1)[line 3]בדיק להו רחבהBADIK LEHU RACHVA- Rachva asked the following question in order to see if the Chachamim to whom he posed it were able to answer properly
2)[line 4]ב' חצרות וב' בתים ביניהםSHTEI CHATZEROS V'SHNEI BATIM BEINEIHEM- two houses attached back to back, which are in two different Chatzeros. Instead of joining the two Chatzeros with a joint Eruv, each Chatzer made their own Eruv and placed in the far house; i.e. the one in the other Chatzer. Therefore, from the viewpoint of one Chatzer the first house is a Beis Sha'ar and the second a Bayis, and vice versa from the opposite direction.
3)[line 14]וערבV'AREV- and make an Eruv [Chatzeros]
4)[line 19]שניהם קנו עירובSHENEIHEM KANEI ERUV- It is unclear whether Bein ha'Shemashos is nighttime or daytime. Since we are always lenient when it comes to the laws of Eruvin, we assume that when the first person ate his Eruv during Bein ha'Shemashos, Shabbos had already begun, and yet for the second person we assume that when the Eruv was placed during Bein ha'Shemashos it was not yet Shabbos.
5)[line 20]לא מינכרא מילתאLO MINKERA MILSA- the ruling of the Chachamim does not appear to contradict itself
PEREK #7 CHALON
6)[line 25]מערבין שנים ואם רצו מערבין א'ME'ARVIN SHENAYIM V'IM RATZU ME'ARVIN ECHAD- these two Chatzeros have a choice: they may make two separate Eruvin, in which case the residents of one may not carry to the other, or they may join in one single Eruv which may be placed in either of the two Chatzeros.
7)[line 29]כלבודLAVUD
(a)The Torah requires Mechitzos (partitions) for various Halachos (e.g. defining a Reshus ha'Yachid for the purposes of carrying on Shabbos and creating a Kosher Sukah). A Mechitzah must be ten Tefachim high and enclose an area of four by four Tefachim.
(b)Certain Halachos l'Moshe mi'Sinai allow one to consider certain incomplete Mechitzos as complete for Halachic purposes (Sukah 5b).
(c)One of these cases is Lavud (lit. a branch or connection). This Halachah states that when there is a space less than three full Tefachim between the Mechitzah and the surface (or object) next to, above, or below it, we consider it to be a complete Mechitzah in which the surfaces or objects are connected without any gaps. (The space itself is not ignored, but rather measured along with and as a part of the existing segment of the partition.)
(d)Raban Shimon ben Gamliel is of the opinion that the distance which this Halachah l'Moshe mi'Sinai considers to be "connected" is four Tefachim, not three. The Gemara suggests that this is why our Mishnah requires a window connecting two Reshuyos to be at least four Tefachim — any hole small enough to be considered attached through Lavud cannot be considered a significant enough breach in the wall to be a Pesach.
8)[line 42]בהיקפוHEKEFO- its circumference
9)[line 43]ושנים ומשהו מהן בתוך י'U'SHENAYIM U'MASHEHU MEHEN B'SOCH ASARAH...- that is, a bit more than two Tefachim aside from an additional four Tefachim of the circumference (that is, 6-plus Tefachim of the circumference) is within ten Tefachim from the ground, in order for the lower edge of the four-by-four square circumscribed by the circle to be within ten Tefachim of the ground. (RASHI, see SEFAS EMES. See also Insights.)
76b----------------------------------------76b
10)[line 1]בריבועאRIBU'A- a square
11)[line 2]כמה מרובע יתר על העגול? רביע!KAMAH MERUBA YESER AL HA'IGUL? REVI'A!- how much greater is the perimeter of a square than the circumference of a circle (whose diameter is the same length as the side of the square)? One fourth (of the perimeter of the square which is one third of the circumference of the circle)! (See Insights and Graphic.)
12a)[line 3]עיגולא דנפיק מגו ריבועאIGULA D'NAFIK MIGO RIBU'A- a circle that is inscribed within a square
b)[line 4]ריבועא דנפיק מגו עיגולאRIBU'A D'NAFIK MIGO IGULA- a square that is inscribed within a circle
13)[line 5]מורשא דקרנתאMURSHA D'KARNASA- the projections of the corners
14)[line 6]כל אמתא בריבוע אמתא ותרי חומשי באלכסונאKOL AMSA B'RIBU'A, AMSA U'TREI CHUMSHEI B'ALACHSONA- for every Amah along the side of a square, the diagonal increases by one and two-fifths Amos
15)[line 7]בשיבסר נכי חומשאSHIVSAR NAKI CHUMSHA- 17 less a fifth, i.e. 16 4/5, as follows:
1.The diagonal of a square with a side of four Tefachim is 4 X 1 2/5 = 4 8/5 = 5 3/5 Tefachim.
2.The circumference of a circle with a diameter of 5 3/5 Tefachim is 3 X 5 3/5 = 15 9/5 = 16 4/5 Tefachim (using 3 as the rounded value of pi, as the Gemara states on the last line of 76a).
16)[line 10]ריבועא מגו עיגולא פלגאRIBU'A MIGO IGULA PALGA- [when] a square [is] inscribed within a circle, [the circumference of that circle is] half [again the perimeter of the square]
17)[line 14]כמאן דמלי דמיK'MAN D'MALI DAMI- is as if it is filled up (i.e. the whole house is considered to be within ten Tefachim from the ground)
18)[line 21]לול הפתוח מן בית לעלייהLUL HA'PASU'ACH MIN HA'BAYIS LA'ALIYAH- a [four-by-four Tefach] window in the ceiling of a house (higher than ten Tefachim), connecting it to an attic [owned by someone else]
19)[line 31]ורוחב ארבעהROCHAV ARBA'AH- four Tefachim thick. This detail is mentioned only because it affects the case of the Seifa, in which fruit is upon the wall, since it is considered a separate Reshus unto itself. In terms of being considered a Mechitzah, any thickness would suffice.
20)[last line]מלא נימאMELO NIMA- a hairbreadth