内容 第10卷 · 301
命题 Propositio X.24
The rectangle contained by medial straight lines commensurable in length is medial.
由长度可公度的中项线段所围成的矩形是中项面。
本页以“中项线段的矩形仍为中项”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。
分步证明Step-by-step proof
1 / 4For let the rectangle AC be contained by the medial straight lines AB, BC which are commensurable in length; I say that AC is medial.
设矩形AC由长度可公度的中项线段AB、BC围成。
For on AB let the square AD be described; therefore AD is medial.
在AB上作正方形AD，则AD是中项面。
And, since AB is commensurable in length with BC, while AB is equal to BD, therefore DB is also commensurable in length with BC; so that DA is also commensurable with AC.
因为AB与BC长度可公度，且AB等于BD，所以DB与BC长度可公度，从而DA与AC可公度。
由于DA是中项面，且与AC可公度，故AC也是中项面。
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