[ 3§6 ] 
commenfurable to each other, they may each be di- 
vided into the fame equal parts, which being done, 
and the ball W thrown, the probability it will reft 
fomewhere upon any number of thefe equal parts 
will be the fum of the probabilities it has to reft upon 
each one of them, becaufe its refting upon any differ- 
ent parts of the plane AC are fo many inconfiftent 
events ; and this fum, becaufe the probability it fhould 
reft upon any one equal part as another is the fame, is 
the probability it fhould reft upon any one equal part 
multiplied by the number of parts. Confequently, the 
probability there is that the ball W fhould reft fome- 
where upon is the probability it has to reft upon one 
equal part multiplied by the number of equal parts in F b; 
and the probability it refts fomewhere upon Cy'or LA, 
i.e. that it dont reft upon Fb (becaule it muft reft fome- 
where upon A C) is the probability it refts upon one 
equal part multiplied by the number of equal parts in 
C/, LA taken together. Wherefore, the probability 
it refts upon F b is to the probability it dont as the 
number of equal parts in F b is to the number of 
equal parts in Cf LA together, or as F b to CJ] 
LA together, or as/£ to B f A b together. Where- 
fore the probability it reft upon F b is to the proba- 
bility it dont as f b to B f, A b together. And ( coni- 
ponendo inverfe ) the probability it refts upon F b is to 
the probability it refts upon F b added to the proba- 
bility it dont, as fb to AB, or as the ratio of fb to 
A B to the ratio of A B to A B. But the probabi- 
lity of any event added to the probability of its failure 
is the ratio of equality ; wherefore, the probability it 
reft upon F b is to the ratio of equality as the ratio of 
jb to AB to the ratio of AB to AB, or the ratio 
of equality i and therefore the probability it reft upon 
