elem.3.30
给定一段圆弧，求作其平分点。
本页以“平分给定圆弧”整体图解辅助阅读；点、线、角、圆索引已按命题文字和证明步骤校订，可与证明和问答联动。
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 ADB be the given circumference; thus it is required to bisect the circumference ADB.
设ADB为给定圆弧，连接AB，取AB中点C。
Let AB be joined and bisected at C; from the point C let CD be drawn at right angles to the straight line AB, and let AD, DB be joined.
从C作AB的垂线CD，交圆弧于D，连接AD、DB。
Then, since AC is equal to CB, and CD is common, the two sides AC, CD are equal to the two sides BC, CD; and the angle ACD is equal to the angle BCD, for each is right; therefore the base AD is equal to the base DB.
因为AC=CB，CD公共，且∠ACD=∠BCD=直角，所以AD=DB。
[I. 4] But equal straight lines cut off equal circumferences, the greater equal to the greater, and the less to the less; [III. 28] and each of the circumferences AD, DB is less than a semicircle; therefore the circumference AD is equal to the circumference DB.
等弦截等弧，且AD、DB均小于半圆，故弧AD=弧DB。