ii SIMPLIFICATION OF EUCLID 243 



although it may be multiplied indefinitely, can be 

 divided only into two parts ; all its lines, it is understood, 

 consisting of fila or rows of atoms ; 1 that the circle 

 has not an infinite number of radii, for from the 

 circumference to the centre only six such lines can be 

 drawn ; 2 that not every line can be divided into two 

 equal parts, for the physical line orjilum may, naturally, 

 consist of an odd number of atoms ; 3 in any case 

 geometrical bisection can at best be a near approximation, 

 though the two halves be apparently equal, they may 

 really differ by many atoms. On this basis, in the 

 fourth and fifth books of the De Minimo, Bruno offers 

 a simplification of the geometry of Euclid. As nature 

 itself is the highest unification of the manifold, and the 

 monad is the unity and essence of all number, so we 

 are taught to pass " from the infinite forms and images 

 of art to the definite forms of nature, which the mind 

 in harmony with nature grasps in a few forms, while 

 the first mind has at once the potentiality and the 

 reality of all particular things in the (simple) monad." 4 

 In accordance with the method of simplification sug- 

 gested by this doctrine, Bruno sets himself to show 

 that the greater part of Euclid may be intuitively 

 presented in three complicated figures, named respec- 

 tively the Atrium Appollinis, Atrium Palladis^ and 

 Atrium Veneris. He hoped that by this means, "if 

 not always, for the most part at any rate, without 

 further explanation, the demonstration and the very 

 evidence of the thing might be presented to the senses 

 of all, without numbers, not after the partial method 

 of others, who in considering a statue take now the 

 foot, now the eyes, now the forehead, now other parts 



1 Op. Lot. i. 3. p. 243 (bk. iii. ch. 3). 2 P. 245 (bk. in. ch. 4.), cf. p. 323 



(bk. v. c. 9), 324 (c. 10). * P. 306 (bk. v. ch. 5.). 4 P. 270. 14. 



