论文部分内容阅读
五§10.三角形中有所謂類似中綫,這是我們所熟知的,類似中綫被三角形的外接圓所截的部分,我們特别稱它為類似弦。設作△ABC的類似弦AD,則ABDC稱為調和四邊形,因為用外接圓上任一點為反演中心而施行反演法,可以把這四邊形的頂點反演為調和點列的原故。這些知識,下面將要用及,希望讀者在前面所舉的書籍中參考一下。定理 I、I_1、I_2、I_3為△ABC的四等心,設將(?)倍增為(?)又各作(?)IBC、ICA、IAB的一類似弦IK_1、IK_2、IK_3,則A′、B′、C′、I_1、I_2、I_3、K_1、K_2、K_3九點共圓。餘類推。 (證) 因為I是△I_1I_2I_3的垂心,所以(?)
Five §10. There is a so-called similar middle line in the triangle. This is what we are familiar with. It is similar to the part where the midline is cut by the circumcircle of the triangle. We call it a similar string. Let us assume a similar string AD of △ABC. Then ABDC is called a harmonic quadrilateral. Since inversion is performed by using any point on the circumscribed circle as the inversion center, the vertices of the quadrilateral can be inverted to the point of harmonic points. This knowledge will be used in the following, and I hope the reader will refer to it in the previously cited books. The theorems I, I_1, I_2, I_3 are the quadratic isocenters of △ABC. Let (?) be multiplied to (?) and each be a similar string of IBC, ICA, IAB, IK_1, IK_2, IK_3, then A′. Nine points of B, C’, I_1, I_2, I_3, K_1, K_2, and K_3 are co-circular. More analogy. (Certificate) Because I is the heart of △I_1I_2I_3, (?)