elem.3.26
在等圆中，相等的角（无论是圆心角还是圆周角）所对的弧相等。
本页以“等圆中等角对等弧”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 them let there be equal angles, namely at the centres the angles BGC, EHF, and at the circumferences the angles BAC, EDF; I say that the circumference BKC is equal to the circumference ELF. For let BC, EF be joined.
设ABC和DEF为等圆，圆心角BGC和EHF相等，圆周角BAC和EDF相等。
Now, since the circles ABC, DEF are equal, the radii are equal. Thus the two straight lines BG, GC are equal to the two straight lines EH, HF; and the angle at G is equal to the angle at H; therefore the base BC is equal to the base EF.
连接BC和EF。由于两圆相等，半径相等，故BG=EH，GC=HF，且角G等于角H，所以底边BC等于底边EF。
[I. 4] And, since the angle at A is equal to the angle at D, the segment BAC is similar to the segment EDF; [III. Def. 11] and they are upon equal straight lines. But similar segments of circles on equal straight lines are equal to one another; [III. 24] therefore the segment BAC is equal to EDF.
因为角A等于角D，所以弓形BAC与弓形EDF相似，且它们立于相等的线段上。
But the whole circle ABC is also equal to the whole circle DEF; therefore the circumference BKC which remains is equal to the circumference ELF.
根据III.24，立于相等线段上的相似弓形相等，因此弓形BAC等于弓形EDF。整个圆ABC等于整个圆DEF，所以剩余的弧BKC等于弧ELF。