elem.3.28
在等圆中，相等的弦截出相等的弧，较大的弧等于较大的弧，较小的弧等于较小的弧。
本页以“等圆中等弦截等弧”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 ABC, DEF be equal circles, and in the circles let AB, DE be equal straight lines cutting off ACB, DFE as greater circumferences and AGB, DHE as lesser; I say that the greater circumference ACB is equal to the greater circumference DFE, and the less circumference AGB to DHE. For let the centres K, L of the circles be taken, and let AK, KB, DL, LE be joined.
设ABC和DEF为等圆，AB和DE为相等的弦，截出较大的弧ACB和DFE，以及较小的弧AGB和DHE。
Now, since the circles are equal, the radii are also equal; therefore the two sides AK, KB are equal to the two sides DL, LE; and the base AB is equal to the base DE; therefore the angle AKB is equal to the angle DLE.
取圆心K和L，连接AK、KB、DL、LE。由于两圆相等，半径相等，故AK、KB分别等于DL、LE，且底边AB等于DE，因此角AKB等于角DLE。
[I. 8] But equal angles stand on equal circumferences, when they are at the centres; [III. 26] therefore the circumference AGB is equal to DHE.
根据III.26，等圆心角对等弧，故弧AGB等于弧DHE。
And the whole circle ABC is also equal to the whole circle DEF; therefore the circumference ACB which remains is also equal to the circumference DFE which remains.
整个圆ABC等于整个圆DEF，因此剩余的弧ACB等于剩余的弧DFE。