BERKELEY'S ANALYST (1734) 61 



. . . Ali which seems a most inconsistent way of 

 arguing, and such as would not be allowed of in 

 Divinity (§ 14). . . . Nothing is plainer than that 

 no just conclusion can be directly drawn from 

 two inconsistent suppositions (§15). . . . It may 

 perhaps be said that [in the calculus differentialis\ 

 the quantity being infinitely diminished becomes 

 nothing, and so nothing is rejected. But, accord- 

 ing to the received principles, it is evident that no 

 geometrica! quantity can by any division or sub- 

 division Yvhatsoever be exhausted, or reduced to 

 nothing. Considering the various arts and devices 

 used by the great author of the fluxionary method ; 

 in how many lights he placeth his fluxions ; and in 

 what different ways he attempts to demonstrate the 

 same point ; one would be inclined to think, he was 

 himself suspicious of the justness of his own demon- 

 strations, and that he was not enough pleased with 

 any notion steadily to adhere to it " (§17). . . . 



80. ''And yet it should seem that, whatever 

 errors [in the calculus differentialis\ are admitted 

 in the premìses, proportional errors ought to be 

 apprehended in the conclusion, be they finite or 

 infinitesimal : and that therefore the aKpl^eia of 

 geometry requires nothing should be neglected or 

 rejected. In answer to this you will perhaps say, 

 that the conclusions are accurately true, and that 

 therefore the principles and methods from whence 

 they are derived must be so too. But . . . the 

 truth of the conclusion will not prove either the form 

 or the matter of a syllogism to be true" (§ 19). 



