MECHANISM OF NATURE 



Annexed is the table of the increase of cubes : 



1 + 7 = 8 It will be seen that the 



8 + 7 + 12 = 27 additional identical cubes 



19 required for the increase 



27 + 19 + 18 = 64 -of cubes form an arith- 



37 metical progression whose 



64 + 37 -j- 24 = 125 common difference is six. 



61 Therefore, the increase, 



125 + 61+ 30=216 etc. 

 etc 



PROPOSITION IV. 



The increase of every plane figure is after the 

 square, and the increase of every form is after the 

 cube. 



Let A be any triangle, then it is evident that 

 four similar triangles in B make up a similar tri- 



angle, every side of which is twice as long as the 

 corresponding side of the first identical triangle. 



The triangle C is built up of nine triangles, 

 each one similar to the triangle A. Therefore, 

 40 



