ANCIENT SCIENCE. 25 



conveyed by the veins ; the existence of nerves is unknown to him. 

 It is, indeed, only of the most obvious anatomical facts that he takes 

 any notice. 



Plato and other ancient philosophers applied to physical ques- 

 tions the abstract relations of number and figure, in a manner very 

 different from that of the modern mathematician. The properties 

 of numbers had been demonstrated irrefragably, and had so possessed 

 men's minds with the conviction of their absolute certainty, that num- 

 bers were even supposed to contain the secret of the universe. Thus 

 we read in the "Timaeus," that when the Creator had compounded 

 the material of the universe, " He began to divide it in this wise : 

 first of all, He took away one part of the whole, and then He sepa- 

 rated a second part, which was double the first, and then He took 

 away a third part, which was half as much again as the second and 

 three times as much again as the first, and then He took a fourth part, 

 which was twice as much as the second, and a fifth part, which was 

 three times as much as the third, and a sixth part, which was eight 

 times as much as the first, and a seventh part, which was twenty- 

 seven times the first." The proportions thus assigned (represented 

 by the figures i, 2, 3, 4, 9, 8, 27) were then filled up in two series 

 by placing in the intervals certain intermediate terms which Plato 

 indicates, pointing out the relations between the several terms, so 

 that finally these two series emerge, viz. : 



i : A : I : 2 : f : 3 : 4 : tf : 6 : S. 

 i : I : 2 : 3 : a : 6 : 9 : V : 18 : 2 7. 



These numbers probably represent musical scales, or have some 

 connection with Pythagorean doctrines of harmonic relations which 

 were current in Plato', c time. 



The elerr^nts are themselves formed of triangles, as four of the 

 regular geometrical solids may be formed of certain combinations of 

 triangles. To each element Plato assigns a geometrical solid : to earth, 

 the cube ; to fire, the pyramid ; to air, the octahedron ; to water, the 

 icosahedron. The elements may be transformed into one another, as 

 one of these figures may be changed into another. This susceptibility 

 of transformation illustrates one characteristic of Plato's scheme, a 

 view of nature which is very noteworthy, and that is, the conception 

 of unity which underlies it. Another example would be his notion 

 about living things. These he imagines are descended from man by a 

 process of degradation from the higher forms into lower. The race 

 of birds was created out of innocent and light-minded men; land 

 animals were the habitations of those souls which had no philosophy 

 and never looked up to heaven ; while the fishes were formed from 

 only the lowest and most ignorant, who were thus made to respire in 

 water, instead of in the finer element, air. 



