If there be as many numbers as we please in continued proportion, and each by multiplying itself make some number, the products will be proportional; and, if the original numbers by multiplying the products make certain numbers, the latter will also be proportional.
若有任意多个数成连比例，则每个数自乘所得的积也成连比例；且若原数乘这些积所得的数，也成连比例。
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Let there be as many numbers as we please, A, B, C, in continued proportion, so that, as A is to B, so is B to C; let A, B, C by multiplying themselves make D, E, F, and by multiplying D, E, F let them make G, H, K; I say that D, E, F and G, H, K are in continued proportion. For let A by multiplying B make L, and let the numbers A, B by multiplying L make M.
设A、B、C成连比例，即A比B等于B比C。令A、B、C自乘得D、E、F，再乘D、E、F得G、H、K。
N respectively.
令A乘B得L，A、B分别乘L得M、N；又令B乘C得O，B、C分别乘O得P、Q。
And again let B by multiplying C make O, and let the numbers B, C by multiplying O make P, Q respectively. Then, in manner similar to the foregoing, we can prove that D, L, E and G, M, N, H are continuously proportional in the ratio of A to B, and further E, O, F and H, P, Q, K are continuously proportional in the ratio of B to C.
仿前可证：D、L、E与G、M、N、H均以A比B为连比例；E、O、F与H、P、Q、K均以B比C为连比例。
Now, as A is to B, so is B to C; therefore D, L, E are also in the same ratio with E, O, F, and further G, M, N, H in the same ratio with H, P, Q, K.
因A比B等于B比C，故D、L、E与E、O、F同比例，且G、M、N、H与H、P、Q、K同比例，从而D、E、F与G、H、K成连比例。