To determine the catenary curves of arches, he would tack a sketch of a foundation plan on the ceiling, hang loops of string, and attach weights along the loops in proportion to down forces.

为了确定拱顶的链状曲线，他会用大头针将基座草稿钉到天花板上，吊上几圈绳子，在绳子上加重，与向下的力相符。

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In the terminology of the next section, these three utility functions would have identical indifference curves even though they attach different Numbers to the curves.

如果以下一节的术语来表述，则是三个效用函数具有同样的无差异曲线，尽管它们为各曲线标上了不同的效用值。

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