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Thus the just also involves four terms at least, and the ratio between the first pair of terms is the same as that between the second pair. For the two lines representing the persons and shares are similarly divided1;

1 Here was another diagram (one would expect the sentence to run ‘Let two lines representing . . . have been similarly divided’). Two segments, A and B, of one line represented two persons, two segments, C and D, of another their shares. It is shown that, if A:B::C:D, then A+C:B+D::A:B, i.e., if the shares are proportioned to the persons, their relative condition after receiving them will be the same as it was before.

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