vf JofeBed Equations. 
■quantity, and in mold of them with great eafe and expedition. 
The method which is to be purfued in each cafe will readily 
p relent itfelf to a Ikilful analyft, who attends carefully to what 
has been already faid, and to the examples which follow. 
IV. The formula in the four preceding tables may be greatly 
varied by fuppofmg x, the unknown quantity, to be fome part 
or parts of the fine, tangent, &c. as f, 4, d, I, &c. or dome 
multiple of it, as twice, thrice, &c. Or x may be the fquare, 
or the fquare root, or any other power of the file, tangent, 
fecant, or verfed fine, of an arc ; in every one of which cafes 
the formula will put on different appearances, either with re* 
fped to the powers or co-efficients of the unknown quantity, 
and vet admit of the fame kind of application. 
V. The tables may be rendered yet more extenfively ufeful by 
mferting expreffions for the fines, cofnes, and tangents, of 
half the arc which has x for its fine, tangent, fecant, or verfed 
fine ; and alfo for the fines, cofnes, and tangents, of the odd 
multiples of this half arc, which .expreffions, together with 
thofe already inferred, may be confidered as the fines, cofines, 
and tangents, of the multiples of an arc, the unknown quan- 
tity, being the fine, tangent, &c. of twice that arc. And 
this confideration may fometimes be applied to very ufetul 
purpofes. 
VI. I11 order to render the formula in the tables more general, 
I have put r for the radius of the circle ; whereas it will fre- 
quently happen, that the equation, finally reiulting from the 
refolution of a problem, efpecially thofe which relate to the 
doctrine of the fphere, will prefent itfelf in a form where the 
radius muft be taken equal to unity ; what thefe forms are will 
readily appear by fubftituting unity for r and its powers every 
where in the expreffioa. 
P p p 2 
