To draw a straight line at right angles to a given straight line from a given point on it.
给定直线 AB 及其上一点 C，从 C 作一条直线与 AB 成直角。
直线 AB 上点 C，左侧取 D，右侧取 E 使 CD=CE；在 DE 上作等边三角形 DFE；连 CF，CF 垂直 AB。
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, and C the given point on it. Thus it is required to draw from the point C a straight line at right angles to the straight line AB.
在直线 AB 上点 C 两侧取 CD 等于 CE，并在 DE 上作等边三角形 DFE。
Let a point D be taken at random on AC; let CE be made equal to CD; [I. 3] on DE let the equilateral triangle FDE be constructed, [I. 1] and let FC be joined; I say that the straight line FC has been drawn at right angles to the given straight line AB from C the given point on it.
连接 FC。三角形 DCF 与 ECF 有 CD=CE、DF=EF、CF 公共。
For, since DC is equal to CE, and CF is common, the two sides DC, CF are equal to the two sides EC, CF respectively; and the base DF is equal to the base FE; therefore the angle DCF is equal to the angle ECF; [I. 8] and they are adjacent angles. But, when a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is right; [Def. 10] therefore each of the angles DCF, FCE is right.
由 euclid-elements/book1-prop-008，角 DCF 等于角 FCE。
Therefore the straight line CF has been drawn at right angles to the given straight line AB from the given point C on it.
这两个相邻角在直线 DE 上相等，所以各为直角，FC 垂直 AB。