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1. Of Quantity, one kind is continuous, but another discrete. And the one consists from parts which have position with reference to each other, but the other from parts which are without position.
2. And discrete quantity, indeed, is such as number, and sentence; but continued quantity, is such as line, superficies, body; and besides these, place and time.
3. For of the parts of number, there is no common boundary, through which the parts of it are conjoined. Thus, if five is a part of ten, five and five are not conjoined by a common boundary but are separated. Three and seven also, are not conjoined by a common boundary; and, in short, you cannot obtain a common boundary of the parts in number, by they are always separated; so that number belongs to things which are discrete.
4. In a similar manner also a sentence belongs to discrete quantity. For that a sentence is quantity is evident, since it is measured by a short and long syllable. But I mean a sentence produced in conjunction with voice. For the parts of it are conjoined by no common boundary; because there is not a common boundary by which syllables are conjoined, but each of them is separated by itself.
5. But a line is continuous; for a common boundary may be assumed, viz. a point through which the parts of it are conjoined.
6. The common boundary also of a superficies, is a line; for the parts of a superficies are conjoined through an individual common boundary.
7. In a similar manner also in a body you may assume as a common boundary, a line or a superficies, through which the parts of the body are conjoined.
8. Time also and place are things of this kind; for the present time is conjoined to the past and future.
9. Again, place is among the number of things continuous; for the parts of a body possess an individual place, which are conjoined through an individual common boundary. Hence also the parts of the place which each of the parts of the body possesses, are conjoined through the same boundary, as the parts of the body. So that place also will be continued; for the parts of it are conjoined through one common boundary.
10. Farther still, some things consist from parts which have position with respect to each other; but others consist from parts which have not position.
11. Thus, the parts of a line have position with reference to each other. For each of them is situated somewhere, and you can explain and show where each of them is situated in a superficies, and with which of the remaining parts it is conjoined.
12. In a similar manner also the parts of a superficies have an individual position; for in like manner it may be explained where each of them is situated, and through what they are conjoined to each other.
13. Thus, also the parts of a solid, and the parts of a place are conjoined.
14. In number, however, no one can show that the parts of it have an individual position with respect to each other, or that they are situated any where, or which of the parts are conjoined to each other. Nor can anyone show this in the parts of time; for no one of the parts of time endures; and how can that have any position which does not endure? But you may rather say that the parts of time have an individual order; because one part of time is prior, but another posterior. The like also takes place in number; because one is numerated prior to two, and two prior to three; and thus, numbers may have an individual order, but you can by no means assume that they have any position.
15. In a similar manner likewise in speech; for no one of its parts endures, but it is spoken, and what is said, can be no longer assumed. Hence there will not be a position of its parts, since no one of them endures.
16. Some things therefore consist from parts which have position, but others from parts which have not position.
17. Those things, however, which have been mentioned are alone properly said to be quantities; but all the rest are so denominated from accident. For looking to these, we say that other things also are quantities. Thus, the whiteness is said to be much, because the superficies is great; and an action is said to be long, because the time in which it was performed is much; and for the same reason motion is much. For each of these is not said to be a quantity by itself. Thus, if anyone should explain what the quantity of an action is, he will define it by time, and say, that it was accomplished in a year, or will explain its quantity in some such way. And explaining what the quantity if of whiteness, he will define it by superficies; for such as is the quantity of the superficies, such also he will say is the quantity of the whiteness. So that the particulars which we have mentioned, are alone properly called quantities essentially; but of other things, no one is so called essentially, but from accident.
18. Nothing is contrary to quantity. For in definite quantities, it is evident that nothing is contrary; as for instance, to two cubits, or three cubits, or to superficies, or to any thing of this kind. For nothing is contrary to them.
19. Perhaps some one should say that the much is contrary to the few, or the great to the small.
20. No one of these, however, is a quantity, but rather belongs to Relatives. For nothing, itself considered by itself, is said to be great or small, but in consequence of being referred to something else. Thus, a mountain is said indeed to be small, but a grain of millet seed to be large; because the one is greater than things of the same kind, but the other is less than things of the same kind. The reference therefore is to something else; for if they were said to be small or great by themselves, the mountain could never be said to be small, but the grain of millet seed large. Again, we say that there are many men in the village, and but few in Athens, though there is a far greater multitude in the latter than in the former. We also say that there are many in the house, and but few in the theatre, though the multitude in the latter far exceeds that in the former.
21. Farther still, two cubits, three cubits, and everything of this kind signify quantities; but the great or the small, does not signify quantity, but rather relation; for the great and the small are surveyed with reference to something else. And hence it is evident that they are among the number of Relatives.
22. Again, whether anyone admits, or does not admit that things of this kind are quantities, there is not any thing contrary to them. For how will any thing be contrary to that which cannot be assumed itself by itself, but is referred to another thing?
23. Farther still, if the great and the small are contraries, it will happen that the same thing will at the same time receive contraries, and that the same things will be contrary to themselves. For it happens that the same thing is at the same time both great and small. Thus, something with reference to this thing is small, but the very same thing with reference to something else is great. Hence it happens that the same thing is at the same time both great and small; so that at one and the same time it receives contraries. Nothing, however, appears at on and the same time to receive contraries; as, for instance, in essence. For this indeed appears to be capable of receiving contraries. No one, however, is at the same time ill and well; nor is any thing at the same time white and black; nor does any thing else at one and the same time receive contraries. It will happen also that the same things will be contrary to themselves. For if the great is contrary to the small, but the same thing is at the same time great and small; the same thing also will be contrary to itself. It is, however, among the number of things impossible, that the same thing should be contrary to itself. The great therefore is not contrary to the small, nor the much to the few. Hence, though some one should say that these do not belong to Relatives, but to quantity, yet they will have nothing contrary.
24. But the contrariety of quantity especially appears to subsist about place. For they admit that the upward is contrary to the downward, asserting asserting that the place towards the middle is downward; because there is the greatest interval from the middle to the extremities of the world. They also appear to derive the definition of other contraries from these; for they define contraries to be those things which being in the same Genus are most distant from each other.
25. But quantity does not appear to receive the more and the less; as for instance, the quantity of two cubits; for one thing is not more two cubits than another. Nor is there the more and the less in number. Thus, three or five of one thing are not said to be more than three or five of another thing, nor is five more five, than three is three. Nor is one time said to be more time than another. And, in short, in the above-mentioned Species of quantity, no one of them is said to be more or less.
26. It is, however, especially the peculiarity of quantity, to be said to be equal and unequal. For each of the above-mentioned quantities are said to be equal and unequal. Thus, body is said to be equal and unequal; and also number and time are said to be equal and unequal. In a similar manner too in the rest of the above-mentioned particulars, each of them is said to be equal and unequal. Of the residue, however, such as are not quantities do not entirely appear to be called equal and unequal. Thus, for instance, disposition, is not entirely said to be equal and unequal, but rather similar and dissimilar. Whiteness also is not entirely said to be equal and unequal, but rather similar or dissimilar. Hence it will be especially the peculiarity of quantity, to be said to be equal and unequal.
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