Mr . wales on the Refolution , &c. 
461 
Obfervathris on the foregoing tables. 
EACH of the formulas in thefe tables may be confidered as' 
one fide of an equation, involving the unknown quantity x to 
different dimenfions. In feme of the formulae the odd powers 
of x are only found, in others the even ones alone, and in 
others both ; but they are all equally ufeful in finding the value 
of the unknown quantity in ad feet ed equations which contain 
all the powers of that quantity, as will plainly appear from 
the following confiderations. 
I. If, on bringing the folution of any problem to an equa- 
tion with fome known quantity, it be found to correfpond with 
any of the formula in thefe tables ; or, if by any means it can 
be reduced to any of them, it is manifeft, that nothing remains to : 
be done but to divide, the known fide of the equation by the 
value of the quantity which is here denoted by r, and to feek 
for the quotient in the tables of fines, cofines, or tangents, as 
the cafe may require, and the value of the unknown quantity 
will be the fine, tangent, fecant, or verfed fine,, of 2 given 
part of that arc (according as the expreffion is found in the 
firft, fecond, third, or fourth table) multiplied by the value 
of r. 
II. If, as will more frequently happen, the final equation of 
an operation be found equivalent to .the fum, difference, pro- 
duct, or quotient, of fome two or more of thefe formula; or 
to the fum, difference, produd, or quotient, of fome two or 
more of them multiplied or divided, increafed or leffened, by 
fome known quantity or quantities ; then, having taken away 
O o o 5 the 
