24 MATHEMATICS. 



Arithmetical and Geometrical Magnitudes. 



When two points describe two different lines, the 

 one with a constant velocity, and the other with a 

 velocity always increasing in the ratio of the space 

 gone over ; the first of these generates magnitudes 

 in arithmetical, the second in geometrical progression. 

 Hence all numbers whatever would find their place 

 among numbers so generated. 



Probability. 



The grounds of probability are the two following ; 

 viz. the conformity of any thing with our own par- 

 ticular knowledge, experience, or observation, and 

 the assertion of others, on whose testimony reliance 

 can be placed. 



We may call any thing improbable if the measure 

 of the chance for its happening be less than one 

 half(l). 



If one premise only of an argument be probable, 

 the conclusion is necessarily probable ; but if there 

 be two or more premises probable, the conclusion 

 will not necessarily be probable. Supposing the 

 probability of each premise (say two premises) ex- 

 pressed by -j^, the probability of the conclusion will 

 be T T ff x -TO T 4 o% consequently improbable, and this 

 would increase with every additional premise. We 

 might therefore safely bet 4 to 1 against the truth of 

 a conclusion, founded on four probable independent 

 premises, all singly more than J in favour of it. 

 Hence it is easy to account how it happens that the 

 most plausible political and physical reasonings lead 

 so often to conclusions false in fact. 



Probability of Life. 



For the sake of easy calculation De Moivre assumed 

 86 as the boundary of human life, from which having 

 deducted the person's age (if 30 or upwards), the 



