You wrote "SQUARE" and I believe it should be "CIRCLE"
you take away 1/2 of what's left IN THE CIRCLE. THE SQYARE IS IN THE CIRCLE. The remaining around the square (IN THE CIRCLE) is circle-space.
Explanation #1: Rashi explains that when you make a square inside a circle, you take away half of what is left in the square, which means one third of the entire circle. Therefore, for a square of sixteen one requires a circle that surrounds it (i.e. circumference) to be twenty four.
Rafael Aryeh Smith
Shalom u'vrachah,
Thank you for your thoughtful comment!
Maybe this can be rendered more clearly as follows:
"Rashi explains that when you make a square inside a circle, [the area of the portion] you are taking away [from the circle, i.e. the portion of the circle that lies outside the square] is half the area of the portion remaining inside [the circle, i.e. the portion of the circle that lies inside the square], which means one third [the area] of the entire circle."
Bi'Vrachah,
Yishai Rasowsky