From a medial straight line there arise irrational straight lines infinite in number, and none of them is the same as any of the preceding.
从一条中项线可以产生无穷多条无理线段，且其中没有一条与前面任何一条相同。
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Let A be a medial straight line; I say that from A there arise irrational straight lines infinite in number, and none of them is the same as any of the preceding. Let a rational straight line B be set out, and let the square on C be equal to the rectangle B, A; therefore C is irrational; [X. Def. 4] for that which is contained by an irrational and a rational straight line is irrational.
设A是一条中项线，取一条有理线段B，作线段C使得以C为边的正方形等于以B、A为边的矩形，则C是无理线，且不与前面任何一条相同。
[deduction from X. 20] And it is not the same with any of the preceding; for the square on none of the preceding, if applied to a rational straight line produces as breadth a medial straight line.
因为无理线与有理线所成矩形是无理的，且前面任何一条线段以有理线为边作正方形时，其宽度都不是中项线。
Again, let the square on D be equal to the rectangle B, C; therefore the square on D is irrational.
再作线段D使得以D为边的正方形等于以B、C为边的矩形，则D是无理线。
[deduction from X. 20] Therefore D is irrational; [X. Def. 4] and it is not the same with any of the preceding, for the square on none of the preceding, if applied to a rational straight line, produces C as breadth.
同样，D不与前面任何一条相同，因为前面任何一条线段以有理线为边作正方形时，其宽度都不是C。