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we abfolutely know nothing antecedently to any 
trials made concerning it, feems to appear from the 
following confideration ; viz. that concerning fuch 
an event I have no reafon to think that, in a certain 
number of trials, it fhould rather happen any one 
poffible number of times than another. For, on 
this account, I may juffly reafon concerning it as if 
its probability had been at firft unfixed, and then 
determined in fuch a manner as to give me no reafon 
to think that, in a certain number of trials, it fhould 
rather happen any one pofifible number of times 
than another. But this is exactly the cafe of the 
event M- For before the ball W is thrown, which 
determines it’s probability in a Angle trial, (by cor. 
prop. 8.) the probability it has to happen p times 
and fail q in p -j- q or n trials is the ratio of A i B to 
C A, which ratio is the fame when p -j- q or n is 
given, whatever number p is ; as will appear by 
computing the magnitude of A i B by the method 
* of fluxions. And confequently before the place 
of the point o is difcovered or the number of times 
the event M has happened in n trials, I can have no 
reafon to think it fhould rather happen one pof- 
fible number of times than another. 
In what follows therefore I (hall take for granted 
that the rule given concerning the event M in 
prop. 9. is alfo the rule to be ufed in relation to any 
event concerning the probability of which nothing 
* It will be proved prefently in art. 4. by computing in the 
method here mentioned that A / B contracted in the ratio of E 
to 1 is to C A as 1 to n + 1 X E : from whence it plainly follows 
that, antecedently to this contraction, A i B muft be to C A in 
the ratio of 1 to n + 1, which is a conftant ratio when n is given, 
whatever p is. 
at 
