We find R. Elazar b. Ya'akov in the Mishnah in Midos.

Three of the four Lishakos are identified.

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

Aba Shaul identified the 'unidentified' Lishkah.

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.