elem.6.9
从给定线段AB上截取指定部分，例如三分之一。
在已知直线 AB 上截取规定分数：从 A 作斜线，依次截等长段 AD=DE=EF；连接 FB，过 D 作平行于 FB 的直线交 AB 于 C，则 AC = AB / 3。
正文图形由校订坐标生成；点、线、角、圆可与证明和问答联动。
Let AB be the given straight line; thus it is required to cut off from AB a prescribed part. Let the third part be that prescribed.
从点A作直线AC与AB成任意角，在AC上取点D，使AD等于DE等于EC。
Let a straight line AC be drawn through from A containing with AB any angle; let a point D be taken at random on AC, and let DE, EC be made equal to AD.
连接BC，过D作DF平行于BC。
[I. 3] Let BC be joined, and through D let DF be drawn parallel to it. [I. 31] Then, since FD has been drawn parallel to BC, one of the sides of the triangle ABC, therefore, proportionally, as CD is to DA, so is BF to FA.
由于DF平行于BC，根据VI.2，CD与DA之比等于BF与FA之比。
[VI. 2] But CD is double of DA; therefore BF is also double of FA; therefore BA is triple of AF.
因为CD是DA的两倍，所以BF也是FA的两倍，因此BA是AF的三倍。