If as many numbers as we please be in continued proportion, and there be subtracted from the second and the last numbers equal to the first, then, as the excess of the second is to the first, so will the excess of the last be to all those before it.
若任意多个数成连比例，且从第二项和末项各减去等于第一项的数，则第二项的余项与第一项之比等于末项的余项与所有前面各项之和之比。
连比例 A、BC、D、EF；从 BC 取 BG=A，从 EF 取 FH=A；构造 FK=BC、FL=D；则 GC:A = EH:(A+BC+D)（连比例求和公式）。
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Let there be as many numbers as we please in continued proportion, A, BC, D, EF, beginning from A as least, and let there be subtracted from BC and EF the numbers BG, FH, each equal to A; I say that, as GC is to A, so is EH to A, BC, D. For let FK be made equal to BC, and FL equal to D.
设连比例数A, BC, D, EF，以A为最小，从BC和EF分别减去BG和FH，各等于A。
Then, since FK is equal to BC, and of these the part FH is equal to the part BG, therefore the remainder HK is equal to the remainder GC. And since, as EF is to D, so is D to BC, and BC to A, while D is equal to FL, BC to FK, and A to FH, therefore, as EF is to FL, so is LF to FK, and FK to FH.
作FK等于BC，FL等于D。因FK等于BC，且FH等于BG，故余量HK等于GC。
Separando, as EL is to LF, so is LK to FK, and KH to FH. [VII. 11, 13] Therefore also, as one of the antecedents is to one of the consequents, so are all the antecedents to all the consequents; [VII. 12] therefore, as KH is to FH, so are EL, LK.
由比例EF:D = D:BC = BC:A，且D=FL，BC=FK，A=FH，得EF:FL = LF:FK = FK:FH。
KH to LF, FK, HF. But KH is equal to CG, FH to A, and LF, FK, HF to D, BC, A; therefore, as CG is to A, so is EH to D, BC, A.
用分比定理得EL:LF = LK:FK = KH:FH，进而KH:FH = (EL+LK+KH):(LF+FK+FH)。代入KH=CG，FH=A，LF+FK+FH=D+BC+A，得CG:A = EH:D+BC+A。