226 Of the SOLIDS 
_ Bur BC =a.tanz; and therefore KC, the fluxion of BC, is 
, 
eer 
z 
ae = 3 if, then, CE =a, m=CExCK =n. 
=a. 
and fubftituting this for m’, we get f—n2z. fine. 
Next, to exprefs fine, in terms of z, if we make E = BAL, 
the angle fubtended by the vertical columns, when it is great- 
eft, or the inclination of the plane ADM, to the plane ACN, 
then we may confider the angle CAD, as meafured by the fide 
of a right angled fpherical triangle, of which the other fide is 
go—x, and E the angle, adjacent to that fide, and therefore 
tane = fin (go — i tanE = cofz.tanE. But tanE = 
tan. BAL = Bea ? fappofing BL, or CD =. 
Me fine 2D ‘ 
THEREFORE tane= = cof z, or =" cof 2. 
HENCE fine _ 8 cofst, or ants ASD cofz*, and 
ENC cole a 9 1—fine — a 40 
2 
, b 
fne = 2 .cofz? — fine’. 2 cofz?; and therefore fine = 
Ir this value of fine be fubftituted for it, we have 
% A bnz col z 
fanz. fne= ee 
2 
alr +5 cof z* 
LE? 
