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Eruvin 76

ERUVIN 76 - dedicated by Dick and Beverly Horowitz and sons Sam and Mike, in memory of Beverly's mother, Miriam Kurtz.

*****PEREK #7 CHALON*****

*1*) [line 43] U'SHNAYIM U'MASHEHU MEHEN B'SOCH ASARAH - that is, a bit more than two Tefachim *besides another four Tefachim* of the circumference (that is, 6 Tefachim+ of the circumference) is within 10 Tefachim from the ground. (RASHI, see SEFAS EMES)

2) [last line] HEKEFO - its circumference


3) [line 1] RIBU'A - a square
4) [line 2] KAMAH MERUBA YESER AL HA'IGUL? REVI'A! - how much is the perimeter of a square greater 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.)

5a) [line 3] IGULA D'NAFIK MIGO RIBU'A - a circle that is inscribed inside a square
b) [line 4] RIBU'A D'NAFIK MIGO IGULA - a square that is inscribed inside a circle

6) [line 5] MURSHA D'KARNASA - the projections of the corners
7) [line 6] KOL AMSA B'RIBU'A, AMSA U'TREI CHUMSHEI B'ALACHSONA - for every Amah along each side of a square the diagonal increases by an one and two-fifths of an Amah

8) [line 7] SHIVSAR NAKI CHUMSA - 17 less a fifth, i.e. 16 4/5 The diagonal of a square with a side of four Tefachim is 4 X 1 2/5 = 4 8/5 = 5 3/5 Tefachim
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)

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