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关于平面截对顶圆锥的问题,我们的做法主要是基于下面的定理: Desargues定理:若两个三角形对应的顶点的连线共点,则对应边所在直线的交点共线,其逆也真。 这个定理的适应范围很广,不仅在平面内成立,而且对于空间也成立,作为空间的情况在立体几何中常作为习题出现在参考书中,我们只应用其结论,不给证明。 定理还包含平行的情况,认为是交于无穷远点。 那么,应用定理来处理“求作通过不在一条直线上的三个已知点确定的平面与已知几何体的截面”(图1)就可以应用定理而采取以下步骤:
Regarding the problem of plane truncated top cone, our approach is based on the following theorem: Desargues theorem: If the two lines of the corresponding vertices of the corresponding point, then the corresponding point of the line where the intersection of the line is collinear, the inverse is true. This theorem has a wide range of adaptation, not only in the plane, but also in space, as a space in the three-dimensional geometry often used as an exercise in the reference book, we only apply its conclusions, not to prove. The theorem also contains parallel situations that are considered to be at infinity. Then, applying theorem to deal with “see the plane and the known geometry of a section determined by three known points not on a straight line” (Fig. 1) can apply the theorem and take the following steps: