584 Dr WHEWELL, ON PLATO'S SURVEY OF THE SCIENCES. 



treats of plane figures ; Astronomy treats of solids in motion, that is, of spheres in motion ; 

 for the astronomy of Plato's time was mainly the doctrine of the sphere. But before treating 

 of solids in motion, we must have a science which treats of solids simply. After taking space 

 of two dimensions, we must take space of three dimensions, length, breadth and depth, as in 

 cubes and the like*. But such a Science, it is remarked, has not yet been discovered. Plato 

 " notes as deficient" this branch of knowledge ; to use the expression employed by Bacon on 

 the like occasions in his Review. Plato goes on to say, that the cultivators of such a science 

 have not received due encouragement ; and that though scorned and starved by the public, 

 and not recommended by any obvious utility, it has still made great progress, in virtue of its 

 own attractiveness. 



In fact, researches in Solid Geometry had been pursued with great zeal by Plato and his 

 friends, and with remarkable success. The five Regular Solids, the Tetrahedron or Pyramid, 

 Cube, Octahedron, Dodecahedron and Icosahedron, had been discovered ; and the curious 

 theorem, that of Regular Solids there can be just so many, these and no others, was known. 

 The doctrine of these Solids was already applied in a way, fanciful and arbitrary, no doubt, 

 but ingenious and lively, to the theory of the Universe. In the Timceus, the elements have 

 these forms assigned to them respectively. Earth has the Cube: Fire has the Pyramid: 

 Water has the Octahedron : Air has the Icosahedron : and the Dodecahedron is the plan of 

 the Universe itself. This application of the doctrine of the Regular Solids shews that the 

 knowledge of those figures was already established ; and that Plato had a right to speak of 

 Solid Geometry as a real and interesting Science. And that this subject was so recondite and 

 profound, — that these five Regular Solids had so little application in the geometry which has 

 a bearing on man's ordinary thoughts and actions, — made it all the more natural for Plato to 

 suppose that these solids had a bearing on the constitution of the Universe ; and we shall find 

 that such a belief in later times found a ready acceptance in the minds of mathematicians who 

 followed in the Platonic line of speculation. 



Plato next proceeds to consider Astronomy ; and here we have an amusing touch of 

 philosophical drama. Glaucon, the hearer and pupil in the Dialogue, is desirous of shewing 

 that he has profited by what his instructor had said about the real uses of Science. He says 

 Astronomy is a very good branch of education. It is such a very useful science for seamen 

 and husbandmen and the like. Socrates says, with a smile, as we may suppose : " You are 

 very amusing with your zeal for utility. I suppose you are afraid of being condemned by the 

 good people of Athens for diffusing Useless Knowledge." A little afterwards Glaucon tries to 

 do better, but still with no great success. He says, " you blamed me for praising Astronomy 

 awkwardly : but now I will follow your lead. Astronomy is one of the sciences which you 

 require, because it makes men's minds look upwards, and study things above. Any one can 

 see that." " Well," says Socrates, " perhaps any one can see it except me — I cannot see it." 

 Glaucon is surprized, but Socrates goes on: "Your notion of 'the study of things above' is 

 certainly a very magnificent one. You seem to think that if a man bends his head back and 

 looks at the ceiling he ' looks upwards' with his mind as well as his eyes. You may be right 



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