elem.5.14
若第一量比第二量等于第三量比第四量，且第一量大于第三量，则第二量也大于第四量；若相等则相等；若小于则小于。
A:B = C:D，且 A > C；由比例性质推出 B > D。两列分别置 A、B（左）与 C、D（右）。
正文图形由校订坐标生成；点、线、角、圆可与证明和问答联动。
For let a first magnitude A have the same ratio to a second B as a third C has to a fourth D; and let A be greater than C; I say that B is also greater than D. For, since A is greater than C, and B is another, chance, magnitude, therefore A has to B a greater ratio than C has to B.
设第一量A比第二量B等于第三量C比第四量D，且A大于C。
[V. 8] But, as A is to B, so is C to D; therefore C has also to D a greater ratio than C has to B.
因A大于C，且B为任意量，故A比B的比大于C比B的比（V.8）。
[V. 13] But that to which the same has a greater ratio is less; [V. 10] therefore D is less than B; so that B is greater than D.
但A比B等于C比D，故C比D的比也大于C比B的比（V.13）。
Similarly we can prove that, if A be equal to C, B will also be equal to D; and, if A be less than C, B will also be less than D.
同一量对之具有更大比的量较小（V.10），故D小于B，即B大于D。同理可证相等和小于的情形。