TEXT-BOOKS, 1736-1741 167 



for, '*if they have not a first Ratio, they have not 

 a second nor a third Ratio, etc. Therefore they 

 have no Ratio in the Time T ; but in the Time T 

 they are Ouantities, " and * * two quantities of the same 

 kind, as soon or so long as they have any Quantity, 

 Being or Existence {i.e. are not absolutely nothing], 

 have a Ratio the one to the other," that is, *'they 

 have a Ratio and they have not a Ratio in the 

 Time T, which is absurd." Smith argues also that 

 since two quantities ''cannot be in their first Ratio, 

 neither before nor after the Beginning of the Time 

 T, they must have been in their first Ratio at the 

 very Beginning of the Time T, just as they began 

 to exist." Near the dose of this part of his hook, 

 Smith reveals some of the subtleties of his topic 

 by stating an **Objection" and the ''Answer" to 

 it. The Objection : *'Nascent and evanescent 

 Quantities are Something or Nothing ; for, Inter ens 

 et non-ens non daiur medium. If Something, then 

 the Ratio of evanescent Ouantities is the same 

 with the Ratio before they were evanescent, 

 or when they had any finite Magnitude. . . . 

 If they are mere Nothing, or Non-quanta ; then 

 B^/E^ = 0/0 = 0; . . . which is absurd." In the 

 *'Answer" Smith says : "Evanescent Quantities 

 are really nothing, or Non-quanta ; for it is evident 

 . . . that upon ^'s coinciding with B, and /s co- 

 inciding with E, the Increments B/; and E^ are 

 annihilated, and evanescent Quantities are never 

 accurately evanescent, but upon this or the like 

 Coincidence. And yet it does not follow that their 



