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may proceed if there be ever fo many fuch events j 
from whence the proportion is manifeft. 
Cor. 1. If there be feveral independent events, the 
probability that the 1 ft happens the 2d fails, the 3d 
fails and the 4th happens, &c. is a ratio compound- 
ed of the probability of the ift, and the probability 
of the failure of the 2d, and the probability of the 
failure of the 3d, and the probability of the 4th, &c. 
For the failure of an event may always be confidered 
as the happening of its contrary. 
Cor. 2. If there be feveral independent events, and 
the probability of each one be a , and that of its fail- 
ing be by the probability that the ift happens and the 
2d fails, and the 3d fails and the 4th happens, &c. 
will be abbdy &c. For, according to the algebraic 
way of notation, if a denote any ratio and b another, 
abba denotes the ratio compounded of the ratios 
a t by by a. This corollary therefore is only a particular 
cafe of the foregoing. 
Definition. If in confequence of certain data 
there arifes a probability that a certain event fhould 
happen, its happening or failing, in confequence 
of thefe data, I call it’s happening or failing in 
the ift trial. And if the fame data be again re- 
repeated, the happening or failing of the event in 
confequence of them I call its happening or failing 
in the 2d trial , and fo on as often as the fame data 
are repeated. And hence it is manifeft that the hap- 
pening or failing of the fame event in fo many diffe- 
trials, is in reality the happening or failing of fo 
many diftindt independent events exadtly fimilar to 
each other. 
Ddd 2 
PROP* 
