Mishnah
Mishnah

Commentary for Eruvin 1:3

הַקּוֹרָה שֶׁאָמְרוּ, רְחָבָה כְּדֵי לְקַבֵּל אָרִיחַ. וְאָרִיחַ, חֲצִי לְבֵנָה שֶׁל שְׁלֹשָׁה טְפָחִים. דַּיָּה לַקּוֹרָה שֶׁתְּהֵא רְחָבָה טֶפַח, כְּדֵי לְקַבֵּל אָרִיחַ לְאָרְכּוֹ:

The aforementioned "korah" must be wide enough to receive an ariach (a small brick) [so that a permanent structure could be built upon it.] And an ariach is half a brick of three tefachim, [so that an ariach is a tefach and a half wide.] It is sufficient that the korah be a tefach wide to receive an ariach along its length. [This is what is meant: If the korah is a tefach wide, the additional half tefach by which the ariach is wider (the ariach being a tefach and a half) can be plastered the width of a finger on either side, so that it will be wide enough to receive an ariach. Thus is it explained in the gemara.]

Bartenura on Mishnah Eruvin

רחבה כדי לקבל אריח – that it would be appropriate to build upon it a fixed, permanent building.
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English Explanation of Mishnah Eruvin

Introduction This mishnah discusses the size of the cross-beam about which Bet Hillel and Bet Shammai debated in yesterday’s mishnah.
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Bartenura on Mishnah Eruvin

והאריח חצי לבנה של שלשה טפחים – it is found that the אריח/small bricks/bond-timber is a handbreadth and-a-half wide.
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English Explanation of Mishnah Eruvin

The cross-beam of which they spoke must be wide enough to hold a small brick (, a small brick which is half of a regular brick, the size of three handbreadths. The width of the cross-beam must be one and half handbreadths, in order to support an “ariah”, a half-brick, which would, at least potentially, be placed on top of it.
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Bartenura on Mishnah Eruvin

דיה לקורה ברוחב טפח – this is how it should be read: since the crossbeam is a handbreadth wide, that one-half handbreadth that remains – since the small brick is one-and-one-half handbreadths wide, it is possible to rub a salve of plaster a finger [width] here and a finger [width] from there and through this it will be wide enough to hold the small bricks and this is how it is explained in the Gemara (Talmud Eruvin 14a).
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English Explanation of Mishnah Eruvin

It is enough for the cross-beam to be one handbreadth wide in order to hold the width of a small brick. The length of the cross-beam need only be one handbreadth. This way when the brick is placed on the cross-beam there will be a little space on each side (a finger on each side), where they can put the mortar to attach the brick to the beam. Even if the cross-beam is not actually attached to the brick, at least it looks as if it will be. This lends it more of an air of permanence.
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