We find R. Elazar b. Ya'akov in the Mishnah in Midos that says: The Ezras Nashim was 135 Amos by 135 Amos.

It had four Lishakos in its four corners that served the following roles:

The southwestern one was the Lishkas ha'Nezirim where the Nezirim cooked their Shelamim, cut their hair, and cast it under the cooking pot;

The northeastern one was Lishkas Dir Eitzim where Kohanim who had Mumin (physical deformities) would select wood for the Mizbe'ach, because wood that contained worms is unfit for the the Mizbe'ach;

The northwestern one was Lishkas ha'Metzora'in;

R. Elazar b. Ya'akov said that he did not recall the use of the southwestern Lishkah, thus indicating that he was the author of the Mishnah.

Aba Shaul: This Lishkah was used to store wine and oil and was called Lishkas Beis Shemania.

There is another indication that the Mishnah in Midos is R. Elazar b. Ya'akov.

All the walls were tall except for the Eastern wall.

This was to allow the Kohen burning the Parah to see through the opening to the Heichal during the Haza'ah.

All the gates were 20 Amos tall, with wall above them.

By calculating the elevations of each level, we can see that the Eastern wall, if left at its 20-plus Amos of height, would block his view, and was thus shortened.

This is only true if the measurements are being given by R. Elazar b. Ya'akov, not the Rabanan.

R. Ada b. Ahavah entertains the possibility that the measurements were those of R. Yehudah.

R. Yehudah had taught the positioning of the Mizbe'ach.

The Mishnah in Midos teaches the overall dimensions of the Azarah (187 x 135 Amos).

If the Mishnah in Midos were R. Yehudah, the Mizbe'ach would not be in the middle, but slightly to the South.

The difficulty involved in such a possibility establishes the Mishnah as the teaching of R. Elazar b. Ya'akov.