22 LIMITS AND FLUXIONS 



36. ''Fluxions are very nearly as the augments 

 of the fluents generateci in equal but very small 

 particles of time, and, to speak accurately, they are 

 in the first ratio of the nascent augments ; but they 

 may be expounded by any lines which are pro- 

 portional to them. 



37. ''Thus if the area's ABC, ABDG be 

 described by the ordinates BC, BD moving along 

 the base AB with an uniform motion, the fluxions of 

 these area's shall be to one another as the describ- 

 ing ordinates BC and BD, and may be expounded by 

 these ordinates, because that these ordinates are as 

 the nascent augments of the area's. 



38. " Let the ordinate BC advance from it's 

 place into any new place bc. Complete the par- 

 allelogram BCE^, and draw the right line VTH 

 touching the curve in C, and meeting the two lines 

 bc and BA produc'd in T and V : and B^, E<: and 

 Qc will be the augments now generated of the 

 absciss AB, the ordinate BC and the curve line 

 AC^; and the sides of the triangle CET are in the 



first ratio of these augments considered as nascent, 

 therefore the fluxions of AB, BC and AC are as 

 the sides CE, ET and CT of that triangle CET, 

 and may be expounded by these same sides, or, 

 which is the same thing, by the sides of the triangle 

 VBC, which is similar to the triangle CET. 



39. '*lt Comes to the same purpose to take the 

 fluxions in the ultimate ratio of the evanescent 

 parts. Draw the right line Qc, and produce it to 

 K. Let the ordinate bc return into it's former 



