Eruvin 165

תנא וחצי חצי חציה לטמא טומאת אוכלין ותנא דידן מ"ט לא תני טומאת אוכלין משום דלא שוו שיעורייהו להדדי

One taught: And half of the half of its half<span class="x" onmousemove="('comment',' Of the size of the loaf prescribed in our Mishnah by R. Johanan and R. Simeon respectively.');">¹</span> is the size susceptible to levitical uncleanness of food.<span class="x" onmousemove="('comment',' According to R. Johanan the size is three quarters of an egg. For, since he defined the size of a whole loaf as a quarter of a lab, or six eggs, the 'half of the half of its half' must be equal to 6/2 X 2 X 2 = 3/4 of an egg. According to R. Simeon, since a whole loaf is equal to 1/3 of a kab, or 24/3 = 8 eggs, the 'half of the half of its half' must be equal to 8/2 X 2 X 2 = 1 egg.');">²</span> But why did not our Tanna mention<span class="x" onmousemove="('comment',' In our MISHNAH:');">³</span>

דתניא כמה שיעור חצי פרס ב' ביצים חסר קימעא דברי רבי יהודה ר' יוסי אומר ב' ביצים שוחקות שיער רבי ב' ביצים ועוד כמה ועוד אחד מעשרים בביצה

the levitical uncleanness of food? - Because their prescribed sizes<span class="x" onmousemove="('comment',' That for (a) the defilement of one's body and (b) the defilement of food.');">⁴</span> are not in exact proportions.<span class="x" onmousemove="('comment',' Sc. the size of the latter (cf. prev. n.) is not exactly a half of the former.');">⁵</span> For it was taught: How much is half a peras?<span class="x" onmousemove="('comment',' Lit., 'a broken piece' Sc. of bread that, if levitically unclean, renders one's body unfit to eat terumah.');">⁶</span>

ואילו גבי טומאת אוכלין תניא רבי נתן ורבי דוסא אמרו כביצה שאמרו כמוה וכקליפתה וחכ"א כמוה בלא קליפתה

The size of two<span class="x" onmousemove="('comment',' Small sized (cf. infra) .');">⁷</span> eggs minus a fraction;<span class="x" onmousemove="('comment',' In agreement with R. Simeon's standard in our MISHNAH:');">⁸</span> so R'Judah.

אמר רפרם בר פפא אמר רב חסדא זו דברי רבי יהודה ורבי יוסי אבל חכ"א כביצה ומחצה שוחקות ומאן חכמים רבי יוחנן בן ברוקה

R'Jose ruled: Two large sized<span class="x" onmousemove="('comment',' Lit., 'laughing'.');">⁹</span> eggs. This was calculated by Rabbi<span class="x" onmousemove="('comment',' On examining a Se'ah measure whose capacity is nominally that of six kab or 6 X 24 = 144 eggs, but whose actual capacity was greater than that number of eggs.');">¹⁰</span>

פשיטא שוחקות אתא לאשמועינן

to be the size of two eggs and a slight surplus.<span class="x" onmousemove="('comment',' Lit., 'and more'.');">¹¹</span> How much was that surplus? - A twentieth part of an egg.<span class="x" onmousemove="('comment',' In respect of each egg of capacity.');">¹²</span> In respect of the levitical uncleanness of food, however, it was taught: R'Nathan and R'Dosa explained that the size of the egg of which the Rabbis have spoken<span class="x" onmousemove="('comment',' As being susceptible to levitical uncleanness.');">¹³</span>

כי אתא רב דימי אמר שיגר בוניוס לרבי מודיא דקונדיס דמן נאוסא ושיער רבי מאתן ושבע עשרה ביעין

includes the egg itself and its shell,<span class="x" onmousemove="('comment',' Lit., 'like itself and like etc. This size obviously is not exactly a half of any of the sizes prescribed by (a) R. Judah, (b) R. Jose or (c) Rabbi for the defilement of one's body according to whom it should have been either (a) an egg minus a fraction or (b) a large sized egg and its shell, or (c) in egg and a twentieth.');">¹⁴</span> but the Sages explained: The egg only, exclusive of its shell.<span class="x" onmousemove="('comment',' A size which is smaller even than half of the one prescribed by R. Judah and much more so than those prescribed by the others.');">¹⁵</span> Rafram B'Papa citing R'Hisda stated: This<span class="x" onmousemove="('comment',' The Baraitha prescribing the size of half a peras.');">¹⁶</span>

הא סאה דהיכא אי דמדברית קמ"ד הויא

is the ruling of R'Judah and R'Jose, but the Sages ruled: The size is one and a half large sized eggs. But who are the Sages? R'Johanan B'Beroka of course;<span class="x" onmousemove="('comment',' Whose standard for 'erub, as explained Supra by R. Hisda, is that of a loaf of a quarter of a kab or six eggs, the half of the half of which is obviously 6/2 X 2 = 1 1/2 eggs.');">¹⁷</span>

ואי דירושלמית קע"ג הויא

is not this then obvious?<span class="x" onmousemove="('comment',' Apparently it is. What need then was there for R. Hisda to repeat what he had once stated?');">¹⁸</span> - His purpose was<span class="x" onmousemove="('comment',' Lit., 'he came'.');">¹⁹</span> to inform us that the eggs must be large sized.

ואי דציפורית ר"ז הויין

When R'Dimi came<span class="x" onmousemove="('comment',' From Palestine to Babylon.');">²⁰</span> he related that Bonios once sent to Rabbi a modius<span class="x" onmousemove="('comment',' A Roman measure of the same capacity as a Se'ah,');">²¹</span> of artichokes that came from Nausa,<span class="x" onmousemove="('comment',' Or 'copied from the standard measure of Nausa' (Jast. q.v.) .');">²²</span>

לעולם דציפורית אייתי חלתא שדי עלייהו

and Rabbi calculated its capacity to be two hundred and Seventeen eggs. What kind of se'ah,<span class="x" onmousemove="('comment',' Cf. supra n. 9');">²³</span> however, was it?

חלתא כמה הויין תמני אכתי בצר ליה

If it was the desert se'ah<span class="x" onmousemove="('comment',' Sc. the se'ah measure used by the Israelites in the time of Moses in the wilderness.');">²⁴</span> it should have contained a hundred and forty-four eggs,<span class="x" onmousemove="('comment',' A Se'ah equals six kab = 6 X 4 log = 6 X 4 X 6 = 144 eggs.');">²⁵</span> and if it was the Jerusalem se'al<span class="x" onmousemove="('comment',' Which exceeds that of the desert by a fifth.');">²⁶</span>

אלא אייתי ועודות דרבי שדי עלייהו

it should have contained a hundred and seventy-three eggs,<span class="x" onmousemove="('comment',' Since 144 + 144/5 = 144 + 28 4/5 = 172 4/5 or 173 eggs approx.');">²⁷</span> and if again it was the one of Sepphoris<span class="x" onmousemove="('comment',' Which exceeded that of Jerusalem by a fifth.');">²⁸</span> It should have contained two hundred and seven eggs.<span class="x" onmousemove="('comment',' 173 + 173/5 = 173 + 34 3/5 = 207 3/5 or 207 eggs approx.');">²⁹</span>

אי הכי הוי ליה טפי כיון דלא הוי כביצה לא חשיב ליה

It was in fact a Sepphoris measure but the quantity of the dough-offering was added to them.<span class="x" onmousemove="('comment',' Lit., 'bring . . throw upon them', sc. Rabbi's calculations which show a higher figure include also the quantity of the dough-offering that is due from a Se'ah or two hundred and seven eggs of dough.');">³⁰</span> But how much is the dough-offering? Nine<span class="x" onmousemove="('comment',' So with R. Han. as cited by Tosaf. a.l. Cur. edd., 'eight'.');">³¹</span>

ת"ר סאה ירושלמית יתירה על מדברית שתות ושל ציפורית יתירה על ירושלמית שתות נמצאת של ציפורית יתירה על מדברית שליש

eggs;<span class="x" onmousemove="('comment',' A twenty-fourth part of the dough (cf. supra 81a) . 217/24 = 9 1/24 or 9 approx.');">³²</span> would not then the number still be less?<span class="x" onmousemove="('comment',' Than two hundred and seventeen (cf. prev. n.) .');">³³</span> - The fact is that the surpluses spoken of by Rabbi<span class="x" onmousemove="('comment',' Not the quantity of the dough-offering.');">³⁴</span>

שליש דמאן אילימא שליש דמדברית מכדי שליש דמדברית כמה הוי ארבעין ותמניא ואילו עודפא שיתין ותלת

were added to them.<span class="x" onmousemove="('comment',' Sc. Rabbi's surpluses which amount to 1/20 of an egg for each egg amount to 1/20 X 207 or 10 7/20 eggs for a se'ah of the size of 207 eggs');">³⁵</span> If so, would not the number be greater?<span class="x" onmousemove="('comment',' Than the number 217, by 7/20');">³⁶</span> - As it does not amount to the size of a whole egg<span class="x" onmousemove="('comment',' It amounts only to seven twentieths (Cf. nn. 4 and 5) .');">³⁷</span>

ואלא שליש דירושלמית שליש דידה כמה הוי חמשין ותמניא נכי תילתא ואילו עודפא שתין ותלת ואלא דציפורי שליש דידה כמה הוי שבעין נכי חדא ואילו עודפא ס"ג

he does not reckon it. Our Rabbis taught: The Jerusalem se'ah exceeds that of the desert one by a sixth,<span class="x" onmousemove="('comment',' Of the latter measure, sc. a fifth of the former.');">³⁸</span> and that of Sepphoris exceeds that of Jerusalem by a sixth.<span class="x" onmousemove="('comment',' Of the latter measure, sc. a fifth of the former.');">³⁸</span>

אלא א"ר ירמיה ה"ק נמצאת סאה של ציפורי יתירה על מדברית קרוב לשליש שלה ושליש שלה קרוב למחצה דמדברית

Thus it follows that the measure of Sepphoris exceeds that of the desert by a third. A third of which? Would you suggest: A third of the desert measure?

מתקיף לה רבינא מידי קרוב קרוב קתני אלא אמר רבינא ה"ק נמצאת שליש של ציפורי בועודיות של רבי יתירה על מחצה של מדברית שליש ביצה

Observe then: How much is a third of the desert measure? Forty-eight eggs;<span class="x" onmousemove="('comment',' 144/3 = 48.');">³⁹</span> whereas the surplus amounts to sixty-three!<span class="x" onmousemove="('comment',' 207 144 = 63.');">⁴⁰</span>

תנו רבנן (במדבר טו, כ) ראשית עריסותיכם

If again a third of the Jerusalem measure was meant, how much, [it could be retorted,] is a third of it? Fifty-eight minus one third;<span class="x" onmousemove="('comment',' 173/3 = 57 2/3.');">⁴¹</span> whereas the surplus is sixty-three! Is then the reference to the measure of Sepphoris? How much, [it may be asked,] is a third of it? Seventy minus one;<span class="x" onmousemove="('comment',' 207/3 = 69.');">⁴²</span> whereas the surplus is sixty-three! - Rather, explained R'Jeremiah it is this that was meant: It follows that the se'ah of Sepphoris exceeds that of the desert by nearly a third of itself<span class="x" onmousemove="('comment',' Since 207 - 144 = 63 and 207/3 = 69. 63 is nearly equal to 69.');">⁴³</span> and that a third of itself<span class="x" onmousemove="('comment',' 69.');">⁴⁴</span> is nearly equal to a half of th desert measure.<span class="x" onmousemove="('comment',' 144/2 = 72. This figure is quite near to 69.');">⁴⁵</span> Rabina demurred: Was any mention at all made of approximation?<span class="x" onmousemove="('comment',' Lit., 'near, near he taught'. How then could it be maintained by R. Jeremiah that 'nearly' a third etc. was meant.');">⁴⁶</span> - Rather, explained Rabina, it is this that was meant: It follows that a third of the Sepphoris measure together with the surpluses spoken of by Rabbi<span class="x" onmousemove="('comment',' Sc. (207 + 207 X 1/20) X 1/3 = (207 + 10 7/20) X 1/3 = 217/3 approx. = 72 1/3 approx.');">⁴⁷</span> exceeds the half of the desert measure<span class="x" onmousemove="('comment',' 144/2 = 72.');">⁴⁸</span> by a third of an egg.<span class="x" onmousemove="('comment',' Since (cf. prev. two notes) 72 1/3 - 72 = 1/3.');">⁴⁹</span> Our Rabbis taught: Of the first of your dough<span class="x" onmousemove="('comment',' Ye shall set apart a cake for a gift (sc. as a dough-offering) ; Num. XV, 20.');">⁵⁰</span>