The rectangle contained by rational straight lines commensurable in length is rational.
由长度可公度的有理线段所围成的矩形是有理的。
本页以“有理线段所成矩形为有理”整体图解辅助阅读；点、线、角、圆索引已按命题文字和证明步骤校订，可与证明和问答联动。
正文图形由校订坐标生成；点、线、角、圆可与证明和问答联动。
For let the rectangle AC be contained by the rational straight lines AB, BC commensurable in length; I say that AC is rational. For on AB let the square AD be described; therefore AD is rational.
设矩形AC由长度可公度的有理线段AB、BC围成。
[X. Def. 4] And, since AB is commensurable in length with BC, while AB is equal to BD, therefore BD is commensurable in length with BC.
在AB上作正方形AD，则AD是有理的。
And, as BD is to BC, so is DA to AC. [VI. 1] Therefore DA is commensurable with AC.
由于AB与BC长度可公度，且AB等于BD，故BD与BC长度可公度。
[X. 11] But DA is rational; therefore AC is also rational.
由BD比BC等于DA比AC，得DA与AC可公度，而DA为有理，故AC也为有理。