TEXT-BOOKS, 1736-1741 163 



not vers'd in mathematica! Speculations. 'Grant,' 

 says he, ' that two infinite Quantities, differing from 

 one another by a finite Quantity, may be esteemed 

 equal. ' Such would imagine that there could not 

 be two infinite Quantities ; or that if there could, 

 they must necessarily be absolutely and not only 

 reputedly equal. But however Hobbes or Berkeley 

 may talk of geometrica! Fallacies, or these unex- 

 perienced People think, the Adepts in this Science 

 very well know, that more infinite Quantities than 

 two are possible, and that one Quantity may be in- 

 finitely greater than an infinite one, and yet be itself 

 infinitely less than a third. But enough of these 

 Ludibria Scientiae, that I may inform the Publick of 

 the more useful Theorems ..." (pp. 422, 423). 



Muller considers in his text a curve generated 

 by a point " urged by two powers acting in two 

 dififerent directions, the one parallel to the Abscisses 

 and the other parallel to the Ordinates. I prove 

 from thence, that if this point (when arrived at a 

 given place) did continue to move with the velocity 

 it has there, it would proceed in a right line touch- 

 ing the Curve in that place ... So that the three 

 Directions being known in each place, the propor- 

 tion between the velocities of the urging powers is 

 likewise known." Fluxions are defined as velocities. 

 To find the fluxion of j^^^ he puts y'^=x\ the sub- 

 tangent of the parabola is 2y'^ Since the subtangent 

 is to the ordinate as the velocities along the abscissa 

 and ordinate, he has 2y^ -. y \ \x \ y, or ,r=2yy, and 

 2yy is the required fluxion. Similarly, to find the 



