If a straight line be cut at random, the rectangle contained by the whole and both of the segments is equal to the square on the whole.
若一条直线任意分割，则整线分别与各段所成矩形之和等于整线上的正方形。
正方形 ADEB 建于 AB 上；C 把 AB 分成两段，过 C 作 CF 与 AD、BE 平行，将正方形切成 AF 与 CE 两块矩形。
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 straight line AB be cut at random at the point C; I say that the rectangle contained by AB, BC together with the rectangle contained by BA, AC is equal to the square on AB. For let the square ADEB be described on AB [I. 46], and let CF be drawn through C parallel to either AD or BE.
把一条线任意分成若干段，并在整线上作正方形。
[I. 31] Then AE is equal to AF, CE.
从分点作与边平行的线，正方形被分成若干矩形。
Now AE is the square on AB; AF is the rectangle contained by BA, AC, for it is contained by DA, AC, and AD is equal to AB; and CE is the rectangle AB, BC, for BE is equal to AB.
这些矩形分别是整线与各段所成的矩形。
Therefore the rectangle BA, AC together with the rectangle AB, BC is equal to the square on AB.
合起来正好填满整线上的正方形。