If there be two straight lines, and one of them be cut into any number of segments whatever, the rectangle contained by the two straight lines is equal to the rectangles contained by the uncut straight line and each of the segments.
若有两条直线，其中一条被分成若干段，则两线所成矩形等于未分割直线与各段所成矩形之和。
BC 横向矩形被分点 D、E 切成 BK、DL、EH 三块，每块高都等于另一条线 A（即 BG）。
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Let A, BC be two straight lines, and let BC be cut at random at the points D, E; I say that the rectangle contained by A, BC is equal to the rectangle contained by A, BD, that contained by A, DE and that contained by A, EC. For let BF be drawn from B at right angles to BC; [I. 11] let BG be made equal to A, [I. 3] through G let GH be drawn parallel to BC, [I. 31] and through D, E, C let DK, EL, CH be drawn parallel to BG.
把一条线分成若干段，并在另一条线的方向上作同高矩形。
Then BH is equal to BK, DL, EH.
整矩形被分割线切成若干小矩形。
Now BH is the rectangle A, BC, for it is contained by GB, BC, and BG is equal to A; BK is the rectangle A, BD, for it is contained by GB, BD, and BG is equal to A; and DL is the rectangle A, DE, for DK, that is BG [I. 34], is equal to A. Similarly also EH is the rectangle A, EC.
每个小矩形的底分别是原线的一段，高是未分割的另一条线。
Therefore the rectangle A, BC is equal to the rectangle A, BD, the rectangle A, DE and the rectangle A, EC.
由整体等于各部分之和，整线与另一线所成矩形等于这些小矩形之和。