TEXT-BOOKS OF MIDDLE OFCENTUR Y 197 



Nicholas S aunder soìi, 1756 



173. At the age of twelve months Saunderson 

 lost his eyesight by small-pox ; nevertheless, he 

 rose to prominence. He studied at Christ's College, 

 Cambridge, and in 171 1 succeeded VVhiston as 

 Lucasian professor of mathematics at Cambridge. 

 His Fluxions ^ is a posthumous vvork. 



VVe read (p. i) : *' Let AB represent any 

 Moment of Time, whether finite or infinitely small 

 it matters not, terminated by the two Instants 

 A and B. Let x be the Value of any flowing or 

 growing Quantity at any Instant A, whose Velocity 

 at that Instant is such, that if it was to flow during 

 the whole Moment AB with this Velocity, it would 

 gain a certain Increment represented by x ; then is 

 this Quantity x called the Fluxion of x at the 

 Instant A, when the Value of the flowing Quantity 

 was X.'' In the scholium which follows, it is 

 explained that if the velocity is variable, then the 

 increment of the velocity " gained in the time AB 

 will not be the same with its Fluxion above defined, 

 . . . but if the Time AB be infinitely small, then 

 though the Velocity of x at the Instant B be 

 not the same, mathematically speaking, with the 

 Velocity at the Instant A ; yet the Difference being 

 infinitely small in Respect of the whole Velocity, it 

 may safely be neglected, where the finite Ratios of 

 Fluxions are only considered ; and so this Increment 



^ The Method of Fluxions Applied to a select Number of Useful 

 Problems. . . . By Nicholas Saunderson, Late Professor of Mathematics 

 in the University of Cambridge. London, MDCCLVL 



