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Thus let there be three straight lines equal to one another. From one of them cut off a portion, and add as much to another of them. The whole line thus made will exceed the remainder of the first-named line, by twice the portion added, and will exceed the untouched line by that portion. And these terms loss and gain are derived from voluntary exchange: that is to say, the having more than what was one’s own is called gaining, and the having less than one’s original stock is called losing; for instance, in buying or selling, or any other transactions which are guaranteed by law: but when the result is neither more nor less, but exactly the same as there was originally, people say they have their own, and neither lose nor gain.

So then the Just we have been speaking of is a mean between loss and gain arising in involuntary transactions; that is, it is the having the same after the transaction as one had before it took place.

V] There are people who have a notion that Reciprocation is simply just, as the Pythagoreans said: for they defined the Just simply and without qualification as “That which reciprocates with another.” But this simple Reciprocation will not fit on either to the Distributive Just, or the Corrective (and yet this is the interpretation they put on the Rhadamanthian rule of Just, If a man should suffer what he hath done, then there would be straightforward justice”), for in many cases differences arise: as, for instance, suppose one in authority has struck a man, he is not to be struck in turn; or if a man has struck one in authority, he must not only be struck but punished also. And again, the voluntariness or involuntariness of actions makes a great difference.

II33a] But in dealings of exchange such a principle of Justice as this Reciprocation forms the bond of union, but then it must be Reciprocation according to proportion and not exact equality, because by proportionate reciprocity of action the social community is held together, For either Reciprocation of evil is meant, and if this be not allowed it is thought to be a servile condition of things: or else Reciprocation of good, and if this be not effected then there is no admission to participation which is the very bond of their union.

And this is the moral of placing the Temple of the Graces ([Greek: charites]) in the public streets; to impress the notion that there may be requital, this being peculiar to [Greek: charis] because a man ought to requite with a good turn the man who has done him a favour and then to become himself the originator of another [Greek: charis], by doing him a favour.

Now the acts of mutual giving in due proportion may be represented by the diameters of a parallelogram, at the four angles of which the parties and their wares are so placed that the side connecting the parties be opposite to that connecting the wares, and each party be connected by one side with his own ware, as in the accompanying diagram.

The builder is to receive from the shoemaker of his ware, and to give him of his own: if then there be first proportionate equality, and then the Reciprocation takes place, there will be the just result which we are speaking of: if not, there is not the equal, nor will the connection stand: for there is no reason why the ware of the one may not be better than that of the other, and therefore before the exchange is made they must have been equalised. And this is so also in the other arts: for they would have been destroyed entirely if there were not a correspondence in point of quantity and quality between the producer and the consumer. For, we must remember, no dealing arises between two of the same kind, two physicians, for instance; but say between a physician and agriculturist, or, to state it generally, between those who are different and not equal, but these of course must have been equalised before the exchange can take place.

It is therefore indispensable that all things which can be exchanged should be capable of comparison, and for this purpose money has come in, and comes to be a kind of medium, for it measures all things and so likewise the excess and defect; for instance, how many shoes are equal to a house or a given quantity of food. As then the builder to the shoemaker, so many shoes must be to the house (or food, if instead of a builder an agriculturist be the exchanging party); for unless there is this proportion there cannot be exchange or dealing, and this proportion cannot be unless the terms are in some way equal; hence the need, as was stated above, of some one measure of all things. Now this is really and truly the Demand for them, which is the common bond of all such dealings. For if the parties were not in want at all or not similarly of one another’s wares, there would either not be any exchange, or at least not the same.

And money has come to be, by general agreement, a representative of Demand: and the account of its Greek name [Greek: nomisma] is this, that it is what it is not naturally but by custom or law ([Greek: nomos]), and it rests with us to change its value, or make it wholly useless.

1113b] Very well then, there will be Reciprocation when the terms have been equalised so as to stand in this proportion; Agriculturist : Shoemaker : : wares of Shoemaker : wares of Agriculturist; but you must bring them to this form of proportion when they exchange, otherwise the one extreme will combine both exceedings of the mean: but when they have exactly their own then they are equal and have dealings, because the same equality can come to be in their case. Let A represent an agriculturist, C food, B a shoemaker, D his wares equalised with A’s. Then the proportion will be correct, A:B::C:D; now Reciprocation will be practicable, if it were not, there would have been no dealing.

Now that what connects men in such transactions is Demand, as being some one thing, is shown by the fact that, when either one does not want the other or neither want one another, they do not exchange at all: whereas they do when one wants what the other man has, wine for instance, giving in return corn for exportation.

And further, money is a kind of security to us in respect of exchange at some future time (supposing that one wants nothing now that we shall have it when we do): the theory of money being that whenever one brings it one can receive commodities in exchange: of course this too is liable to depreciation, for its purchasing power is not always the same, but still it is of a more permanent nature than the commodities it represents. And this is the reason why all things should have a price set upon them, because thus there may be exchange at any time, and if exchange then dealing. So money, like a measure, making all things commensurable equalises them: for if there was not exchange there would not have been dealing, nor exchange if there were not equality, nor equality if there were not the capacity of being commensurate: it is impossible that things so greatly different should be really commensurate, but we can approximate sufficiently for all practical purposes in reference to Demand. The common measure must be some one thing, and also from agreement (for which reason it is called [Greek: nomisma]), for this makes all things commensurable: in fact, all things are measured by money. Let B represent ten min, A a house worth five min, or in other words half B, C a bed worth 1/10th of B: it is clear then how many beds are equal to one house, namely, five.

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