of adfedied Equations.. 463 
3d. If the equation, finally /refill ting from the refolutibn 
any problem, prefent itfelf in an exprefilon which is compofed 
of the fum or difference of the fine, cofine, or tangent, of an 
arc, of which the unknown quantity is the fine, cofine, tan- 
gent, or verfed fine, and the fine, coline, or tangent, of fome 
multiple of that arc, it will then be convenient to have two 
tables of fines and tangents ; and in running the eye along 
them to find the two arcs immediately following one another, 
of which the fum or difference of the fine, cofine, or tangent, 
of one of them, and the fine, cofine, or tangent, of fome 
multiple of it, may be lefs, and the fum or difference of the 
fine, cofine, or tangent, of the other, and the fine, cofine, or 
tangent, of the fame multiple of it, may be greater than the 
number which conftitutes the known fide of the equation, for 
.every minute of a degree that the finger is moved over in one, 
it rauft be moved over a number of minutes in the other, 
which is equal to the number of times that the fingle arc is 
contained in the multiple one. When thefe two arcs are 
found, the operation will not differ fo materially from that 
-which is pointed out in the firft rule as to merit repetition. 
4th, If, inftead of the fum or difference of the fine, cofine, 
or tangent, of an arc, and the fine, cofine, or tangent, of 
fome multiple of it, the form of the equation be fuch as to be 
conftituted of the product of them, or the quotient of one di- 
vided by the other, the laft rule will frill hold good, ufing only 
the logarithmic fines and tangents inftead of the natural ones, 
and comparing the fum or difference of them, according as the 
equation is compofed of the product: or quotient of the two 
faftors, with the logarithm of the number which conftitutes the 
known fide of the equation, inftead of that number itfelf. 
Vql. LXXL P P p 5th. 
