To bisect a given finite straight line.
给定一条有限直线，作出它的中点，把它平分。
在线段 AB 上作等边三角形 ABC，CD 平分顶角 ACB 交 AB 于 D，即 D 是 AB 的中点。
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Let AB be the given finite straight line. Thus it is required to bisect the finite straight line AB.
在给定线段 AB 上作等边三角形 ABC（euclid-elements/book1-prop-001）。
Let the equilateral triangle ABC be constructed on it, [I. 1] and let the angle ACB be bisected by the straight line CD; [I. 9] I say that the straight line AB has been bisected at the point D.
平分顶角 ACB（euclid-elements/book1-prop-009），令平分线交 AB 于 D。
For, since AC is equal to CB, and CD is common, the two sides AC, CD are equal to the two sides BC, CD respectively; and the angle ACD is equal to the angle BCD; therefore the base AD is equal to the base BD.
三角形 ACD 与 BCD 有 AC=BC、CD 公共、夹角相等，由 euclid-elements/book1-prop-004 全等。
[I. 4] Therefore the given finite straight line AB has been bisected at D.
于是 AD 等于 DB，D 平分 AB。