Through a given point to draw a straight line parallel to a given straight line.
过给定点作一条直线，平行于给定直线。
给定直线 BC、外点 A；D 在 BC 上，连接 AD；在 A 处作角 DAE 等于角 ADC（内错相等）；EAF 是经过 A 平行于 BC 的直线。
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 A be the given point, and BC the given straight line; thus it is required to draw through the point A a straight line parallel to the straight line BC.
取给定直线上的一点，并连接到给定点。
Let a point D be taken at random on BC, and let AD be joined; on the straight line DA, and at the point A on it, let the angle DAE be constructed equal to the angle ADC [I. 23]; and let the straight line AF be produced in a straight line with EA.
在给定点处作一个角，等于连接线与给定直线形成的内错角（euclid-elements/book1-prop-023）。
Then, since the straight line AD falling on the two straight lines BC, EF has made the alternate angles EAD, ADC equal to one another, therefore EAF is parallel to BC.
让新直线通过给定点沿此角方向作出。
[I. 27] Therefore through the given point A the straight line EAF has been drawn parallel to the given straight line BC.
内错角相等，由 euclid-elements/book1-prop-027，新直线平行于给定直线。