Sukkah

— That1 applies only to a circle, but in the case of a square, a greater perimeter is required.2 But consider: By how much is a square greater than its [inscribed] circle? By a quarter. Should it then not suffice if only sixteen [men can be seated around it]?3 -That4 is so in the case of a circle inscribed within a square, but if a square is to be inscribed within a circle a greater circumference is required on account of the projection of the corners.5 But consider: If the side of a square is a cubit, its diagonal is approximately one and two fifths cubits.6 Should not then [a circumference equivalent to] sixteen and four fifths [cubits]7 suffice?8 — [R. Johanan] gave only an approximate figure. But is it not to be maintained that one may be assumed to give all approximate figure only [where the discrepancy is] small, but could such all assumption be made [where the discrepancy is] big? — Mar Kashisha the son of R. Hisda said to R. Ashi: Do you think that a man occupies one cubit? [The fact is that] three men occupy two cubits. How much then does this [amount to for twenty-four men]? Sixteen cubits; and we [really] demand here sixteen and four fifths,9 [because, as has been said, R. Johanan] gave only an approximate figure. But is it not to be maintained that one may be assumed to give approximate figures only when the law is thereby restricted, but could such an assumption be made where a law is thereby relaxed?-R. Assi answered R. Ashi: In truth, a man occupies a cubit-space, but R. Johanan does not include the space occupied by the men.10 How many [cubits] does this11 [amount to]? Eighteen;12 while sixteen and four-fifths suffice. That is [then] what was meant [when it was stated] that he only gave an approximate figure; and in this case it is in the direction of stringency.13 The Rabbis of Caesarea14 (and some say, The judges of Caesarea) maintain, The circumference of a circle inscribed in a square is a quarter; 15 diameter of four cubits accommodates four times three is twelve men, a square of four cubits provides seating capacity for four times four is sixteen men. A circumference of sixteen cubits should, therefore, have sufficed. one of twelve cubits. approximately equivalent to three, a circumference of 3 X 5 3/5 cubits 16-4/5 cubits ought to suffice. (For this whole discussion of Feldman, op. cit., pp. 28-30). Cf. also ‘Er., Sonc. ed., p. 531ff, notes. of twenty-four cubits (equivalent to the space occupied by twenty-four men) with a diameter of eight cubits. But the inner circumference formed by the Sukkah is smaller since its diameter is eight minus two (the space occupied lengthways by the legs of two men, one sitting at each end) is six cubits. 3/5= 2/5) is even less Caesarea’ are often quoted. V. Bacher, Die Gelehrten von Caesarea in MGWJ.XLV, p. 298.