Mr. wales on the Refolution 
5 tb. Sometimes the final equation will come out in expref- 
fjotis which are confiituted of the fum, difference, product, or 
quotient, of the line, coline, or tangent,, of fome multiple of 
an arc, of which the unknown quantity is the fine,, tangent, 
recant, or veiled fine, and the fine, cofine, or tangent, of fome 
other multiple of the fame are. And in any of thefe cafes it 
is manifeif, that the method of proceeding, in order to obtain 
one of the multiple arcs, and from thence the fingle one, of 
which tire unknown quantity is the line,, tangent, &c. will 
not be g; ready different from thofe which have been deferibed in 
the third and fourth rules. The moff material difference con* 
lifts in this, that inffead of proceeding minute by minute, ac- 
r 
cording to the directions in the third rule to find the finrfe arc, 
it will now be moft convenient to proceed in each table by as- 
many minutes at each ffep as are equal in number to the num- 
ber of times which the fingle arc is contained’ in the multiple 
ones refipeffively. 
6th. Equations will frequently make their appearance in for- 
mulae which exprefs the fquare, cube, &c. of the fine, cofine, 
or tangent, of the multiple of fome are, of which the un- 
known quantity is the fine, tangent, fecant, or verfed fine ; 
or in formulae which are expreflive of the fum, difference, pro- 
duct, &c. of the fine, cofine, or tangent, of an are,, and fome 
power of the fine, cofine, or tangent, of the fame arc ; or of 
fome multiple of it, the unknown quantity being fome other 
trigonometrical line belonging to that arc. Or the equation 
may be compounded of the- fum, difFerence, product, &c, of 
the fame, or different powers of the fines, tangents, or cofines, 
of different multiples of an arc, the unknown quantity being, 
the fine, tangent, fecant, or verfed fine, of that arc.. In every 
one of thefe cafes the tables will give the value, of the unknown 
quantity. 
