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On Generation and corruption   

straight line in either direction, since otherwise an infinite

number of contrarieties would attach to the single 'element'. Let E

stand for Earth, W for Water, A for Air, and F for Fire. Then (i)

since A is transformed into F and W, there will be a contrariety

belonging to A F. Let these contraries be whiteness and blackness.

Again (ii) since A is transformed into W, there will be another

contrariety: for W is not the same as F. Let this second contrariety

be dryness and moistness, D being dryness and M moistness. Now if,

when A is transformed into W, the 'white' persists, Water will be

moist and white: but if it does not persist, Water will be black since

change is into contraries. Water, therefore, must be either white or

black. Let it then be the first. On similar grounds, therefore, D

(dryness) will also belong to F. Consequently F (Fire) as well as

Air will be able to be transformed into Water: for it has qualities

contrary to those of Water, since Fire was first taken to be black and

then to be dry, while Water was moist and then showed itself white.

Thus it is evident that all the 'elements' will be able to be

transformed out of one another; and that, in the instances we have

taken, E (Earth) also will contain the remaining two 'complementary

factors', viz. the black and the moist (for these have not yet been


We have dealt with this last topic before the thesis we set out to

prove. That thesis-viz. that the process cannot continue ad

infinitum-will be clear from the following considerations. If Fire

(which is represented by F) is not to revert, but is to be transformed

in turn into some other 'element' (e.g. into Q), a new contrariety,

other than those mentioned, will belong to Fire and Q: for it has been

assumed that Q is not the same as any of the four, E W A and F. Let K,

then, belong to F and Y to Q. Then K will belong to all four, E W A

and F: for they are transformed into one another. This last point,

however, we may admit, has not yet been proved: but at any rate it

is clear that if Q is to be transformed in turn into yet another

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