If, as whole is to whole, so is a number subtracted to a number subtracted, the remainder will also be to the remainder as whole to whole.
若整体与整体之比等于减数与减数之比，则余数与余数之比也等于整体与整体之比。
本页以“减数比与余数比定理”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。
As the whole AB is to the whole CD, so let AE subtracted be to CF subtracted; I say that the remainder EB is also to the remainder FD as the whole AB to the whole CD.
设整体AB与整体CD之比等于减数AE与减数CF之比。
Since, as AB is to CD, so is AE to CF, whatever part or parts AB is of CD, the same part or the same parts is AE of CF also; [VII. Def. 20] Therefore also the remainder EB is the same part or parts of FD that AB is of CD.
根据定义20，AB是CD的几部分或几分之几，AE也是CF的相同部分或几分之几。
由第七卷命题7和8，余数EB是FD的相同部分或几分之几，如同AB是CD的相同部分或几分之几。
因此，余数EB与余数FD之比等于整体AB与整体CD之比。