of adfe&ed Equations, 
3d. if the equation, finally refulting from the refolutlon q- 
any problem, prefent itfelf in an expreffion 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, cofine, 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 line, coiine, or tangent,- 
of one of them, and the fine, cofine, or tangent, of fame 
'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 con flit utes the known fide of the equation, for 
every minute of a degree that the finger is moved over in one, 
it muff be moved over a number of minutes in the other, 
which is equal to the number of times that .the fingie 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 fiiff rule as to merit repetition. 
4th. If, in head 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 fiuch as to be 
conftituted of the produff of them, or the quotient of one di- 
vided by the other, the laff rule will ftill 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 produff or quotient of the tw r o 
faffors, with the logarithm of the number which conihtutes- the 
known fide of the equation, inftead of that number it fid ft 
Vol. LX XL P.PP 5 iff 
