Eruvin

Our Rabbis taught: If [a circular] town is to be [circumscribed by a] square1 [the sides must be] drawn in the shape of a square tablet. The Sabbath limits also are then drawn in the shape of a square tablet.2 When the measurements1 are taken one should not measure the two thousand cubits3 from the middle point of the town corner,4 because, thereby, one loses the corners.5 One should rather imagine6 that a square tablet of the size of two thousand cubits by two thousand cubits is applied to each corner diagonally,7 so that the town gains thereby four hundred cubits in each corner,8 the Sabbath limits gain eight hundred cubits in each corner,9 while the town and the Sabbath limits together gain twelve hundred cubits10 in each corner.11 This12 is possible, Abaye explained. in a town of the size of two thousand by two thousand cubits.13 It was taught: R. Eliezer son of R. Jose stated: The limit of the allotted land beyond the confines of the levitical cities14 was two thousand cubits.15 Deducting from these16 an open space of one thousand cubits,17 such open space would represent a quarter of the entire area18 the remainder of which consisted of fields and vineyards.19 Whence is this20 deduced? — Raba replied: From Scripture which says. [And the open land,..] from the wall of the city and outward a thousand cubits round about,21 the Torah has thus enjoined, ‘Surround the city by an open space of one thousand cubits’. ‘Such an open space [it was said] would represent a quarter of the entire area’ — ‘A quarter’! Is it not in fact one [in the neighbourhood] of a half?22 — Raba replied: The surveyor Bar Adda23 explained this to me. Such a proportion is possible in the case of a town whose area is two thousand by two thousand cubits. For what is the area of its limits?24 Sixteen [million square cubits].25 What is the area of the corners?26 Also sixteen [million square cubits].27 Deducting [for the open spaces] eight [million square cubits]28 front the limits, and four [million square cubits]29 from the corners, to what area would this space amount? To one of twelve [million square cubits].30 Would then ‘such an open space represent a quarter’? Is it not in fact more than a third of the entire area?31 — Take the four [million square cubits] of the town area itself and add to them.32 Does not this, however, still amount to a third?33 — Do you imagine that a quadrilateral town was spoken off? No, a circular town was meant. For by how much does the area of a square exceed that of a circle? By one quarter [approximately] — Deduct a quarter from the measurements given and there would remain nine [million square cubits];34 and nine [million] represents one quarter of thirty six [million].35 Abaye said: This36 is also possible in the case of a town that has an area of a thousand by a thousand cubits For what are its limits?37 Eight [million square cubits].38 What is the area of the corners? Sixteen [million square cubits].39 form a larger square. square, the diagonal of the latter forming a straight line with that of the former. shape and the diameter of which is two thousand cubits. By enclosing it in an imaginary square the diagonal of which (on the rule that the diagonal of a square exceeds its side by two fifths approx.) the town is extended in each of its four corners by ((2000 X 2/5)/2) = 4000/10 = 400 cubits (cf. foll. n.). square tablet of the size of two thousand cubits by two thousand cubits applied to each corner diagonally’ would consequently add to each corner two thousand cubits plus (2000 x 2)/5 = 800 cubits. fields and vineyards as will be specified below. open space on the present assumption would, of course, be less than a half of the total area, since an inner belt of the width of a thousand cubits is smaller in area than one of equal width around it. 16,000,000 square cubits. cubits on each of the four sides 2,000,000 X 4 = 8,000,000 sq. cubits. shape has only an area of 4,000,000 X 3/4 = 3,000,000 sq. cubits approx. The belt of open spaces around it, which was originally assumed to have an area of 12,000,000 sq. cubits would similarly amount to 4,000 (city, 2,000, and open spaces on two of its sides 2,000) by 4,000 X 3/4 (difference between area of sq. and circle) 3,000,000 approx. (area of circular city). 4,000 X 4,000 X 3/4 — 3,000,000 = 12,000,000 — 3,000,000 = 9,000.000 sq. cubits. vineyards allowed to each levitical city. The shape of the city does not affect this outer area which always extends to a perpendicular distance of 2,000 cubits from it in all directions of the city. 16,000,000 sq. cubits.