finding a circle whose area is the same as that of a square (the reverse of squaring the circle).

Draw half its diagonal about the centre towards the East–West line; then describe a circle together with a third part of that which lies outside the square.

Explanation:

• Draw the half-diagonal of the square, which is larger than the half-side by 
  {displaystyle x={a over 2}{sqrt {2}}-{a over 2}}.
• Then draw a circle with radius 
  {displaystyle {a over 2}+{x over 3}}, or

  {displaystyle {a over 2}+{a over 6}({sqrt {2}}-1)}, which equals

  {displaystyle {a over 6}(2+{sqrt {2}})}.

• Now 
  {displaystyle (2+{sqrt {2}})^{2}approx 11.66approx {36.6 over pi }}, so the area

  {displaystyle {pi }r^{2}approx pi times {a^{2} over 6^{2}}times {36.6 over pi }approx a^{2}}.