elem.3.29
在相等的圆中，相等的圆周所对的弦相等。
本页以“等圆中等弧所对弦相等”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 equal circumferences BGC, EHF be cut off; and let the straight lines BC, EF be joined; I say that BC is equal to EF.
设ABC和DEF为相等的圆，且截取相等的圆周BGC和EHF，连接BC和EF。
For let the centres of the circles be taken, and let them be K, L; let BK, KC, EL, LF be joined.
取圆心K和L，连接BK、KC、EL、LF。
Now, since the circumference BGC is equal to the circumference EHF, the angle BKC is also equal to the angle ELF.
因为圆周BGC等于圆周EHF，所以角BKC等于角ELF（III.27）。
[III. 27] And, since the circles ABC, DEF are equal, the radii are also equal; therefore the two sides BK, KC are equal to the two sides EL, LF; and they contain equal angles; therefore the base BC is equal to the base EF.
又因为圆相等，半径相等，所以BK、KC分别等于EL、LF，且夹角相等，故底边BC等于底边EF（I.4）。