[ 39i ] 
to their common confequent, i. e. the ratio of fb % 
e /, c i, bk together to CA; which ratio is lefs 
than that of D to C A, becaufe D is greater 
than fb, ei, ci, bk together. And therefore, the 
probability that the point o will lie between f and 
and withal that the event M will happen p times 
and fail q in p -p q trials, is lefs than the ratio of 
D to CA; but it was fuppofed the fame which is 
abfurd. And in like manner, by infcribing redangles 
within the figure, as eg , dh , dk , cm , you may prove 
that the laft mentioned probability is greater than the 
ratio of any figure lefs than fg h ik m b to CA. 
Wherefore, that probability mud be the ratio of 
fg h i km b to C A. 
Cor. Before the ball W is thrown the probability 
that the point o will lie fomewhere between A and B, 
or fomewhere upon the line A B, and withal that the 
event M will happen p times, and fail q in p -j- q 
trials is the ratio of the whole figure A z B to C A. 
But it is certain that the point o will lie fomewhere 
upon A B. Wherefore, before the ball W is thrown 
the probability the event M will happen p times and 
fail q in p q trials is the ratio of At B to C A. 
PROP. 9. 
If before any thing is difcovered concerning the 
place of the point#, it fhould appear that the event 
M had happened p times and failed q in p -f- q trials, 
and from hence I guefs that the point 0 lies bet ween 
any two points in the line A B, as jfand b , and con- 
lequently that the probability of the event M in a lin- 
gle trial was fomewhere between the ratio of A b to 
A B and that of A f to A B : the probability I am in 
E c e 2 the 
