[ 3§9 ] 
ctilars terminated by the line Jb, and the curve 
A in i g B \ and the points e } d, c being fo many and 
fo placed that the redangles, b k, c /, £> /, fh taken 
together fhall differ lefs from Jghikm'b than D 
does ; all which may be eafily done by the help of the 
equation of the curve, and the difference between D 
and the figure fghikmb given. Then fince di is 
the longed: of the perpendicular ordinates that infid: 
upon j b, the red; will gradually decreafe as they are 
farther and farther from it on each fide, as appears 
from the conftrudion of the figure, and confequently 
e h Is greater than gf or any other ordinate that in- 
fills upon e f 
Now if Ao were equal to Ae , then by lem. 2. 
the probability of the event M in a fingle trial would 
be tne ratio of A e to A B, and confequently by cor. 
Prop. 1. the probability of it’s failure would be the 
ratio of Be to A B. Wherefore, if x and r be the 
two forementioned ratios refpedively, by Prop. 7. the 
probability of the event M happening p times and 
failing q in p -j- q trials would be r q . But a: 
and r being refpedively the ratios of Ae to A B 
and Be to AB, if y is the ratio of eh to A B, then, 
by conftrudion of the figure A i B, y — Ex* r q \ 
Wherefore, if A 0 were equal to Ar the probability 
of the event M happening p times and failing q in 
p \-q trials would be y , or the ratio of eh to A B. 
And if A 0 were equal to A f or were any mean be- 
tween Ae and Af, the lad mentioned probability 
for the fame reafons would be the ratio of fg or fome 
other of the ordinates inditing upon ef to AB. But 
e £ is the greated: of all the ordinates that infid: upon 
ef. Wherefore, upon fuppofition the point ffould lie 
Vol. LIII. Eee 
