If two numbers by multiplying one another make a square number, they are similar plane numbers.
若两数相乘得平方数，则它们是相似平面数。
数 A、B 与它们的积 C（设为平方数）以堆叠水平线段表示；令 D = A·A 也为平方数，由 D 与 C 之间比例中项可推 A、B 之间也有比例中项，故 A、B 为相似平面数。
正文图形由校订坐标生成；点、线、角、圆可与证明和问答联动。
Let A, B be two numbers, and let A by multiplying B make the square number C; I say that A, B are similar plane numbers. For let A by multiplying itself make D; therefore D is square.
设A、B两数，A乘B得平方数C。
Now, since A by multiplying itself has made D, and by multiplying B has made C, therefore, as A is to B, so is D to C.
令A自乘得D，则D为平方数。
[VII. 17] And, since D is square, and C is so also, therefore D, C are similar plane numbers. Therefore one mean proportional number falls between D, C.
因A自乘得D，乘B得C，故A比B等于D比C。
[VIII. 18] And, as D is to C, so is A to B; therefore one mean proportional number falls between A, B also.
D、C均为平方数，故为相似平面数，其间有一个比例中项；因此A、B之间也有一个比例中项，故A、B为相似平面数。