Commentary for Eruvin 113:12

וכן ג' כפרים המשולשין אם יש בין שנים חיצונים מאה וארבעים ואחת ושליש עשה אמצעי את שלשתן להיות אחד:

only six hundred and sixty-seven minus a third?<span class="x" onmousemove="('comment',' If the difference between a square and a circle is a quarter of the former it is also (since the proportion of the two figures is 3:4) a third of the latter. The difference consequently between a line of two thousand cubits (which may be regarded as the diameter of a circle) and the diagonal of a square whose sides measure two thousand cubits should be a third of two thousand 2000/3 = 666 2/3 or 667 - 1/3.');">²²</span> - The other replied: This<span class="x" onmousemove="('comment',' That the approximate difference between the area of a square and that of a circle is a quarter of the former or a third of the latter.');">²³</span> applies only to a circle inscribed within a square, but in the case of the diagonal - of a square<span class="x" onmousemove="('comment',' In relation to any of its sides.');">²⁴</span>

Explore commentary for Eruvin 113:12. In-depth commentary and analysis from classical Jewish sources.