DISPLACEMENT 

 PROPOSITION IV. 



OCCULAB DEMONSTRATION. 



The primary spheres, which constitute the void 

 matter of the Universe, cannot all be, each to two 

 others, in as close contact as three spheres can be 

 to one another. 



Let the bottom of a box be filled with a layer 

 of spheres, each to two others in the closest possi- 

 ble contact. Then it is impossible to put on the 

 layer of spheres another layer, which shall be in 

 the closest possible contact, each sphere to two 

 adjoining ones of both layers. And since the void 

 matter of the Universe consists of many layers of 

 spheres, therefore, the primary spheres constitut- 

 ing the void matter of the Universe cannot all be 

 in as close contact as three spheres can be to one 

 another. 



PROPOSITION V. 



All bodies directly perceptible to our senses are 

 composed of particles. 



Let a ball of iron be heated to 1,000 degrees 

 Fahrenheit. Let it be measured. Let it be 

 weighed. Let it cool to 100 degrees. Then, be- 

 cause it weighs no less when cooled, there has been 

 no loss of iron. (Axiom IV.) 



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