350 A Theory of Fluxions. 



ced, the three bases of the pyramids are supposed to be in- 

 variable, and by their motion to generate the three parallel- 

 opipedons of a red color, (fig. 3. 4. 5.) representing the three 

 terms of the first fluxion x 2 x'-\-x 2 x'-\-x 2 x\ or 3x a x: Next, the 

 two flowing sides in each of the red parallelopipedons by 

 their motion, produce the six parallelopipedons of a yellow 

 color, (fig. 3. 4. 5.) representing the second fluxion 6xx' 2 . 

 And lastly, the ends of the yellow parallelopipedons, that are 

 supposed to flow, produce the six cubes of a blue color, (fig. 

 3. 4. 5.) representing the third fluxion 6x* 3 . To construct 

 the whole solid figure representing the higher orders of flux- 

 ions in the cube, we are to imagine the sections fig. 3. to be 

 placed at the bottom of the cube (fig. 2.) ; those of fig. 4. at 

 the side opposite ; and those of fig. 5. at the end opposite to 

 the corner A, at which the fluent originated. These figures 

 are to be placed about the cube in such a manner as to make 

 the same letters stand together. To the fluent, add the first 

 fluxion, half the second fluxion, and one sixth of the third 

 fluxion, and it constitutes the cube NLCKMO, (fig. 6.) com- 

 posed of the original fluent EGCDBF, (fig. 2.) and the in- 

 crement. 



N. B. The reader will notice that the position of the cube 

 in fig. 6. is different from that in fig. 2. as is denoted by the 

 letters. The side ACBD, fronts the reader. BDFH is the 

 base of the fluent, the edge FH being the more distant one 

 of the base. ABFE, the left hand side. EGFH is the side 

 opposite, and farther distant from the reader, of which the 

 edge EF only should be seen, after the whole figure is form- 

 ed, the plane NOMP is the base. 



Tallmadge, Ohio, April, 1828. 



See the annexed plate, in which the figures are reduced 

 to half their original size. — Ed. 



