elem.6.12
给定三条线段A、B、C，求作一条线段X，使得A比B等于C比X。
求三条已知量 A、B、C 的第四比例项（DE、EF、DG 分别表示 A、B、C）：在两条相交线上分别截取已知段，过 F 作平行于 EG 的直线交另一线于 H，则 GH 为所求第四比例项。
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Let A, B, C be the three given straight lines; thus it is required to find a fourth proportional to A, B, C.
作任意角∠EDF，在DE上截取DG等于A，GE等于B，在DF上截取DH等于C。
Let two straight lines DE, DF be set out containing any angle EDF; let DG be made equal to A, GE equal to B, and further DH equal to C; let GH be joined, and let EF be drawn through E parallel to it.
连接GH，过E作EF平行于GH（I.31）。
[I. 31] Since, then, GH has been drawn parallel to EF, one of the sides of the triangle DEF, therefore, as DG is to GE, so is DH to HF.
因为GH平行于三角形DEF的一边EF，所以DG比GE等于DH比HF（VI.2）。
[VI. 2] But DG is equal to A, GE to B, and DH to C; therefore, as A is to B, so is C to HF.
由于DG等于A，GE等于B，DH等于C，因此A比B等于C比HF，即HF为所求第四比例项。