We make [the city] a rectangle, according to the directions of the world, so west is in the west of the world, and south is in the south of the world.

(R. Yosah): If he does not know the directions of the world, he can learn from the Tekufah (solstice). From the place from which the sun rises (i.e. the northeast) on the first day of Tekufas Tamuz (the longest day of the year in the northern hemisphere. It is always about June 21), to the place from which it rises (i.e. the southeast) in Tekufas Teves (the shortest day, about December 21), this is the east.

From the place (southeast) where the sun sets in Tekufas Teves (the southwest), to the place where it sets in Tekufas Tamuz (the northwest), this is the west. The remaining directions are north and south. (The line between southeast and southwest is south.)

Source: "Holech El Darom v'Sovev El Tzafon'' - the sun [always] travels along the south by day and circles around the north by night [out of our sight, on the other side of the earth];

"Sovev Sovev Holech ha'Ru'ach v'Al Sevivosav Shav ha'Ru'ach'' - these are the east and west. (Sometimes, i.e. in summer, the sun travels along the east and west by day, when we see it. Sometimes, i.e. in winter, it circles around the east and west, i.e. traverses these sides at night, out of our sight.)

Remark: Granted, in the Beis ha'Mikdash and [the building made for the Mishkan] in Shilo [they were able to measure this to build in the proper directions];

(R. Acha citing R. Shmuel bar Rav Yitzchak): Early Nevi'im toiled greatly to make the eastern gate [perfectly north-south,] so that the sun will be exact on it in Tekufas Teves and in Tekufas Tamuz.

Note: Presumably, he means that on the two days each year when the sun rises due east, it will shine on the gate. These are the last days of Tekufas Teves and Tekufas Tamuz (b'Dochak, we can explain our text like this; it would be better if the text said 'the first of Tekufas Nisan and Tekufas Tishrei'). The gate had to be precisely north-south for the sunrise sun to shine directly on (perpendicular to) the gate on these days. Alternatively, precision was needed because the eastern walls of the Azarah, Ezras Nashim and Har ha'Bayis were all parallel, and the sun needed to enter through gates in the latter walls aligned with the eastern gate. All these gates were 10 Amos wide (Midos 2:3). If the walls were roughly north-south (i.e. tilted slightly to the southeast or northeast), when the sun rises due east, it would shine on part of the eastern gate. The walls had to be precisely north-south for the sun to shine on the entire eastern gate. If R. Acha discusses the first days of Tekufas Teves and Tekufas Tamuz, the sun cannot shine on the gate [due to the other walls] until it rises a few degrees above the horizon. And then, there is no reason to discuss specifically these two days! - PF

It is called seven names - Sha'ar Sur, Sha'ar ha'Yesod, Sha'ar Charisi, Sha'ar Eisun, Sha'ar ha'Tavech, Sha'ar Chadash, Sha'ar ha'Elyon.

It is called Sha'ar Sur, for there Temei'im separate (for they may not enter). This is based on "Suru Tamei Kar'u Lamo.''

It is called Sha'ar ha'Yesod, for there they establish the Halachah. (The Sanhedrin sits there);

It is called Sha'ar Charisi, for it is corresponds to where the sun shines. This is based on "ha'Omer la'Cheres v'Lo Yizrach.''

It is called Sha'ar Eisun, for it is the entrance and exit [to the Azarah. Eisun is an expression of coming - "v'Asa me'Rivevos Kodesh.''

It is called Sha'ar ha'Tavech, for it is based [in the middle] between two [other] gates (of the Ezras Nashim, and of the Heichal).

It is called Sha'ar Chadash, because Chachamim made a new law (that a Tevul Yom may not enter the Ezras Nashim).

It is called Sha'ar ha'Elyon, for it was above Ezras Nashim. There was an extra attribute in the Beis ha'Mikdash (there was Ezras Nashim, which had Kedushas Machaneh Levi. No part of the Mishkan had Kedushas Machaneh Levi - PNEI MEIR.)

Question: In the Midbar, who coordinated the directions for them? (They did not see the sun, due to the clouds (PNEI MOSHE). Also, they erected the Mishkan the day they arrived. They did not have time to see where the sun rises and sets in Tekufas Teves and Tekufas Tamuz!)

Answer (R. Acha): The Aron coordinated the directions for them;

Source: "V'Nas'u ha'Kehasim Nos'ei ha'Mikdash'' - this is the Aron. (They did not carry the Aron itself.) "V'Hekimu'' - Bnei Merari. "Es ha'Mishkan Ad Bo'am'' (before the coming of) Bnei Kehas, on whom the Aron was put. (The Aron is called the Mikdash, for it coordinated the directions for the Mikdash.)

Question: How did Bnei Yisrael go in the Midbar?

Answers: R. Chama bar Chaninah and R. Hoshayah argued about this. One of them said that they went like a [square] box, and one said that they went [in a line,] like a beam;

The one who said like a box [learns from] "Ka'asher Yachanu Ken Yisa'u.'' The one who said like a beam [learns from] "Me'asef l'Chol ha'Machanos l'Tziv'osam.''

Question: The one who said like a beam, how does he fulfill [the source of the one who said] like a box "Ka'asher Yachanu Ken Yisa'u''?

Answer: Just like they camped according to Hash-m's word, so they traveled according to Hash-m's word.

Question: The one who said like a box, how does he fulfill [the source of the one who said] like a beam "Me'asef l'Chol ha'Machanos l'Tziv'osam''?

Answer: Because Shevet Dan had many people, they traveled at the end, and anyone who lost something, [Shevet Dan] would return it to him. This is why it says "Me'asef l'Chol ha'Machanos l'Tziv'osam.''

(Beraisa): In the name of R. Yehudah, they said that even [a house's] ledges and walls are measured with it.

Question (R. Hoshayah): The air (unenclosed area) of a [breached] Chatzer - is it measured with it?

Answer: We learn from the following [Beraisa]. If a house was breached from one side, it is measured with it. If it was breached from two sides, it is not measured with it;

[And] R. Avin said that in the name of that this is when its roof was removed, but if it was not removed, it is measured with it.

Summation of answer: If its roof was removed, is it not like the air of a Chatzer?!

Rejection: There, [a house] was made to dwell in it. (If its roof was removed, and it is breached from two sides, it is totally Batel from its purpose). Here, [a Chatzer] was not made to dwell in it. (Even without a roof, it serves its purpose. Therefore, it is measured with it. We explained this like CHASAM SOFER.)

When he measures [the Techum of 2000 Amos], he does not measure from the middle [of the corner on the diagonal], for he would lose [the excess of the diagonal over the side]. Rather, [he measures straight, i.e. east, north, west or south] from the corner [and completes the rectangle].