get cubic fingers, such that 6 * 3 * 9 = 162.} Thus, 162 cubic fingers are found to be 15 reviit.

Thus, to each reviit is 11 fingerbreadths - 1/5 {thus, 10 4/5 fingerbreadths = 10.8 cubic fingerbreadths, by simple division of 162/15}, which is the same as 2 X 2 X 2 + 1/2 + 1/5 fingerbreadths high {since 2 * 2 * 2.7 = 10.8} in this division.

And this is the calculation {since Rif cannot rely on the simpler, modern arithmetic}: The portion of 2 X 2 is 4. By a height of 2 = 8 cubic fingerbreadths.

And when you add to this 1/2 a fingerbreadth X 4 {the area}, you have {an additional} 2 cubic fingerbreadths.

And you already had 8 cubic fingerbreadths in hand, so now there are 10 cubic fingerbreadths.

And there is an additional 1/5 X 4, which is 1 - 1/5 {=4/5}.

And you already had 10 cubic fingerbreadths in hand, so now there are 11 cubic fingerbreadths - 1/5 fingerbreadth.

And they are a reviit.

Thus, the reviit of the Torah is discovered to be 2 X 2 X 2 + 1/2 + 1/5 high figerbreadths, no less and no more.

"And they should not give him less than 4 cups of wine, even from the charity plate":

How could the Sages establish a decree which brings to danger? But they learnt {in a brayta}: One should not eat in pairs nor drink in pairs.

Rav Nachman bar Yitzchak {our gemara: just R Nachman} said: Scriptures stated {Shemot 12:42}:

Rava said: The cup of blessing {of birkat haMazon} combines for good but not for bad.

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