elem.3.6
如果两个圆彼此相切，则它们不会有相同的圆心。
本页以“两圆相切不同心”整体图解辅助阅读；点、线、角、圆索引已按命题文字和证明步骤校订，可与证明和问答联动。
正文图形由校订坐标生成；点、线、角、圆可与证明和问答联动。
For let the two circles ABC, CDE touch one another at the point C; I say that they will not have the same centre. For, if possible, let it be F; let FC be joined, and let FEB be drawn through at random.
设两圆ABC和CDE在点C处相切。
Then, since the point F is the centre of the circle ABC, FC is equal to FB.
假设它们有相同的圆心F，连接FC，并任意作直线FEB。
Again, since the point F is the centre of the circle CDE, FC is equal to FE. But FC was proved equal to FB; therefore FE is also equal to FB, the less to the greater: which is impossible.
因为F是圆ABC的圆心，所以FC等于FB；又因为F是圆CDE的圆心，所以FC等于FE。
Therefore F is not the centre of the circles ABC, CDE.
因此FE等于FB，即较小者等于较大者，矛盾。所以F不是两圆的公共圆心。