Middos, Chapter 3, Mishnah 1. Chapter Two took us through the courtyards and the gates of the Har Habayit. Now the Mishnah brings us to the center of the Azarah itself and begins a detailed survey of the outer mizbeach: its measurements, how those measurements changed between the first Beit Hamikdash and the second, and the markings on its walls that the kohanim relied on in their avodah.
How the mizbeach was built
Before the numbers, it helps to picture the construction. At the bottom they laid a base, the yesod, formed by setting stones inside a hollow wooden frame and pouring in a concrete-like mixture that hardened into a solid block. On top of that first block they set up another wooden form, packed it with smooth stones, and again poured in the mixture. That second level is the sovev, the ledge. The same method produced the third level above it, and the keranot, the horns at the four corners of the top.
Level by level
The Mishnah opens with the footprint of the structure: "Hamizbeach haya," the mizbeach was, and here come the numbers, "sheloshim ushtayim" amot by "sheloshim ushtayim" amot. Where it rested on the floor of the Azarah it formed a square measuring thirty two amot in each direction.
"Ala amah," it climbed a single amah, and then "vechanas amah," it stepped back by an amah on each of its four sides. "Zeh hayesod": this lowest tier carries the name yesod, the foundation of the mizbeach.
"Nimtza sheloshim al sheloshim." Having pulled in one amah all around, the mizbeach at this height measures thirty amot by thirty amot.
"Ala chamesh vechanas amah, zeh hasovev." From there it rose another five amot and again drew inward one amah. This tier is called the sovev, the ledge, because its recessed top formed a walkway on which the kohanim circled the mizbeach when their avodah required it.
"Nimtza," the outcome is, "esrim ushmoneh" by "esrim ushmoneh." With a second amah given up on every one of the four faces, the mizbeach at this height spans twenty eight amot in each direction.
It then rose a further three amot, forming the top level of the mizbeach.
The top surface
"Mekom hakeranot": on each of the four corners of the upper surface sat a keren, a horn shaped as a cube, one amah high, one amah long and one amah wide. The strip reserved for these horns therefore claimed, in the Mishnah's words, "amah mizeh ve'amah mizeh," an amah along one edge of the top and an amah along the edge facing it.
"Nimtza": take away those two strips and what is left is "esrim vashesh" by "esrim vashesh," a square measuring twenty six amot on each side.
"Mekom hiluch raglei hakohanim," the place where the feet of the kohanim travelled. Running along the inner edge of the horns, a lane was kept clear for the kohanim as they made their circuit over the top of the mizbeach and tended the fires. Why could they not simply use the amah wide strips that stretch from one horn to the next? Because at every corner a keren would stand in their path and stop them. A free passage had to be designated immediately beside the keranot.
"Amah mizeh ve'amah mizeh." That walkway took another amah from this side and another amah from that side.
"Nimtza": with all the strips deducted, there remain "esrim ve'arba" amot in one direction and "esrim ve'arba" in the other. That square of twenty four by twenty four is the "mekom ma'arachah," the surface on which the wood of the fire was arranged.
The mizbeach of the first Beit Hamikdash
Rabbi Yose adds a historical note: "Amar Rabbi Yose." The mizbeach erected by Shlomo Hamelech, he teaches, was of more modest dimensions. "Mitechilah lo haya ela," at the outset it was nothing more than "shemoneh ve'esrim" amot in each direction: twenty eight by twenty eight where it stood on the ground, and not thirty two by thirty two.
"Kones ve'oleh bemidah zo": it drew inward and rose according to this identical scheme, tier upon tier, "ad shenimtza mekom hama'arachah esrim al esrim," until the area of the fire came out at twenty amot by twenty amot. Follow the arithmetic: starting from twenty eight amot to a side, the indentation at the ledge leaves twenty six; the tier above it brings the top to twenty four; an amah on every side goes to the horns; a further amah on every side goes to the lane where the kohanim trod; and a square of twenty by twenty remains for the ma'arachah.
The addition of the returnees from Bavel
"Keshe'alu benei hagolah": once the first Beit Hamikdash lay in ruins, the nation was carried off to Bavel, and the Mishnah now turns to the generation that came back up from there to raise the second Beit Hamikdash. They "hosifu alav," they made an addition to the mizbeach: "arba amot" on the side facing south, "min hadarom," and "arba amot" on the side facing west, "min hama'arav." The shape of that addition is given as "kemin gamma," like the Greek letter gamma, which looks like a nun stood on its head, or, in the alphabet we use, a capital L. The new construction wrapped along two neighbouring faces of the mizbeach in precisely that L formation.
Why was the enlargement necessary? The answer lies in the route travelled by the libations, nisuch hayayin and nisuch hamayim, the poured wine and the poured water, as they made their way down to the shitin, the hollow space beneath the Beit Hamikdash. Shlomo Hamelech held that the libations were meant to run down the outer wall of the mizbeach, cross the pavement of the courtyard, and enter an opening in that pavement near the southwestern corner which led into the shitin. The Chachamim of the second Beit Hamikdash held differently: the libations were to descend through the body of the mizbeach itself. The structure was therefore extended until it stood over that opening, and from then on the poured liquids ran down a channel inside the mizbeach and passed directly into the shitin.
The verse in Yechezkel
"Shene'emar": the Mishnah anchors these measurements in the prophecy of Yechezkel, which describes the outer mizbeach of the second Beit Hamikdash and of the third. "Veha'ariel," the Ariel, the title the pasuk gives to the upper surface of the mizbeach, is "sheteim esreh orech," twelve amot in length, "bishteim esreh rochav," by twelve amot in width, "ravu'a," squared.
"Yachol she'eino ela": reading only that much, a person might have concluded that the entire top of the mizbeach amounted to no more than "sheteim esreh al sheteim esreh," twelve amot in each direction.
"Keshehu omer, el arba'at riv'av, melamed shemin ha'emtza hu moded shetayim." When the pasuk continues, "to its four quarters," it teaches that the prophet is measuring outward from the center. The upper surface is divided into four equal quarters, each one twelve by twelve amot, so that twelve and twelve in each direction yield a total of twenty four by twenty four amot.
The red line
"Vechut shel sikra chogro be'emtza." A stripe of crimson paint was drawn around the mizbeach, belting it at half its height. From the ground up to the tops of the keranot the mizbeach stood ten amot tall, so the stripe encircled it at the level of five amot.
"Lehavdil," to draw a distinction, "bein hadamim ha'elyonim," between the bloods placed higher up, "ladamim hatachtonim," and those placed lower down. The blood of some korbanot was applied to the wall of the mizbeach above this stripe, and the blood of others beneath it. The crimson band told a kohen at a glance which zone he was standing in, so that every application of blood landed exactly where the halachah places it.
Where the base actually projected
The Mishnah stated that the yesod measured thirty two by thirty two amot, which sounds like a perfect square. It was not.
"Vehayesod haya mehalech": the yesod, meaning the ledge of the base that protrudes beyond the tier resting upon it, extended "al penei chol hatzafon," along the entire northern face of the mizbeach, "ve'al penei chol hama'arav," and along the entire western face.
"Ve'ochel," and it eats, "badarom amah achat," a single amah on the southern side, "uvamizrach amah achat," and a single amah on the eastern side. Along those two faces the base sent out no ledge whatsoever; it simply turned the corner and took up one amah of length in each of those two directions. The figure of thirty two amot to a side is thus exact along the north and along the west, where the yesod stands out an amah beyond the level above it. Toward the south and toward the east no such projection existed, apart from that lone amah at the northeastern corner and at the southeastern corner, where the base came around and filled the space that would otherwise have remained empty.