Menachos Daf 77 מנחוס דַף 77

The eighth Perek begins: התודה היתה באה חמש סאין ירושלמיות – [the breads of] the todah came from five Yerushalmi סאה of flour, which are equal to six מדבריות – se’ah of the מדבר, i.e., when the Torah was given (which was increased when they entered Eretz Yisroel). These equal two איפות, which is twenty עשרון, which allows for ten עשרון for the חמץ loaves and ten עשרון for the מצה loaves. This resulted in one עשרון per מצה loaf (of which there were ten), but of the חמץ loaves, of which there were three types (חלות, רקיקין, and רבוכה) of ten loaves each, each type was made of three and a third עשרון, so there were three loaves per עשרון. The Gemara proves that an איפה equals three סאה, because a passuk says that a "בת" is identical to an איפה, and another passuk says that a בת is one-tenth of a כור. Since a כור is thirty סאה, an איפה equals three סאה, so the six סאה מדבריות of the Mishnah equal two איפה.

Shmuel said three rulings: אין מוסיפין על המדות יותר משתות – [A city] cannot increase the sizes of their measures by more than a sixth, ולא על המטבע יתר משתות – nor can they increase the value of coins by more than a sixth, והמשתכר אל ישתכר יותר משתות – and one should not profit through selling by more than a sixth. The Gemara’s first two explanations for Shmuel’s first ruling about increased measures are rejected, and the Gemara suggests another: דלא ליהוי פסידא לתגרא – It is so the merchant does not suffer a loss of principal if he mistakenly sells a new measure for the old price (unaware of the increased volume), since a merchant usually profits by a sixth. The Gemara objects that if so, increasing the measure by a sixth should also be prohibited, since he will have no profit: זבן וזבין תגרא איקרי – does he buy and sell merchandise just to be called a merchant, without making any profit?! The Gemara concludes that Shmuel has a source in a passuk that coins (and measures) may be increased by a sixth, which is calculated מלבר – externally (i.e., a sixth of the final total, which is a fifth of the original amount). Shmuel’s ruling is supported by our Mishnah, which taught that five סאין ירושלמיות are equal to six original סאין, reflecting an increase of a “sixth.”

The next Mishnah states: מכולם היה נוטל אחד מעשרה תרומה – from all [the four types of bread], he would take one of ten as “terumah,” as the passuk says: והקריב ממנו אחד מכל קרבן תרומה לה' – he shall offer from it one of each [bread] offering, as terumah to Hashem. The word "אחד" implies שלא יטול פרוס – that he should not take a broken piece, but a whole loaf. "מכל קרבן" implies שיהו כל הקרבנות שוות – that all the bread offerings should be equal, ten loaves each, שלא יטול מקרבן על חבירו – so he will not take [terumah] from one bread offering for another, but should take from each type for itself. A Baraisa derives from תרומת מעשר with a gezeirah shavah (תרומה תרומה) that the terumah taken from לחמי תודה is a tenth of the breads. It proceeds to derive from the שתי הלחם that the חמץ breads of todah are similarly made of one עשרון per loaf, for a total of ten עשרונות. It then derives that the מצה loaves are also made of a total of ten עשרונות, and since there are three types of מצות (חלות, רקיקין, and רבוכה), each of which is made as ten loaves, the result is that there were three מצה loaves per עשרון.