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logous media fall between them ; and each of the media will 

 have two sides of the extremes situated next to it, and the 

 remaining side from the other extreme. Hence, since fire 

 has for its three physical sides the triple powers, tenuity, 

 acuteness, and facility of motion, by taking away the middle 

 power, acuteness, and introducing instead of it obtuseness, 

 we shall produce air, which has two sides of fire, but one of 

 earth, or two powers of fire, but one of earth ; as it is fit 

 that what is near should rather communicate with it, than 

 what is separated in the third rank from it. 



"Again, since earth has three physical powers, contrary to 

 the powers of fire, viz. grossness of parts, obtuseness, and 

 difficulty of motion ; by taking away difficulty of motion, 

 and introducing facility of motion, we shall produce water, 

 which consists of gross parts, is obtuse, and is easily moved ; 

 and which has indeed two sides or powers common with 

 earth, but receives one from fire. And thus these media 

 will be spontaneously conjoined with each other ; communi- 

 cating indeed in twofold powers, but differing in similitude 

 by one power; and the extremes will be bound together by 

 two media. Each element also will thus be in a greater de- 

 gree conjoined to, than separated from, the element which 

 is near to it; and one world will be perfectly effected 

 through all of them, and one harmonious order, through 

 the predominance of analogy. Thus also, of the two cubes 

 8 and 27, the medium 12 being placed next to 8, will have 

 two sides of this, but one side of 27. For 12 is produced 

 by 2 X 2 X 3 But it is vice versa with 18. For this is 

 produced by 3 X 3 X 2. And the side of 27 is 3, in the same 

 manner as 2 is the side of 8. The physical dogmas, there- 

 fore, of Plato, about the elements of the universe, accord 

 with mathematical speculations. 



