of aclfeBed Equations* 4^5 
quantity, and in moft of them with great ’eafe and expedition. 
The method which is to be purfued in each cafe will readily 
p relent itfelf to a Ikilfoi analyft, who attends carefully to what 
has been already fa id, and to the examples which follow. 
IV. The formula in the four preceding tables may be greatly 
varied by fuppofing the Unknown quantity, to be feme part 
or parts of the fine, tangent, &c. as §, 4, *, 1, &c. or feme) 
.multiple of it, as twice, thrice, &c. Or y may be the fqu are, 
or the fquare root, or any other power of the fine, tangent, 
decant, or verfod fine, of an arc ; in every One of which cafes 
the formula will put on different appearances, eithef with re- 
fpe<Si to the powers or co-efficients of the unknown quantity:^., 
and yet admit of the lame kind of application. 
V. The tables may be rendered yet more extenfively ufeful by 
inferring expreffions for the fines, cofines, and tangents^ of 
half the arc which has x for its fine, tangent, feca'nt, or verfed’ 
fine; and alfo for the fines, cofines, and tangents,- of the odd 
multiples of this half arc, which expreffions, together with 
thole already inferted, may be confidered as the fines, - colines, 
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 ufefui 
purpofes. 
VI. In order to render the formula In the tables rnore general, 
I have put r for the radius of the circle ; whereas it will fre- 
quently happen, that the equation, finally refulting from the 
refolution of a problem, efpecially thofe which relate to the 
doctrine of the lphere, will prefent itfelf in a form where the 
radius muft be taken equal to unity : what theie forms are will 
readily appear by fubftituting unity for r and its powers- every 
where in the expreffion. 
p p P 2 
it 
