242 GIORDANO BRUNO PART 



ever exactly equal. In exact geometry the number of 

 one species of figure has nothing in common with that 

 of another. It is clear, however, that even on his own 

 ground Bruno was in error in this regard ; for example, 

 the seventh triangle and the fifth square are each com- 

 posed of thirty-six minima. 1 But it is hardly necessary 

 to take seriously his teaching in this respect. He was 

 wholly governed by the belief in the infinite diversity 

 of nature, and the absolute incommensurability of any 

 member of one species of beings with one of a different 

 species. " Since a definite minimum exists, it is not 

 possible either in reality or in thought for a square to 

 be equalled by a circle, nor even a square by a pentagon, 

 a triangle by a square, nor in fine any species of figure 

 by a figure of another species ; for difference in the 

 number of sides implies also difference in the order 

 and number of parts. As figures in this respect are as 

 numbers, and one species of number cannot be equalled 

 by another either { formally ' or fundamentally (i.e. 

 either in idea or in fact), we can never make an 

 equilateral figure of any kind equal to one of another 

 by first parts/' 2 Where this transformation is ap- 

 parently carried out, as where a cube of wax is moulded 

 to another figure, the result is due to the varying 

 degrees of density in the different parts of the material ; 

 no solid parts are added or subtracted, but the dis- 

 position and extent of the pores or vacua are altered. 

 But no argument can be drawn from this rough method, 

 for the principles of practice are different from those of 



science. 3 



The latter principles are then applied boldly to 

 geometrical science : thus it is shown that an angle, 



1 Lasswitz, p. 26, note, where it is said the eighth triangle and the sixth circle are 

 equal. 2 Op. Lat. i. 3. p. 217. 9. 3 Pp. 219, 221. 



