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我在讲授高中平面几何时,结合教材内容,设计了一种简单的几何作图仪器。利用它,能够很快地分一条不十分长的线段成若干部分,使它们的比等于已知的比。这种仪器,我把它叫做定比分割仪。定比分割仪是根据关于比例线段的一个定理:“如果一个角的两边被若干条平行线所截,那末这两边被这些平行线分为成比例的线段”的原理制成的。根据需要,它可以用木条、竹条或赛璐珞等制成。它的构造很简单,可以用下面的略图来说明。(图1)
When I was teaching high school plane geometry, I combined the teaching materials and designed a simple geometric mapping instrument. With it, it is possible to quickly divide a line segment that is not very long into parts so that their ratio is equal to the known ratio. This instrument, I call it fixed splitter. The split ratio divider is based on a theorem about proportional line segments: “If two sides of a corner are cut by several parallel lines, then the two sides are divided into proportional segments by these parallel lines.” According to needs, it can be made of wood strips, bamboo strips or cellophane. Its construction is very simple and can be illustrated with the following sketch. (figure 1)