NEWTON 23 



place BC, and when the points C and e coalesce, 

 the right line CK will coincide with the tangent 

 CH, and the evanescent triangle CE<:in it's ultimate 

 form will become similar to the triangle CET, and 

 it's evanescent sides CE, E^ and Qc will be ulti- 

 mately among themselves as the sides CE, ET and 

 CT of the other triangle CET, are, and therefore 

 the fluxions of the lines AB, BC and AC are in the 

 same ratio. If the points C and e are distant from 

 one another by any small distance, the right line 

 CK will likewise be distant from the tangent CH 

 by a small distance. That the right line CK may 

 coincide with the tangent CH, and the ultimate 

 ratios of the lines CE, E^ and Qc may be found, the 

 points C and e ought to coalesce and exactly co- 

 incide. The very smallest errors in mathematical 

 matters are not to be neglected. 



40. ''By the like way of reasoning, if a circle 

 describ'd with the center B and radius BC be drawn 

 at right angles along the absciss AB, with an uni- 

 form motion, the fluxion of the generated solid 

 ABC will be as that generating circle, and the 

 fluxion of it's superficies will be as the perimeter of 

 that circle and the fluxion of the curve line AC 

 jointly. Por in whatever time the solid ABC is 

 generated by drawing that circle along the length 

 of the absciss, in the same time it's superficies is 

 generated by drawing the perimeter of that circle 

 along the length of the curve AC. ..." 



41. ''' Let the quantity x flow uniformly, and let it 

 b e propose ci to find the fluxion of x". 



