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在解析几何里,曲面是看作适合某种条件的动点的軌迹,据此論点可以証明曲线依某种規律移动必可产生曲面(見§1)。按前者所建立的曲面方程的方法,叫做直譯几何条件法,而后者則謂消参数法。前法理論較簡进行容易,而后者則理論較难但用处较多。本文拟对后者作扼要的論述,并以此观点建立三类直紋曲面(柱面、錐面和劈錐曲面)以及迴轉曲面的方程。一般书中所論,則仅为此处的特例。
In analytical geometry, a surface is a trajectory that is considered to be a moving point that fits a certain condition. From this point of view, it can be shown that the curve moves according to a certain law to produce surfaces (see § 1). According to the method of the surface equation established by the former, it is called the literal translation conditional method, while the latter is called the parametric elimination method. The theory of the former law is easier to perform, while the latter theory is more difficult but useful. This article intends to give a brief discussion of the latter, and from this point of view, establishes the equations for the three types of ruled surfaces (cylindrical, conical, and truncated conical surfaces) and the surface of revolution. In the general book, it is only a special case here.