משנה: הָרוֹצֶה לַעֲשׂוֹת שָׂדֵהוּ קָרַחַת קָרַחַת מִכָּל־מִין עוֹשֶׂה עֶשְׂרִים וְאַרְבַּע קְרָחוֹת לְבֵית סְאָה מִקָּרַחַת בֵּית רוֹבַע וְזוֹרֵעַ בְּתוֹכָהּ כָּל־מִין שֶׁיִּרְצֶה. הָֽיְתָה קָרַחַת אַחַת אוֹ שְׁתַּיִם זוֹרְעָן חַרְדָּל. שָׁלֹשׁ לֹא יִזְרְעֵם חַרְדָּל מִפְּנֵי שֶׁהִיא נִרְאֵית כִּשְׂדֵה חַרְדָּל דִּבְרֵי רִבִּי מֵאִיר. וַחֲכָמִים אוֹמְרִין תֵּשַׁע קְרָחוֹת מוּתָּרוֹת וְעֶשֶׂר אֲסוּרוֹת. רִבִּי אֱלִיעֶזֶר בֶּן יַעֲקֹב אוֹמֵר אֲפִילוּ כָּל־שָׂדֵהוּ בֵּית כּוֹר לֹא יַעֲשֶׂה בְּתוֹכָהּ חוּץ מִקָּרַחַת אַחַת. MISHNAH: He who wants to turn his field into patches150Arabic קַרָאח “terrain appropriate for being sown,” used here for equal patches all sown or planted with different kinds. Clearly, R. Meïr cannot require the patches all to be square and equal, since 24 is not a square number. Since a seah contains 24 rova‘, each plot will have just the minimal size that allows different seeds to be sown. Since the patches have to be rectangular and equal in shape, on a field of 50 by 50 cubits the sides of the rectangles are 50/4=12.5 by 50/6=8. 3̄ cubits (or 50/3=16.6̄ by 50/8=6.25 cubits.) for all different kinds makes 24 patches per bet seah, each patch one bet rova‘, and sows in each one any kind that he desires. If there were one or two patches151A new statement. If an otherwise continuous field has two square excisions of a bet rova‘ each, separated from one another, he may sow both of them with mustard because that is still less than a commercial crop. Three he may not sow because the yield would be enough for a commercial crop and would make the remainder kilaim., he may sow them with mustard; three he should not sow because that would look like a mustard field, the words of Rebbi Meïr152The entire Mishnah up to here is R. Meïr’s.. But the Sages say, nine patches are permitted, ten are forbidden153This is explained in the Halakhah. Maimonides, who insists that a קרחת must be square, takes as model of the 50 by 50 cubits field a five-by-five square checkerboard. All white fields in the first, third, and fifth rows are squares of a bet rova‘ each (squares of √2500/24 = 10.207 cubits edge length) while the black fields in these rows are rectangles of edge lengths 10.207 and 9.69 cubits. In rows 2 and 4, the black fields are squares of a bet rova‘, the white fields are rectangles of edge lengths 9.69 and 10.207 cubits. Together, they fill the large square, but only the nine fields selected first may be sown and all others must lie fallow.
According to Maimonides, the number 9 as maximum of patches is a mathematical fact. In the interpretation of R. Simson who admits rectangular patches, 10 patches would be possible but are forbidden. In a 4-by-6 checkerbord, a valid centrally symmetric configuration of 10 patches might contain (1,1) (1,4) (2,2) (3,1) (3,3) (4,2) (4,4) (5,3) (6,1) (6,4). The expression “ten are forbidden” supports R. Simson.. Rebbi Eliezer ben Jacob says, even if its field is a bet kor1541 kor = 30 seah. 1 bet kor =75’000 square cubits, larger than the bet kor appearing in cuneiform documents., he should not make in it more than one patch.
הלכה: רִבִּי חִזְקִיָּה רִבִּי יָסָא בְשֵׁם רִבִּי יוֹחָנָן עַל רֹאשָׁהּ רִבִּי מֵאִיר אוֹמֵר אֲפִילוּ חֲבוּשׁוֹת אֲפִילוּ סְמוּכוֹת. וְרַבָּנִין אָֽמְרִין וּבִלְבַד שֶׁלֹּא יְהוּ לֹא חֲבוּשׁוֹת וְלֹא סְמוּכוֹת. הֵיךְ עֲבִידָא תְּלַת וְתַרְתֵּיי וְחָדָא וְתַרְתֵּיי וְחָדָא. HALAKHAH: Rebbi Ḥizqiah, Rebbi Yasa, in the name of Rebbi Joḥanan: For the first part, Rebbi Meïr says, even jailed, even adjacent, but the rabbis say, on condition that they were neither jailed nor adjacent155Two rectangular fields may meet one another at a vertex, since each one is ראש תור for the other. “Jailed” means here that a rectangular field forms ראש תור at all four of its vertices. Rebbi Meïr permits to sow rectangular fields, each of the minimum size of bet rova‘, even if they are adjacent, i. e., they are joined at an edge, and even if they are jailed at all corners, which means that he permits to use the entire field. The Sages do not disagree that a קרחת must have a minimum size of bet rova‘. If the field is divided into equal rectangles, one may imagine that the different rectangles are alternately black and white in checkerboard fashion. Since the rabbis do not permit adjacent rectangles to be sown, the first condition is that only rectangles of the same color are chosen. The second condition is that no chosen rectangle can be surrounded by 4 chosen rectangles. The opinion of Maimonides about the position of the rabbis was explained in the Mishnah. His opinion is difficult to accept, since he does not permit any two fields to touch at all, so the mention of “jailing” is totally redundant. It is therefore better to look for a partition of the 50 by 50 field into 24 equal parts. The rabbis cannot speak about division of the field into squares since their number would have to be either 16 (with 7 chosen squares) or 25 (where 12 chosen squares are possible.) Also, the squares in the second case would be smaller than a bet rova‘. If the Sages would follow the division of R. Meïr and cover the field by a 4-by-6 checkerboard, they could accomodate 10 chosen rectangles (fields 1,3,5 in the first row, 2,4,6 in the second, 1,5 in the third, 2,4 in the fourth.) Hence, it seems that the rabbis insist that the area for קרחת should be strictly larger than a bet rova‘, and on a 5-by-4 board one may select at most nine (e. g., fields 1,3,5 in row 1; 2,4 in row 2; 1,5 in row 3; 2,4 in row 4.) The area of each plot is then 125 sq. cubits. (Explanation of R. Eliahu Fulda.). How is that done? 3,2,1,2,l156This statement fails in two respects. First, the underlying checkerboard is 5-by-5, allowing only 100 sq. cubits per plot, and second, on such a checkerboard that has 13 white and 12 black fields, one may choose all white fields with the exception of the central one (#3 in row 3), for a total of 12 admissible fields. Hence, this sentence (choosing 3 plots in the first row, 2 in the second, 1 in the third, 2 in the fourth, 1 in the fifth) must be a later addition. Even if one chooses the central element in row three, one still could accomodate 10 plots (1,3,5 in the first row, 2,4 in the second, 3 in the third, 1,5,in the fourth, 2,4 in the fifth).
The argument is not part of R. Joḥanan’s statement since it is in Aramaic. R. I. J. Kanievski proposes to read תְּלַת תַּרְתֵּי וְחָדָא תַּרְתֵּיי וְחָדָא, eliminating two conjunctions and translating “three [times] two and one each.” The syntax is very unusual..