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《画法几何》一书中对“两个回转二次曲面的相贯线在回转轴公共平面上的投影”有四条基本定理,其中第四条为:两个轴线相交的二次回转曲面相交,相贯线在公共对称面上的投影是双曲线。本文对此定理做了一些补充,补充意见为:回转轴相交的回转二次曲面相交,若其中有一个是扁椭球面,则相贯线在回转轴公共面上的投影是椭圆,在其它惰况下,投影皆为双曲线。
There are four basic theorems in “Painting Geometry” in the book “The projection of the intersecting line of two revolving conics on the common plane of the revolving axis”. The fourth one is the intersection of the two revolving surfaces where the two axes intersect , The projection of the intersecting line on the common symmetry plane is hyperbola. In this paper, we make some additions to this theorem, with the following suggestions: the intersection of the revolving conics and the intersecting surfaces of the revolving axes intersect, and if one of them is an oblate ellipsoid, the projection of the intersecting line on the common plane of the revolving axis is elliptical. Under the circumstances, the projection is hyperbolic.