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prop. I. the probability that fome way or other it 
happens p times and fails q times in p -|- q trials i 
E a* b*. 
SECTION II. 
is 
Populate, i. I Suppofe the fquare table or plane 
A B C D to be fo made and levelled, that if either 
of the balls o or W be thrown upon it, there fhali 
be the fame probability that it relfs upon any one 
equal part of the plane as another, and that it mud 
necelTarily red fome where upon it. 
2. I luppofe that the ball W fhali be id thrown, 
and through the point where it reds a line os diall be 
drawn parallel to A D, and meeting C D and A B in 
s and o and that afterwards the ball O fhali be 
thrown p 4. q or n times, and that its reding between 
AD and os after a dngle throw be called the hap- 
pening of the event M in a dngle trial. Thefe things 
fuppofed, 
Lem. 1. The proba-Q 
bility that the point 0 
will fall between any 
two points in the line 
A B is the ratio of the 
didance between the 
two points to the whole 
line AB. 
Let any two points 
be named, as f and b 
in the line A B, and B 
through them parallel 
to A D draw fF, b L 
meeting CD in F and 
L. Then if the rect- 
angles CfFb,LA are 
com- 
