ii PART AND LIMIT 239 



thing is therefore no part of it, and by implication not 

 a minimal part. Hence there are two kinds of minima 

 concerned that of the touching body, or part, and the 

 minimum of that by which the contact is effected, the 

 terminus. 1 The atom, which is the minimal sphere, 

 touches in the absolutely minimal point, the smallest 

 terminus. Other spheres do not touch in a point 

 simply, but in more than one, or in a plane circle. 2 

 By adding limit to limit we never obtain a magni- 

 tude ; the terminus is no part, and therefore if in 

 contact it would touch with its whole self, so that 

 magnitude is not made up of termini, whether points, 

 atoms, lines, or surfaces which are termini ; and this 

 was the false ground on which the Aristotelians denied 

 the possibility of the atom. It remained to ask if the 

 termini were infinite, since the atoms were not ; but it 

 was clear that their number was determined by that of 

 the atoms. For two limits do not touch one another : 

 " They do not cohere or make a quantum, but through 

 them others in contact with one another make a con- 

 tiguum or continuum" 3 It may be added that if the 

 parts of a divisible body were infinite in number, the 

 parts of the whole would be equalled by the parts of the 

 half, for in the infinite there can be no greater and 

 less. In the infinite, as we have seen above, there 

 is no difference between palms, digits, miles, between 

 units and thousands, nor in the infinite time that has 

 elapsed are there more months than years, more years 

 than centuries. If any one set of these were less than 

 the others it would be finite, and if one finite number 

 may be applied to the whole, then the whole is finite. 4 

 The force of the Achilles dilemma was derived from the 

 false idea that the minimum of one kind had some 



1 De Min. p. 173. 9 ; cf. 173. 7, 180. 2 P. 160. 3 P. 161. 4 P. 162. 



