Sukkah 15

Chapter 15

א הני מילי בעיגולא אבל בריבועא בעיא טפי
1 That applies only to a circle, but in the case of a square, a greater perimeter is required.
ב מכדי כמה מרובע יותר על העיגול רביע בשיתסר סגי
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]?
ג ה"מ בעיגול דנפיק מגו ריבועא <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAD8AAAA/CAYAAABXXxDfAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAQ9SURBVGhD7ZotUMNAEIUrkUgkEolEIpFIJBKJxCGRSCQSiUQikUgkEolEhvk62ZmXm1fu8tP2SvvN7EyaXC737mdvs+ms2WJ24reVnfhtxYp/eXlpDg8Pm9lstvGGjsfHx1ZZFyv+4ODAVrSptre31yrrYsW7CjbdHFnxY3h/f29ub2+b4+PjTp0lxnS9urpqXl9f29r6o/U5liKeBg8RvMjoiKenp7b2crQOx6TiPz4+mvPz8879Yay7i4uL+Ux4eHiYd5AaTolrjPYin3NycjIvW4re65hM/PX1dec+bH9/fy7m+fm5LVXO29vbvE6369CJ39/fbcnF6D2O0eJpxOnpaeceRpmGlzQwx8/PT3N3dzfvSH3G0dHRfKb9hZZ3jBLPw2mElj87O2s+Pz/bEtNBRzKL9Fl0yF+zSss6BotHeDoaNzc37dXlgeNjZulzFzlDLeMYJJ5R0LVIY4Z446GwhabPx0ekxHXM0Vs8a1DXOA/u44Gn4uvrq9MB7BDpcotrmKO3+HTdrXLEU9Klx1bI4ATaTkcv8Uw3vbaKNZ6DlzBt0/39fXtlYvEawHBcC2yF0S6mP0sC4hzmKBbPlhLnWOfxgBpgqmtUSIwB8RtzFIvXWD0qrwnC42hfDE78xhxF4vHm8ZseVqdSEzpAvD/EMeYoEo9ji981jnqgo5+G3I4i8bqfrmNPL4XgK9rJ1I9jzJEVz14ax+yptZOOeJgjK559M44vLy/bEvWi7VVzZMXretcAolbUOas5suIZ7TheZyhbCvG9tj/MkRWva6hmZxeo01NzZMVrsmIZSYplkHp6zJEVr9vcpoh3CVBHVrxOe5cwqBFtf5gjK55MaRwPycKumkkdHuFsHC/64FcTzE5tf5gjK54PCXFcQ/IiB9uxtj/MkRWvmRI8f+1oXKLmyIrn9VXzZDV7/LStao6seFCnR8qoVjS0TT+mOIrE6zoiYVArmmPUdxLMUSSekFGnU40xfppZTn87isSDvirWmMrSYCwyy/EbcxSLR6yGujWtfc0sY4w66DlHsXhI09c1vOWln61wzkGcwxy9xAOfhOIafmCdWx+zMW2Pfk+I85ijt3jE6lsT3n9d6z/9bkhApug1R2/xwHTXd2Z6f5VfcOjsVLhLsel1xyDxkH4UYN2Fo1kmdLJOdUzXuaJlHIPFQ5opZTbQKcuCGafODUP4omWn5RyjxAM7QBpP4wfS9TcGZhT/9dFnYLlsspZ1jBYPNC4dEYzAY0wChHdzfa8Io7NL6tV7HJOIB0JgEh8uecg5RJAM+Ss2oBMRhTNzeTiM6K10e9X7HJOJD2iYGy1nCEzfvhYZs6ivQ9X7HZOLD/jGN/RPx2EsJWbB0MSp1uVYmniF2cAugNNiBN2UZmlwDaPTptg2tX5HVvx/MYc965zWppvDntV/N/0Hw284fJdsCTvx28pO/HbSNL+mIBO4Y4g7cgAAAABJRU5ErkJggg=="> אבל ריבועא דנפיק מגו עגולא <img src="data:image/png;base64,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"> בעיא טפי משום מורשא דקרנתא
3 That 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....
ד מכדי כל אמתא בריבועא אמתא ותרי חומשא באלכסונא בשיבסר נכי חומשי סגיא לא דק
4 But consider: If the side of a square is a cubit, its diagonal is approximately one and two fifths cubits. Should not then [a circumference equivalent to] sixteen and four fifths [cubits] suffice? [R. Johanan] gave only an approximate figure.
ה אימור דאמרינן לא דק פורתא טובא מי אמרינן לא דק
5 Say that we say that [where the discrepancy is] small he might approximate, but could such an assumption be made [where the discrepancy is] big?
ו א"ל מר קשישא בריה דרב חסדא לרב אשי מי סברת גברא באמתא יתיב תלתא גברי בתרתי אמתא יתבי כמה הוו להו שיתסר אנן שיבסר נכי חומשא בעינן לא דק
6 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. [Because, as has been said, R. Yohanan] gave only an approximate figure...
ז אימור דאמרינן לא דק לחומרא לקולא מי אמרינן לא דק
7 Say that we give approximate figures in order to create a where this makes the law lenient?
ח אמר ליה רב אסי לרב אשי לעולם גברא באמתא יתיב ורבי יוחנן מקום גברי לא קחשיב
8 R. Assi said to R. Ashi: In truth, a man occupies a cubitspace, but R. Yohanan does not include the space occupied by the men.
ט כמה הוו להו תמני סרי בשיבסר נכי חומשא סגיא היינו דלא דק ולחומרא לא דק
9 How many [cubits] does this[amount to]? Eighteen; while sixteen and four-fifths would be enough. 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.
י רבנן דקיסרי ואמרי לה דייני דקיסרי אמרי עיגולא דנפיק מגו ריבועא רבעא
10 The rabbis of Caesarea (and some say, the judges of Caesarea) say: The circumference of a circle inscribed in a square is a quarter;
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