' £ 509 
Number is applicable to fomethings, to which it is 
not commonly applied by the Vulgar. Thus, by atten- 
tive Confideration, Lots and Chances of various Kinds 
appear to be made up of a determinate Number of 
Chances that are allowed to be equal; and bynum- 
- bering thefe, the Values and Proportions of thofe 
which arc compounded of them may be demon- 
ft rated. 
Velocity, the Quantity of Motion, Denfity, Elafti- 
city, the Vis infita , and impreffa, the various Kinds of 
centripetal Forces, and different Orders of Fluxions, 
are all Improper Quantities; which therefore ought 
not to be admitted into Mathematics, without hav- 
ing a Meafure of them alligned. The Meafure of 
an improper Quantity ought always to be included 
in the Definition of it; for it is the giving it a 
Meafure that makes it a proper Subject of mathe- 
matical Reafoning. If all Mathematicians had con- 
fidered,this as carefully as Sklfaac Newton appears 
to have done, forne Labour had been faved both to 
themfelves and to their Readers. That Great Man, 
whofe clear and comprehenfive TJnderftanding ap- 
pears, even in his Definitions, having frequent Oc- 
cafion to treat of fuch improper Quantities, never 
fails to define them, fo as to give a Meafure of 
them, either in proper Quantities, or in luch as 
had a known Meafure. This.may be feen in the De- 
finitions prefixed to his Princip . 'Phil. Nat. Math. 
It is not eafy to fay how many Kinds of impro- 
per Quantity, may in time, be introduced into Ma- 
thematics, or to what new Subjects Meafures may 
be applied: But this I think we may conclude, 
X x x 2 that 
I 
