292 LIMITS AND FLUXIONS 



o ; for properly speaking there is no Product. It is 

 true, this of Multiplication has no influence upon 

 Practice, but that of Division has. From hence it 

 appears, that a Curve is saicl to meet with its Asymp- 

 tote, when the Ordinate is infinitely little." Then 

 follows a startling view which had been held about 

 sixty years before by John Wallis in his Arithmetica 

 Infinitoruin, 1655,^ but Craig makes no reference to 

 him. Craig argues (p. 169): "This same Notion 

 does explain how it comes to pass that i divided by 

 a negative Number gives a Ouotient greater than 

 Infinite." Curiously, he represents the logarithmic 

 curve j/ = log;r as crossing the r-axis at y= —00, 

 for since the curve approaches the y - axis in- 

 finitely near when positive x approaches zero, '*we 

 may conceive the Logarithmic Curve continued as 

 intersecting " the y-axis, so as to form " one con- 

 tinued Curve." Accordingly negative numbers have 

 logarithms that are real and negative. His further 

 argument amounts to this : For values of x that are 

 equal to i divided by a negative number, yìny — log jr 

 is negative and is less than its value — oo arising 

 when x= (presumably in the sense that — 2 < — i). 

 " Ergo ;ir is a Number greater than infinite." Con- 

 sidering the approach of the logarithmic curve 

 towards its asymptote, Craig says (p. 170) that 

 "bere it is observable, that there are affirmative 

 Numbers less than nothing denoted by the several 

 Powers oidx, as dx'^, dx^, ec. , or by the second, third, 

 ec. Differences, and these Numbers may be aptly 



1 Wallis, Opera, I, p. 409, Prop. CIV. 



