If two numbers have to one another the ratio which a square number has to a square number, and the first be square, the second will also be square.
若两数之比等于一个平方数与另一个平方数之比，且第一个数是平方数，则第二个数也是平方数。
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For let the two numbers A, B have to one another the ratio which the square number C has to the square number D, and let A be square; I say that B is also square.
设两数A、B之比等于平方数C与平方数D之比，且A是平方数。
For, since C, D are square, C, D are similar plane numbers.
由于C、D是平方数，它们是相似面数，因此C、D之间有一个比例中项数。
Therefore one mean proportional number falls between C, D.
因为C比D等于A比B，所以A、B之间也有一个比例中项数。
[VIII. 18] And, as C is to D, so is A to B; therefore one mean proportional number falls between A, B also.
由于A是平方数，且A、B之间有一个比例中项数，故B也是平方数。