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Now proportionate requital is effected by diagonal conjunction. For example, let A be a builder, B a shoemaker, C a house, and D a shoe. It is required that the builder shall receive from the shoemaker a portion of the product of his labor, and give him a portion of the product of his own. Now1 if proportionate equality between the products be first established, and then reciprocation take place, the requirement indicated will have been achieved; but if this is not done, the bargain is not equal, and intercourse does not continue. For it may happen that the product of one of the parties is worth more than that of the other, and in that case therefore they have to be equalized.

1 The relative value of the units of the two products must be ascertained, say one house must be taken as worth n. Then the four terms are and cross-conjunction gives totals A+nD, B+C, which are in ‘arithmetical proportion’ (see first note on 5.4.3) with the two first terms, i.e. the differentce between each pair is the same; the builder and the shoemaker after the transaction are by an equal amount richer than they were before they began to make the articles.

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