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双紐曲線係高次曲線的一种,它的性質已在解析幾何与數学分析中略述一二,本文的目的,在於用初等幾何的方法來研究它的性質,假使達到这个目的,那末我們就可以用同样的方法來研究其他高次曲線了。本文中利用反演法將直角双曲線反演成双紐曲線然後利用直角双曲線的性質來得出双紐曲線的性質。用直角双曲線的中心O为反演中心,以其輔助圓(即以实軸AA′为直徑之圓)为反演基圓而將直角双曲線反演,本文始終採用这种方法。 設S及占S′为直角双曲線之焦點,A,A′为其頂點,則OS=OS′=a2~(1/2),OA=OA′=a(因直角双曲線中e=2~(1/2)),取O为反演中心,a真为反演半徑求S,S’之反點,設这兩點之反點
The double-nine curve is a kind of high-order curve. Its properties have been outlined in analytic geometry and mathematical analysis. The purpose of this paper is to study its properties by means of elementary geometry. If this is achieved, then we The same method can be used to study other higher-order curves. In this paper, the inversion method is used to invert the right angle hyperbola into a binary curve and then use the properties of the right angle hyperbola to get the properties of the double helix curve. The center O of the hyperbola is used as the inversion center, and the auxiliary circle (that is, the circle with the real axis AA′ as the diameter) is used to invert the square hyperbola for the inversion base circle. This method has always been adopted in this paper. Let S and S’ be the focus of the hyperbola, A and A’ are their vertices, then OS=OS’=a2~(1/2), OA=OA’=a(Since the hyperbola has e=2~ 1/2)), take O as the inversion center, a is really the inversion radius, find the opposite point of S, S’, set the inverse point of these two points