464 Mr. wales on the Resolution 
5th* Sometimes the- final equation will come out in expref- 
fions. which are conftituted of the fum, difFerence, product, or 
quotient, of the fine } cofine, or tangent, of fome multiple of 
an arc, of which the unknown quantity is the fine, tangent* 
fecant,. or verfed fine, and the- fine, cofine, or tangent, of lbmc 
other multiple of the fame arc. And in any of thele cafes it 
is manifeft, that the method of proceeding, in order to obtain 
one of the- multiple arcs, and from thence the tingle one, of 
which the unknown quantity is the fine, tangent, &c. wilt 
not be greatly different from thole which have been defcribed in 
the third and fourth rules. The moft material difFerence con- 
lifts in this, that inftead of proceeding minute by minute, ac- 
cording to the directions in the third rule to find the fingle arc* 
it will now be moft: convenient to proceed in each table by as 
many minutes at each ftep as are equal in number to the num- 
ber of times which the fingle arc is contained in the multiple 
ones relpeftively. 
6th. Equations will frequently make their appearance in for- 
mulae which exprefs the fquare, cube, &c. of the fine, cofine* f 
or tangent, of the multiple of Ibme arc, of which the un- 
known quantity is the fine, tangent, fecant, or verfed fine ; 
or in formulae which are expreffive of the fum, difference, pro- 
duct, &c. of the fine, cofine, or tangent, of an arc* 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, produdt, &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. I11 every 
©ae of tkefe cafes the tables will give the value of the unknown 
quantity t 
