CHANGING IDENTITIES 



any side of the triangle C is three times as long as 

 the corresponding side of the triangle A, and the 

 whole area of the triangle C is nine times the 

 area of triangle A. Circles are to one another as 

 the squares on their diameters. (Euclid.) 



The cubic contents of any solid are determined 

 by multiplying the length and breadth by the 

 height. This holds good of every solid in any 

 shape. 



Therefore, if two horses are similar in shape, 

 which is identity of form, then if one is fourteen 

 hands high and the other sixteen, the little horse 



14 14 14 

 will displace X X as much water as the 



16 16 16 

 larger horse. 



Therefore, etc. 



PROPOSITION V. 



The mass of any substance is that number of 

 primary spheres which are held together in the 

 constitution of the substance. 



Because every substance is built up of primary 

 spheres. (Prop. XIX, B. 1.) Therefore, every 

 substance can be compared with any other sub- 

 stance in common origin. 



And since force is not inherent in matter (Prop. 

 II, B. 1) ; and as it cannot be stored up in any 

 substance (Prop. XIII, B. 1) ; therefore, when the 



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