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reft fomewhere upon D o or between A D and so is 
is the ratio of A o to A B. But the refting of the 
ball o between A D and r o after a fingle throw is 
the happening of the event M in a fingle trial. 
Wherefore the lemma is manifeft. 
PROP. 8. 
If upon BA you erefl the figure Bg hi k m A 
whofe property is this, that (the bale B A being di- 
vided into any two parts, as Ab, and bb and at the 
point of divifion b a perpendicular being erected and 
terminated by the figure in m ; and y, x, r repre- 
fenting refpedtively the ratio of bm> A b, and bb to 
AB, and E being the the coefficient of the term in 
which occurs a p b q when the binomial a-\-b \ J is 
expanded) y = E x p r q . I fay that before the ball W 
is thrown, the probability the point o lhould fall be- 
tween j and by any two points named in the line 
A B, and withall that the event M fliould happen p 
times and fail q in p q trials, is the ratio of 
f g hi km by the part of the figure bghi k m A in- 
tercepted between the perpendiculars J g, bm raifed 
upon the line AB, to C A the fquare upon AB. 
DEMONSTRATION. 
For if not; ift let it be the ratio of D a figure 
greater than fghikmb to C A, and through the 
points e,d>c draw perpendiculars to jb meeting the 
curve A tn i g B in h y i, k ; the point d being io 
placed that di fhall be the longeft of the perpendi- 
r culars 
