i6 LIMITS AND FLUXIONS 



generation of curves by locai motion are always 

 increased or diminished, and by their fluxions he 

 understands the velocity of increase or decrease. 

 For, however difficult of comprehension flowing 

 quaìttities and their fluxions appear at first sight 

 (for new things are usually perceived with diffi- 

 culty), yet he thinks a notion of them will be 

 obtained more easily than the notion of moments 

 either oi least pai'ts or of infinitely small diffei^ences ; 

 because the generation of figures and quantities is 

 more naturally and easily conceived, and the draw- 

 ings in this method are usually more simple than in 

 that of parts." 



25. Page 392: " Let the flowing quantities be 

 designated v, x^ j', 2, and their fluxions by the 

 marks v, x, j>, i, respectively. And since these 

 fluxions are likewise indeterminate quantities, and 

 by perpetuai motion become greater or lesser, he 

 considers the velocities by which they are increased 

 or diminished as their fluxions, and marks them 

 with doublé dots in this way i), x, y, i, and he con- 

 siders the perpetuai increase or decrease of these 

 fluxions as fluxions of themselves. ..." 



26. Page 392: ** Let be an infinitely small 

 quantity, and 02^ oy, ox the synchronous moments 

 or momentaneous increments of the flowing quanti- 

 ties z, y, X \ and these quantities at the next 

 moment of time, by the accession of the momen- 

 taneous increments become z-\-02, y-\-oy, x + ox: 

 . . ." After substituting these in -r3—;i7j/-j-^(3:<3' = o, 

 then subtracting the originai expression and divid- 



