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And the invcftigations naturally fall under two 
heads. 
Firft, The Confideration of Amounts. 
Secondly, The Conlideration of Difcounts. 
Under the firft head an Equation is to be obtained 
between the Annuity, Time, Rate and Amount, 
from the known proportion that fubfifts between 
films of money put to intereft, during the fame 
length of time, and the amounts of the principal 
and intereft together. 
Under the lecond head another Equation is to be 
formed between the Annuity, Rate, Time and pre- 
fent Worth, from the known proportion that l'ub- 
iifts between the fums difeounted, and their prefent 
worths, when done for the fame time. 
As thefe Equations involve quantities common to 
both of them, therefore other Equations may be 
thence deduced, containing all the five terms before 
fpecified. And hence, any three of the five terms 
being given, the other two are to be found, which 
admits of 20 Cafes. 
Some of thefe Cafes will produce Adfe&ed Equa- 
tions, where the index of the higheft power of the 
unknown quantity will be the number of times the 
Rent is to continue, or to be paid : Therefore, the 
folution of thofe Cafes will be given by a method of 
Approximation, as no better way has yet been dis- 
covered for the folution of Adfe&ed Equations, in 
aumbers, above the third or fourth degree. 
In 
