462 Mr. wales on the Refolution 
the known quantities by the common algebraic rules, obferve 
the following ones. 
1 ft. When the equation is found to correfpond with the fum 
or difference of two formula in thefe tables, which are the fine 
and tangent, fine and cofine, or cofine and tangent, of the fame 
arc, by running the eye along the tables of natural fines and 
tangents, find thefe two arcs, immediately following one ano- 
ther, the fum or difference of the fine and tangent, fine and 
cofine, or cofine and tangent, of which are one of them 
greater, and the other lefs than the number which conftitutes 
the known fide of the equation. Take the excefs of one of 
thefe fums or differences above, and what the other fum or 
difference wants of the faid given number, add thefe two errors 
together, and fay, as the fum of them is to 60", fo is that 
error whicffbelongs to the lefs arc to a number of feconds ; 
which being added to the lefs arc will give one, the fum or dif- 
ference of whofe fine and tangent, fine and cofine, or cofine 
and tangent, is exadtly equal to the number which conftitutes 
the known fide of the equation. Of the arc, thus found, let 
fuch a part be taken as the table in which the formula are found 
directs, and the natural fine, tangent, fecant, or verfed fine (as 
the cafe may require) of this part, being multiplied by the 
value of r, if r be found in the equation, will be the value of 
x fought. 
2d. When the equation happens to be the produft or quo- 
tient of two formulae which exprefs the fine and cofine, fine 
and tangent, or cofine and tangent, of the fame arc, take the 
logarithm of the number which conftitutes the known fide of 
the equation, and then follow exactly the direftions given in 
the firft cafe, ufing the tables of logarithmic fines and tangents 
-inftead of the tables of natural ones. 
4 
