THINGS THAT ARE DETRIMENTAL TO HEALTH
Answer: Garlic and leeks are good, and other vegetables are bad. (Some say vice-versa).
(Beraisa): Garlic is a full vegetable (it is very good. Some say that it is very bad.) Leeks are a half vegetable.
Radishes are an elixir of life.
Contradiction (Beraisa): Radishes are a lethal poison.
Version #1 (Tosfos) Resolution: The leaves are bad and the roots are good in one season (winter or summer). In the other season they are vice-versa.
Version #2 (Tosfos) Resolution #1: The leaves are bad, and the roots are good.
Resolution #2: The leaves are good in one season, but bad in the other. (The roots are always good.) (end of Version #2)
(Rav Yehudah): If there are inclines in a city, people and animals die after half their normal lifetime [due to the strain].
Objection: This cannot be!
Answer: Rather, they start aging after half their normal lifetime;
(Rav Huna brei d'Rav Yehoshua): The inclines between Bei Biri and Bei Narash aged me.
THE FOUR TEKUFOS
(Beraisa #1): One squares a city according to the directions of the world -- north-south and east-west;
[If one does not know which way is north,] he can learn from the constellations. The calf is in the north, and scorpion is in the south.
R. Yosi says, if he does not know the directions, he can square it according to the [trajectory of the sun in] different seasons;
On a long day (summer), the sun rises in the north[east] and sets in the north[west]. The line between these is north (i.e. the north border should be parallel to this line. The Gemara always assumes that one is in the northern hemisphere. The same method may be used in the southern hemisphere, between Iyar and Elul. However, there, these are short winter days.)
On a short winter day, the sun rises in the south[east] and sets in the south[west]. The line between these is south.
In Tekufas Nisan and Tekufas Tishrei (the equinoxes), the sun rises due east and sets due west.
"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" - sometimes (i.e. in summer) the sun travels along the east and west [by day, when we see it. I.e. it rises in the northeast and goes to the southeast, and later goes from the southwest to the northwest, and sets there.] Sometimes (i.e. in winter) it circles around the east and west (traverses these sides at night, out of our sight).
(Rav Mesharshiya): These rules are not always true!
(Beraisa #2): The sun never rose [due] northeast and set [due] northwest. It never rose [due] southeast and set [due] southwest. (See note 21 in Appendix.)
(Shmuel): Tekufas Nisan always occurs at one of the four quarters of the day, i.e. the beginning of the day or night, or the middle of the day or night. (This is the moment [at the start of spring] when the sun is directly overhead at the equator. It is also directly overhead there at Tekufas Tishrei (the start of fall). Tekufas Tamuz and Teves are, respectively, when the sun is as far north and south as it ever gets [23 and a half degrees north and south of the equator]. These are the longest and shortest days of the year. A year of [four] Tekufos is 365 and a quarter days. Each Tekufah occurs six hours later in the day than it did the previous year. See note 22 in Appendix.)
Tekufas Tamuz always occurs at one and a half hours of the day, or seven and a half hours, or at one of these two times in the night. (This is because the interval between successive Tekufos is a quarter of 365 days and six hours, i.e. 91 days, seven and a half hours.)
Tekufas Tishrei always occurs at three or nine hours of the day or night. Tekufas Teves always occurs at four and a half or 10 and a half hours of the day or night.
The interval successive Tekufos is 91 days and seven and a half hours. Each Tekufah is a half hour past the previous one [regarding the seven Kochvei Lechet. These are the five closest planets, the sun and the moon. Every hour, one of them dominates (has a supernatural influence on earth), according to a fixed rotation that repeats itself every seven hours. The interval between Tekufos is 13 weeks (a week has 24 full rotations of dominations of the Kochvei Lechet) and seven and a half hours, i.e. a rotation and an extra half hour.]
(Shmuel): When Tekufas Nisan falls during [the dominant hour of] Tzedek (Jupiter), trees break (perhaps from great winds - PF). When Tekufas Teves falls during Tzedek, crops dry up;
These apply only if the Molad (new moon, of that month) occurred when the moon or Tzedek was dominant.
SQUARING A CITY
(Beraisa): One who squares a city makes it like a square board. He then squares the Techum, and makes it like a square board.
We do not measure 2000 Amos from the middle of the corner (i.e. on the diagonal), for then he would lose [due to] the corners. (In Rashi's diagram, the Techum would be the line below the top line. This is too small);
Rather, we add a square of 2000 Amos by 2000 Amos in the corner on the diagonal. The city gains 400 Amos in each direction (we will explain when this is true), and the Techum gains 800 Amos in each direction (the excess of the diagonal of a square of side 2000 over the side), altogether 1200 in each direction. (See Perush Chai diagram, Perek 5 number 49, in the English Charts section.)
(Abaye): This applies to a [round] city that is 2000 by 2000 Amos. (If we divide it into four quadrants, each is a quarter-circle in a square whose side is 1000 Amos. The diagonal adds 400 Amos.)
(Beraisa - R. Eliezer b'Ribi Yosi): The Techum of cities of Leviyim is 2000 Amos. One thousand Amos are Migrash (they are left vacant). This is a quarter. (This will be explained.) The rest is for fields and vineyards.
Question: What is the source of this?
Answer (Rava): "Mi'Kir ha'Ir va'Chutzah Elef Amah Soviv" teaches that we must surround the city with 1000 Amos.
Question: The Beraisa says that the Migrash is a quarter. Really, it is half! (The entire Techum is 2000.)
Answer #1 (Rava citing Rav Ada of Shucha'ah): The case is, the city is 2000 by 2000 Amos. (The Migrash is a quarter of the area of the Techum. We shall calculate the area in square Mil. One Mil is 1000 Amos. A square Mil is a million square Amos):
The Techum [itself, two Mil in every direction without the corners] is four [square Mil, i.e. a square of two by two in each of four directions]; the corners are another [four squares of the same size, i.e.] 16. (In all, it is 32);
The Migrash [itself, without the corners] is eight [square Mil, i.e. a rectangle one by two Mil in each of four directions]; the corners are another [four squares of one by one, i.e.] four; altogether it is 12.
Question: The Migrash is not a quarter! Rather, it is [12 divided by 32, which is] more than a third!
Answer #1: The Migrash is a quarter of the city and the Techum together. We must add another four for the area of the city.
Question: The Migrash is [12 divided by 36, i.e.] a third!
Answer: Your calculations are for a square [city and Migrash]. Really, they are circles!
A circle is three quarters of the area of the square around it. Therefore, the area of the Migrash is three quarters of [our previous calculation of] 12, i.e. nine. (The city with the Migrash is a circle of radius two [Mil] and area 12. The radius of the city itself is one, so its area is three, so the area of the Migrash is nine);
Nine is a quarter of 36. (The Techum is still square.)