Keilim, Chapter 6, Mishnah 3. This chapter deals with the kirah, the simple stove of the Mishnah's world: not a manufactured vessel but stones set down beside one another, with the fire burning in the space between them and the pot resting on their tops. The previous mishnah taught the principle that when several such stone arrangements stand side by side, each one is judged on its own, so that tumah which enters one stove does not automatically carry over to its neighbor. Our mishnah takes that rule and works it out in a case where two stoves are not merely neighbors but actually share a stone between them.
"Shalosh avanim she'asa'an shetei kirayim": three stones were set in a row and formed into two stoves. Count them: stone one, stone two, stone three. A fire burns between the first and the second, and a pot rests across their tops; a second fire burns between the second and the third, with a second pot resting across those tops. The middle stone is doing double duty. It is a partner in the stove on its right and a partner in the stove on its left.
When one outer stone becomes tamei
"Nitme'et achat min hachitzonot": one of the two outer stones contracted tumah. Picture a dead sheretz that came into the space between that outer stone and the middle stone, that is, into the airspace of that stove. The other outer stone, along with its own fire and its own pot, was untouched and remains fully tahor.
What of the middle stone, which belongs to both stoves at once? Here the mishnah draws a line through the stone itself: "ha'emtza'it hameshameshet et hateme'ah, teme'ah; hameshameshet et hatehorah, tehorah." Whichever side of it functions as a wall of the stove that received the tumah, paired with the tamei outer stone, is itself tamei; whichever side of it works together with the untouched outer stone stays tahor. A single stone, and yet halachah divides it: the surface turned toward the tumah has become tamei, while the surface turned toward the clean stove is unaffected.
When one of the outer stones is taken away
"Nitlah hatehorah, huchleta ha'emtza'it lateme'ah." Should the tahor outer stone be taken away, the clean stove has ceased to be. Only a single function is left for the middle stone, to serve as a side of the tamei stove, and it is therefore assigned in full to that side: the stone in its entirety is tamei.
"Nitlah hateme'ah, huchleta ha'emtza'it latehorah." The reverse is equally true. Remove the tamei outer stone, so that the tamei stove is gone, and the middle stone is now wholly bound up with the tahor stone alone. It is completely tahor.
When both outer stones become tamei
Now the mishnah turns to the case where tumah entered both stoves, a sheretz having fallen into each one: "nitme'u shetei hachitzonot." Here the ruling for the middle stone depends on its size. "Im haytah ha'emtza'it gedolah, venoten lazo kedei shefitah mikan velazo kedei shefitah mikan, vehashe'ar tahor." If the middle stone is large, so that a pot rests on one portion of it for the first stove and another pot rests on a different portion of it for the second stove, while the stretch of stone between those two resting places is not being used for anything, then only the two used portions are tamei, each one the place where a pot actually sits, and the remainder of the stone stays tahor.
The small stone is treated otherwise: "ve'im haytah ketanah, hakol tamei." Where the central stone offers no surface beyond what the two pots occupy, no idle stretch is left over to be called tahor. Every part of it is in the service of the two tamei stoves, and so the stone is tamei throughout.
When the middle stone is removed
Both stoves are tamei, and now "nitlah ha'emtza'it": the central stone is lifted out, while the two tamei outer stones stay standing where they were. The mishnah rules: "im yachol lishpot aleha" a "yorah gedolah, teme'ah." If the space now opened between the two remaining stones is narrow enough that an oversized cauldron could be balanced across them, then a working stove still stands there, built of two tamei stones, and its tumah remains with it.
"Hechzirah, tehorah." Once he sets the central stone back where it had been, the whole arrangement is tahor. Trace the sequence of events. Lifting out that stone dissolved the two ordinary stoves that had stood there, and in their place stood one unusually wide stove resting on the pair of outer stones. Replacing the stone now dismantles that wide stove as well. Not one of the structures that carried the tumah is left standing, and the entire setup begins again as something fresh and clean.
"Mirechah betit, mekabelet tum'ah mishe'yasikenah kedei levashel aleha et habeitzah." Should he go further and smear clay around the stones, fastening the whole thing to the ground, it counts as a stove freshly built. Such a stove is susceptible to tumah, though not from the moment it is set up: as with every new stove, it must first be fired, and the measure is heat sufficient to boil an egg upon its surface. Only after that heating is it a stove in halachah, able to take on tumah once again.