Page:The Elements of Euclid for the Use of Schools and Colleges - 1872.djvu/273

Rh ABCD, because, by hypothesis, the space T is greater than the circle EFGH. [V. 14.

Therefore the square on FH is to the square on BD as the circle EFGH is to some space less than the circle ABCD; which has been shewn to be impossible. Therefore the square on BD is not to the square on FH as the circle ABCD is to any space greater than the circle EFGH.

And it has been shewn that the square on BD is not to the square on FH as the circle ABCD is to any space less than the circle EFGH. Therefore the square on BD is to the square on FH as the circle ABCD is to the circle EFGH,

Wherefore, circles &c.